Mercurial > cpython-lru_cache-weakref
annotate Lib/decimal.py @ 58925:eecf1bef052d 2.6
Merged revisions 78207 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
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r78207 | ezio.melotti | 2010-02-17 01:26:09 +0200 (Wed, 17 Feb 2010) | 1 line
#7930: fix stripid
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| author | Ezio Melotti <ezio.melotti@gmail.com> |
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| date | Tue, 16 Feb 2010 23:29:44 +0000 |
| parents | 86bf440bf9bf |
| children | ecc32e2f4656 |
| rev | line source |
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1 # Copyright (c) 2004 Python Software Foundation. |
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2 # All rights reserved. |
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3 |
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4 # Written by Eric Price <eprice at tjhsst.edu> |
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5 # and Facundo Batista <facundo at taniquetil.com.ar> |
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6 # and Raymond Hettinger <python at rcn.com> |
| 32456 | 7 # and Aahz <aahz at pobox.com> |
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8 # and Tim Peters |
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9 |
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10 # This module is currently Py2.3 compatible and should be kept that way |
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11 # unless a major compelling advantage arises. IOW, 2.3 compatibility is |
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12 # strongly preferred, but not guaranteed. |
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13 |
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14 # Also, this module should be kept in sync with the latest updates of |
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15 # the IBM specification as it evolves. Those updates will be treated |
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16 # as bug fixes (deviation from the spec is a compatibility, usability |
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17 # bug) and will be backported. At this point the spec is stabilizing |
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18 # and the updates are becoming fewer, smaller, and less significant. |
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19 |
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20 """ |
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21 This is a Py2.3 implementation of decimal floating point arithmetic based on |
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22 the General Decimal Arithmetic Specification: |
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23 |
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24 www2.hursley.ibm.com/decimal/decarith.html |
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25 |
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26 and IEEE standard 854-1987: |
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27 |
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28 www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html |
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29 |
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30 Decimal floating point has finite precision with arbitrarily large bounds. |
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31 |
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32 The purpose of this module is to support arithmetic using familiar |
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33 "schoolhouse" rules and to avoid some of the tricky representation |
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34 issues associated with binary floating point. The package is especially |
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35 useful for financial applications or for contexts where users have |
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36 expectations that are at odds with binary floating point (for instance, |
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37 in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead |
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38 of the expected Decimal('0.00') returned by decimal floating point). |
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39 |
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40 Here are some examples of using the decimal module: |
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41 |
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42 >>> from decimal import * |
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43 >>> setcontext(ExtendedContext) |
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44 >>> Decimal(0) |
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45 Decimal('0') |
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46 >>> Decimal('1') |
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47 Decimal('1') |
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48 >>> Decimal('-.0123') |
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49 Decimal('-0.0123') |
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50 >>> Decimal(123456) |
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51 Decimal('123456') |
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52 >>> Decimal('123.45e12345678901234567890') |
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53 Decimal('1.2345E+12345678901234567892') |
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54 >>> Decimal('1.33') + Decimal('1.27') |
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55 Decimal('2.60') |
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56 >>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41') |
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57 Decimal('-2.20') |
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58 >>> dig = Decimal(1) |
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59 >>> print dig / Decimal(3) |
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60 0.333333333 |
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61 >>> getcontext().prec = 18 |
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62 >>> print dig / Decimal(3) |
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63 0.333333333333333333 |
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64 >>> print dig.sqrt() |
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65 1 |
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66 >>> print Decimal(3).sqrt() |
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67 1.73205080756887729 |
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68 >>> print Decimal(3) ** 123 |
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69 4.85192780976896427E+58 |
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70 >>> inf = Decimal(1) / Decimal(0) |
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71 >>> print inf |
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72 Infinity |
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73 >>> neginf = Decimal(-1) / Decimal(0) |
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74 >>> print neginf |
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75 -Infinity |
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76 >>> print neginf + inf |
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77 NaN |
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78 >>> print neginf * inf |
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79 -Infinity |
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80 >>> print dig / 0 |
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81 Infinity |
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82 >>> getcontext().traps[DivisionByZero] = 1 |
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83 >>> print dig / 0 |
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84 Traceback (most recent call last): |
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85 ... |
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86 ... |
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87 ... |
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88 DivisionByZero: x / 0 |
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89 >>> c = Context() |
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90 >>> c.traps[InvalidOperation] = 0 |
| 32560 | 91 >>> print c.flags[InvalidOperation] |
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92 0 |
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93 >>> c.divide(Decimal(0), Decimal(0)) |
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94 Decimal('NaN') |
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95 >>> c.traps[InvalidOperation] = 1 |
| 32560 | 96 >>> print c.flags[InvalidOperation] |
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97 1 |
| 32560 | 98 >>> c.flags[InvalidOperation] = 0 |
| 99 >>> print c.flags[InvalidOperation] | |
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100 0 |
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101 >>> print c.divide(Decimal(0), Decimal(0)) |
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102 Traceback (most recent call last): |
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103 ... |
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104 ... |
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105 ... |
| 32560 | 106 InvalidOperation: 0 / 0 |
| 107 >>> print c.flags[InvalidOperation] | |
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108 1 |
| 32560 | 109 >>> c.flags[InvalidOperation] = 0 |
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110 >>> c.traps[InvalidOperation] = 0 |
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111 >>> print c.divide(Decimal(0), Decimal(0)) |
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112 NaN |
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114 1 |
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115 >>> |
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116 """ |
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117 |
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118 __all__ = [ |
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119 # Two major classes |
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120 'Decimal', 'Context', |
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121 |
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122 # Contexts |
| 32482 | 123 'DefaultContext', 'BasicContext', 'ExtendedContext', |
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124 |
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125 # Exceptions |
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126 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', |
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127 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', |
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128 |
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129 # Constants for use in setting up contexts |
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130 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', |
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131 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP', |
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132 |
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133 # Functions for manipulating contexts |
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134 'setcontext', 'getcontext', 'localcontext' |
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135 ] |
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136 |
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137 import copy as _copy |
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138 import numbers as _numbers |
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139 |
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140 try: |
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141 from collections import namedtuple as _namedtuple |
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142 DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent') |
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143 except ImportError: |
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144 DecimalTuple = lambda *args: args |
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145 |
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146 # Rounding |
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147 ROUND_DOWN = 'ROUND_DOWN' |
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148 ROUND_HALF_UP = 'ROUND_HALF_UP' |
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149 ROUND_HALF_EVEN = 'ROUND_HALF_EVEN' |
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150 ROUND_CEILING = 'ROUND_CEILING' |
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151 ROUND_FLOOR = 'ROUND_FLOOR' |
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152 ROUND_UP = 'ROUND_UP' |
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153 ROUND_HALF_DOWN = 'ROUND_HALF_DOWN' |
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154 ROUND_05UP = 'ROUND_05UP' |
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155 |
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156 # Errors |
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157 |
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158 class DecimalException(ArithmeticError): |
| 32560 | 159 """Base exception class. |
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160 |
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161 Used exceptions derive from this. |
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162 If an exception derives from another exception besides this (such as |
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163 Underflow (Inexact, Rounded, Subnormal) that indicates that it is only |
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164 called if the others are present. This isn't actually used for |
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165 anything, though. |
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166 |
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167 handle -- Called when context._raise_error is called and the |
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168 trap_enabler is set. First argument is self, second is the |
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169 context. More arguments can be given, those being after |
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170 the explanation in _raise_error (For example, |
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171 context._raise_error(NewError, '(-x)!', self._sign) would |
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172 call NewError().handle(context, self._sign).) |
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173 |
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174 To define a new exception, it should be sufficient to have it derive |
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175 from DecimalException. |
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176 """ |
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177 def handle(self, context, *args): |
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178 pass |
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179 |
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180 |
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181 class Clamped(DecimalException): |
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182 """Exponent of a 0 changed to fit bounds. |
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183 |
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184 This occurs and signals clamped if the exponent of a result has been |
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185 altered in order to fit the constraints of a specific concrete |
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186 representation. This may occur when the exponent of a zero result would |
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187 be outside the bounds of a representation, or when a large normal |
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188 number would have an encoded exponent that cannot be represented. In |
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189 this latter case, the exponent is reduced to fit and the corresponding |
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190 number of zero digits are appended to the coefficient ("fold-down"). |
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191 """ |
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192 |
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193 class InvalidOperation(DecimalException): |
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194 """An invalid operation was performed. |
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195 |
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196 Various bad things cause this: |
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197 |
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198 Something creates a signaling NaN |
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199 -INF + INF |
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200 0 * (+-)INF |
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201 (+-)INF / (+-)INF |
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202 x % 0 |
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203 (+-)INF % x |
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204 x._rescale( non-integer ) |
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205 sqrt(-x) , x > 0 |
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206 0 ** 0 |
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207 x ** (non-integer) |
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208 x ** (+-)INF |
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209 An operand is invalid |
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210 |
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211 The result of the operation after these is a quiet positive NaN, |
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212 except when the cause is a signaling NaN, in which case the result is |
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213 also a quiet NaN, but with the original sign, and an optional |
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214 diagnostic information. |
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215 """ |
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216 def handle(self, context, *args): |
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217 if args: |
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218 ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True) |
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219 return ans._fix_nan(context) |
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220 return _NaN |
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221 |
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222 class ConversionSyntax(InvalidOperation): |
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223 """Trying to convert badly formed string. |
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224 |
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225 This occurs and signals invalid-operation if an string is being |
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226 converted to a number and it does not conform to the numeric string |
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227 syntax. The result is [0,qNaN]. |
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228 """ |
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229 def handle(self, context, *args): |
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230 return _NaN |
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231 |
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232 class DivisionByZero(DecimalException, ZeroDivisionError): |
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233 """Division by 0. |
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234 |
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235 This occurs and signals division-by-zero if division of a finite number |
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236 by zero was attempted (during a divide-integer or divide operation, or a |
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237 power operation with negative right-hand operand), and the dividend was |
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238 not zero. |
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239 |
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240 The result of the operation is [sign,inf], where sign is the exclusive |
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241 or of the signs of the operands for divide, or is 1 for an odd power of |
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242 -0, for power. |
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243 """ |
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244 |
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245 def handle(self, context, sign, *args): |
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246 return _SignedInfinity[sign] |
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247 |
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248 class DivisionImpossible(InvalidOperation): |
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249 """Cannot perform the division adequately. |
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250 |
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251 This occurs and signals invalid-operation if the integer result of a |
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252 divide-integer or remainder operation had too many digits (would be |
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253 longer than precision). The result is [0,qNaN]. |
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254 """ |
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255 |
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256 def handle(self, context, *args): |
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257 return _NaN |
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258 |
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259 class DivisionUndefined(InvalidOperation, ZeroDivisionError): |
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260 """Undefined result of division. |
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261 |
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262 This occurs and signals invalid-operation if division by zero was |
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263 attempted (during a divide-integer, divide, or remainder operation), and |
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264 the dividend is also zero. The result is [0,qNaN]. |
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265 """ |
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266 |
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267 def handle(self, context, *args): |
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268 return _NaN |
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269 |
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270 class Inexact(DecimalException): |
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271 """Had to round, losing information. |
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272 |
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273 This occurs and signals inexact whenever the result of an operation is |
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274 not exact (that is, it needed to be rounded and any discarded digits |
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275 were non-zero), or if an overflow or underflow condition occurs. The |
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276 result in all cases is unchanged. |
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277 |
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278 The inexact signal may be tested (or trapped) to determine if a given |
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279 operation (or sequence of operations) was inexact. |
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280 """ |
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281 |
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282 class InvalidContext(InvalidOperation): |
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283 """Invalid context. Unknown rounding, for example. |
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284 |
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285 This occurs and signals invalid-operation if an invalid context was |
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286 detected during an operation. This can occur if contexts are not checked |
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287 on creation and either the precision exceeds the capability of the |
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288 underlying concrete representation or an unknown or unsupported rounding |
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289 was specified. These aspects of the context need only be checked when |
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290 the values are required to be used. The result is [0,qNaN]. |
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291 """ |
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292 |
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293 def handle(self, context, *args): |
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294 return _NaN |
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295 |
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296 class Rounded(DecimalException): |
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297 """Number got rounded (not necessarily changed during rounding). |
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298 |
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299 This occurs and signals rounded whenever the result of an operation is |
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300 rounded (that is, some zero or non-zero digits were discarded from the |
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301 coefficient), or if an overflow or underflow condition occurs. The |
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302 result in all cases is unchanged. |
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303 |
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304 The rounded signal may be tested (or trapped) to determine if a given |
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305 operation (or sequence of operations) caused a loss of precision. |
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306 """ |
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307 |
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308 class Subnormal(DecimalException): |
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309 """Exponent < Emin before rounding. |
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310 |
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311 This occurs and signals subnormal whenever the result of a conversion or |
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312 operation is subnormal (that is, its adjusted exponent is less than |
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313 Emin, before any rounding). The result in all cases is unchanged. |
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314 |
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315 The subnormal signal may be tested (or trapped) to determine if a given |
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316 or operation (or sequence of operations) yielded a subnormal result. |
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317 """ |
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318 |
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319 class Overflow(Inexact, Rounded): |
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320 """Numerical overflow. |
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321 |
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322 This occurs and signals overflow if the adjusted exponent of a result |
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323 (from a conversion or from an operation that is not an attempt to divide |
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324 by zero), after rounding, would be greater than the largest value that |
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325 can be handled by the implementation (the value Emax). |
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326 |
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327 The result depends on the rounding mode: |
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328 |
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329 For round-half-up and round-half-even (and for round-half-down and |
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330 round-up, if implemented), the result of the operation is [sign,inf], |
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331 where sign is the sign of the intermediate result. For round-down, the |
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332 result is the largest finite number that can be represented in the |
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333 current precision, with the sign of the intermediate result. For |
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334 round-ceiling, the result is the same as for round-down if the sign of |
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335 the intermediate result is 1, or is [0,inf] otherwise. For round-floor, |
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336 the result is the same as for round-down if the sign of the intermediate |
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337 result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded |
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338 will also be raised. |
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339 """ |
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340 |
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341 def handle(self, context, sign, *args): |
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342 if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, |
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343 ROUND_HALF_DOWN, ROUND_UP): |
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344 return _SignedInfinity[sign] |
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345 if sign == 0: |
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346 if context.rounding == ROUND_CEILING: |
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347 return _SignedInfinity[sign] |
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348 return _dec_from_triple(sign, '9'*context.prec, |
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349 context.Emax-context.prec+1) |
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350 if sign == 1: |
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351 if context.rounding == ROUND_FLOOR: |
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352 return _SignedInfinity[sign] |
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353 return _dec_from_triple(sign, '9'*context.prec, |
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354 context.Emax-context.prec+1) |
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355 |
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356 |
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357 class Underflow(Inexact, Rounded, Subnormal): |
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358 """Numerical underflow with result rounded to 0. |
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359 |
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360 This occurs and signals underflow if a result is inexact and the |
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361 adjusted exponent of the result would be smaller (more negative) than |
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362 the smallest value that can be handled by the implementation (the value |
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363 Emin). That is, the result is both inexact and subnormal. |
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364 |
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365 The result after an underflow will be a subnormal number rounded, if |
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366 necessary, so that its exponent is not less than Etiny. This may result |
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367 in 0 with the sign of the intermediate result and an exponent of Etiny. |
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368 |
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369 In all cases, Inexact, Rounded, and Subnormal will also be raised. |
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370 """ |
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371 |
| 32560 | 372 # List of public traps and flags |
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373 _signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, |
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374 Underflow, InvalidOperation, Subnormal] |
| 32560 | 375 |
| 376 # Map conditions (per the spec) to signals | |
| 377 _condition_map = {ConversionSyntax:InvalidOperation, | |
| 378 DivisionImpossible:InvalidOperation, | |
| 379 DivisionUndefined:InvalidOperation, | |
| 380 InvalidContext:InvalidOperation} | |
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381 |
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382 ##### Context Functions ################################################## |
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383 |
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384 # The getcontext() and setcontext() function manage access to a thread-local |
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385 # current context. Py2.4 offers direct support for thread locals. If that |
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386 # is not available, use threading.currentThread() which is slower but will |
| 34184 | 387 # work for older Pythons. If threads are not part of the build, create a |
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388 # mock threading object with threading.local() returning the module namespace. |
| 34184 | 389 |
| 390 try: | |
| 391 import threading | |
| 392 except ImportError: | |
| 393 # Python was compiled without threads; create a mock object instead | |
| 394 import sys | |
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395 class MockThreading(object): |
| 34184 | 396 def local(self, sys=sys): |
| 397 return sys.modules[__name__] | |
| 398 threading = MockThreading() | |
| 399 del sys, MockThreading | |
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400 |
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401 try: |
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402 threading.local |
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403 |
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404 except AttributeError: |
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405 |
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406 # To fix reloading, force it to create a new context |
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407 # Old contexts have different exceptions in their dicts, making problems. |
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408 if hasattr(threading.currentThread(), '__decimal_context__'): |
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409 del threading.currentThread().__decimal_context__ |
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410 |
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411 def setcontext(context): |
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412 """Set this thread's context to context.""" |
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413 if context in (DefaultContext, BasicContext, ExtendedContext): |
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414 context = context.copy() |
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415 context.clear_flags() |
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416 threading.currentThread().__decimal_context__ = context |
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417 |
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418 def getcontext(): |
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419 """Returns this thread's context. |
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420 |
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421 If this thread does not yet have a context, returns |
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422 a new context and sets this thread's context. |
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423 New contexts are copies of DefaultContext. |
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424 """ |
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425 try: |
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426 return threading.currentThread().__decimal_context__ |
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427 except AttributeError: |
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428 context = Context() |
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429 threading.currentThread().__decimal_context__ = context |
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430 return context |
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431 |
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432 else: |
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433 |
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434 local = threading.local() |
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435 if hasattr(local, '__decimal_context__'): |
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436 del local.__decimal_context__ |
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437 |
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438 def getcontext(_local=local): |
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439 """Returns this thread's context. |
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440 |
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441 If this thread does not yet have a context, returns |
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442 a new context and sets this thread's context. |
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443 New contexts are copies of DefaultContext. |
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444 """ |
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445 try: |
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446 return _local.__decimal_context__ |
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447 except AttributeError: |
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448 context = Context() |
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449 _local.__decimal_context__ = context |
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450 return context |
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451 |
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452 def setcontext(context, _local=local): |
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453 """Set this thread's context to context.""" |
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454 if context in (DefaultContext, BasicContext, ExtendedContext): |
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455 context = context.copy() |
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456 context.clear_flags() |
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457 _local.__decimal_context__ = context |
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458 |
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459 del threading, local # Don't contaminate the namespace |
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460 |
|
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461 def localcontext(ctx=None): |
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462 """Return a context manager for a copy of the supplied context |
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463 |
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464 Uses a copy of the current context if no context is specified |
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465 The returned context manager creates a local decimal context |
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466 in a with statement: |
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467 def sin(x): |
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468 with localcontext() as ctx: |
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469 ctx.prec += 2 |
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470 # Rest of sin calculation algorithm |
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471 # uses a precision 2 greater than normal |
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472 return +s # Convert result to normal precision |
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473 |
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474 def sin(x): |
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475 with localcontext(ExtendedContext): |
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476 # Rest of sin calculation algorithm |
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477 # uses the Extended Context from the |
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478 # General Decimal Arithmetic Specification |
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479 return +s # Convert result to normal context |
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480 |
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481 >>> setcontext(DefaultContext) |
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482 >>> print getcontext().prec |
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483 28 |
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484 >>> with localcontext(): |
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485 ... ctx = getcontext() |
| 40770 | 486 ... ctx.prec += 2 |
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487 ... print ctx.prec |
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488 ... |
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489 30 |
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490 >>> with localcontext(ExtendedContext): |
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491 ... print getcontext().prec |
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492 ... |
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493 9 |
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494 >>> print getcontext().prec |
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495 28 |
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496 """ |
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497 if ctx is None: ctx = getcontext() |
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498 return _ContextManager(ctx) |
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499 |
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500 |
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501 ##### Decimal class ####################################################### |
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502 |
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503 class Decimal(object): |
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504 """Floating point class for decimal arithmetic.""" |
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505 |
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506 __slots__ = ('_exp','_int','_sign', '_is_special') |
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507 # Generally, the value of the Decimal instance is given by |
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508 # (-1)**_sign * _int * 10**_exp |
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509 # Special values are signified by _is_special == True |
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510 |
| 33695 | 511 # We're immutable, so use __new__ not __init__ |
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512 def __new__(cls, value="0", context=None): |
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513 """Create a decimal point instance. |
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514 |
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515 >>> Decimal('3.14') # string input |
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516 Decimal('3.14') |
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517 >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) |
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518 Decimal('3.14') |
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519 >>> Decimal(314) # int or long |
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520 Decimal('314') |
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521 >>> Decimal(Decimal(314)) # another decimal instance |
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522 Decimal('314') |
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523 >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay |
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524 Decimal('3.14') |
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525 """ |
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526 |
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527 # Note that the coefficient, self._int, is actually stored as |
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528 # a string rather than as a tuple of digits. This speeds up |
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529 # the "digits to integer" and "integer to digits" conversions |
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530 # that are used in almost every arithmetic operation on |
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531 # Decimals. This is an internal detail: the as_tuple function |
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532 # and the Decimal constructor still deal with tuples of |
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533 # digits. |
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534 |
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535 self = object.__new__(cls) |
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536 |
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537 # From a string |
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538 # REs insist on real strings, so we can too. |
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539 if isinstance(value, basestring): |
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540 m = _parser(value.strip()) |
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541 if m is None: |
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542 if context is None: |
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543 context = getcontext() |
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544 return context._raise_error(ConversionSyntax, |
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545 "Invalid literal for Decimal: %r" % value) |
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546 |
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547 if m.group('sign') == "-": |
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548 self._sign = 1 |
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549 else: |
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550 self._sign = 0 |
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551 intpart = m.group('int') |
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552 if intpart is not None: |
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553 # finite number |
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554 fracpart = m.group('frac') or '' |
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555 exp = int(m.group('exp') or '0') |
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556 self._int = str(int(intpart+fracpart)) |
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557 self._exp = exp - len(fracpart) |
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558 self._is_special = False |
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559 else: |
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560 diag = m.group('diag') |
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561 if diag is not None: |
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562 # NaN |
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563 self._int = str(int(diag or '0')).lstrip('0') |
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564 if m.group('signal'): |
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565 self._exp = 'N' |
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566 else: |
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567 self._exp = 'n' |
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568 else: |
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569 # infinity |
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570 self._int = '0' |
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571 self._exp = 'F' |
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572 self._is_special = True |
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573 return self |
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574 |
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575 # From an integer |
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576 if isinstance(value, (int,long)): |
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577 if value >= 0: |
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578 self._sign = 0 |
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579 else: |
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580 self._sign = 1 |
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581 self._exp = 0 |
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582 self._int = str(abs(value)) |
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583 self._is_special = False |
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584 return self |
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585 |
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|
586 # From another decimal |
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587 if isinstance(value, Decimal): |
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588 self._exp = value._exp |
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589 self._sign = value._sign |
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590 self._int = value._int |
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591 self._is_special = value._is_special |
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592 return self |
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|
593 |
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|
594 # From an internal working value |
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595 if isinstance(value, _WorkRep): |
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596 self._sign = value.sign |
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597 self._int = str(value.int) |
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598 self._exp = int(value.exp) |
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599 self._is_special = False |
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600 return self |
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|
601 |
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|
602 # tuple/list conversion (possibly from as_tuple()) |
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603 if isinstance(value, (list,tuple)): |
|
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604 if len(value) != 3: |
|
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605 raise ValueError('Invalid tuple size in creation of Decimal ' |
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606 'from list or tuple. The list or tuple ' |
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607 'should have exactly three elements.') |
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608 # process sign. The isinstance test rejects floats |
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609 if not (isinstance(value[0], (int, long)) and value[0] in (0,1)): |
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610 raise ValueError("Invalid sign. The first value in the tuple " |
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611 "should be an integer; either 0 for a " |
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612 "positive number or 1 for a negative number.") |
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613 self._sign = value[0] |
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|
614 if value[2] == 'F': |
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615 # infinity: value[1] is ignored |
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616 self._int = '0' |
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617 self._exp = value[2] |
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618 self._is_special = True |
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619 else: |
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620 # process and validate the digits in value[1] |
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621 digits = [] |
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622 for digit in value[1]: |
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623 if isinstance(digit, (int, long)) and 0 <= digit <= 9: |
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624 # skip leading zeros |
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625 if digits or digit != 0: |
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626 digits.append(digit) |
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627 else: |
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628 raise ValueError("The second value in the tuple must " |
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629 "be composed of integers in the range " |
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630 "0 through 9.") |
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631 if value[2] in ('n', 'N'): |
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632 # NaN: digits form the diagnostic |
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633 self._int = ''.join(map(str, digits)) |
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634 self._exp = value[2] |
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635 self._is_special = True |
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636 elif isinstance(value[2], (int, long)): |
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637 # finite number: digits give the coefficient |
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|
638 self._int = ''.join(map(str, digits or [0])) |
|
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639 self._exp = value[2] |
|
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640 self._is_special = False |
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641 else: |
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642 raise ValueError("The third value in the tuple must " |
|
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|
643 "be an integer, or one of the " |
|
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|
644 "strings 'F', 'n', 'N'.") |
|
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|
645 return self |
|
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|
646 |
|
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|
647 if isinstance(value, float): |
|
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648 raise TypeError("Cannot convert float to Decimal. " + |
|
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|
649 "First convert the float to a string") |
|
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|
650 |
|
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|
651 raise TypeError("Cannot convert %r to Decimal" % value) |
|
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|
652 |
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|
653 def _isnan(self): |
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654 """Returns whether the number is not actually one. |
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|
655 |
|
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|
656 0 if a number |
|
44352
f7bc79112bcf
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|
657 1 if NaN |
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|
658 2 if sNaN |
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|
659 """ |
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|
660 if self._is_special: |
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|
661 exp = self._exp |
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662 if exp == 'n': |
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|
663 return 1 |
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664 elif exp == 'N': |
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|
665 return 2 |
|
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|
666 return 0 |
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|
667 |
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|
668 def _isinfinity(self): |
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669 """Returns whether the number is infinite |
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|
670 |
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671 0 if finite or not a number |
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672 1 if +INF |
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|
673 -1 if -INF |
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|
674 """ |
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|
675 if self._exp == 'F': |
|
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|
676 if self._sign: |
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|
677 return -1 |
|
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|
678 return 1 |
|
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|
679 return 0 |
|
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|
680 |
|
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|
681 def _check_nans(self, other=None, context=None): |
|
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682 """Returns whether the number is not actually one. |
|
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|
683 |
|
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|
684 if self, other are sNaN, signal |
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parents:
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|
685 if self, other are NaN return nan |
|
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|
686 return 0 |
|
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|
687 |
|
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parents:
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|
688 Done before operations. |
|
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|
689 """ |
|
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|
690 |
|
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|
691 self_is_nan = self._isnan() |
|
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|
692 if other is None: |
|
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|
693 other_is_nan = False |
|
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|
694 else: |
|
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|
695 other_is_nan = other._isnan() |
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|
696 |
|
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|
697 if self_is_nan or other_is_nan: |
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|
698 if context is None: |
|
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|
699 context = getcontext() |
|
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|
700 |
|
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|
701 if self_is_nan == 2: |
|
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|
702 return context._raise_error(InvalidOperation, 'sNaN', |
|
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|
703 self) |
|
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|
704 if other_is_nan == 2: |
|
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diff
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|
705 return context._raise_error(InvalidOperation, 'sNaN', |
|
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diff
changeset
|
706 other) |
|
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|
707 if self_is_nan: |
|
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diff
changeset
|
708 return self._fix_nan(context) |
|
63f3154c731d
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Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
709 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
710 return other._fix_nan(context) |
|
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diff
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|
711 return 0 |
|
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Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
712 |
|
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diff
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|
713 def _compare_check_nans(self, other, context): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
changeset
|
714 """Version of _check_nans used for the signaling comparisons |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
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|
715 compare_signal, __le__, __lt__, __ge__, __gt__. |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
changeset
|
716 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
changeset
|
717 Signal InvalidOperation if either self or other is a (quiet |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
changeset
|
718 or signaling) NaN. Signaling NaNs take precedence over quiet |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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parents:
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diff
changeset
|
719 NaNs. |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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parents:
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diff
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|
720 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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parents:
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diff
changeset
|
721 Return 0 if neither operand is a NaN. |
|
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diff
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|
722 |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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|
723 """ |
|
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|
724 if context is None: |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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|
725 context = getcontext() |
|
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|
726 |
|
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|
727 if self._is_special or other._is_special: |
|
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|
728 if self.is_snan(): |
|
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|
729 return context._raise_error(InvalidOperation, |
|
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|
730 'comparison involving sNaN', |
|
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|
731 self) |
|
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changeset
|
732 elif other.is_snan(): |
|
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|
733 return context._raise_error(InvalidOperation, |
|
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changeset
|
734 'comparison involving sNaN', |
|
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|
735 other) |
|
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diff
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|
736 elif self.is_qnan(): |
|
f55a4f119141
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changeset
|
737 return context._raise_error(InvalidOperation, |
|
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parents:
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changeset
|
738 'comparison involving NaN', |
|
f55a4f119141
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diff
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|
739 self) |
|
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|
740 elif other.is_qnan(): |
|
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|
741 return context._raise_error(InvalidOperation, |
|
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|
742 'comparison involving NaN', |
|
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|
743 other) |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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|
744 return 0 |
|
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|
745 |
|
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|
746 def __nonzero__(self): |
|
43454
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Made the various is_* operations return booleans. This was discussed
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diff
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|
747 """Return True if self is nonzero; otherwise return False. |
|
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Made the various is_* operations return booleans. This was discussed
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|
748 |
|
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Made the various is_* operations return booleans. This was discussed
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|
749 NaNs and infinities are considered nonzero. |
|
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|
750 """ |
|
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|
751 return self._is_special or self._int != '0' |
|
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|
752 |
|
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|
753 def _cmp(self, other): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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parents:
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diff
changeset
|
754 """Compare the two non-NaN decimal instances self and other. |
|
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parents:
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changeset
|
755 |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
changeset
|
756 Returns -1 if self < other, 0 if self == other and 1 |
|
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parents:
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diff
changeset
|
757 if self > other. This routine is for internal use only.""" |
|
33519
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|
758 |
|
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parents:
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|
759 if self._is_special or other._is_special: |
|
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|
760 self_inf = self._isinfinity() |
|
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|
761 other_inf = other._isinfinity() |
|
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|
762 if self_inf == other_inf: |
|
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|
763 return 0 |
|
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|
764 elif self_inf < other_inf: |
|
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|
765 return -1 |
|
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Merged revisions 68920 via svnmerge from
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|
766 else: |
|
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|
767 return 1 |
|
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changeset
|
768 |
|
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diff
changeset
|
769 # check for zeros; Decimal('0') == Decimal('-0') |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
770 if not self: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
771 if not other: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
772 return 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
773 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
774 return -((-1)**other._sign) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
42605
diff
changeset
|
775 if not other: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
776 return (-1)**self._sign |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
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parents:
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diff
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|
777 |
|
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parents:
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diff
changeset
|
778 # If different signs, neg one is less |
|
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|
779 if other._sign < self._sign: |
|
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diff
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|
780 return -1 |
|
d2c1c7ae7cf4
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parents:
diff
changeset
|
781 if self._sign < other._sign: |
|
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diff
changeset
|
782 return 1 |
|
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Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
783 |
|
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parents:
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diff
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|
784 self_adjusted = self.adjusted() |
|
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|
785 other_adjusted = other.adjusted() |
|
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parents:
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diff
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|
786 if self_adjusted == other_adjusted: |
|
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parents:
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diff
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|
787 self_padded = self._int + '0'*(self._exp - other._exp) |
|
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|
788 other_padded = other._int + '0'*(other._exp - self._exp) |
|
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|
789 if self_padded == other_padded: |
|
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|
790 return 0 |
|
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|
791 elif self_padded < other_padded: |
|
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|
792 return -(-1)**self._sign |
|
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|
793 else: |
|
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|
794 return (-1)**self._sign |
|
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|
795 elif self_adjusted > other_adjusted: |
|
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|
796 return (-1)**self._sign |
|
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parents:
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|
797 else: # self_adjusted < other_adjusted |
|
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|
798 return -((-1)**self._sign) |
|
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diff
changeset
|
799 |
|
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changeset
|
800 # Note: The Decimal standard doesn't cover rich comparisons for |
|
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changeset
|
801 # Decimals. In particular, the specification is silent on the |
|
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changeset
|
802 # subject of what should happen for a comparison involving a NaN. |
|
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Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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changeset
|
803 # We take the following approach: |
|
f55a4f119141
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|
804 # |
|
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changeset
|
805 # == comparisons involving a NaN always return False |
|
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parents:
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diff
changeset
|
806 # != comparisons involving a NaN always return True |
|
f55a4f119141
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diff
changeset
|
807 # <, >, <= and >= comparisons involving a (quiet or signaling) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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diff
changeset
|
808 # NaN signal InvalidOperation, and return False if the |
|
45269
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Typos in decimal comment and documentation
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45201
diff
changeset
|
809 # InvalidOperation is not trapped. |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
810 # |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
811 # This behavior is designed to conform as closely as possible to |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
812 # that specified by IEEE 754. |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
813 |
|
32505
191796b7a054
* Add __eq__ and __ne__ so that things like list.index() work properly
Raymond Hettinger <python@rcn.com>
parents:
32499
diff
changeset
|
814 def __eq__(self, other): |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
815 other = _convert_other(other) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
816 if other is NotImplemented: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
817 return other |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
818 if self.is_nan() or other.is_nan(): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
819 return False |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
820 return self._cmp(other) == 0 |
|
32505
191796b7a054
* Add __eq__ and __ne__ so that things like list.index() work properly
Raymond Hettinger <python@rcn.com>
parents:
32499
diff
changeset
|
821 |
|
191796b7a054
* Add __eq__ and __ne__ so that things like list.index() work properly
Raymond Hettinger <python@rcn.com>
parents:
32499
diff
changeset
|
822 def __ne__(self, other): |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
823 other = _convert_other(other) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
824 if other is NotImplemented: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
825 return other |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
826 if self.is_nan() or other.is_nan(): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
827 return True |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
828 return self._cmp(other) != 0 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
829 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
830 def __lt__(self, other, context=None): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
831 other = _convert_other(other) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
832 if other is NotImplemented: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
833 return other |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
834 ans = self._compare_check_nans(other, context) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
835 if ans: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
836 return False |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
837 return self._cmp(other) < 0 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
838 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
839 def __le__(self, other, context=None): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
840 other = _convert_other(other) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
841 if other is NotImplemented: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
842 return other |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
843 ans = self._compare_check_nans(other, context) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
844 if ans: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
845 return False |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
846 return self._cmp(other) <= 0 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
847 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
848 def __gt__(self, other, context=None): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
849 other = _convert_other(other) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
850 if other is NotImplemented: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
851 return other |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
852 ans = self._compare_check_nans(other, context) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
853 if ans: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
854 return False |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
855 return self._cmp(other) > 0 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
856 |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
857 def __ge__(self, other, context=None): |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
858 other = _convert_other(other) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
859 if other is NotImplemented: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
860 return other |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
861 ans = self._compare_check_nans(other, context) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
862 if ans: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
863 return False |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
864 return self._cmp(other) >= 0 |
|
32505
191796b7a054
* Add __eq__ and __ne__ so that things like list.index() work properly
Raymond Hettinger <python@rcn.com>
parents:
32499
diff
changeset
|
865 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
866 def compare(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
867 """Compares one to another. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
868 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
869 -1 => a < b |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
870 0 => a = b |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
871 1 => a > b |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
872 NaN => one is NaN |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
873 Like __cmp__, but returns Decimal instances. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
874 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
875 other = _convert_other(other, raiseit=True) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
876 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
877 # Compare(NaN, NaN) = NaN |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
878 if (self._is_special or other and other._is_special): |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
879 ans = self._check_nans(other, context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
880 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
881 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
882 |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
883 return Decimal(self._cmp(other)) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
884 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
885 def __hash__(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
886 """x.__hash__() <==> hash(x)""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
887 # Decimal integers must hash the same as the ints |
|
44593
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
888 # |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
889 # The hash of a nonspecial noninteger Decimal must depend only |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
890 # on the value of that Decimal, and not on its representation. |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
891 # For example: hash(Decimal('100E-1')) == hash(Decimal('10')). |
|
34758
50509ee96364
Bug #1163325: "special" decimals aren't hashable
Raymond Hettinger <python@rcn.com>
parents:
34638
diff
changeset
|
892 if self._is_special: |
|
50509ee96364
Bug #1163325: "special" decimals aren't hashable
Raymond Hettinger <python@rcn.com>
parents:
34638
diff
changeset
|
893 if self._isnan(): |
|
50509ee96364
Bug #1163325: "special" decimals aren't hashable
Raymond Hettinger <python@rcn.com>
parents:
34638
diff
changeset
|
894 raise TypeError('Cannot hash a NaN value.') |
|
50509ee96364
Bug #1163325: "special" decimals aren't hashable
Raymond Hettinger <python@rcn.com>
parents:
34638
diff
changeset
|
895 return hash(str(self)) |
|
43409
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
896 if not self: |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
897 return 0 |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
898 if self._isinteger(): |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
899 op = _WorkRep(self.to_integral_value()) |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
900 # to make computation feasible for Decimals with large |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
901 # exponent, we use the fact that hash(n) == hash(m) for |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
902 # any two nonzero integers n and m such that (i) n and m |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
903 # have the same sign, and (ii) n is congruent to m modulo |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
904 # 2**64-1. So we can replace hash((-1)**s*c*10**e) with |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
905 # hash((-1)**s*c*pow(10, e, 2**64-1). |
|
357cf07a23fe
Issue #1772851. Optimization of __hash__ to behave better for big big
Facundo Batista <facundobatista@gmail.com>
parents:
43391
diff
changeset
|
906 return hash((-1)**op.sign*op.int*pow(10, op.exp, 2**64-1)) |
|
44593
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
907 # The value of a nonzero nonspecial Decimal instance is |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
908 # faithfully represented by the triple consisting of its sign, |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
909 # its adjusted exponent, and its coefficient with trailing |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
910 # zeros removed. |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
911 return hash((self._sign, |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
912 self._exp+len(self._int), |
|
057de46ea17e
Issue #1757: The hash of a Decimal instance is no longer affected
Facundo Batista <facundobatista@gmail.com>
parents:
44352
diff
changeset
|
913 self._int.rstrip('0'))) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
914 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
915 def as_tuple(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
916 """Represents the number as a triple tuple. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
917 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
918 To show the internals exactly as they are. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
919 """ |
|
44631
3cd9b877eae0
Have Decimal.as_tuple return a named tuple.
Raymond Hettinger <python@rcn.com>
parents:
44593
diff
changeset
|
920 return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
921 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
922 def __repr__(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
923 """Represents the number as an instance of Decimal.""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
924 # Invariant: eval(repr(d)) == d |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
925 return "Decimal('%s')" % str(self) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
926 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
927 def __str__(self, eng=False, context=None): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
928 """Return string representation of the number in scientific notation. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
929 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
930 Captures all of the information in the underlying representation. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
931 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
932 |
|
44120
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
933 sign = ['', '-'][self._sign] |
|
35113
adf189eb4f58
Apply the _is_special guard.
Raymond Hettinger <python@rcn.com>
parents:
35035
diff
changeset
|
934 if self._is_special: |
|
44120
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
935 if self._exp == 'F': |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
936 return sign + 'Infinity' |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
937 elif self._exp == 'n': |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
938 return sign + 'NaN' + self._int |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
939 else: # self._exp == 'N' |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
940 return sign + 'sNaN' + self._int |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
941 |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
942 # number of digits of self._int to left of decimal point |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
943 leftdigits = self._exp + len(self._int) |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
944 |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
945 # dotplace is number of digits of self._int to the left of the |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
946 # decimal point in the mantissa of the output string (that is, |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
947 # after adjusting the exponent) |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
948 if self._exp <= 0 and leftdigits > -6: |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
949 # no exponent required |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
950 dotplace = leftdigits |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
951 elif not eng: |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
952 # usual scientific notation: 1 digit on left of the point |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
953 dotplace = 1 |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
954 elif self._int == '0': |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
955 # engineering notation, zero |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
956 dotplace = (leftdigits + 1) % 3 - 1 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
957 else: |
|
44120
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
958 # engineering notation, nonzero |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
959 dotplace = (leftdigits - 1) % 3 + 1 |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
960 |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
961 if dotplace <= 0: |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
962 intpart = '0' |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
963 fracpart = '.' + '0'*(-dotplace) + self._int |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
964 elif dotplace >= len(self._int): |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
965 intpart = self._int+'0'*(dotplace-len(self._int)) |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
966 fracpart = '' |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
967 else: |
|
44120
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
968 intpart = self._int[:dotplace] |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
969 fracpart = '.' + self._int[dotplace:] |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
970 if leftdigits == dotplace: |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
971 exp = '' |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
972 else: |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
973 if context is None: |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
974 context = getcontext() |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
975 exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
976 |
|
fe6bedafb46a
Speedup and cleaning of __str__. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44068
diff
changeset
|
977 return sign + intpart + fracpart + exp |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
978 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
979 def to_eng_string(self, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
980 """Convert to engineering-type string. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
981 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
982 Engineering notation has an exponent which is a multiple of 3, so there |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
983 are up to 3 digits left of the decimal place. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
984 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
985 Same rules for when in exponential and when as a value as in __str__. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
986 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
987 return self.__str__(eng=True, context=context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
988 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
989 def __neg__(self, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
990 """Returns a copy with the sign switched. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
991 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
992 Rounds, if it has reason. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
993 """ |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
994 if self._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
995 ans = self._check_nans(context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
996 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
997 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
998 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
999 if not self: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1000 # -Decimal('0') is Decimal('0'), not Decimal('-0') |
|
44352
f7bc79112bcf
Some minor cleanups. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44328
diff
changeset
|
1001 ans = self.copy_abs() |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1002 else: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1003 ans = self.copy_negate() |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1004 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1005 if context is None: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1006 context = getcontext() |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1007 return ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1008 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1009 def __pos__(self, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1010 """Returns a copy, unless it is a sNaN. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1011 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1012 Rounds the number (if more then precision digits) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1013 """ |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1014 if self._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1015 ans = self._check_nans(context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1016 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1017 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1018 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1019 if not self: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1020 # + (-0) = 0 |
|
44352
f7bc79112bcf
Some minor cleanups. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44328
diff
changeset
|
1021 ans = self.copy_abs() |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1022 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1023 ans = Decimal(self) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1024 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1025 if context is None: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1026 context = getcontext() |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1027 return ans._fix(context) |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1028 |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1029 def __abs__(self, round=True, context=None): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1030 """Returns the absolute value of self. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1031 |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1032 If the keyword argument 'round' is false, do not round. The |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1033 expression self.__abs__(round=False) is equivalent to |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1034 self.copy_abs(). |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1035 """ |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1036 if not round: |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1037 return self.copy_abs() |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1038 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1039 if self._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1040 ans = self._check_nans(context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1041 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1042 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1043 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1044 if self._sign: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1045 ans = self.__neg__(context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1046 else: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1047 ans = self.__pos__(context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1048 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1049 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1050 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1051 def __add__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1052 """Returns self + other. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1053 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1054 -INF + INF (or the reverse) cause InvalidOperation errors. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1055 """ |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1056 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1057 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1058 return other |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1059 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1060 if context is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1061 context = getcontext() |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1062 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1063 if self._is_special or other._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1064 ans = self._check_nans(other, context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1065 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1066 return ans |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1067 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1068 if self._isinfinity(): |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
1069 # If both INF, same sign => same as both, opposite => error. |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1070 if self._sign != other._sign and other._isinfinity(): |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1071 return context._raise_error(InvalidOperation, '-INF + INF') |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1072 return Decimal(self) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1073 if other._isinfinity(): |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
1074 return Decimal(other) # Can't both be infinity here |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1075 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1076 exp = min(self._exp, other._exp) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1077 negativezero = 0 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1078 if context.rounding == ROUND_FLOOR and self._sign != other._sign: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
1079 # If the answer is 0, the sign should be negative, in this case. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1080 negativezero = 1 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1081 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1082 if not self and not other: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1083 sign = min(self._sign, other._sign) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1084 if negativezero: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1085 sign = 1 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1086 ans = _dec_from_triple(sign, '0', exp) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1087 ans = ans._fix(context) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1088 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1089 if not self: |
|
33845
032f342efcd2
Very few little improvements.
Facundo Batista <facundobatista@gmail.com>
parents:
33803
diff
changeset
|
1090 exp = max(exp, other._exp - context.prec-1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1091 ans = other._rescale(exp, context.rounding) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1092 ans = ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1093 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1094 if not other: |
|
33845
032f342efcd2
Very few little improvements.
Facundo Batista <facundobatista@gmail.com>
parents:
33803
diff
changeset
|
1095 exp = max(exp, self._exp - context.prec-1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1096 ans = self._rescale(exp, context.rounding) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1097 ans = ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1098 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1099 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1100 op1 = _WorkRep(self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1101 op2 = _WorkRep(other) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1102 op1, op2 = _normalize(op1, op2, context.prec) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1103 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1104 result = _WorkRep() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1105 if op1.sign != op2.sign: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1106 # Equal and opposite |
| 33851 | 1107 if op1.int == op2.int: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1108 ans = _dec_from_triple(negativezero, '0', exp) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1109 ans = ans._fix(context) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1110 return ans |
| 33851 | 1111 if op1.int < op2.int: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1112 op1, op2 = op2, op1 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
1113 # OK, now abs(op1) > abs(op2) |
| 33851 | 1114 if op1.sign == 1: |
| 1115 result.sign = 1 | |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1116 op1.sign, op2.sign = op2.sign, op1.sign |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1117 else: |
| 33851 | 1118 result.sign = 0 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
1119 # So we know the sign, and op1 > 0. |
| 33851 | 1120 elif op1.sign == 1: |
| 1121 result.sign = 1 | |
| 1122 op1.sign, op2.sign = (0, 0) | |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1123 else: |
| 33851 | 1124 result.sign = 0 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
1125 # Now, op1 > abs(op2) > 0 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1126 |
| 33851 | 1127 if op2.sign == 0: |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1128 result.int = op1.int + op2.int |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1129 else: |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1130 result.int = op1.int - op2.int |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1131 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1132 result.exp = op1.exp |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1133 ans = Decimal(result) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1134 ans = ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1135 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1136 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1137 __radd__ = __add__ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1138 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1139 def __sub__(self, other, context=None): |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1140 """Return self - other""" |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1141 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1142 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1143 return other |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1144 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1145 if self._is_special or other._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1146 ans = self._check_nans(other, context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1147 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1148 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1149 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1150 # self - other is computed as self + other.copy_negate() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1151 return self.__add__(other.copy_negate(), context=context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1152 |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1153 def __rsub__(self, other, context=None): |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1154 """Return other - self""" |
|
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Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1155 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1156 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1157 return other |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1158 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1159 return other.__sub__(self, context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1160 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1161 def __mul__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1162 """Return self * other. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1163 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1164 (+-) INF * 0 (or its reverse) raise InvalidOperation. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1165 """ |
|
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SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1166 other = _convert_other(other) |
|
34812
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* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1167 if other is NotImplemented: |
|
b016236dfbd9
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Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1168 return other |
|
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parents:
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diff
changeset
|
1169 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1170 if context is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1171 context = getcontext() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1172 |
|
32561
6f351b1bcf53
* Update the test suite to reflect that ConversionSyntax was no longer
Raymond Hettinger <python@rcn.com>
parents:
32560
diff
changeset
|
1173 resultsign = self._sign ^ other._sign |
|
33519
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Raymond Hettinger <python@rcn.com>
parents:
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diff
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|
1174 |
|
139a4012bead
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parents:
33198
diff
changeset
|
1175 if self._is_special or other._is_special: |
|
139a4012bead
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Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1176 ans = self._check_nans(other, context) |
|
139a4012bead
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diff
changeset
|
1177 if ans: |
|
139a4012bead
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parents:
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diff
changeset
|
1178 return ans |
|
139a4012bead
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Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1179 |
|
139a4012bead
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Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1180 if self._isinfinity(): |
|
139a4012bead
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parents:
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diff
changeset
|
1181 if not other: |
|
139a4012bead
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Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1182 return context._raise_error(InvalidOperation, '(+-)INF * 0') |
|
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Merged revisions 68191 via svnmerge from
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parents:
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diff
changeset
|
1183 return _SignedInfinity[resultsign] |
|
33519
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diff
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|
1184 |
|
139a4012bead
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parents:
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diff
changeset
|
1185 if other._isinfinity(): |
|
139a4012bead
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parents:
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diff
changeset
|
1186 if not self: |
|
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parents:
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diff
changeset
|
1187 return context._raise_error(InvalidOperation, '0 * (+-)INF') |
|
50480
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parents:
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diff
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|
1188 return _SignedInfinity[resultsign] |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1189 |
|
d2c1c7ae7cf4
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parents:
diff
changeset
|
1190 resultexp = self._exp + other._exp |
|
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Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1191 |
|
d2c1c7ae7cf4
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Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1192 # Special case for multiplying by zero |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1193 if not self or not other: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1194 ans = _dec_from_triple(resultsign, '0', resultexp) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1195 # Fixing in case the exponent is out of bounds |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1196 ans = ans._fix(context) |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1197 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1198 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1199 # Special case for multiplying by power of 10 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1200 if self._int == '1': |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1201 ans = _dec_from_triple(resultsign, other._int, resultexp) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1202 ans = ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1203 return ans |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1204 if other._int == '1': |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1205 ans = _dec_from_triple(resultsign, self._int, resultexp) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1206 ans = ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1207 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1208 |
|
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SF patch #1020845: Decimal performance enhancements
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parents:
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diff
changeset
|
1209 op1 = _WorkRep(self) |
|
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SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1210 op2 = _WorkRep(other) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
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parents:
33198
diff
changeset
|
1211 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1212 ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1213 ans = ans._fix(context) |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1214 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1215 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1216 __rmul__ = __mul__ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1217 |
|
46651
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1218 def __truediv__(self, other, context=None): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1219 """Return self / other.""" |
|
33519
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SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1220 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1221 if other is NotImplemented: |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1222 return NotImplemented |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1223 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1224 if context is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1225 context = getcontext() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1226 |
|
32561
6f351b1bcf53
* Update the test suite to reflect that ConversionSyntax was no longer
Raymond Hettinger <python@rcn.com>
parents:
32560
diff
changeset
|
1227 sign = self._sign ^ other._sign |
|
33519
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SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1228 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1229 if self._is_special or other._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1230 ans = self._check_nans(other, context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1231 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1232 return ans |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1233 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1234 if self._isinfinity() and other._isinfinity(): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1235 return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1236 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1237 if self._isinfinity(): |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
1238 return _SignedInfinity[sign] |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1239 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1240 if other._isinfinity(): |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1241 context._raise_error(Clamped, 'Division by infinity') |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1242 return _dec_from_triple(sign, '0', context.Etiny()) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
1243 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1244 # Special cases for zeroes |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1245 if not other: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1246 if not self: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1247 return context._raise_error(DivisionUndefined, '0 / 0') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1248 return context._raise_error(DivisionByZero, 'x / 0', sign) |
|
33519
139a4012bead
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parents:
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diff
changeset
|
1249 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1250 if not self: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1251 exp = self._exp - other._exp |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1252 coeff = 0 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1253 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1254 # OK, so neither = 0, INF or NaN |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1255 shift = len(other._int) - len(self._int) + context.prec + 1 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1256 exp = self._exp - other._exp - shift |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1257 op1 = _WorkRep(self) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1258 op2 = _WorkRep(other) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1259 if shift >= 0: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1260 coeff, remainder = divmod(op1.int * 10**shift, op2.int) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1261 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1262 coeff, remainder = divmod(op1.int, op2.int * 10**-shift) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1263 if remainder: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1264 # result is not exact; adjust to ensure correct rounding |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1265 if coeff % 5 == 0: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1266 coeff += 1 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1267 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1268 # result is exact; get as close to ideal exponent as possible |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1269 ideal_exp = self._exp - other._exp |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1270 while exp < ideal_exp and coeff % 10 == 0: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1271 coeff //= 10 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1272 exp += 1 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1273 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1274 ans = _dec_from_triple(sign, str(coeff), exp) |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1275 return ans._fix(context) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1276 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1277 def _divide(self, other, context): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1278 """Return (self // other, self % other), to context.prec precision. |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1279 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1280 Assumes that neither self nor other is a NaN, that self is not |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1281 infinite and that other is nonzero. |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1282 """ |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1283 sign = self._sign ^ other._sign |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1284 if other._isinfinity(): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1285 ideal_exp = self._exp |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1286 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1287 ideal_exp = min(self._exp, other._exp) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1288 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1289 expdiff = self.adjusted() - other.adjusted() |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1290 if not self or other._isinfinity() or expdiff <= -2: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1291 return (_dec_from_triple(sign, '0', 0), |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1292 self._rescale(ideal_exp, context.rounding)) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1293 if expdiff <= context.prec: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1294 op1 = _WorkRep(self) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1295 op2 = _WorkRep(other) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1296 if op1.exp >= op2.exp: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1297 op1.int *= 10**(op1.exp - op2.exp) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1298 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1299 op2.int *= 10**(op2.exp - op1.exp) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1300 q, r = divmod(op1.int, op2.int) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1301 if q < 10**context.prec: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1302 return (_dec_from_triple(sign, str(q), 0), |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1303 _dec_from_triple(self._sign, str(r), ideal_exp)) |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1304 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1305 # Here the quotient is too large to be representable |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1306 ans = context._raise_error(DivisionImpossible, |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1307 'quotient too large in //, % or divmod') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1308 return ans, ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1309 |
|
46651
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1310 def __rtruediv__(self, other, context=None): |
|
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1311 """Swaps self/other and returns __truediv__.""" |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1312 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1313 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1314 return other |
|
46651
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1315 return other.__truediv__(self, context=context) |
|
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1316 |
|
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1317 __div__ = __truediv__ |
|
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
1318 __rdiv__ = __rtruediv__ |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1319 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1320 def __divmod__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1321 """ |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1322 Return (self // other, self % other) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1323 """ |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1324 other = _convert_other(other) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1325 if other is NotImplemented: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1326 return other |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1327 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1328 if context is None: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1329 context = getcontext() |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1330 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1331 ans = self._check_nans(other, context) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1332 if ans: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1333 return (ans, ans) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1334 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1335 sign = self._sign ^ other._sign |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1336 if self._isinfinity(): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1337 if other._isinfinity(): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1338 ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1339 return ans, ans |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1340 else: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
1341 return (_SignedInfinity[sign], |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1342 context._raise_error(InvalidOperation, 'INF % x')) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1343 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1344 if not other: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1345 if not self: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1346 ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1347 return ans, ans |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1348 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1349 return (context._raise_error(DivisionByZero, 'x // 0', sign), |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1350 context._raise_error(InvalidOperation, 'x % 0')) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1351 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1352 quotient, remainder = self._divide(other, context) |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1353 remainder = remainder._fix(context) |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1354 return quotient, remainder |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1355 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1356 def __rdivmod__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1357 """Swaps self/other and returns __divmod__.""" |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1358 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1359 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1360 return other |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1361 return other.__divmod__(self, context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1362 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1363 def __mod__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1364 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1365 self % other |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1366 """ |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1367 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1368 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1369 return other |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1370 |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1371 if context is None: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1372 context = getcontext() |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1373 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1374 ans = self._check_nans(other, context) |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1375 if ans: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1376 return ans |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1377 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1378 if self._isinfinity(): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1379 return context._raise_error(InvalidOperation, 'INF % x') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1380 elif not other: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1381 if self: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1382 return context._raise_error(InvalidOperation, 'x % 0') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1383 else: |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1384 return context._raise_error(DivisionUndefined, '0 % 0') |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1385 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1386 remainder = self._divide(other, context)[1] |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
1387 remainder = remainder._fix(context) |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1388 return remainder |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1389 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1390 def __rmod__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1391 """Swaps self/other and returns __mod__.""" |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
1392 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1393 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
1394 return other |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1395 return other.__mod__(self, context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1396 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1397 def remainder_near(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1398 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1399 Remainder nearest to 0- abs(remainder-near) <= other/2 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1400 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1401 if context is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1402 context = getcontext() |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1403 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1404 other = _convert_other(other, raiseit=True) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1405 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1406 ans = self._check_nans(other, context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1407 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1408 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1409 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1410 # self == +/-infinity -> InvalidOperation |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1411 if self._isinfinity(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1412 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1413 'remainder_near(infinity, x)') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1414 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1415 # other == 0 -> either InvalidOperation or DivisionUndefined |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1416 if not other: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1417 if self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1418 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1419 'remainder_near(x, 0)') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1420 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1421 return context._raise_error(DivisionUndefined, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1422 'remainder_near(0, 0)') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1423 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1424 # other = +/-infinity -> remainder = self |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1425 if other._isinfinity(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1426 ans = Decimal(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1427 return ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1428 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1429 # self = 0 -> remainder = self, with ideal exponent |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1430 ideal_exponent = min(self._exp, other._exp) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1431 if not self: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1432 ans = _dec_from_triple(self._sign, '0', ideal_exponent) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1433 return ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1434 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1435 # catch most cases of large or small quotient |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1436 expdiff = self.adjusted() - other.adjusted() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1437 if expdiff >= context.prec + 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1438 # expdiff >= prec+1 => abs(self/other) > 10**prec |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1439 return context._raise_error(DivisionImpossible) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1440 if expdiff <= -2: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1441 # expdiff <= -2 => abs(self/other) < 0.1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1442 ans = self._rescale(ideal_exponent, context.rounding) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1443 return ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1444 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1445 # adjust both arguments to have the same exponent, then divide |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1446 op1 = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1447 op2 = _WorkRep(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1448 if op1.exp >= op2.exp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1449 op1.int *= 10**(op1.exp - op2.exp) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1450 else: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1451 op2.int *= 10**(op2.exp - op1.exp) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1452 q, r = divmod(op1.int, op2.int) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1453 # remainder is r*10**ideal_exponent; other is +/-op2.int * |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1454 # 10**ideal_exponent. Apply correction to ensure that |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1455 # abs(remainder) <= abs(other)/2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1456 if 2*r + (q&1) > op2.int: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1457 r -= op2.int |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1458 q += 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1459 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1460 if q >= 10**context.prec: |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
1461 return context._raise_error(DivisionImpossible) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1462 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1463 # result has same sign as self unless r is negative |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1464 sign = self._sign |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1465 if r < 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1466 sign = 1-sign |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1467 r = -r |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1468 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1469 ans = _dec_from_triple(sign, str(r), ideal_exponent) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1470 return ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1471 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1472 def __floordiv__(self, other, context=None): |
|
d2c1c7ae7cf4
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Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1473 """self // other""" |
|
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|
1474 other = _convert_other(other) |
|
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diff
changeset
|
1475 if other is NotImplemented: |
|
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diff
changeset
|
1476 return other |
|
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parents:
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diff
changeset
|
1477 |
|
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parents:
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diff
changeset
|
1478 if context is None: |
|
b9236a75a6e5
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parents:
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diff
changeset
|
1479 context = getcontext() |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
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parents:
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diff
changeset
|
1480 |
|
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parents:
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diff
changeset
|
1481 ans = self._check_nans(other, context) |
|
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Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1482 if ans: |
|
b9236a75a6e5
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Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1483 return ans |
|
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parents:
43383
diff
changeset
|
1484 |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1485 if self._isinfinity(): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1486 if other._isinfinity(): |
|
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
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diff
changeset
|
1487 return context._raise_error(InvalidOperation, 'INF // INF') |
|
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changeset
|
1488 else: |
|
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diff
changeset
|
1489 return _SignedInfinity[self._sign ^ other._sign] |
|
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changeset
|
1490 |
|
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changeset
|
1491 if not other: |
|
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parents:
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diff
changeset
|
1492 if self: |
|
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parents:
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diff
changeset
|
1493 return context._raise_error(DivisionByZero, 'x // 0', |
|
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parents:
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diff
changeset
|
1494 self._sign ^ other._sign) |
|
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parents:
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diff
changeset
|
1495 else: |
|
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diff
changeset
|
1496 return context._raise_error(DivisionUndefined, '0 // 0') |
|
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|
1497 |
|
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changeset
|
1498 return self._divide(other, context)[0] |
|
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|
1499 |
|
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Raymond Hettinger <python@rcn.com>
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diff
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|
1500 def __rfloordiv__(self, other, context=None): |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1501 """Swaps self/other and returns __floordiv__.""" |
|
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|
1502 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
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|
1503 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
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changeset
|
1504 return other |
|
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parents:
diff
changeset
|
1505 return other.__floordiv__(self, context=context) |
|
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|
1506 |
|
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Raymond Hettinger <python@rcn.com>
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|
1507 def __float__(self): |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
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changeset
|
1508 """Float representation.""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
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|
1509 return float(str(self)) |
|
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diff
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|
1510 |
|
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changeset
|
1511 def __int__(self): |
|
34638
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Fix small grammatical error in a docstring.
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34545
diff
changeset
|
1512 """Converts self to an int, truncating if necessary.""" |
|
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|
1513 if self._is_special: |
|
139a4012bead
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changeset
|
1514 if self._isnan(): |
|
55886
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|
1515 raise ValueError("Cannot convert NaN to integer") |
|
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|
1516 elif self._isinfinity(): |
|
55886
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changeset
|
1517 raise OverflowError("Cannot convert infinity to integer") |
|
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|
1518 s = (-1)**self._sign |
|
34023
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SF bug #1071588 coercing decimal to int doesn't work between -1 and 1
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changeset
|
1519 if self._exp >= 0: |
|
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|
1520 return s*int(self._int)*10**self._exp |
|
34023
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|
1521 else: |
|
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|
1522 return s*int(self._int[:self._exp] or '0') |
|
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|
1523 |
|
44923
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diff
changeset
|
1524 __trunc__ = __int__ |
|
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Add support for trunc().
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|
1525 |
|
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diff
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|
1526 def real(self): |
|
4ca70663a79d
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diff
changeset
|
1527 return self |
|
50601
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|
1528 real = property(real) |
|
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|
1529 |
|
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|
1530 def imag(self): |
|
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changeset
|
1531 return Decimal(0) |
|
50601
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changeset
|
1532 imag = property(imag) |
|
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|
1533 |
|
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changeset
|
1534 def conjugate(self): |
|
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diff
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|
1535 return self |
|
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diff
changeset
|
1536 |
|
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diff
changeset
|
1537 def __complex__(self): |
|
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parents:
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diff
changeset
|
1538 return complex(float(self)) |
|
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|
1539 |
|
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|
1540 def __long__(self): |
|
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Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
1541 """Converts to a long. |
|
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Move Decimal from the sandbox into production.
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diff
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|
1542 |
|
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changeset
|
1543 Equivalent to long(int(self)) |
|
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diff
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|
1544 """ |
|
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parents:
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|
1545 return long(self.__int__()) |
|
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changeset
|
1546 |
|
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changeset
|
1547 def _fix_nan(self, context): |
|
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diff
changeset
|
1548 """Decapitate the payload of a NaN to fit the context""" |
|
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changeset
|
1549 payload = self._int |
|
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changeset
|
1550 |
|
63f3154c731d
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diff
changeset
|
1551 # maximum length of payload is precision if _clamp=0, |
|
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diff
changeset
|
1552 # precision-1 if _clamp=1. |
|
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diff
changeset
|
1553 max_payload_len = context.prec - context._clamp |
|
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changeset
|
1554 if len(payload) > max_payload_len: |
|
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diff
changeset
|
1555 payload = payload[len(payload)-max_payload_len:].lstrip('0') |
|
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changeset
|
1556 return _dec_from_triple(self._sign, payload, self._exp, True) |
|
43383
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diff
changeset
|
1557 return Decimal(self) |
|
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|
1558 |
| 33695 | 1559 def _fix(self, context): |
|
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|
1560 """Round if it is necessary to keep self within prec precision. |
|
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|
1561 |
|
d2c1c7ae7cf4
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changeset
|
1562 Rounds and fixes the exponent. Does not raise on a sNaN. |
|
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Move Decimal from the sandbox into production.
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|
1563 |
|
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|
1564 Arguments: |
|
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Move Decimal from the sandbox into production.
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|
1565 self - Decimal instance |
|
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Move Decimal from the sandbox into production.
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|
1566 context - context used. |
|
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|
1567 """ |
|
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|
1568 |
|
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|
1569 if self._is_special: |
|
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|
1570 if self._isnan(): |
|
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changeset
|
1571 # decapitate payload if necessary |
|
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changeset
|
1572 return self._fix_nan(context) |
|
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|
1573 else: |
|
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diff
changeset
|
1574 # self is +/-Infinity; return unaltered |
|
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43362
diff
changeset
|
1575 return Decimal(self) |
|
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changeset
|
1576 |
|
63f3154c731d
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diff
changeset
|
1577 # if self is zero then exponent should be between Etiny and |
|
63f3154c731d
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diff
changeset
|
1578 # Emax if _clamp==0, and between Etiny and Etop if _clamp==1. |
|
63f3154c731d
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diff
changeset
|
1579 Etiny = context.Etiny() |
|
63f3154c731d
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diff
changeset
|
1580 Etop = context.Etop() |
|
63f3154c731d
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diff
changeset
|
1581 if not self: |
|
63f3154c731d
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diff
changeset
|
1582 exp_max = [context.Emax, Etop][context._clamp] |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1583 new_exp = min(max(self._exp, Etiny), exp_max) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1584 if new_exp != self._exp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1585 context._raise_error(Clamped) |
|
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Major change in the internal structure of the Decimal
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diff
changeset
|
1586 return _dec_from_triple(self._sign, '0', new_exp) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
1587 else: |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1588 return Decimal(self) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1589 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
1590 # exp_min is the smallest allowable exponent of the result, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1591 # equal to max(self.adjusted()-context.prec+1, Etiny) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1592 exp_min = len(self._int) + self._exp - context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1593 if exp_min > Etop: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1594 # overflow: exp_min > Etop iff self.adjusted() > Emax |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1595 context._raise_error(Inexact) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1596 context._raise_error(Rounded) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1597 return context._raise_error(Overflow, 'above Emax', self._sign) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1598 self_is_subnormal = exp_min < Etiny |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1599 if self_is_subnormal: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1600 context._raise_error(Subnormal) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1601 exp_min = Etiny |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1602 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1603 # round if self has too many digits |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1604 if self._exp < exp_min: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1605 context._raise_error(Rounded) |
|
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30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1606 digits = len(self._int) + self._exp - exp_min |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1607 if digits < 0: |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1608 self = _dec_from_triple(self._sign, '1', exp_min-1) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1609 digits = 0 |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1610 this_function = getattr(self, self._pick_rounding_function[context.rounding]) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1611 changed = this_function(digits) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1612 coeff = self._int[:digits] or '0' |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1613 if changed == 1: |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1614 coeff = str(int(coeff)+1) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1615 ans = _dec_from_triple(self._sign, coeff, exp_min) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1616 |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1617 if changed: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1618 context._raise_error(Inexact) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1619 if self_is_subnormal: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1620 context._raise_error(Underflow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1621 if not ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1622 # raise Clamped on underflow to 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1623 context._raise_error(Clamped) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1624 elif len(ans._int) == context.prec+1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1625 # we get here only if rescaling rounds the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1626 # cofficient up to exactly 10**context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1627 if ans._exp < Etop: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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diff
changeset
|
1628 ans = _dec_from_triple(ans._sign, |
|
a4a140486691
Major change in the internal structure of the Decimal
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diff
changeset
|
1629 ans._int[:-1], ans._exp+1) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1630 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1631 # Inexact and Rounded have already been raised |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1632 ans = context._raise_error(Overflow, 'above Emax', |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1633 self._sign) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
1634 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1635 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1636 # fold down if _clamp == 1 and self has too few digits |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1637 if context._clamp == 1 and self._exp > Etop: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1638 context._raise_error(Clamped) |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
1639 self_padded = self._int + '0'*(self._exp - Etop) |
|
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
1640 return _dec_from_triple(self._sign, self_padded, Etop) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1641 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1642 # here self was representable to begin with; return unchanged |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1643 return Decimal(self) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
1644 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1645 _pick_rounding_function = {} |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1646 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1647 # for each of the rounding functions below: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1648 # self is a finite, nonzero Decimal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1649 # prec is an integer satisfying 0 <= prec < len(self._int) |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1650 # |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1651 # each function returns either -1, 0, or 1, as follows: |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1652 # 1 indicates that self should be rounded up (away from zero) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1653 # 0 indicates that self should be truncated, and that all the |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1654 # digits to be truncated are zeros (so the value is unchanged) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1655 # -1 indicates that there are nonzero digits to be truncated |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1656 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1657 def _round_down(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1658 """Also known as round-towards-0, truncate.""" |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1659 if _all_zeros(self._int, prec): |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1660 return 0 |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1661 else: |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1662 return -1 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1663 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1664 def _round_up(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1665 """Rounds away from 0.""" |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1666 return -self._round_down(prec) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1667 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1668 def _round_half_up(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1669 """Rounds 5 up (away from 0)""" |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
1670 if self._int[prec] in '56789': |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1671 return 1 |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1672 elif _all_zeros(self._int, prec): |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1673 return 0 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1674 else: |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1675 return -1 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1676 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1677 def _round_half_down(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1678 """Round 5 down""" |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1679 if _exact_half(self._int, prec): |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1680 return -1 |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
1681 else: |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1682 return self._round_half_up(prec) |
|
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63f3154c731d
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|
1683 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1684 def _round_half_even(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1685 """Round 5 to even, rest to nearest.""" |
|
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Faster _fix function, and some reordering for a more elegant
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|
1686 if _exact_half(self._int, prec) and \ |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
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|
1687 (prec == 0 or self._int[prec-1] in '02468'): |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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|
1688 return -1 |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1689 else: |
|
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diff
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|
1690 return self._round_half_up(prec) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1691 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
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|
1692 def _round_ceiling(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1693 """Rounds up (not away from 0 if negative.)""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1694 if self._sign: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1695 return self._round_down(prec) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1696 else: |
|
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Faster _fix function, and some reordering for a more elegant
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diff
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|
1697 return -self._round_down(prec) |
|
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|
1698 |
|
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|
1699 def _round_floor(self, prec): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
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|
1700 """Rounds down (not towards 0 if negative)""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1701 if not self._sign: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1702 return self._round_down(prec) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
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|
1703 else: |
|
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Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1704 return -self._round_down(prec) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1705 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1706 def _round_05up(self, prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1707 """Round down unless digit prec-1 is 0 or 5.""" |
|
44121
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Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1708 if prec and self._int[prec-1] not in '05': |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
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parents:
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diff
changeset
|
1709 return self._round_down(prec) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
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|
1710 else: |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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diff
changeset
|
1711 return -self._round_down(prec) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1712 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1713 def fma(self, other, third, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1714 """Fused multiply-add. |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1715 |
|
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|
1716 Returns self*other+third with no rounding of the intermediate |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1717 product self*other. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1718 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1719 self and other are multiplied together, with no rounding of |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1720 the result. The third operand is then added to the result, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1721 and a single final rounding is performed. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1722 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1723 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1724 other = _convert_other(other, raiseit=True) |
|
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|
1725 |
|
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changeset
|
1726 # compute product; raise InvalidOperation if either operand is |
|
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|
1727 # a signaling NaN or if the product is zero times infinity. |
|
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|
1728 if self._is_special or other._is_special: |
|
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|
1729 if context is None: |
|
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|
1730 context = getcontext() |
|
53320d544bc7
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|
1731 if self._exp == 'N': |
|
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|
1732 return context._raise_error(InvalidOperation, 'sNaN', self) |
|
44148
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parents:
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diff
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|
1733 if other._exp == 'N': |
|
44352
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Some minor cleanups. Thanks Mark Dickinson.
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parents:
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diff
changeset
|
1734 return context._raise_error(InvalidOperation, 'sNaN', other) |
|
44148
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parents:
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|
1735 if self._exp == 'n': |
|
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|
1736 product = self |
|
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|
1737 elif other._exp == 'n': |
|
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parents:
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|
1738 product = other |
|
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parents:
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|
1739 elif self._exp == 'F': |
|
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|
1740 if not other: |
|
53320d544bc7
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|
1741 return context._raise_error(InvalidOperation, |
|
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changeset
|
1742 'INF * 0 in fma') |
|
50480
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Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
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|
1743 product = _SignedInfinity[self._sign ^ other._sign] |
|
44148
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|
1744 elif other._exp == 'F': |
|
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|
1745 if not self: |
|
53320d544bc7
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changeset
|
1746 return context._raise_error(InvalidOperation, |
|
53320d544bc7
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changeset
|
1747 '0 * INF in fma') |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
1748 product = _SignedInfinity[self._sign ^ other._sign] |
|
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|
1749 else: |
|
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diff
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|
1750 product = _dec_from_triple(self._sign ^ other._sign, |
|
53320d544bc7
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|
1751 str(int(self._int) * int(other._int)), |
|
53320d544bc7
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|
1752 self._exp + other._exp) |
|
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|
1753 |
|
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changeset
|
1754 third = _convert_other(third, raiseit=True) |
|
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|
1755 return product.__add__(third, context) |
|
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|
1756 |
|
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|
1757 def _power_modulo(self, other, modulo, context=None): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1758 """Three argument version of __pow__""" |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1759 |
|
63f3154c731d
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changeset
|
1760 # if can't convert other and modulo to Decimal, raise |
|
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|
1761 # TypeError; there's no point returning NotImplemented (no |
|
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changeset
|
1762 # equivalent of __rpow__ for three argument pow) |
|
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|
1763 other = _convert_other(other, raiseit=True) |
|
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|
1764 modulo = _convert_other(modulo, raiseit=True) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
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|
1765 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
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changeset
|
1766 if context is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
1767 context = getcontext() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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diff
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|
1768 |
|
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changeset
|
1769 # deal with NaNs: if there are any sNaNs then first one wins, |
|
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|
1770 # (i.e. behaviour for NaNs is identical to that of fma) |
|
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|
1771 self_is_nan = self._isnan() |
|
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|
1772 other_is_nan = other._isnan() |
|
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|
1773 modulo_is_nan = modulo._isnan() |
|
63f3154c731d
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|
1774 if self_is_nan or other_is_nan or modulo_is_nan: |
|
63f3154c731d
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|
1775 if self_is_nan == 2: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1776 return context._raise_error(InvalidOperation, 'sNaN', |
|
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|
1777 self) |
|
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|
1778 if other_is_nan == 2: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1779 return context._raise_error(InvalidOperation, 'sNaN', |
|
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|
1780 other) |
|
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|
1781 if modulo_is_nan == 2: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1782 return context._raise_error(InvalidOperation, 'sNaN', |
|
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Some minor cleanups. Thanks Mark Dickinson.
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|
1783 modulo) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1784 if self_is_nan: |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
1785 return self._fix_nan(context) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
1786 if other_is_nan: |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
1787 return other._fix_nan(context) |
|
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
1788 return modulo._fix_nan(context) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1789 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1790 # check inputs: we apply same restrictions as Python's pow() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1791 if not (self._isinteger() and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1792 other._isinteger() and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1793 modulo._isinteger()): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1794 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1795 'pow() 3rd argument not allowed ' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1796 'unless all arguments are integers') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1797 if other < 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1798 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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|
1799 'pow() 2nd argument cannot be ' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1800 'negative when 3rd argument specified') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
1801 if not modulo: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1802 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1803 'pow() 3rd argument cannot be 0') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1804 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1805 # additional restriction for decimal: the modulus must be less |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1806 # than 10**prec in absolute value |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1807 if modulo.adjusted() >= context.prec: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1808 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1809 'insufficient precision: pow() 3rd ' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1810 'argument must not have more than ' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1811 'precision digits') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1812 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1813 # define 0**0 == NaN, for consistency with two-argument pow |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1814 # (even though it hurts!) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1815 if not other and not self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1816 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1817 'at least one of pow() 1st argument ' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1818 'and 2nd argument must be nonzero ;' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1819 '0**0 is not defined') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1820 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1821 # compute sign of result |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1822 if other._iseven(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1823 sign = 0 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
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diff
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|
1824 else: |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1825 sign = self._sign |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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|
1826 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1827 # convert modulo to a Python integer, and self and other to |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1828 # Decimal integers (i.e. force their exponents to be >= 0) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1829 modulo = abs(int(modulo)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1830 base = _WorkRep(self.to_integral_value()) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1831 exponent = _WorkRep(other.to_integral_value()) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1832 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1833 # compute result using integer pow() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1834 base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1835 for i in xrange(exponent.exp): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1836 base = pow(base, 10, modulo) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1837 base = pow(base, exponent.int, modulo) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1838 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1839 return _dec_from_triple(sign, str(base), 0) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1840 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1841 def _power_exact(self, other, p): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1842 """Attempt to compute self**other exactly. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1843 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1844 Given Decimals self and other and an integer p, attempt to |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1845 compute an exact result for the power self**other, with p |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
1846 digits of precision. Return None if self**other is not |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1847 exactly representable in p digits. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1848 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1849 Assumes that elimination of special cases has already been |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1850 performed: self and other must both be nonspecial; self must |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1851 be positive and not numerically equal to 1; other must be |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1852 nonzero. For efficiency, other._exp should not be too large, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1853 so that 10**abs(other._exp) is a feasible calculation.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1854 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1855 # In the comments below, we write x for the value of self and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1856 # y for the value of other. Write x = xc*10**xe and y = |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1857 # yc*10**ye. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1858 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1859 # The main purpose of this method is to identify the *failure* |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1860 # of x**y to be exactly representable with as little effort as |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1861 # possible. So we look for cheap and easy tests that |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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|
1862 # eliminate the possibility of x**y being exact. Only if all |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1863 # these tests are passed do we go on to actually compute x**y. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1864 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1865 # Here's the main idea. First normalize both x and y. We |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1866 # express y as a rational m/n, with m and n relatively prime |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1867 # and n>0. Then for x**y to be exactly representable (at |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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|
1868 # *any* precision), xc must be the nth power of a positive |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
1869 # integer and xe must be divisible by n. If m is negative |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1870 # then additionally xc must be a power of either 2 or 5, hence |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1871 # a power of 2**n or 5**n. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1872 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1873 # There's a limit to how small |y| can be: if y=m/n as above |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1874 # then: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1875 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1876 # (1) if xc != 1 then for the result to be representable we |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1877 # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1878 # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
1879 # 2**(1/|y|), hence xc**|y| < 2 and the result is not |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
1880 # representable. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1881 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1882 # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1883 # |y| < 1/|xe| then the result is not representable. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1884 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1885 # Note that since x is not equal to 1, at least one of (1) and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1886 # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1887 # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1888 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1889 # There's also a limit to how large y can be, at least if it's |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1890 # positive: the normalized result will have coefficient xc**y, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1891 # so if it's representable then xc**y < 10**p, and y < |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1892 # p/log10(xc). Hence if y*log10(xc) >= p then the result is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1893 # not exactly representable. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1894 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1895 # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1896 # so |y| < 1/xe and the result is not representable. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1897 # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1898 # < 1/nbits(xc). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1899 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1900 x = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1901 xc, xe = x.int, x.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1902 while xc % 10 == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1903 xc //= 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1904 xe += 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1905 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1906 y = _WorkRep(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1907 yc, ye = y.int, y.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1908 while yc % 10 == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1909 yc //= 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1910 ye += 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1911 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1912 # case where xc == 1: result is 10**(xe*y), with xe*y |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1913 # required to be an integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1914 if xc == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1915 if ye >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1916 exponent = xe*yc*10**ye |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1917 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1918 exponent, remainder = divmod(xe*yc, 10**-ye) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1919 if remainder: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1920 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1921 if y.sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1922 exponent = -exponent |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1923 # if other is a nonnegative integer, use ideal exponent |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1924 if other._isinteger() and other._sign == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1925 ideal_exponent = self._exp*int(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1926 zeros = min(exponent-ideal_exponent, p-1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1927 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1928 zeros = 0 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1929 return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1930 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1931 # case where y is negative: xc must be either a power |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1932 # of 2 or a power of 5. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1933 if y.sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1934 last_digit = xc % 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1935 if last_digit in (2,4,6,8): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1936 # quick test for power of 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1937 if xc & -xc != xc: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1938 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1939 # now xc is a power of 2; e is its exponent |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1940 e = _nbits(xc)-1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1941 # find e*y and xe*y; both must be integers |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1942 if ye >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1943 y_as_int = yc*10**ye |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1944 e = e*y_as_int |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1945 xe = xe*y_as_int |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1946 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1947 ten_pow = 10**-ye |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1948 e, remainder = divmod(e*yc, ten_pow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1949 if remainder: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1950 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1951 xe, remainder = divmod(xe*yc, ten_pow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1952 if remainder: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1953 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1954 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1955 if e*65 >= p*93: # 93/65 > log(10)/log(5) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1956 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1957 xc = 5**e |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1958 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1959 elif last_digit == 5: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1960 # e >= log_5(xc) if xc is a power of 5; we have |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1961 # equality all the way up to xc=5**2658 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1962 e = _nbits(xc)*28//65 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1963 xc, remainder = divmod(5**e, xc) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1964 if remainder: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1965 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1966 while xc % 5 == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1967 xc //= 5 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1968 e -= 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1969 if ye >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1970 y_as_integer = yc*10**ye |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1971 e = e*y_as_integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1972 xe = xe*y_as_integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1973 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1974 ten_pow = 10**-ye |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1975 e, remainder = divmod(e*yc, ten_pow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1976 if remainder: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1977 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1978 xe, remainder = divmod(xe*yc, ten_pow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
1979 if remainder: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1980 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1981 if e*3 >= p*10: # 10/3 > log(10)/log(2) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1982 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1983 xc = 2**e |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1984 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1985 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1986 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1987 if xc >= 10**p: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1988 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1989 xe = -e-xe |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
1990 return _dec_from_triple(0, str(xc), xe) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1991 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1992 # now y is positive; find m and n such that y = m/n |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1993 if ye >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1994 m, n = yc*10**ye, 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1995 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1996 if xe != 0 and len(str(abs(yc*xe))) <= -ye: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1997 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
1998 xc_bits = _nbits(xc) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
1999 if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2000 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2001 m, n = yc, 10**(-ye) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2002 while m % 2 == n % 2 == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2003 m //= 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2004 n //= 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2005 while m % 5 == n % 5 == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2006 m //= 5 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2007 n //= 5 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2008 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2009 # compute nth root of xc*10**xe |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2010 if n > 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2011 # if 1 < xc < 2**n then xc isn't an nth power |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2012 if xc != 1 and xc_bits <= n: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2013 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2014 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2015 xe, rem = divmod(xe, n) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2016 if rem != 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2017 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2018 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2019 # compute nth root of xc using Newton's method |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2020 a = 1L << -(-_nbits(xc)//n) # initial estimate |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2021 while True: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2022 q, r = divmod(xc, a**(n-1)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2023 if a <= q: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2024 break |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2025 else: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2026 a = (a*(n-1) + q)//n |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2027 if not (a == q and r == 0): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2028 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2029 xc = a |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2030 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2031 # now xc*10**xe is the nth root of the original xc*10**xe |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2032 # compute mth power of xc*10**xe |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2033 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2034 # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2035 # 10**p and the result is not representable. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2036 if xc > 1 and m > p*100//_log10_lb(xc): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2037 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2038 xc = xc**m |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2039 xe *= m |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2040 if xc > 10**p: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2041 return None |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2042 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2043 # by this point the result *is* exactly representable |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2044 # adjust the exponent to get as close as possible to the ideal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2045 # exponent, if necessary |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2046 str_xc = str(xc) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2047 if other._isinteger() and other._sign == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2048 ideal_exponent = self._exp*int(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2049 zeros = min(xe-ideal_exponent, p-len(str_xc)) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2050 else: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2051 zeros = 0 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2052 return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2053 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2054 def __pow__(self, other, modulo=None, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2055 """Return self ** other [ % modulo]. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2056 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2057 With two arguments, compute self**other. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2058 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2059 With three arguments, compute (self**other) % modulo. For the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2060 three argument form, the following restrictions on the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2061 arguments hold: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2062 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2063 - all three arguments must be integral |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2064 - other must be nonnegative |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2065 - either self or other (or both) must be nonzero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2066 - modulo must be nonzero and must have at most p digits, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2067 where p is the context precision. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2068 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2069 If any of these restrictions is violated the InvalidOperation |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2070 flag is raised. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2071 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2072 The result of pow(self, other, modulo) is identical to the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2073 result that would be obtained by computing (self**other) % |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2074 modulo with unbounded precision, but is computed more |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2075 efficiently. It is always exact. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2076 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2077 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2078 if modulo is not None: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2079 return self._power_modulo(other, modulo, context) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2080 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2081 other = _convert_other(other) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2082 if other is NotImplemented: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2083 return other |
|
33519
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|
2084 |
|
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|
2085 if context is None: |
|
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Move Decimal from the sandbox into production.
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|
2086 context = getcontext() |
|
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|
2087 |
|
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|
2088 # either argument is a NaN => result is NaN |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2089 ans = self._check_nans(other, context) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2090 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2091 return ans |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2092 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2093 # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) |
|
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|
2094 if not other: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2095 if not self: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2096 return context._raise_error(InvalidOperation, '0 ** 0') |
|
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|
2097 else: |
|
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|
2098 return _One |
|
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|
2099 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2100 # result has sign 1 iff self._sign is 1 and other is an odd integer |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2101 result_sign = 0 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2102 if self._sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2103 if other._isinteger(): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2104 if not other._iseven(): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2105 result_sign = 1 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2106 else: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2107 # -ve**noninteger = NaN |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2108 # (-0)**noninteger = 0**noninteger |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2109 if self: |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2110 return context._raise_error(InvalidOperation, |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2111 'x ** y with x negative and y not an integer') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2112 # negate self, without doing any unwanted rounding |
|
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|
2113 self = self.copy_negate() |
|
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|
2114 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2115 # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2116 if not self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2117 if other._sign == 0: |
|
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Major change in the internal structure of the Decimal
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|
2118 return _dec_from_triple(result_sign, '0', 0) |
|
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|
2119 else: |
|
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|
2120 return _SignedInfinity[result_sign] |
|
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|
2121 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2122 # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 |
|
32451
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Move Decimal from the sandbox into production.
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|
2123 if self._isinfinity(): |
|
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|
2124 if other._sign == 0: |
|
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|
2125 return _SignedInfinity[result_sign] |
|
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|
2126 else: |
|
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Major change in the internal structure of the Decimal
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|
2127 return _dec_from_triple(result_sign, '0', 0) |
|
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|
2128 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2129 # 1**other = 1, but the choice of exponent and the flags |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2130 # depend on the exponent of self, and on whether other is a |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2131 # positive integer, a negative integer, or neither |
|
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|
2132 if self == _One: |
|
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|
2133 if other._isinteger(): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2134 # exp = max(self._exp*max(int(other), 0), |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2135 # 1-context.prec) but evaluating int(other) directly |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2136 # is dangerous until we know other is small (other |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2137 # could be 1e999999999) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2138 if other._sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2139 multiplier = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2140 elif other > context.prec: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2141 multiplier = context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2142 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2143 multiplier = int(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2144 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2145 exp = self._exp * multiplier |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2146 if exp < 1-context.prec: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2147 exp = 1-context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2148 context._raise_error(Rounded) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2149 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2150 context._raise_error(Inexact) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2151 context._raise_error(Rounded) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2152 exp = 1-context.prec |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2153 |
|
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Major change in the internal structure of the Decimal
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|
2154 return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) |
|
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|
2155 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2156 # compute adjusted exponent of self |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2157 self_adj = self.adjusted() |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2158 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2159 # self ** infinity is infinity if self > 1, 0 if self < 1 |
|
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|
2160 # self ** -infinity is infinity if self < 1, 0 if self > 1 |
|
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|
2161 if other._isinfinity(): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2162 if (other._sign == 0) == (self_adj < 0): |
|
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|
2163 return _dec_from_triple(result_sign, '0', 0) |
|
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|
2164 else: |
|
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|
2165 return _SignedInfinity[result_sign] |
|
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|
2166 |
|
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|
2167 # from here on, the result always goes through the call |
|
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|
2168 # to _fix at the end of this function. |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2169 ans = None |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2170 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2171 # crude test to catch cases of extreme overflow/underflow. If |
|
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|
2172 # log10(self)*other >= 10**bound and bound >= len(str(Emax)) |
|
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|
2173 # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence |
|
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|
2174 # self**other >= 10**(Emax+1), so overflow occurs. The test |
|
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|
2175 # for underflow is similar. |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
2176 bound = self._log10_exp_bound() + other.adjusted() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2177 if (self_adj >= 0) == (other._sign == 0): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2178 # self > 1 and other +ve, or self < 1 and other -ve |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2179 # possibility of overflow |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2180 if bound >= len(str(context.Emax)): |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2181 ans = _dec_from_triple(result_sign, '1', context.Emax+1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2182 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2183 # self > 1 and other -ve, or self < 1 and other +ve |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2184 # possibility of underflow to 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2185 Etiny = context.Etiny() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2186 if bound >= len(str(-Etiny)): |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2187 ans = _dec_from_triple(result_sign, '1', Etiny-1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2188 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2189 # try for an exact result with precision +1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2190 if ans is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2191 ans = self._power_exact(other, context.prec + 1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2192 if ans is not None and result_sign == 1: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2193 ans = _dec_from_triple(1, ans._int, ans._exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2194 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2195 # usual case: inexact result, x**y computed directly as exp(y*log(x)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2196 if ans is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2197 p = context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2198 x = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2199 xc, xe = x.int, x.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2200 y = _WorkRep(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2201 yc, ye = y.int, y.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2202 if y.sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2203 yc = -yc |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2204 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2205 # compute correctly rounded result: start with precision +3, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2206 # then increase precision until result is unambiguously roundable |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2207 extra = 3 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2208 while True: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2209 coeff, exp = _dpower(xc, xe, yc, ye, p+extra) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2210 if coeff % (5*10**(len(str(coeff))-p-1)): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2211 break |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2212 extra += 3 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2213 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2214 ans = _dec_from_triple(result_sign, str(coeff), exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2215 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2216 # the specification says that for non-integer other we need to |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2217 # raise Inexact, even when the result is actually exact. In |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2218 # the same way, we need to raise Underflow here if the result |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2219 # is subnormal. (The call to _fix will take care of raising |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2220 # Rounded and Subnormal, as usual.) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2221 if not other._isinteger(): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2222 context._raise_error(Inexact) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2223 # pad with zeros up to length context.prec+1 if necessary |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2224 if len(ans._int) <= context.prec: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2225 expdiff = context.prec+1 - len(ans._int) |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2226 ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2227 ans._exp-expdiff) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2228 if ans.adjusted() < context.Emin: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2229 context._raise_error(Underflow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2230 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2231 # unlike exp, ln and log10, the power function respects the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2232 # rounding mode; no need to use ROUND_HALF_EVEN here |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2233 ans = ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2234 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2235 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2236 def __rpow__(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2237 """Swaps self/other and returns __pow__.""" |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2238 other = _convert_other(other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
2239 if other is NotImplemented: |
|
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
Raymond Hettinger <python@rcn.com>
parents:
34758
diff
changeset
|
2240 return other |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2241 return other.__pow__(self, context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2242 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2243 def normalize(self, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2244 """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2245 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2246 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2247 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2248 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2249 if self._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2250 ans = self._check_nans(context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2251 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2252 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2253 |
| 33695 | 2254 dup = self._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2255 if dup._isinfinity(): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2256 return dup |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2257 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2258 if not dup: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2259 return _dec_from_triple(dup._sign, '0', 0) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2260 exp_max = [context.Emax, context.Etop()][context._clamp] |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2261 end = len(dup._int) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2262 exp = dup._exp |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2263 while dup._int[end-1] == '0' and exp < exp_max: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2264 exp += 1 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2265 end -= 1 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2266 return _dec_from_triple(dup._sign, dup._int[:end], exp) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2267 |
|
43362
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2268 def quantize(self, exp, rounding=None, context=None, watchexp=True): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2269 """Quantize self so its exponent is the same as that of exp. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2270 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2271 Similar to self._rescale(exp._exp) but with error checking. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2272 """ |
|
43362
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2273 exp = _convert_other(exp, raiseit=True) |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
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parents:
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diff
changeset
|
2274 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2275 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2276 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2277 if rounding is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2278 rounding = context.rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2279 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2280 if self._is_special or exp._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2281 ans = self._check_nans(exp, context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
2282 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2283 return ans |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2284 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2285 if exp._isinfinity() or self._isinfinity(): |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2286 if exp._isinfinity() and self._isinfinity(): |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2287 return Decimal(self) # if both are inf, it is OK |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2288 return context._raise_error(InvalidOperation, |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2289 'quantize with one INF') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2290 |
|
43362
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2291 # if we're not watching exponents, do a simple rescale |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2292 if not watchexp: |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2293 ans = self._rescale(exp._exp, rounding) |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2294 # raise Inexact and Rounded where appropriate |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2295 if ans._exp > self._exp: |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2296 context._raise_error(Rounded) |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2297 if ans != self: |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2298 context._raise_error(Inexact) |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2299 return ans |
|
c8c7a947a641
Put the parameter watchexp back in (changed watchexp from an int
Facundo Batista <facundobatista@gmail.com>
parents:
43360
diff
changeset
|
2300 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2301 # exp._exp should be between Etiny and Emax |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2302 if not (context.Etiny() <= exp._exp <= context.Emax): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2303 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2304 'target exponent out of bounds in quantize') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2305 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2306 if not self: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2307 ans = _dec_from_triple(self._sign, '0', exp._exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2308 return ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2309 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2310 self_adjusted = self.adjusted() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2311 if self_adjusted > context.Emax: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2312 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2313 'exponent of quantize result too large for current context') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2314 if self_adjusted - exp._exp + 1 > context.prec: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2315 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2316 'quantize result has too many digits for current context') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2317 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2318 ans = self._rescale(exp._exp, rounding) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2319 if ans.adjusted() > context.Emax: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2320 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2321 'exponent of quantize result too large for current context') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2322 if len(ans._int) > context.prec: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2323 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2324 'quantize result has too many digits for current context') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2325 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2326 # raise appropriate flags |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2327 if ans._exp > self._exp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2328 context._raise_error(Rounded) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2329 if ans != self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2330 context._raise_error(Inexact) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2331 if ans and ans.adjusted() < context.Emin: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2332 context._raise_error(Subnormal) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2333 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2334 # call to fix takes care of any necessary folddown |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2335 ans = ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2336 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2337 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2338 def same_quantum(self, other): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2339 """Return True if self and other have the same exponent; otherwise |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2340 return False. |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2341 |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2342 If either operand is a special value, the following rules are used: |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2343 * return True if both operands are infinities |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2344 * return True if both operands are NaNs |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2345 * otherwise, return False. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2346 """ |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2347 other = _convert_other(other, raiseit=True) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2348 if self._is_special or other._is_special: |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2349 return (self.is_nan() and other.is_nan() or |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2350 self.is_infinite() and other.is_infinite()) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2351 return self._exp == other._exp |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2352 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2353 def _rescale(self, exp, rounding): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2354 """Rescale self so that the exponent is exp, either by padding with zeros |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2355 or by truncating digits, using the given rounding mode. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2356 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2357 Specials are returned without change. This operation is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2358 quiet: it raises no flags, and uses no information from the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2359 context. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2360 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2361 exp = exp to scale to (an integer) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2362 rounding = rounding mode |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2363 """ |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2364 if self._is_special: |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2365 return Decimal(self) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2366 if not self: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2367 return _dec_from_triple(self._sign, '0', exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2368 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2369 if self._exp >= exp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2370 # pad answer with zeros if necessary |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
43602
diff
changeset
|
2371 return _dec_from_triple(self._sign, |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2372 self._int + '0'*(self._exp - exp), exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2373 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2374 # too many digits; round and lose data. If self.adjusted() < |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2375 # exp-1, replace self by 10**(exp-1) before rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2376 digits = len(self._int) + self._exp - exp |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2377 if digits < 0: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2378 self = _dec_from_triple(self._sign, '1', exp-1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2379 digits = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2380 this_function = getattr(self, self._pick_rounding_function[rounding]) |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
44120
diff
changeset
|
2381 changed = this_function(digits) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
44120
diff
changeset
|
2382 coeff = self._int[:digits] or '0' |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
44120
diff
changeset
|
2383 if changed == 1: |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
44120
diff
changeset
|
2384 coeff = str(int(coeff)+1) |
|
30f54977828b
Faster _fix function, and some reordering for a more elegant
Facundo Batista <facundobatista@gmail.com>
parents:
44120
diff
changeset
|
2385 return _dec_from_triple(self._sign, coeff, exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2386 |
|
45566
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2387 def _round(self, places, rounding): |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2388 """Round a nonzero, nonspecial Decimal to a fixed number of |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2389 significant figures, using the given rounding mode. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2390 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2391 Infinities, NaNs and zeros are returned unaltered. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2392 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2393 This operation is quiet: it raises no flags, and uses no |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2394 information from the context. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2395 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2396 """ |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2397 if places <= 0: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2398 raise ValueError("argument should be at least 1 in _round") |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2399 if self._is_special or not self: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2400 return Decimal(self) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2401 ans = self._rescale(self.adjusted()+1-places, rounding) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2402 # it can happen that the rescale alters the adjusted exponent; |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2403 # for example when rounding 99.97 to 3 significant figures. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2404 # When this happens we end up with an extra 0 at the end of |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2405 # the number; a second rescale fixes this. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2406 if ans.adjusted() != self.adjusted(): |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2407 ans = ans._rescale(ans.adjusted()+1-places, rounding) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2408 return ans |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
2409 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2410 def to_integral_exact(self, rounding=None, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2411 """Rounds to a nearby integer. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2412 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2413 If no rounding mode is specified, take the rounding mode from |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2414 the context. This method raises the Rounded and Inexact flags |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2415 when appropriate. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2416 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2417 See also: to_integral_value, which does exactly the same as |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2418 this method except that it doesn't raise Inexact or Rounded. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2419 """ |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2420 if self._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2421 ans = self._check_nans(context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2422 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2423 return ans |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2424 return Decimal(self) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2425 if self._exp >= 0: |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2426 return Decimal(self) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2427 if not self: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2428 return _dec_from_triple(self._sign, '0', 0) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2429 if context is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2430 context = getcontext() |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2431 if rounding is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2432 rounding = context.rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2433 context._raise_error(Rounded) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2434 ans = self._rescale(0, rounding) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2435 if ans != self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2436 context._raise_error(Inexact) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2437 return ans |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2438 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2439 def to_integral_value(self, rounding=None, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2440 """Rounds to the nearest integer, without raising inexact, rounded.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2441 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2442 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2443 if rounding is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2444 rounding = context.rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2445 if self._is_special: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2446 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2447 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2448 return ans |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2449 return Decimal(self) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2450 if self._exp >= 0: |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2451 return Decimal(self) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2452 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2453 return self._rescale(0, rounding) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2454 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2455 # the method name changed, but we provide also the old one, for compatibility |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2456 to_integral = to_integral_value |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2457 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2458 def sqrt(self, context=None): |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2459 """Return the square root of self.""" |
|
46082
22bd02293efa
Issue #2478: Decimal(sqrt(0)) failed when the decimal context
Mark Dickinson <dickinsm@gmail.com>
parents:
45568
diff
changeset
|
2460 if context is None: |
|
22bd02293efa
Issue #2478: Decimal(sqrt(0)) failed when the decimal context
Mark Dickinson <dickinsm@gmail.com>
parents:
45568
diff
changeset
|
2461 context = getcontext() |
|
22bd02293efa
Issue #2478: Decimal(sqrt(0)) failed when the decimal context
Mark Dickinson <dickinsm@gmail.com>
parents:
45568
diff
changeset
|
2462 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2463 if self._is_special: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2464 ans = self._check_nans(context=context) |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2465 if ans: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2466 return ans |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2467 |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2468 if self._isinfinity() and self._sign == 0: |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2469 return Decimal(self) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2470 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2471 if not self: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2472 # exponent = self._exp // 2. sqrt(-0) = -0 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2473 ans = _dec_from_triple(self._sign, '0', self._exp // 2) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2474 return ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2475 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2476 if self._sign == 1: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2477 return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2478 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2479 # At this point self represents a positive number. Let p be |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2480 # the desired precision and express self in the form c*100**e |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2481 # with c a positive real number and e an integer, c and e |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2482 # being chosen so that 100**(p-1) <= c < 100**p. Then the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2483 # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2484 # <= sqrt(c) < 10**p, so the closest representable Decimal at |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2485 # precision p is n*10**e where n = round_half_even(sqrt(c)), |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2486 # the closest integer to sqrt(c) with the even integer chosen |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2487 # in the case of a tie. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2488 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2489 # To ensure correct rounding in all cases, we use the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2490 # following trick: we compute the square root to an extra |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2491 # place (precision p+1 instead of precision p), rounding down. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2492 # Then, if the result is inexact and its last digit is 0 or 5, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2493 # we increase the last digit to 1 or 6 respectively; if it's |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2494 # exact we leave the last digit alone. Now the final round to |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2495 # p places (or fewer in the case of underflow) will round |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2496 # correctly and raise the appropriate flags. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2497 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2498 # use an extra digit of precision |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2499 prec = context.prec+1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2500 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2501 # write argument in the form c*100**e where e = self._exp//2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2502 # is the 'ideal' exponent, to be used if the square root is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2503 # exactly representable. l is the number of 'digits' of c in |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2504 # base 100, so that 100**(l-1) <= c < 100**l. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2505 op = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2506 e = op.exp >> 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2507 if op.exp & 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2508 c = op.int * 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2509 l = (len(self._int) >> 1) + 1 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2510 else: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2511 c = op.int |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2512 l = len(self._int)+1 >> 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2513 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
42605
diff
changeset
|
2514 # rescale so that c has exactly prec base 100 'digits' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2515 shift = prec-l |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2516 if shift >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2517 c *= 100**shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2518 exact = True |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2519 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2520 c, remainder = divmod(c, 100**-shift) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2521 exact = not remainder |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2522 e -= shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2523 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2524 # find n = floor(sqrt(c)) using Newton's method |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2525 n = 10**prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2526 while True: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2527 q = c//n |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2528 if n <= q: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2529 break |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2530 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2531 n = n + q >> 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2532 exact = exact and n*n == c |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2533 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2534 if exact: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2535 # result is exact; rescale to use ideal exponent e |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2536 if shift >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2537 # assert n % 10**shift == 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2538 n //= 10**shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2539 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2540 n *= 10**-shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2541 e += shift |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2542 else: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2543 # result is not exact; fix last digit as described above |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2544 if n % 5 == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2545 n += 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2546 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2547 ans = _dec_from_triple(0, str(n), e) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2548 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2549 # round, and fit to current context |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2550 context = context._shallow_copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2551 rounding = context._set_rounding(ROUND_HALF_EVEN) |
| 33695 | 2552 ans = ans._fix(context) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2553 context.rounding = rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2554 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2555 return ans |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2556 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2557 def max(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2558 """Returns the larger value. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2559 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2560 Like max(self, other) except if one is not a number, returns |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2561 NaN (and signals if one is sNaN). Also rounds. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2562 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2563 other = _convert_other(other, raiseit=True) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2564 |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2565 if context is None: |
|
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2566 context = getcontext() |
|
8890be9386b7
The methods always return Decimal classes, even if they're
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parents:
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diff
changeset
|
2567 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2568 if self._is_special or other._is_special: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
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parents:
40770
diff
changeset
|
2569 # If one operand is a quiet NaN and the other is number, then the |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2570 # number is always returned |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2571 sn = self._isnan() |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
2572 on = other._isnan() |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2573 if sn or on: |
|
50116
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2574 if on == 1 and sn == 0: |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2575 return self._fix(context) |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2576 if sn == 1 and on == 0: |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2577 return other._fix(context) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
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parents:
33198
diff
changeset
|
2578 return self._check_nans(other, context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2579 |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
2580 c = self._cmp(other) |
|
33157
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
2581 if c == 0: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
2582 # If both operands are finite and equal in numerical value |
|
33157
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
2583 # then an ordering is applied: |
|
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
2584 # |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
2585 # If the signs differ then max returns the operand with the |
|
33157
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
2586 # positive sign and min returns the operand with the negative sign |
|
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
2587 # |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
2588 # If the signs are the same then the exponent is used to select |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2589 # the result. This is exactly the ordering used in compare_total. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2590 c = self.compare_total(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2591 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2592 if c == -1: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2593 ans = other |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2594 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2595 ans = self |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2596 |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
2597 return ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2598 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2599 def min(self, other, context=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2600 """Returns the smaller value. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2601 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
2602 Like min(self, other) except if one is not a number, returns |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2603 NaN (and signals if one is sNaN). Also rounds. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2604 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2605 other = _convert_other(other, raiseit=True) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2606 |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2607 if context is None: |
|
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2608 context = getcontext() |
|
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
2609 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2610 if self._is_special or other._is_special: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
2611 # If one operand is a quiet NaN and the other is number, then the |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2612 # number is always returned |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2613 sn = self._isnan() |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2614 on = other._isnan() |
|
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2615 if sn or on: |
|
50116
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2616 if on == 1 and sn == 0: |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2617 return self._fix(context) |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2618 if sn == 1 and on == 0: |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
48847
diff
changeset
|
2619 return other._fix(context) |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2620 return self._check_nans(other, context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2621 |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
2622 c = self._cmp(other) |
|
33157
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
2623 if c == 0: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2624 c = self.compare_total(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2625 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2626 if c == -1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2627 ans = self |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2628 else: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2629 ans = other |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
2630 |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
2631 return ans._fix(context) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2632 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2633 def _isinteger(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2634 """Returns whether self is an integer""" |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2635 if self._is_special: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2636 return False |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2637 if self._exp >= 0: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2638 return True |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2639 rest = self._int[self._exp:] |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2640 return rest == '0'*len(rest) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2641 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2642 def _iseven(self): |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2643 """Returns True if self is even. Assumes self is an integer.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2644 if not self or self._exp > 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2645 return True |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2646 return self._int[-1+self._exp] in '02468' |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2647 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2648 def adjusted(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2649 """Return the adjusted exponent of self""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2650 try: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2651 return self._exp + len(self._int) - 1 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
2652 # If NaN or Infinity, self._exp is string |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2653 except TypeError: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2654 return 0 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
2655 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2656 def canonical(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2657 """Returns the same Decimal object. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2658 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2659 As we do not have different encodings for the same number, the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2660 received object already is in its canonical form. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2661 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2662 return self |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2663 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2664 def compare_signal(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2665 """Compares self to the other operand numerically. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2666 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2667 It's pretty much like compare(), but all NaNs signal, with signaling |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2668 NaNs taking precedence over quiet NaNs. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2669 """ |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
2670 other = _convert_other(other, raiseit = True) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
2671 ans = self._compare_check_nans(other, context) |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
2672 if ans: |
|
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
2673 return ans |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2674 return self.compare(other, context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2675 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2676 def compare_total(self, other): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2677 """Compares self to other using the abstract representations. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2678 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2679 This is not like the standard compare, which use their numerical |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2680 value. Note that a total ordering is defined for all possible abstract |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2681 representations. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2682 """ |
|
56971
53e38005d507
Merged revisions 75943-75945 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
56854
diff
changeset
|
2683 other = _convert_other(other, raiseit=True) |
|
53e38005d507
Merged revisions 75943-75945 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
56854
diff
changeset
|
2684 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2685 # if one is negative and the other is positive, it's easy |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2686 if self._sign and not other._sign: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2687 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2688 if not self._sign and other._sign: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2689 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2690 sign = self._sign |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2691 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2692 # let's handle both NaN types |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2693 self_nan = self._isnan() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2694 other_nan = other._isnan() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2695 if self_nan or other_nan: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2696 if self_nan == other_nan: |
|
55741
1f1b4c03e892
Merged revisions 74564 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2697 # compare payloads as though they're integers |
|
1f1b4c03e892
Merged revisions 74564 via svnmerge from
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parents:
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diff
changeset
|
2698 self_key = len(self._int), self._int |
|
1f1b4c03e892
Merged revisions 74564 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2699 other_key = len(other._int), other._int |
|
1f1b4c03e892
Merged revisions 74564 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2700 if self_key < other_key: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2701 if sign: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
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diff
changeset
|
2702 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2703 else: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2704 return _NegativeOne |
|
55741
1f1b4c03e892
Merged revisions 74564 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
55519
diff
changeset
|
2705 if self_key > other_key: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2706 if sign: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2707 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2708 else: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2709 return _One |
|
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2710 return _Zero |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2711 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2712 if sign: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2713 if self_nan == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2714 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2715 if other_nan == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
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diff
changeset
|
2716 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2717 if self_nan == 2: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2718 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2719 if other_nan == 2: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2720 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2721 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2722 if self_nan == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2723 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2724 if other_nan == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2725 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2726 if self_nan == 2: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2727 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2728 if other_nan == 2: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2729 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2730 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2731 if self < other: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2732 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2733 if self > other: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2734 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2735 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2736 if self._exp < other._exp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2737 if sign: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2738 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2739 else: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2740 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2741 if self._exp > other._exp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2742 if sign: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2743 return _NegativeOne |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2744 else: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2745 return _One |
|
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2746 return _Zero |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2747 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2748 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2749 def compare_total_mag(self, other): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2750 """Compares self to other using abstract repr., ignoring sign. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2751 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2752 Like compare_total, but with operand's sign ignored and assumed to be 0. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2753 """ |
|
56971
53e38005d507
Merged revisions 75943-75945 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
56854
diff
changeset
|
2754 other = _convert_other(other, raiseit=True) |
|
53e38005d507
Merged revisions 75943-75945 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2755 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2756 s = self.copy_abs() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2757 o = other.copy_abs() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2758 return s.compare_total(o) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2759 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2760 def copy_abs(self): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2761 """Returns a copy with the sign set to 0. """ |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2762 return _dec_from_triple(0, self._int, self._exp, self._is_special) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2763 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2764 def copy_negate(self): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2765 """Returns a copy with the sign inverted.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2766 if self._sign: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2767 return _dec_from_triple(0, self._int, self._exp, self._is_special) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2768 else: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2769 return _dec_from_triple(1, self._int, self._exp, self._is_special) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2770 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2771 def copy_sign(self, other): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2772 """Returns self with the sign of other.""" |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2773 return _dec_from_triple(other._sign, self._int, |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2774 self._exp, self._is_special) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2775 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2776 def exp(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2777 """Returns e ** self.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2778 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2779 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2780 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2781 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2782 # exp(NaN) = NaN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2783 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2784 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2785 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2786 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2787 # exp(-Infinity) = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2788 if self._isinfinity() == -1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
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diff
changeset
|
2789 return _Zero |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2790 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2791 # exp(0) = 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2792 if not self: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2793 return _One |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2794 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2795 # exp(Infinity) = Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2796 if self._isinfinity() == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2797 return Decimal(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2798 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2799 # the result is now guaranteed to be inexact (the true |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2800 # mathematical result is transcendental). There's no need to |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2801 # raise Rounded and Inexact here---they'll always be raised as |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2802 # a result of the call to _fix. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2803 p = context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2804 adj = self.adjusted() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2805 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2806 # we only need to do any computation for quite a small range |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2807 # of adjusted exponents---for example, -29 <= adj <= 10 for |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2808 # the default context. For smaller exponent the result is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2809 # indistinguishable from 1 at the given precision, while for |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2810 # larger exponent the result either overflows or underflows. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2811 if self._sign == 0 and adj > len(str((context.Emax+1)*3)): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2812 # overflow |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
2813 ans = _dec_from_triple(0, '1', context.Emax+1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2814 elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2815 # underflow to 0 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2816 ans = _dec_from_triple(0, '1', context.Etiny()-1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2817 elif self._sign == 0 and adj < -p: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2818 # p+1 digits; final round will raise correct flags |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2819 ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2820 elif self._sign == 1 and adj < -p-1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2821 # p+1 digits; final round will raise correct flags |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2822 ans = _dec_from_triple(0, '9'*(p+1), -p-1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2823 # general case |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2824 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2825 op = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2826 c, e = op.int, op.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2827 if op.sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2828 c = -c |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2829 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2830 # compute correctly rounded result: increase precision by |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2831 # 3 digits at a time until we get an unambiguously |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2832 # roundable result |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2833 extra = 3 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2834 while True: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2835 coeff, exp = _dexp(c, e, p+extra) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2836 if coeff % (5*10**(len(str(coeff))-p-1)): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2837 break |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2838 extra += 3 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2839 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2840 ans = _dec_from_triple(0, str(coeff), exp) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2841 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2842 # at this stage, ans should round correctly with *any* |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2843 # rounding mode, not just with ROUND_HALF_EVEN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2844 context = context._shallow_copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2845 rounding = context._set_rounding(ROUND_HALF_EVEN) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2846 ans = ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2847 context.rounding = rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2848 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2849 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2850 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2851 def is_canonical(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2852 """Return True if self is canonical; otherwise return False. |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2853 |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2854 Currently, the encoding of a Decimal instance is always |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2855 canonical, so this method returns True for any Decimal. |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2856 """ |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2857 return True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2858 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2859 def is_finite(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2860 """Return True if self is finite; otherwise return False. |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2861 |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2862 A Decimal instance is considered finite if it is neither |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2863 infinite nor a NaN. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2864 """ |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2865 return not self._is_special |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2866 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2867 def is_infinite(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2868 """Return True if self is infinite; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2869 return self._exp == 'F' |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2870 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2871 def is_nan(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2872 """Return True if self is a qNaN or sNaN; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2873 return self._exp in ('n', 'N') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2874 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2875 def is_normal(self, context=None): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2876 """Return True if self is a normal number; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2877 if self._is_special or not self: |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2878 return False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2879 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2880 context = getcontext() |
|
56854
59505e7e7073
Merged revisions 75561 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
56836
diff
changeset
|
2881 return context.Emin <= self.adjusted() |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2882 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2883 def is_qnan(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2884 """Return True if self is a quiet NaN; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2885 return self._exp == 'n' |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2886 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2887 def is_signed(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2888 """Return True if self is negative; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2889 return self._sign == 1 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2890 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2891 def is_snan(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2892 """Return True if self is a signaling NaN; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2893 return self._exp == 'N' |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2894 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2895 def is_subnormal(self, context=None): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2896 """Return True if self is subnormal; otherwise return False.""" |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2897 if self._is_special or not self: |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2898 return False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2899 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2900 context = getcontext() |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2901 return self.adjusted() < context.Emin |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2902 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2903 def is_zero(self): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
2904 """Return True if self is a zero; otherwise return False.""" |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
2905 return not self._is_special and self._int == '0' |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2906 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2907 def _ln_exp_bound(self): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2908 """Compute a lower bound for the adjusted exponent of self.ln(). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2909 In other words, compute r such that self.ln() >= 10**r. Assumes |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2910 that self is finite and positive and that self != 1. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2911 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2912 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2913 # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2914 adj = self._exp + len(self._int) - 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2915 if adj >= 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2916 # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2917 return len(str(adj*23//10)) - 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2918 if adj <= -2: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2919 # argument <= 0.1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2920 return len(str((-1-adj)*23//10)) - 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2921 op = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2922 c, e = op.int, op.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2923 if adj == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2924 # 1 < self < 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2925 num = str(c-10**-e) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2926 den = str(c) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2927 return len(num) - len(den) - (num < den) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2928 # adj == -1, 0.1 <= self < 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2929 return e + len(str(10**-e - c)) - 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2930 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2931 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2932 def ln(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2933 """Returns the natural (base e) logarithm of self.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2934 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2935 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2936 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2937 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2938 # ln(NaN) = NaN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2939 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2940 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2941 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2942 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2943 # ln(0.0) == -Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2944 if not self: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2945 return _NegativeInfinity |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2946 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2947 # ln(Infinity) = Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2948 if self._isinfinity() == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2949 return _Infinity |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2950 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2951 # ln(1.0) == 0.0 |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
2952 if self == _One: |
|
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
2953 return _Zero |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2954 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2955 # ln(negative) raises InvalidOperation |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2956 if self._sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2957 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2958 'ln of a negative value') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2959 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2960 # result is irrational, so necessarily inexact |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2961 op = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2962 c, e = op.int, op.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2963 p = context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2964 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2965 # correctly rounded result: repeatedly increase precision by 3 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2966 # until we get an unambiguously roundable result |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2967 places = p - self._ln_exp_bound() + 2 # at least p+3 places |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2968 while True: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2969 coeff = _dlog(c, e, places) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2970 # assert len(str(abs(coeff)))-p >= 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
42605
diff
changeset
|
2971 if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
2972 break |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2973 places += 3 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
43602
diff
changeset
|
2974 ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2975 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2976 context = context._shallow_copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2977 rounding = context._set_rounding(ROUND_HALF_EVEN) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2978 ans = ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2979 context.rounding = rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2980 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2981 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2982 def _log10_exp_bound(self): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2983 """Compute a lower bound for the adjusted exponent of self.log10(). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2984 In other words, find r such that self.log10() >= 10**r. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2985 Assumes that self is finite and positive and that self != 1. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2986 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2987 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2988 # For x >= 10 or x < 0.1 we only need a bound on the integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2989 # part of log10(self), and this comes directly from the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
2990 # exponent of x. For 0.1 <= x <= 10 we use the inequalities |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2991 # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
2992 # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
2993 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2994 adj = self._exp + len(self._int) - 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2995 if adj >= 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2996 # self >= 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2997 return len(str(adj))-1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2998 if adj <= -2: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
2999 # self < 0.1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3000 return len(str(-1-adj))-1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3001 op = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3002 c, e = op.int, op.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3003 if adj == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3004 # 1 < self < 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3005 num = str(c-10**-e) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3006 den = str(231*c) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3007 return len(num) - len(den) - (num < den) + 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3008 # adj == -1, 0.1 <= self < 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3009 num = str(10**-e-c) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3010 return len(num) + e - (num < "231") - 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3011 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3012 def log10(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3013 """Returns the base 10 logarithm of self.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3014 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3015 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3016 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3017 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3018 # log10(NaN) = NaN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3019 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3020 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3021 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3022 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3023 # log10(0.0) == -Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3024 if not self: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
3025 return _NegativeInfinity |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3026 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3027 # log10(Infinity) = Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3028 if self._isinfinity() == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
3029 return _Infinity |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3030 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3031 # log10(negative or -Infinity) raises InvalidOperation |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3032 if self._sign == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3033 return context._raise_error(InvalidOperation, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3034 'log10 of a negative value') |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3035 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3036 # log10(10**n) = n |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3037 if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3038 # answer may need rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3039 ans = Decimal(self._exp + len(self._int) - 1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3040 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3041 # result is irrational, so necessarily inexact |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3042 op = _WorkRep(self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3043 c, e = op.int, op.exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3044 p = context.prec |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3045 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3046 # correctly rounded result: repeatedly increase precision |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3047 # until result is unambiguously roundable |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3048 places = p-self._log10_exp_bound()+2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3049 while True: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3050 coeff = _dlog10(c, e, places) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3051 # assert len(str(abs(coeff)))-p >= 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3052 if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3053 break |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3054 places += 3 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3055 ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3056 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3057 context = context._shallow_copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3058 rounding = context._set_rounding(ROUND_HALF_EVEN) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3059 ans = ans._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3060 context.rounding = rounding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3061 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3062 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3063 def logb(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3064 """ Returns the exponent of the magnitude of self's MSD. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3065 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3066 The result is the integer which is the exponent of the magnitude |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3067 of the most significant digit of self (as though it were truncated |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3068 to a single digit while maintaining the value of that digit and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3069 without limiting the resulting exponent). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3070 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3071 # logb(NaN) = NaN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3072 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3073 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3074 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3075 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3076 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3077 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3078 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3079 # logb(+/-Inf) = +Inf |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3080 if self._isinfinity(): |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
50471
diff
changeset
|
3081 return _Infinity |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3082 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3083 # logb(0) = -Inf, DivisionByZero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3084 if not self: |
|
43391
b9236a75a6e5
Speed up of the various division operations (remainder, divide,
Facundo Batista <facundobatista@gmail.com>
parents:
43383
diff
changeset
|
3085 return context._raise_error(DivisionByZero, 'logb(0)', 1) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3086 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3087 # otherwise, simply return the adjusted exponent of self, as a |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3088 # Decimal. Note that no attempt is made to fit the result |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3089 # into the current context. |
|
56836
bd776e01993a
Merged revisions 75275 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
55886
diff
changeset
|
3090 ans = Decimal(self.adjusted()) |
|
bd776e01993a
Merged revisions 75275 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
55886
diff
changeset
|
3091 return ans._fix(context) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3092 |
|
63f3154c731d
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|
3093 def _islogical(self): |
|
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|
3094 """Return True if self is a logical operand. |
|
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|
3095 |
| 44701 | 3096 For being logical, it must be a finite number with a sign of 0, |
|
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|
3097 an exponent of 0, and a coefficient whose digits must all be |
|
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|
3098 either 0 or 1. |
|
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|
3099 """ |
|
63f3154c731d
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changeset
|
3100 if self._sign != 0 or self._exp != 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3101 return False |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3102 for dig in self._int: |
|
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|
3103 if dig not in '01': |
|
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|
3104 return False |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3105 return True |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3106 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3107 def _fill_logical(self, context, opa, opb): |
|
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|
3108 dif = context.prec - len(opa) |
|
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|
3109 if dif > 0: |
|
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|
3110 opa = '0'*dif + opa |
|
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|
3111 elif dif < 0: |
|
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|
3112 opa = opa[-context.prec:] |
|
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|
3113 dif = context.prec - len(opb) |
|
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|
3114 if dif > 0: |
|
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|
3115 opb = '0'*dif + opb |
|
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|
3116 elif dif < 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3117 opb = opb[-context.prec:] |
|
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|
3118 return opa, opb |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3119 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3120 def logical_and(self, other, context=None): |
|
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changeset
|
3121 """Applies an 'and' operation between self and other's digits.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3122 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3123 context = getcontext() |
|
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3124 |
|
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|
3125 other = _convert_other(other, raiseit=True) |
|
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|
3126 |
|
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|
3127 if not self._islogical() or not other._islogical(): |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3128 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3129 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3130 # fill to context.prec |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3131 (opa, opb) = self._fill_logical(context, self._int, other._int) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3132 |
|
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|
3133 # make the operation, and clean starting zeroes |
|
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|
3134 result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) |
|
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|
3135 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
|
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|
3136 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3137 def logical_invert(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3138 """Invert all its digits.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3139 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3140 context = getcontext() |
|
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|
3141 return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), |
|
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|
3142 context) |
|
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|
3143 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3144 def logical_or(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3145 """Applies an 'or' operation between self and other's digits.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3146 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3147 context = getcontext() |
|
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|
3148 |
|
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|
3149 other = _convert_other(other, raiseit=True) |
|
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|
3150 |
|
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changeset
|
3151 if not self._islogical() or not other._islogical(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3152 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3153 |
|
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|
3154 # fill to context.prec |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3155 (opa, opb) = self._fill_logical(context, self._int, other._int) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3156 |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3157 # make the operation, and clean starting zeroes |
|
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|
3158 result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)]) |
|
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|
3159 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
|
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|
3160 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3161 def logical_xor(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3162 """Applies an 'xor' operation between self and other's digits.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3163 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3164 context = getcontext() |
|
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|
3165 |
|
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|
3166 other = _convert_other(other, raiseit=True) |
|
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|
3167 |
|
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changeset
|
3168 if not self._islogical() or not other._islogical(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3169 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3170 |
|
63f3154c731d
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changeset
|
3171 # fill to context.prec |
|
63f3154c731d
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changeset
|
3172 (opa, opb) = self._fill_logical(context, self._int, other._int) |
|
63f3154c731d
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|
3173 |
|
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|
3174 # make the operation, and clean starting zeroes |
|
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|
3175 result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)]) |
|
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|
3176 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
|
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|
3177 |
|
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changeset
|
3178 def max_mag(self, other, context=None): |
|
63f3154c731d
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changeset
|
3179 """Compares the values numerically with their sign ignored.""" |
|
63f3154c731d
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|
3180 other = _convert_other(other, raiseit=True) |
|
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|
3181 |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
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|
3182 if context is None: |
|
8890be9386b7
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|
3183 context = getcontext() |
|
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|
3184 |
|
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|
3185 if self._is_special or other._is_special: |
|
63f3154c731d
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changeset
|
3186 # If one operand is a quiet NaN and the other is number, then the |
|
63f3154c731d
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|
3187 # number is always returned |
|
63f3154c731d
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|
3188 sn = self._isnan() |
|
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|
3189 on = other._isnan() |
|
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changeset
|
3190 if sn or on: |
|
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|
3191 if on == 1 and sn == 0: |
|
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|
3192 return self._fix(context) |
|
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diff
changeset
|
3193 if sn == 1 and on == 0: |
|
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Merged revisions 67694 via svnmerge from
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diff
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|
3194 return other._fix(context) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3195 return self._check_nans(other, context) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
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|
3196 |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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parents:
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diff
changeset
|
3197 c = self.copy_abs()._cmp(other.copy_abs()) |
|
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diff
changeset
|
3198 if c == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
3199 c = self.compare_total(other) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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|
3200 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3201 if c == -1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3202 ans = other |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
3203 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3204 ans = self |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
3205 |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
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diff
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|
3206 return ans._fix(context) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3207 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3208 def min_mag(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3209 """Compares the values numerically with their sign ignored.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3210 other = _convert_other(other, raiseit=True) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3211 |
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43383
8890be9386b7
The methods always return Decimal classes, even if they're
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parents:
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diff
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|
3212 if context is None: |
|
8890be9386b7
The methods always return Decimal classes, even if they're
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parents:
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diff
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|
3213 context = getcontext() |
|
8890be9386b7
The methods always return Decimal classes, even if they're
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parents:
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diff
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3214 |
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
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|
3215 if self._is_special or other._is_special: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3216 # If one operand is a quiet NaN and the other is number, then the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3217 # number is always returned |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3218 sn = self._isnan() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3219 on = other._isnan() |
|
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parents:
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diff
changeset
|
3220 if sn or on: |
|
50116
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Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
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|
3221 if on == 1 and sn == 0: |
|
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Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
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|
3222 return self._fix(context) |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
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parents:
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diff
changeset
|
3223 if sn == 1 and on == 0: |
|
01c023d9218e
Merged revisions 67694 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
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|
3224 return other._fix(context) |
|
43360
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parents:
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diff
changeset
|
3225 return self._check_nans(other, context) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3226 |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
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parents:
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diff
changeset
|
3227 c = self.copy_abs()._cmp(other.copy_abs()) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3228 if c == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3229 c = self.compare_total(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
3230 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3231 if c == -1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
3232 ans = self |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3233 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3234 ans = other |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3235 |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3236 return ans._fix(context) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3237 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3238 def next_minus(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3239 """Returns the largest representable number smaller than itself.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3240 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3241 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
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|
3242 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
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|
3243 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
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|
3244 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3245 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3246 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3247 if self._isinfinity() == -1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
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parents:
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diff
changeset
|
3248 return _NegativeInfinity |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3249 if self._isinfinity() == 1: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
3250 return _dec_from_triple(0, '9'*context.prec, context.Etop()) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3251 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3252 context = context.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3253 context._set_rounding(ROUND_FLOOR) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3254 context._ignore_all_flags() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3255 new_self = self._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3256 if new_self != self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3257 return new_self |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
3258 return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), |
|
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
3259 context) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3260 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3261 def next_plus(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3262 """Returns the smallest representable number larger than itself.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3263 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3264 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3265 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3266 ans = self._check_nans(context=context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3267 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3268 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3269 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3270 if self._isinfinity() == 1: |
|
50480
f2a5d7828b83
Merged revisions 68191 via svnmerge from
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diff
changeset
|
3271 return _Infinity |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3272 if self._isinfinity() == -1: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
changeset
|
3273 return _dec_from_triple(1, '9'*context.prec, context.Etop()) |
|
43360
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3274 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3275 context = context.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3276 context._set_rounding(ROUND_CEILING) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3277 context._ignore_all_flags() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3278 new_self = self._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3279 if new_self != self: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3280 return new_self |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
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diff
changeset
|
3281 return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), |
|
a4a140486691
Major change in the internal structure of the Decimal
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diff
changeset
|
3282 context) |
|
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Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3283 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3284 def next_toward(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3285 """Returns the number closest to self, in the direction towards other. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3286 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3287 The result is the closest representable number to self |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3288 (excluding self) that is in the direction towards other, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3289 unless both have the same value. If the two operands are |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3290 numerically equal, then the result is a copy of self with the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3291 sign set to be the same as the sign of other. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3292 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3293 other = _convert_other(other, raiseit=True) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3294 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3295 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3296 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3297 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3298 ans = self._check_nans(other, context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3299 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3300 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3301 |
|
45201
f55a4f119141
Issue 1979: Make Decimal comparisons (other than !=, ==) involving NaN
Mark Dickinson <dickinsm@gmail.com>
parents:
44923
diff
changeset
|
3302 comparison = self._cmp(other) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3303 if comparison == 0: |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3304 return self.copy_sign(other) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3305 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3306 if comparison == -1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3307 ans = self.next_plus(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3308 else: # comparison == 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3309 ans = self.next_minus(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3310 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3311 # decide which flags to raise using value of ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3312 if ans._isinfinity(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3313 context._raise_error(Overflow, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3314 'Infinite result from next_toward', |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3315 ans._sign) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3316 context._raise_error(Rounded) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3317 context._raise_error(Inexact) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3318 elif ans.adjusted() < context.Emin: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3319 context._raise_error(Underflow) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3320 context._raise_error(Subnormal) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3321 context._raise_error(Rounded) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3322 context._raise_error(Inexact) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3323 # if precision == 1 then we don't raise Clamped for a |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3324 # result 0E-Etiny. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3325 if not ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3326 context._raise_error(Clamped) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3327 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3328 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3329 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3330 def number_class(self, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3331 """Returns an indication of the class of self. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3332 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3333 The class is one of the following strings: |
|
44352
f7bc79112bcf
Some minor cleanups. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44328
diff
changeset
|
3334 sNaN |
|
f7bc79112bcf
Some minor cleanups. Thanks Mark Dickinson.
Facundo Batista <facundobatista@gmail.com>
parents:
44328
diff
changeset
|
3335 NaN |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3336 -Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3337 -Normal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3338 -Subnormal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3339 -Zero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3340 +Zero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3341 +Subnormal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3342 +Normal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3343 +Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3344 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3345 if self.is_snan(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3346 return "sNaN" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3347 if self.is_qnan(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3348 return "NaN" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3349 inf = self._isinfinity() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3350 if inf == 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3351 return "+Infinity" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3352 if inf == -1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3353 return "-Infinity" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3354 if self.is_zero(): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3355 if self._sign: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3356 return "-Zero" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3357 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3358 return "+Zero" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3359 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3360 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3361 if self.is_subnormal(context=context): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3362 if self._sign: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3363 return "-Subnormal" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3364 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3365 return "+Subnormal" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3366 # just a normal, regular, boring number, :) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3367 if self._sign: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3368 return "-Normal" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3369 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3370 return "+Normal" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3371 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3372 def radix(self): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3373 """Just returns 10, as this is Decimal, :)""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3374 return Decimal(10) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3375 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3376 def rotate(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3377 """Returns a rotated copy of self, value-of-other times.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3378 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3379 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3380 |
|
56971
53e38005d507
Merged revisions 75943-75945 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
56854
diff
changeset
|
3381 other = _convert_other(other, raiseit=True) |
|
53e38005d507
Merged revisions 75943-75945 via svnmerge from
Mark Dickinson <dickinsm@gmail.com>
parents:
56854
diff
changeset
|
3382 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3383 ans = self._check_nans(other, context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3384 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3385 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3386 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3387 if other._exp != 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3388 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3389 if not (-context.prec <= int(other) <= context.prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3390 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3391 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3392 if self._isinfinity(): |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
3393 return Decimal(self) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3394 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3395 # get values, pad if necessary |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3396 torot = int(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3397 rotdig = self._int |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3398 topad = context.prec - len(rotdig) |
|
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changeset
|
3399 if topad > 0: |
|
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|
3400 rotdig = '0'*topad + rotdig |
|
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|
3401 elif topad < 0: |
|
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changeset
|
3402 rotdig = rotdig[-topad:] |
|
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changeset
|
3403 |
|
63f3154c731d
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parents:
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diff
changeset
|
3404 # let's rotate! |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3405 rotated = rotdig[torot:] + rotdig[:torot] |
|
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diff
changeset
|
3406 return _dec_from_triple(self._sign, |
|
a4a140486691
Major change in the internal structure of the Decimal
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diff
changeset
|
3407 rotated.lstrip('0') or '0', self._exp) |
|
43360
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|
3408 |
|
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changeset
|
3409 def scaleb(self, other, context=None): |
|
43360
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diff
changeset
|
3410 """Returns self operand after adding the second value to its exp.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3411 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3412 context = getcontext() |
|
63f3154c731d
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|
3413 |
|
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|
3414 other = _convert_other(other, raiseit=True) |
|
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|
3415 |
|
43360
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|
3416 ans = self._check_nans(other, context) |
|
63f3154c731d
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changeset
|
3417 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3418 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3419 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3420 if other._exp != 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3421 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3422 liminf = -2 * (context.Emax + context.prec) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3423 limsup = 2 * (context.Emax + context.prec) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
3424 if not (liminf <= int(other) <= limsup): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3425 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3426 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3427 if self._isinfinity(): |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
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parents:
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diff
changeset
|
3428 return Decimal(self) |
|
43360
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|
3429 |
|
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|
3430 d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) |
|
43360
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|
3431 d = d._fix(context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3432 return d |
|
63f3154c731d
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parents:
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|
3433 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3434 def shift(self, other, context=None): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
3435 """Returns a shifted copy of self, value-of-other times.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3436 if context is None: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3437 context = getcontext() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
3438 |
|
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|
3439 other = _convert_other(other, raiseit=True) |
|
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|
3440 |
|
43360
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|
3441 ans = self._check_nans(other, context) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3442 if ans: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3443 return ans |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3444 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3445 if other._exp != 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3446 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3447 if not (-context.prec <= int(other) <= context.prec): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3448 return context._raise_error(InvalidOperation) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3449 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3450 if self._isinfinity(): |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
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parents:
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diff
changeset
|
3451 return Decimal(self) |
|
43360
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parents:
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changeset
|
3452 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3453 # get values, pad if necessary |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3454 torot = int(other) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3455 rotdig = self._int |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3456 topad = context.prec - len(rotdig) |
|
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changeset
|
3457 if topad > 0: |
|
43993
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parents:
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diff
changeset
|
3458 rotdig = '0'*topad + rotdig |
|
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changeset
|
3459 elif topad < 0: |
|
53e38005d507
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diff
changeset
|
3460 rotdig = rotdig[-topad:] |
|
43360
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parents:
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diff
changeset
|
3461 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
3462 # let's shift! |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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changeset
|
3463 if torot < 0: |
|
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changeset
|
3464 shifted = rotdig[:torot] |
|
43360
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parents:
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changeset
|
3465 else: |
|
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changeset
|
3466 shifted = rotdig + '0'*torot |
|
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changeset
|
3467 shifted = shifted[-context.prec:] |
|
43360
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parents:
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diff
changeset
|
3468 |
|
43993
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parents:
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changeset
|
3469 return _dec_from_triple(self._sign, |
|
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changeset
|
3470 shifted.lstrip('0') or '0', self._exp) |
|
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changeset
|
3471 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
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parents:
40770
diff
changeset
|
3472 # Support for pickling, copy, and deepcopy |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3473 def __reduce__(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
3474 return (self.__class__, (str(self),)) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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diff
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|
3475 |
|
d2c1c7ae7cf4
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diff
changeset
|
3476 def __copy__(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
3477 if type(self) == Decimal: |
|
39120
1d7da8608031
Revert r50706 (Whitespace normalization) and
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parents:
39117
diff
changeset
|
3478 return self # I'm immutable; therefore I am my own clone |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
3479 return self.__class__(str(self)) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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diff
changeset
|
3480 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3481 def __deepcopy__(self, memo): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3482 if type(self) == Decimal: |
|
39120
1d7da8608031
Revert r50706 (Whitespace normalization) and
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parents:
39117
diff
changeset
|
3483 return self # My components are also immutable |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
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|
3484 return self.__class__(str(self)) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3485 |
|
45566
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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parents:
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diff
changeset
|
3486 # PEP 3101 support. See also _parse_format_specifier and _format_align |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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parents:
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diff
changeset
|
3487 def __format__(self, specifier, context=None): |
| 45568 | 3488 """Format a Decimal instance according to the given specifier. |
|
45566
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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diff
changeset
|
3489 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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parents:
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diff
changeset
|
3490 The specifier should be a standard format specifier, with the |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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parents:
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diff
changeset
|
3491 form described in PEP 3101. Formatting types 'e', 'E', 'f', |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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parents:
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diff
changeset
|
3492 'F', 'g', 'G', and '%' are supported. If the formatting type |
|
bce4c40df7df
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parents:
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diff
changeset
|
3493 is omitted it defaults to 'g' or 'G', depending on the value |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
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parents:
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diff
changeset
|
3494 of context.capitals. |
|
bce4c40df7df
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parents:
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diff
changeset
|
3495 |
|
bce4c40df7df
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parents:
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diff
changeset
|
3496 At this time the 'n' format specifier type (which is supposed |
|
bce4c40df7df
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parents:
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diff
changeset
|
3497 to use the current locale) is not supported. |
|
bce4c40df7df
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parents:
45505
diff
changeset
|
3498 """ |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3499 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3500 # Note: PEP 3101 says that if the type is not present then |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3501 # there should be at least one digit after the decimal point. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3502 # We take the liberty of ignoring this requirement for |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3503 # Decimal---it's presumably there to make sure that |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3504 # format(float, '') behaves similarly to str(float). |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3505 if context is None: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3506 context = getcontext() |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3507 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3508 spec = _parse_format_specifier(specifier) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3509 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3510 # special values don't care about the type or precision... |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3511 if self._is_special: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3512 return _format_align(str(self), spec) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3513 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3514 # a type of None defaults to 'g' or 'G', depending on context |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3515 # if type is '%', adjust exponent of self accordingly |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3516 if spec['type'] is None: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3517 spec['type'] = ['g', 'G'][context.capitals] |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3518 elif spec['type'] == '%': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3519 self = _dec_from_triple(self._sign, self._int, self._exp+2) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3520 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3521 # round if necessary, taking rounding mode from the context |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3522 rounding = context.rounding |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3523 precision = spec['precision'] |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3524 if precision is not None: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3525 if spec['type'] in 'eE': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3526 self = self._round(precision+1, rounding) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3527 elif spec['type'] in 'gG': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3528 if len(self._int) > precision: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3529 self = self._round(precision, rounding) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3530 elif spec['type'] in 'fF%': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3531 self = self._rescale(-precision, rounding) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3532 # special case: zeros with a positive exponent can't be |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3533 # represented in fixed point; rescale them to 0e0. |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3534 elif not self and self._exp > 0 and spec['type'] in 'fF%': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3535 self = self._rescale(0, rounding) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3536 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3537 # figure out placement of the decimal point |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3538 leftdigits = self._exp + len(self._int) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3539 if spec['type'] in 'fF%': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3540 dotplace = leftdigits |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3541 elif spec['type'] in 'eE': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3542 if not self and precision is not None: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3543 dotplace = 1 - precision |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3544 else: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3545 dotplace = 1 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3546 elif spec['type'] in 'gG': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3547 if self._exp <= 0 and leftdigits > -6: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3548 dotplace = leftdigits |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3549 else: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3550 dotplace = 1 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3551 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3552 # figure out main part of numeric string... |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3553 if dotplace <= 0: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3554 num = '0.' + '0'*(-dotplace) + self._int |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3555 elif dotplace >= len(self._int): |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3556 # make sure we're not padding a '0' with extra zeros on the right |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3557 assert dotplace==len(self._int) or self._int != '0' |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3558 num = self._int + '0'*(dotplace-len(self._int)) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3559 else: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3560 num = self._int[:dotplace] + '.' + self._int[dotplace:] |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3561 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3562 # ...then the trailing exponent, or trailing '%' |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3563 if leftdigits != dotplace or spec['type'] in 'eE': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3564 echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']] |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3565 num = num + "{0}{1:+}".format(echar, leftdigits-dotplace) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3566 elif spec['type'] == '%': |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3567 num = num + '%' |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3568 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3569 # add sign |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3570 if self._sign == 1: |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3571 num = '-' + num |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3572 return _format_align(num, spec) |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3573 |
|
bce4c40df7df
Add __format__ method to Decimal, to support PEP 3101
Mark Dickinson <dickinsm@gmail.com>
parents:
45505
diff
changeset
|
3574 |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3575 def _dec_from_triple(sign, coefficient, exponent, special=False): |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3576 """Create a decimal instance directly, without any validation, |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3577 normalization (e.g. removal of leading zeros) or argument |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3578 conversion. |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3579 |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3580 This function is for *internal use only*. |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3581 """ |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3582 |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3583 self = object.__new__(Decimal) |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3584 self._sign = sign |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3585 self._int = coefficient |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3586 self._exp = exponent |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3587 self._is_special = special |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3588 |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3589 return self |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
3590 |
|
51294
aea90f5f398b
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
51028
diff
changeset
|
3591 # Register Decimal as a kind of Number (an abstract base class). |
|
aea90f5f398b
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
51028
diff
changeset
|
3592 # However, do not register it as Real (because Decimals are not |
|
aea90f5f398b
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
51028
diff
changeset
|
3593 # interoperable with floats). |
|
aea90f5f398b
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
51028
diff
changeset
|
3594 _numbers.Number.register(Decimal) |
|
aea90f5f398b
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
51028
diff
changeset
|
3595 |
|
aea90f5f398b
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
51028
diff
changeset
|
3596 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3597 ##### Context class ####################################################### |
|
39120
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
3598 |
|
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
3599 |
|
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
3600 # get rounding method function: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3601 rounding_functions = [name for name in Decimal.__dict__.keys() |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3602 if name.startswith('_round_')] |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3603 for name in rounding_functions: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3604 # name is like _round_half_even, goes to the global ROUND_HALF_EVEN value. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3605 globalname = name[1:].upper() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3606 val = globals()[globalname] |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3607 Decimal._pick_rounding_function[val] = name |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3608 |
| 32482 | 3609 del name, val, globalname, rounding_functions |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3610 |
|
39721
2f086d58ca10
Make decimal.ContextManager a private implementation detail of decimal.localcontext()
Nick Coghlan <ncoghlan@gmail.com>
parents:
39707
diff
changeset
|
3611 class _ContextManager(object): |
|
39707
a83957c91fdb
Fix the wrongheaded implementation of context management in the decimal module and add unit tests. (python-dev discussion is ongoing regarding what we do about Python 2.5)
Nick Coghlan <ncoghlan@gmail.com>
parents:
39120
diff
changeset
|
3612 """Context manager class to support localcontext(). |
|
a83957c91fdb
Fix the wrongheaded implementation of context management in the decimal module and add unit tests. (python-dev discussion is ongoing regarding what we do about Python 2.5)
Nick Coghlan <ncoghlan@gmail.com>
parents:
39120
diff
changeset
|
3613 |
|
39721
2f086d58ca10
Make decimal.ContextManager a private implementation detail of decimal.localcontext()
Nick Coghlan <ncoghlan@gmail.com>
parents:
39707
diff
changeset
|
3614 Sets a copy of the supplied context in __enter__() and restores |
|
39707
a83957c91fdb
Fix the wrongheaded implementation of context management in the decimal module and add unit tests. (python-dev discussion is ongoing regarding what we do about Python 2.5)
Nick Coghlan <ncoghlan@gmail.com>
parents:
39120
diff
changeset
|
3615 the previous decimal context in __exit__() |
|
36737
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3616 """ |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3617 def __init__(self, new_context): |
|
39721
2f086d58ca10
Make decimal.ContextManager a private implementation detail of decimal.localcontext()
Nick Coghlan <ncoghlan@gmail.com>
parents:
39707
diff
changeset
|
3618 self.new_context = new_context.copy() |
|
36737
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3619 def __enter__(self): |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3620 self.saved_context = getcontext() |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3621 setcontext(self.new_context) |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3622 return self.new_context |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3623 def __exit__(self, t, v, tb): |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3624 setcontext(self.saved_context) |
|
fa92fe15251a
Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
35379
diff
changeset
|
3625 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3626 class Context(object): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3627 """Contains the context for a Decimal instance. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3628 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3629 Contains: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3630 prec - precision (for use in rounding, division, square roots..) |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3631 rounding - rounding type (how you round) |
|
32576
83cbc025bfc7
Improve Context construction and representation:
Raymond Hettinger <python@rcn.com>
parents:
32561
diff
changeset
|
3632 traps - If traps[exception] = 1, then the exception is |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3633 raised when it is caused. Otherwise, a value is |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3634 substituted in. |
|
46643
ec09ad5bed1a
Backport Raymond's changes in r60508 to Python 2.6.
Mark Dickinson <dickinsm@gmail.com>
parents:
46625
diff
changeset
|
3635 flags - When an exception is caused, flags[exception] is set. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3636 (Whether or not the trap_enabler is set) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3637 Should be reset by user of Decimal instance. |
|
32489
ab0a2b74ddfd
Changed the rounding constant values to match their variable names.
Raymond Hettinger <python@rcn.com>
parents:
32487
diff
changeset
|
3638 Emin - Minimum exponent |
|
ab0a2b74ddfd
Changed the rounding constant values to match their variable names.
Raymond Hettinger <python@rcn.com>
parents:
32487
diff
changeset
|
3639 Emax - Maximum exponent |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3640 capitals - If 1, 1*10^1 is printed as 1E+1. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3641 If 0, printed as 1e1 |
| 32496 | 3642 _clamp - If 1, change exponents if too high (Default 0) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3643 """ |
| 32482 | 3644 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3645 def __init__(self, prec=None, rounding=None, |
|
33722
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3646 traps=None, flags=None, |
|
32489
ab0a2b74ddfd
Changed the rounding constant values to match their variable names.
Raymond Hettinger <python@rcn.com>
parents:
32487
diff
changeset
|
3647 Emin=None, Emax=None, |
| 32496 | 3648 capitals=None, _clamp=0, |
|
33722
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3649 _ignored_flags=None): |
|
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3650 if flags is None: |
|
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3651 flags = [] |
|
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3652 if _ignored_flags is None: |
|
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3653 _ignored_flags = [] |
|
32576
83cbc025bfc7
Improve Context construction and representation:
Raymond Hettinger <python@rcn.com>
parents:
32561
diff
changeset
|
3654 if not isinstance(flags, dict): |
|
46653
1872e1dc035f
Make sure that Context traps and flags dictionaries have values 0 and 1
Mark Dickinson <dickinsm@gmail.com>
parents:
46651
diff
changeset
|
3655 flags = dict([(s, int(s in flags)) for s in _signals]) |
|
32667
941c239cb6d2
* Hide a loop induction variable that was inadvertantly being picked up
Raymond Hettinger <python@rcn.com>
parents:
32666
diff
changeset
|
3656 del s |
|
32576
83cbc025bfc7
Improve Context construction and representation:
Raymond Hettinger <python@rcn.com>
parents:
32561
diff
changeset
|
3657 if traps is not None and not isinstance(traps, dict): |
|
46653
1872e1dc035f
Make sure that Context traps and flags dictionaries have values 0 and 1
Mark Dickinson <dickinsm@gmail.com>
parents:
46651
diff
changeset
|
3658 traps = dict([(s, int(s in traps)) for s in _signals]) |
|
32667
941c239cb6d2
* Hide a loop induction variable that was inadvertantly being picked up
Raymond Hettinger <python@rcn.com>
parents:
32666
diff
changeset
|
3659 del s |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3660 for name, val in locals().items(): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3661 if val is None: |
|
35035
c55899863b9c
Minor namespace clean-up.
Raymond Hettinger <python@rcn.com>
parents:
34812
diff
changeset
|
3662 setattr(self, name, _copy.copy(getattr(DefaultContext, name))) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3663 else: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3664 setattr(self, name, val) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3665 del self.self |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3666 |
|
32487
fa23a9b18967
Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3667 def __repr__(self): |
|
32576
83cbc025bfc7
Improve Context construction and representation:
Raymond Hettinger <python@rcn.com>
parents:
32561
diff
changeset
|
3668 """Show the current context.""" |
|
32487
fa23a9b18967
Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3669 s = [] |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3670 s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3671 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d' |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3672 % vars(self)) |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3673 names = [f.__name__ for f, v in self.flags.items() if v] |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3674 s.append('flags=[' + ', '.join(names) + ']') |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3675 names = [t.__name__ for t, v in self.traps.items() if v] |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3676 s.append('traps=[' + ', '.join(names) + ']') |
|
32487
fa23a9b18967
Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3677 return ', '.join(s) + ')' |
|
fa23a9b18967
Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3678 |
|
32477
bc586db9945a
Work through several open todos:
Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3679 def clear_flags(self): |
|
bc586db9945a
Work through several open todos:
Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3680 """Reset all flags to zero""" |
|
bc586db9945a
Work through several open todos:
Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3681 for flag in self.flags: |
|
32487
fa23a9b18967
Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3682 self.flags[flag] = 0 |
|
32477
bc586db9945a
Work through several open todos:
Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3683 |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3684 def _shallow_copy(self): |
|
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3685 """Returns a shallow copy from self.""" |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
3686 nc = Context(self.prec, self.rounding, self.traps, |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
3687 self.flags, self.Emin, self.Emax, |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
3688 self.capitals, self._clamp, self._ignored_flags) |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3689 return nc |
|
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3690 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3691 def copy(self): |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3692 """Returns a deep copy from self.""" |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3693 nc = Context(self.prec, self.rounding, self.traps.copy(), |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
3694 self.flags.copy(), self.Emin, self.Emax, |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
3695 self.capitals, self._clamp, self._ignored_flags) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3696 return nc |
| 32482 | 3697 __copy__ = copy |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3698 |
| 32560 | 3699 def _raise_error(self, condition, explanation = None, *args): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3700 """Handles an error |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3701 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3702 If the flag is in _ignored_flags, returns the default response. |
|
46643
ec09ad5bed1a
Backport Raymond's changes in r60508 to Python 2.6.
Mark Dickinson <dickinsm@gmail.com>
parents:
46625
diff
changeset
|
3703 Otherwise, it sets the flag, then, if the corresponding |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3704 trap_enabler is set, it reaises the exception. Otherwise, it returns |
|
46643
ec09ad5bed1a
Backport Raymond's changes in r60508 to Python 2.6.
Mark Dickinson <dickinsm@gmail.com>
parents:
46625
diff
changeset
|
3705 the default value after setting the flag. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3706 """ |
| 32560 | 3707 error = _condition_map.get(condition, condition) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3708 if error in self._ignored_flags: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3709 # Don't touch the flag |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3710 return error().handle(self, *args) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3711 |
|
46643
ec09ad5bed1a
Backport Raymond's changes in r60508 to Python 2.6.
Mark Dickinson <dickinsm@gmail.com>
parents:
46625
diff
changeset
|
3712 self.flags[error] = 1 |
|
32576
83cbc025bfc7
Improve Context construction and representation:
Raymond Hettinger <python@rcn.com>
parents:
32561
diff
changeset
|
3713 if not self.traps[error]: |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3714 # The errors define how to handle themselves. |
| 32560 | 3715 return condition().handle(self, *args) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3716 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3717 # Errors should only be risked on copies of the context |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3718 # self._ignored_flags = [] |
|
46651
c97e36abcdd5
Some very minor changes to decimal.py in Python 2.6, aimed
Mark Dickinson <dickinsm@gmail.com>
parents:
46643
diff
changeset
|
3719 raise error(explanation) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3720 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3721 def _ignore_all_flags(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3722 """Ignore all flags, if they are raised""" |
|
32666
c13d911ae05b
* Rename "Signals" to "_signals" making it non-public.
Raymond Hettinger <python@rcn.com>
parents:
32576
diff
changeset
|
3723 return self._ignore_flags(*_signals) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3724 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3725 def _ignore_flags(self, *flags): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3726 """Ignore the flags, if they are raised""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3727 # Do not mutate-- This way, copies of a context leave the original |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3728 # alone. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3729 self._ignored_flags = (self._ignored_flags + list(flags)) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3730 return list(flags) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3731 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3732 def _regard_flags(self, *flags): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3733 """Stop ignoring the flags, if they are raised""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3734 if flags and isinstance(flags[0], (tuple,list)): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3735 flags = flags[0] |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3736 for flag in flags: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3737 self._ignored_flags.remove(flag) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3738 |
|
47961
f9b80a820a25
Issue 2235: __hash__ is once again inherited by default, but inheritance can be blocked explicitly so that collections.Hashable remains meaningful
Nick Coghlan <ncoghlan@gmail.com>
parents:
47872
diff
changeset
|
3739 # We inherit object.__hash__, so we must deny this explicitly |
|
f9b80a820a25
Issue 2235: __hash__ is once again inherited by default, but inheritance can be blocked explicitly so that collections.Hashable remains meaningful
Nick Coghlan <ncoghlan@gmail.com>
parents:
47872
diff
changeset
|
3740 __hash__ = None |
| 32560 | 3741 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3742 def Etiny(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3743 """Returns Etiny (= Emin - prec + 1)""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3744 return int(self.Emin - self.prec + 1) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3745 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3746 def Etop(self): |
| 32496 | 3747 """Returns maximum exponent (= Emax - prec + 1)""" |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3748 return int(self.Emax - self.prec + 1) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3749 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3750 def _set_rounding(self, type): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3751 """Sets the rounding type. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3752 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3753 Sets the rounding type, and returns the current (previous) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3754 rounding type. Often used like: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3755 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3756 context = context.copy() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3757 # so you don't change the calling context |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3758 # if an error occurs in the middle. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3759 rounding = context._set_rounding(ROUND_UP) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3760 val = self.__sub__(other, context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3761 context._set_rounding(rounding) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3762 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3763 This will make it round up for that operation. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3764 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3765 rounding = self.rounding |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3766 self.rounding= type |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3767 return rounding |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3768 |
|
32666
c13d911ae05b
* Rename "Signals" to "_signals" making it non-public.
Raymond Hettinger <python@rcn.com>
parents:
32576
diff
changeset
|
3769 def create_decimal(self, num='0'): |
|
44650
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3770 """Creates a new Decimal instance but using self as context. |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3771 |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3772 This method implements the to-number operation of the |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3773 IBM Decimal specification.""" |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3774 |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3775 if isinstance(num, basestring) and num != num.strip(): |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3776 return self._raise_error(ConversionSyntax, |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3777 "no trailing or leading whitespace is " |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3778 "permitted.") |
|
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
3779 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3780 d = Decimal(num, context=self) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3781 if d._isnan() and len(d._int) > self.prec - self._clamp: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3782 return self._raise_error(ConversionSyntax, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3783 "diagnostic info too long in NaN") |
| 33695 | 3784 return d._fix(self) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3785 |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3786 # Methods |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3787 def abs(self, a): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3788 """Returns the absolute value of the operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3789 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3790 If the operand is negative, the result is the same as using the minus |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
3791 operation on the operand. Otherwise, the result is the same as using |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3792 the plus operation on the operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3793 |
| 32482 | 3794 >>> ExtendedContext.abs(Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3795 Decimal('2.1') |
| 32482 | 3796 >>> ExtendedContext.abs(Decimal('-100')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3797 Decimal('100') |
| 32482 | 3798 >>> ExtendedContext.abs(Decimal('101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3799 Decimal('101.5') |
| 32482 | 3800 >>> ExtendedContext.abs(Decimal('-101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3801 Decimal('101.5') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3802 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3803 return a.__abs__(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3804 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3805 def add(self, a, b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3806 """Return the sum of the two operands. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3807 |
| 32482 | 3808 >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3809 Decimal('19.00') |
| 32482 | 3810 >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3811 Decimal('1.02E+4') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3812 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3813 return a.__add__(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3814 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3815 def _apply(self, a): |
| 33695 | 3816 return str(a._fix(self)) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3817 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3818 def canonical(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3819 """Returns the same Decimal object. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3820 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3821 As we do not have different encodings for the same number, the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3822 received object already is in its canonical form. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3823 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3824 >>> ExtendedContext.canonical(Decimal('2.50')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3825 Decimal('2.50') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3826 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3827 return a.canonical(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3828 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3829 def compare(self, a, b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3830 """Compares values numerically. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3831 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3832 If the signs of the operands differ, a value representing each operand |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3833 ('-1' if the operand is less than zero, '0' if the operand is zero or |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3834 negative zero, or '1' if the operand is greater than zero) is used in |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3835 place of that operand for the comparison instead of the actual |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3836 operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3837 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3838 The comparison is then effected by subtracting the second operand from |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3839 the first and then returning a value according to the result of the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3840 subtraction: '-1' if the result is less than zero, '0' if the result is |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3841 zero or negative zero, or '1' if the result is greater than zero. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3842 |
| 32482 | 3843 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3844 Decimal('-1') |
| 32482 | 3845 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3846 Decimal('0') |
| 32482 | 3847 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3848 Decimal('0') |
| 32482 | 3849 >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3850 Decimal('1') |
| 32482 | 3851 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3852 Decimal('1') |
| 32482 | 3853 >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3854 Decimal('-1') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3855 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3856 return a.compare(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3857 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3858 def compare_signal(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3859 """Compares the values of the two operands numerically. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3860 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3861 It's pretty much like compare(), but all NaNs signal, with signaling |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3862 NaNs taking precedence over quiet NaNs. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3863 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3864 >>> c = ExtendedContext |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3865 >>> c.compare_signal(Decimal('2.1'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3866 Decimal('-1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3867 >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3868 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3869 >>> c.flags[InvalidOperation] = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3870 >>> print c.flags[InvalidOperation] |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3871 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3872 >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3873 Decimal('NaN') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3874 >>> print c.flags[InvalidOperation] |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3875 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3876 >>> c.flags[InvalidOperation] = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3877 >>> print c.flags[InvalidOperation] |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3878 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3879 >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3880 Decimal('NaN') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3881 >>> print c.flags[InvalidOperation] |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3882 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3883 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3884 return a.compare_signal(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3885 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3886 def compare_total(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3887 """Compares two operands using their abstract representation. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3888 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3889 This is not like the standard compare, which use their numerical |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3890 value. Note that a total ordering is defined for all possible abstract |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3891 representations. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3892 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3893 >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3894 Decimal('-1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3895 >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3896 Decimal('-1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3897 >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3898 Decimal('-1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3899 >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3900 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3901 >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3902 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3903 >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3904 Decimal('-1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3905 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3906 return a.compare_total(b) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3907 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3908 def compare_total_mag(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3909 """Compares two operands using their abstract representation ignoring sign. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3910 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3911 Like compare_total, but with operand's sign ignored and assumed to be 0. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3912 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3913 return a.compare_total_mag(b) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3914 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3915 def copy_abs(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3916 """Returns a copy of the operand with the sign set to 0. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3917 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3918 >>> ExtendedContext.copy_abs(Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3919 Decimal('2.1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3920 >>> ExtendedContext.copy_abs(Decimal('-100')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3921 Decimal('100') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3922 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3923 return a.copy_abs() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3924 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3925 def copy_decimal(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3926 """Returns a copy of the decimal objet. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3927 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3928 >>> ExtendedContext.copy_decimal(Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3929 Decimal('2.1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3930 >>> ExtendedContext.copy_decimal(Decimal('-1.00')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3931 Decimal('-1.00') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3932 """ |
|
43383
8890be9386b7
The methods always return Decimal classes, even if they're
Facundo Batista <facundobatista@gmail.com>
parents:
43362
diff
changeset
|
3933 return Decimal(a) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3934 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3935 def copy_negate(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3936 """Returns a copy of the operand with the sign inverted. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3937 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3938 >>> ExtendedContext.copy_negate(Decimal('101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3939 Decimal('-101.5') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3940 >>> ExtendedContext.copy_negate(Decimal('-101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
3941 Decimal('101.5') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
3942 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3943 return a.copy_negate() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3944 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
3945 def copy_sign(self, a, b): |
|
63f3154c731d
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|
3946 """Copies the second operand's sign to the first one. |
|
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3947 |
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|
3948 In detail, it returns a copy of the first operand with the sign |
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|
3949 equal to the sign of the second operand. |
|
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3950 |
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|
3951 >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) |
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|
3952 Decimal('1.50') |
|
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|
3953 >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) |
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3954 Decimal('1.50') |
|
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|
3955 >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) |
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3956 Decimal('-1.50') |
|
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|
3957 >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) |
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3958 Decimal('-1.50') |
|
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|
3959 """ |
|
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|
3960 return a.copy_sign(b) |
|
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3961 |
|
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3962 def divide(self, a, b): |
|
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3963 """Decimal division in a specified context. |
|
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3964 |
| 32482 | 3965 >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) |
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|
3966 Decimal('0.333333333') |
| 32482 | 3967 >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) |
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|
3968 Decimal('0.666666667') |
| 32482 | 3969 >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) |
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3970 Decimal('2.5') |
| 32482 | 3971 >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) |
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3972 Decimal('0.1') |
| 32482 | 3973 >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) |
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3974 Decimal('1') |
| 32482 | 3975 >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) |
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|
3976 Decimal('4.00') |
| 32482 | 3977 >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) |
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3978 Decimal('1.20') |
| 32482 | 3979 >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) |
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3980 Decimal('10') |
| 32482 | 3981 >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) |
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3982 Decimal('1000') |
| 32482 | 3983 >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) |
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3984 Decimal('1.20E+6') |
|
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|
3985 """ |
|
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3986 return a.__div__(b, context=self) |
|
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3987 |
|
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3988 def divide_int(self, a, b): |
|
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3989 """Divides two numbers and returns the integer part of the result. |
|
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3990 |
| 32482 | 3991 >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) |
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3992 Decimal('0') |
| 32482 | 3993 >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) |
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|
3994 Decimal('3') |
| 32482 | 3995 >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) |
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3996 Decimal('3') |
|
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3997 """ |
|
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3998 return a.__floordiv__(b, context=self) |
|
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3999 |
|
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|
4000 def divmod(self, a, b): |
|
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|
4001 """Return (a // b, a % b) |
|
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4002 |
|
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|
4003 >>> ExtendedContext.divmod(Decimal(8), Decimal(3)) |
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|
4004 (Decimal('2'), Decimal('2')) |
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|
4005 >>> ExtendedContext.divmod(Decimal(8), Decimal(4)) |
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|
4006 (Decimal('2'), Decimal('0')) |
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|
4007 """ |
|
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4008 return a.__divmod__(b, context=self) |
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4009 |
|
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|
4010 def exp(self, a): |
|
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4011 """Returns e ** a. |
|
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4012 |
|
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|
4013 >>> c = ExtendedContext.copy() |
|
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|
4014 >>> c.Emin = -999 |
|
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|
4015 >>> c.Emax = 999 |
|
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|
4016 >>> c.exp(Decimal('-Infinity')) |
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|
4017 Decimal('0') |
|
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|
4018 >>> c.exp(Decimal('-1')) |
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|
4019 Decimal('0.367879441') |
|
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|
4020 >>> c.exp(Decimal('0')) |
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|
4021 Decimal('1') |
|
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|
4022 >>> c.exp(Decimal('1')) |
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|
4023 Decimal('2.71828183') |
|
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|
4024 >>> c.exp(Decimal('0.693147181')) |
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|
4025 Decimal('2.00000000') |
|
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|
4026 >>> c.exp(Decimal('+Infinity')) |
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|
4027 Decimal('Infinity') |
|
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|
4028 """ |
|
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|
4029 return a.exp(context=self) |
|
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|
4030 |
|
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|
4031 def fma(self, a, b, c): |
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|
4032 """Returns a multiplied by b, plus c. |
|
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4033 |
|
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|
4034 The first two operands are multiplied together, using multiply, |
|
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|
4035 the third operand is then added to the result of that |
|
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|
4036 multiplication, using add, all with only one final rounding. |
|
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|
4037 |
|
63f3154c731d
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|
4038 >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) |
|
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|
4039 Decimal('22') |
|
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|
4040 >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) |
|
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|
4041 Decimal('-8') |
|
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|
4042 >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) |
|
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|
4043 Decimal('1.38435736E+12') |
|
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|
4044 """ |
|
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|
4045 return a.fma(b, c, context=self) |
|
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|
4046 |
|
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|
4047 def is_canonical(self, a): |
|
43454
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|
4048 """Return True if the operand is canonical; otherwise return False. |
|
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|
4049 |
|
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|
4050 Currently, the encoding of a Decimal instance is always |
|
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|
4051 canonical, so this method returns True for any Decimal. |
|
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|
4052 |
|
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|
4053 >>> ExtendedContext.is_canonical(Decimal('2.50')) |
|
43454
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|
4054 True |
|
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|
4055 """ |
|
43454
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|
4056 return a.is_canonical() |
|
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|
4057 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4058 def is_finite(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4059 """Return True if the operand is finite; otherwise return False. |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4060 |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4061 A Decimal instance is considered finite if it is neither |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4062 infinite nor a NaN. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4063 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4064 >>> ExtendedContext.is_finite(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4065 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4066 >>> ExtendedContext.is_finite(Decimal('-0.3')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4067 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4068 >>> ExtendedContext.is_finite(Decimal('0')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4069 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4070 >>> ExtendedContext.is_finite(Decimal('Inf')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4071 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4072 >>> ExtendedContext.is_finite(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4073 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4074 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4075 return a.is_finite() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4076 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4077 def is_infinite(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4078 """Return True if the operand is infinite; otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4079 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4080 >>> ExtendedContext.is_infinite(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4081 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4082 >>> ExtendedContext.is_infinite(Decimal('-Inf')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4083 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4084 >>> ExtendedContext.is_infinite(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4085 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4086 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4087 return a.is_infinite() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4088 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4089 def is_nan(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4090 """Return True if the operand is a qNaN or sNaN; |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4091 otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4092 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4093 >>> ExtendedContext.is_nan(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4094 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4095 >>> ExtendedContext.is_nan(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4096 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4097 >>> ExtendedContext.is_nan(Decimal('-sNaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4098 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4099 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4100 return a.is_nan() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4101 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4102 def is_normal(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4103 """Return True if the operand is a normal number; |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4104 otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4105 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4106 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4107 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4108 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4109 >>> c.is_normal(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4110 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4111 >>> c.is_normal(Decimal('0.1E-999')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4112 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4113 >>> c.is_normal(Decimal('0.00')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4114 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4115 >>> c.is_normal(Decimal('-Inf')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4116 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4117 >>> c.is_normal(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4118 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4119 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4120 return a.is_normal(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4121 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4122 def is_qnan(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4123 """Return True if the operand is a quiet NaN; otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4124 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4125 >>> ExtendedContext.is_qnan(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4126 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4127 >>> ExtendedContext.is_qnan(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4128 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4129 >>> ExtendedContext.is_qnan(Decimal('sNaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4130 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4131 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4132 return a.is_qnan() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4133 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4134 def is_signed(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4135 """Return True if the operand is negative; otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4136 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4137 >>> ExtendedContext.is_signed(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4138 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4139 >>> ExtendedContext.is_signed(Decimal('-12')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4140 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4141 >>> ExtendedContext.is_signed(Decimal('-0')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4142 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4143 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4144 return a.is_signed() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4145 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4146 def is_snan(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4147 """Return True if the operand is a signaling NaN; |
|
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4148 otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
4149 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4150 >>> ExtendedContext.is_snan(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
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parents:
43409
diff
changeset
|
4151 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4152 >>> ExtendedContext.is_snan(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4153 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4154 >>> ExtendedContext.is_snan(Decimal('sNaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4155 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4156 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4157 return a.is_snan() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4158 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4159 def is_subnormal(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4160 """Return True if the operand is subnormal; otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4161 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4162 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4163 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4164 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4165 >>> c.is_subnormal(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4166 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4167 >>> c.is_subnormal(Decimal('0.1E-999')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4168 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4169 >>> c.is_subnormal(Decimal('0.00')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4170 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4171 >>> c.is_subnormal(Decimal('-Inf')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4172 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4173 >>> c.is_subnormal(Decimal('NaN')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4174 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4175 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
4176 return a.is_subnormal(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4177 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4178 def is_zero(self, a): |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4179 """Return True if the operand is a zero; otherwise return False. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4180 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4181 >>> ExtendedContext.is_zero(Decimal('0')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4182 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4183 >>> ExtendedContext.is_zero(Decimal('2.50')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4184 False |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4185 >>> ExtendedContext.is_zero(Decimal('-0E+2')) |
|
43454
9d6d9ac95ae1
Made the various is_* operations return booleans. This was discussed
Facundo Batista <facundobatista@gmail.com>
parents:
43409
diff
changeset
|
4186 True |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4187 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4188 return a.is_zero() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4189 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4190 def ln(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4191 """Returns the natural (base e) logarithm of the operand. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4192 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4193 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4194 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4195 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4196 >>> c.ln(Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4197 Decimal('-Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4198 >>> c.ln(Decimal('1.000')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4199 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4200 >>> c.ln(Decimal('2.71828183')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4201 Decimal('1.00000000') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4202 >>> c.ln(Decimal('10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4203 Decimal('2.30258509') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4204 >>> c.ln(Decimal('+Infinity')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4205 Decimal('Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4206 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4207 return a.ln(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4208 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4209 def log10(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4210 """Returns the base 10 logarithm of the operand. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4211 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4212 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4213 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4214 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4215 >>> c.log10(Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4216 Decimal('-Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4217 >>> c.log10(Decimal('0.001')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4218 Decimal('-3') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4219 >>> c.log10(Decimal('1.000')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4220 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4221 >>> c.log10(Decimal('2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4222 Decimal('0.301029996') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4223 >>> c.log10(Decimal('10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4224 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4225 >>> c.log10(Decimal('70')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4226 Decimal('1.84509804') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4227 >>> c.log10(Decimal('+Infinity')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4228 Decimal('Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4229 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4230 return a.log10(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4231 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4232 def logb(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4233 """ Returns the exponent of the magnitude of the operand's MSD. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4234 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4235 The result is the integer which is the exponent of the magnitude |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4236 of the most significant digit of the operand (as though the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4237 operand were truncated to a single digit while maintaining the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4238 value of that digit and without limiting the resulting exponent). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4239 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4240 >>> ExtendedContext.logb(Decimal('250')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4241 Decimal('2') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4242 >>> ExtendedContext.logb(Decimal('2.50')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4243 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4244 >>> ExtendedContext.logb(Decimal('0.03')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4245 Decimal('-2') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4246 >>> ExtendedContext.logb(Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4247 Decimal('-Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4248 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4249 return a.logb(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4250 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4251 def logical_and(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
4252 """Applies the logical operation 'and' between each operand's digits. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4253 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
4254 The operands must be both logical numbers. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4255 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4256 >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4257 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4258 >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4259 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4260 >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4261 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4262 >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4263 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4264 >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4265 Decimal('1000') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4266 >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4267 Decimal('10') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4268 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4269 return a.logical_and(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4270 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4271 def logical_invert(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4272 """Invert all the digits in the operand. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4273 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4274 The operand must be a logical number. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4275 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4276 >>> ExtendedContext.logical_invert(Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4277 Decimal('111111111') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4278 >>> ExtendedContext.logical_invert(Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4279 Decimal('111111110') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4280 >>> ExtendedContext.logical_invert(Decimal('111111111')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4281 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4282 >>> ExtendedContext.logical_invert(Decimal('101010101')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4283 Decimal('10101010') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4284 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4285 return a.logical_invert(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4286 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4287 def logical_or(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4288 """Applies the logical operation 'or' between each operand's digits. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4289 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4290 The operands must be both logical numbers. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4291 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4292 >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4293 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4294 >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4295 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4296 >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4297 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4298 >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4299 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4300 >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4301 Decimal('1110') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4302 >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4303 Decimal('1110') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4304 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4305 return a.logical_or(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4306 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4307 def logical_xor(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4308 """Applies the logical operation 'xor' between each operand's digits. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4309 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4310 The operands must be both logical numbers. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4311 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4312 >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4313 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4314 >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4315 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4316 >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4317 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4318 >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4319 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4320 >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4321 Decimal('110') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4322 >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4323 Decimal('1101') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4324 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4325 return a.logical_xor(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4326 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4327 def max(self, a,b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4328 """max compares two values numerically and returns the maximum. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4329 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4330 If either operand is a NaN then the general rules apply. |
| 44701 | 4331 Otherwise, the operands are compared as though by the compare |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4332 operation. If they are numerically equal then the left-hand operand |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4333 is chosen as the result. Otherwise the maximum (closer to positive |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4334 infinity) of the two operands is chosen as the result. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4335 |
| 32482 | 4336 >>> ExtendedContext.max(Decimal('3'), Decimal('2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4337 Decimal('3') |
| 32482 | 4338 >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4339 Decimal('3') |
| 32482 | 4340 >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4341 Decimal('1') |
|
33157
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
4342 >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4343 Decimal('7') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4344 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4345 return a.max(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4346 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4347 def max_mag(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4348 """Compares the values numerically with their sign ignored.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4349 return a.max_mag(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4350 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4351 def min(self, a,b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4352 """min compares two values numerically and returns the minimum. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4353 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4354 If either operand is a NaN then the general rules apply. |
| 44701 | 4355 Otherwise, the operands are compared as though by the compare |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4356 operation. If they are numerically equal then the left-hand operand |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4357 is chosen as the result. Otherwise the minimum (closer to negative |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4358 infinity) of the two operands is chosen as the result. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4359 |
| 32482 | 4360 >>> ExtendedContext.min(Decimal('3'), Decimal('2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4361 Decimal('2') |
| 32482 | 4362 >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4363 Decimal('-10') |
| 32482 | 4364 >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4365 Decimal('1.0') |
|
33157
b2f427db228b
Revise max() and min() to comply with the 8/2/2004 update to the specification
Raymond Hettinger <python@rcn.com>
parents:
33044
diff
changeset
|
4366 >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4367 Decimal('7') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4368 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4369 return a.min(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4370 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4371 def min_mag(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4372 """Compares the values numerically with their sign ignored.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4373 return a.min_mag(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4374 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4375 def minus(self, a): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4376 """Minus corresponds to unary prefix minus in Python. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4377 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4378 The operation is evaluated using the same rules as subtract; the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4379 operation minus(a) is calculated as subtract('0', a) where the '0' |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4380 has the same exponent as the operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4381 |
| 32482 | 4382 >>> ExtendedContext.minus(Decimal('1.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4383 Decimal('-1.3') |
| 32482 | 4384 >>> ExtendedContext.minus(Decimal('-1.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4385 Decimal('1.3') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4386 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4387 return a.__neg__(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4388 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4389 def multiply(self, a, b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4390 """multiply multiplies two operands. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4391 |
|
39120
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
4392 If either operand is a special value then the general rules apply. |
|
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
4393 Otherwise, the operands are multiplied together ('long multiplication'), |
|
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
4394 resulting in a number which may be as long as the sum of the lengths |
|
1d7da8608031
Revert r50706 (Whitespace normalization) and
Martin v. Löwis <martin@v.loewis.de>
parents:
39117
diff
changeset
|
4395 of the two operands. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4396 |
| 32482 | 4397 >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4398 Decimal('3.60') |
| 32482 | 4399 >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4400 Decimal('21') |
| 32482 | 4401 >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4402 Decimal('0.72') |
| 32482 | 4403 >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4404 Decimal('-0.0') |
| 32482 | 4405 >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4406 Decimal('4.28135971E+11') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4407 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4408 return a.__mul__(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4409 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4410 def next_minus(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4411 """Returns the largest representable number smaller than a. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4412 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4413 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4414 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4415 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4416 >>> ExtendedContext.next_minus(Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4417 Decimal('0.999999999') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4418 >>> c.next_minus(Decimal('1E-1007')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4419 Decimal('0E-1007') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4420 >>> ExtendedContext.next_minus(Decimal('-1.00000003')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4421 Decimal('-1.00000004') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4422 >>> c.next_minus(Decimal('Infinity')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4423 Decimal('9.99999999E+999') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4424 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4425 return a.next_minus(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4426 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4427 def next_plus(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4428 """Returns the smallest representable number larger than a. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4429 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4430 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4431 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4432 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4433 >>> ExtendedContext.next_plus(Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4434 Decimal('1.00000001') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4435 >>> c.next_plus(Decimal('-1E-1007')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4436 Decimal('-0E-1007') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4437 >>> ExtendedContext.next_plus(Decimal('-1.00000003')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4438 Decimal('-1.00000002') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4439 >>> c.next_plus(Decimal('-Infinity')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4440 Decimal('-9.99999999E+999') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4441 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4442 return a.next_plus(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4443 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4444 def next_toward(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4445 """Returns the number closest to a, in direction towards b. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4446 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4447 The result is the closest representable number from the first |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4448 operand (but not the first operand) that is in the direction |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4449 towards the second operand, unless the operands have the same |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4450 value. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4451 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4452 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4453 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4454 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4455 >>> c.next_toward(Decimal('1'), Decimal('2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4456 Decimal('1.00000001') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4457 >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4458 Decimal('-0E-1007') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4459 >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4460 Decimal('-1.00000002') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4461 >>> c.next_toward(Decimal('1'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4462 Decimal('0.999999999') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4463 >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4464 Decimal('0E-1007') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4465 >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4466 Decimal('-1.00000004') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4467 >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4468 Decimal('-0.00') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4469 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4470 return a.next_toward(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4471 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4472 def normalize(self, a): |
| 32496 | 4473 """normalize reduces an operand to its simplest form. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4474 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4475 Essentially a plus operation with all trailing zeros removed from the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4476 result. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4477 |
| 32482 | 4478 >>> ExtendedContext.normalize(Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4479 Decimal('2.1') |
| 32482 | 4480 >>> ExtendedContext.normalize(Decimal('-2.0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4481 Decimal('-2') |
| 32482 | 4482 >>> ExtendedContext.normalize(Decimal('1.200')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4483 Decimal('1.2') |
| 32482 | 4484 >>> ExtendedContext.normalize(Decimal('-120')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4485 Decimal('-1.2E+2') |
| 32482 | 4486 >>> ExtendedContext.normalize(Decimal('120.00')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4487 Decimal('1.2E+2') |
| 32482 | 4488 >>> ExtendedContext.normalize(Decimal('0.00')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4489 Decimal('0') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4490 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4491 return a.normalize(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4492 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4493 def number_class(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4494 """Returns an indication of the class of the operand. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4495 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4496 The class is one of the following strings: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4497 -sNaN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4498 -NaN |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4499 -Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4500 -Normal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4501 -Subnormal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4502 -Zero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4503 +Zero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4504 +Subnormal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4505 +Normal |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4506 +Infinity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4507 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4508 >>> c = Context(ExtendedContext) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4509 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4510 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4511 >>> c.number_class(Decimal('Infinity')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4512 '+Infinity' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4513 >>> c.number_class(Decimal('1E-10')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4514 '+Normal' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4515 >>> c.number_class(Decimal('2.50')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4516 '+Normal' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4517 >>> c.number_class(Decimal('0.1E-999')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4518 '+Subnormal' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4519 >>> c.number_class(Decimal('0')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4520 '+Zero' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4521 >>> c.number_class(Decimal('-0')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4522 '-Zero' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4523 >>> c.number_class(Decimal('-0.1E-999')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4524 '-Subnormal' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4525 >>> c.number_class(Decimal('-1E-10')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4526 '-Normal' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4527 >>> c.number_class(Decimal('-2.50')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4528 '-Normal' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4529 >>> c.number_class(Decimal('-Infinity')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4530 '-Infinity' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4531 >>> c.number_class(Decimal('NaN')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4532 'NaN' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4533 >>> c.number_class(Decimal('-NaN')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4534 'NaN' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4535 >>> c.number_class(Decimal('sNaN')) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4536 'sNaN' |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4537 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4538 return a.number_class(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4539 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4540 def plus(self, a): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4541 """Plus corresponds to unary prefix plus in Python. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4542 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4543 The operation is evaluated using the same rules as add; the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4544 operation plus(a) is calculated as add('0', a) where the '0' |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4545 has the same exponent as the operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4546 |
| 32482 | 4547 >>> ExtendedContext.plus(Decimal('1.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4548 Decimal('1.3') |
| 32482 | 4549 >>> ExtendedContext.plus(Decimal('-1.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4550 Decimal('-1.3') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4551 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4552 return a.__pos__(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4553 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4554 def power(self, a, b, modulo=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4555 """Raises a to the power of b, to modulo if given. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4556 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4557 With two arguments, compute a**b. If a is negative then b |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4558 must be integral. The result will be inexact unless b is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4559 integral and the result is finite and can be expressed exactly |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4560 in 'precision' digits. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4561 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4562 With three arguments, compute (a**b) % modulo. For the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4563 three argument form, the following restrictions on the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4564 arguments hold: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4565 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4566 - all three arguments must be integral |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4567 - b must be nonnegative |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4568 - at least one of a or b must be nonzero |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4569 - modulo must be nonzero and have at most 'precision' digits |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4570 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4571 The result of pow(a, b, modulo) is identical to the result |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4572 that would be obtained by computing (a**b) % modulo with |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4573 unbounded precision, but is computed more efficiently. It is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
4574 always exact. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4575 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4576 >>> c = ExtendedContext.copy() |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4577 >>> c.Emin = -999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4578 >>> c.Emax = 999 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4579 >>> c.power(Decimal('2'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4580 Decimal('8') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4581 >>> c.power(Decimal('-2'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4582 Decimal('-8') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4583 >>> c.power(Decimal('2'), Decimal('-3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4584 Decimal('0.125') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4585 >>> c.power(Decimal('1.7'), Decimal('8')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4586 Decimal('69.7575744') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4587 >>> c.power(Decimal('10'), Decimal('0.301029996')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4588 Decimal('2.00000000') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4589 >>> c.power(Decimal('Infinity'), Decimal('-1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4590 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4591 >>> c.power(Decimal('Infinity'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4592 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4593 >>> c.power(Decimal('Infinity'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4594 Decimal('Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4595 >>> c.power(Decimal('-Infinity'), Decimal('-1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4596 Decimal('-0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4597 >>> c.power(Decimal('-Infinity'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4598 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4599 >>> c.power(Decimal('-Infinity'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4600 Decimal('-Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4601 >>> c.power(Decimal('-Infinity'), Decimal('2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4602 Decimal('Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4603 >>> c.power(Decimal('0'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4604 Decimal('NaN') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4605 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4606 >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4607 Decimal('11') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4608 >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4609 Decimal('-11') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4610 >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4611 Decimal('1') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4612 >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4613 Decimal('11') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4614 >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4615 Decimal('11729830') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4616 >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4617 Decimal('-0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4618 >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4619 Decimal('1') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4620 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4621 return a.__pow__(b, modulo, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4622 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4623 def quantize(self, a, b): |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4624 """Returns a value equal to 'a' (rounded), having the exponent of 'b'. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4625 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4626 The coefficient of the result is derived from that of the left-hand |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4627 operand. It may be rounded using the current rounding setting (if the |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4628 exponent is being increased), multiplied by a positive power of ten (if |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4629 the exponent is being decreased), or is unchanged (if the exponent is |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4630 already equal to that of the right-hand operand). |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4631 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4632 Unlike other operations, if the length of the coefficient after the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4633 quantize operation would be greater than precision then an Invalid |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4634 operation condition is raised. This guarantees that, unless there is |
|
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4635 an error condition, the exponent of the result of a quantize is always |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4636 equal to that of the right-hand operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4637 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4638 Also unlike other operations, quantize will never raise Underflow, even |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4639 if the result is subnormal and inexact. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4640 |
| 32482 | 4641 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4642 Decimal('2.170') |
| 32482 | 4643 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4644 Decimal('2.17') |
| 32482 | 4645 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4646 Decimal('2.2') |
| 32482 | 4647 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4648 Decimal('2') |
| 32482 | 4649 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4650 Decimal('0E+1') |
| 32482 | 4651 >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4652 Decimal('-Infinity') |
| 32482 | 4653 >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4654 Decimal('NaN') |
| 32482 | 4655 >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4656 Decimal('-0') |
| 32482 | 4657 >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4658 Decimal('-0E+5') |
| 32482 | 4659 >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4660 Decimal('NaN') |
| 32482 | 4661 >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4662 Decimal('NaN') |
| 32482 | 4663 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4664 Decimal('217.0') |
| 32482 | 4665 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4666 Decimal('217') |
| 32482 | 4667 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4668 Decimal('2.2E+2') |
| 32482 | 4669 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4670 Decimal('2E+2') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4671 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4672 return a.quantize(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4673 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4674 def radix(self): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4675 """Just returns 10, as this is Decimal, :) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4676 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4677 >>> ExtendedContext.radix() |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4678 Decimal('10') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4679 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4680 return Decimal(10) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4681 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4682 def remainder(self, a, b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4683 """Returns the remainder from integer division. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4684 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4685 The result is the residue of the dividend after the operation of |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4686 calculating integer division as described for divide-integer, rounded |
|
41532
4b9fa8092e82
Whitespace normalization. Ugh, we really need to do this more often.
Neal Norwitz <nnorwitz@gmail.com>
parents:
41418
diff
changeset
|
4687 to precision digits if necessary. The sign of the result, if |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4688 non-zero, is the same as that of the original dividend. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4689 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4690 This operation will fail under the same conditions as integer division |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4691 (that is, if integer division on the same two operands would fail, the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4692 remainder cannot be calculated). |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4693 |
| 32482 | 4694 >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4695 Decimal('2.1') |
| 32482 | 4696 >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4697 Decimal('1') |
| 32482 | 4698 >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4699 Decimal('-1') |
| 32482 | 4700 >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4701 Decimal('0.2') |
| 32482 | 4702 >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4703 Decimal('0.1') |
| 32482 | 4704 >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4705 Decimal('1.0') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4706 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4707 return a.__mod__(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4708 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4709 def remainder_near(self, a, b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4710 """Returns to be "a - b * n", where n is the integer nearest the exact |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4711 value of "x / b" (if two integers are equally near then the even one |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4712 is chosen). If the result is equal to 0 then its sign will be the |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4713 sign of a. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4714 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4715 This operation will fail under the same conditions as integer division |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4716 (that is, if integer division on the same two operands would fail, the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4717 remainder cannot be calculated). |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4718 |
| 32482 | 4719 >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4720 Decimal('-0.9') |
| 32482 | 4721 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4722 Decimal('-2') |
| 32482 | 4723 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4724 Decimal('1') |
| 32482 | 4725 >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4726 Decimal('-1') |
| 32482 | 4727 >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4728 Decimal('0.2') |
| 32482 | 4729 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4730 Decimal('0.1') |
| 32482 | 4731 >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4732 Decimal('-0.3') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4733 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4734 return a.remainder_near(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4735 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4736 def rotate(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4737 """Returns a rotated copy of a, b times. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4738 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4739 The coefficient of the result is a rotated copy of the digits in |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4740 the coefficient of the first operand. The number of places of |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4741 rotation is taken from the absolute value of the second operand, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4742 with the rotation being to the left if the second operand is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4743 positive or to the right otherwise. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4744 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4745 >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4746 Decimal('400000003') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4747 >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4748 Decimal('12') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4749 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4750 Decimal('891234567') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4751 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4752 Decimal('123456789') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4753 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4754 Decimal('345678912') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4755 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4756 return a.rotate(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4757 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4758 def same_quantum(self, a, b): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4759 """Returns True if the two operands have the same exponent. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4760 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4761 The result is never affected by either the sign or the coefficient of |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4762 either operand. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4763 |
| 32482 | 4764 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4765 False |
| 32482 | 4766 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4767 True |
| 32482 | 4768 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4769 False |
| 32482 | 4770 >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4771 True |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4772 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4773 return a.same_quantum(b) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4774 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4775 def scaleb (self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4776 """Returns the first operand after adding the second value its exp. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4777 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4778 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4779 Decimal('0.0750') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4780 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4781 Decimal('7.50') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4782 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4783 Decimal('7.50E+3') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4784 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4785 return a.scaleb (b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4786 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4787 def shift(self, a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4788 """Returns a shifted copy of a, b times. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4789 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4790 The coefficient of the result is a shifted copy of the digits |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4791 in the coefficient of the first operand. The number of places |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4792 to shift is taken from the absolute value of the second operand, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4793 with the shift being to the left if the second operand is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4794 positive or to the right otherwise. Digits shifted into the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4795 coefficient are zeros. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4796 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4797 >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4798 Decimal('400000000') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4799 >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4800 Decimal('0') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4801 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4802 Decimal('1234567') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4803 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4804 Decimal('123456789') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4805 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4806 Decimal('345678900') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4807 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4808 return a.shift(b, context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4809 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4810 def sqrt(self, a): |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4811 """Square root of a non-negative number to context precision. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4812 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4813 If the result must be inexact, it is rounded using the round-half-even |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4814 algorithm. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4815 |
| 32482 | 4816 >>> ExtendedContext.sqrt(Decimal('0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4817 Decimal('0') |
| 32482 | 4818 >>> ExtendedContext.sqrt(Decimal('-0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4819 Decimal('-0') |
| 32482 | 4820 >>> ExtendedContext.sqrt(Decimal('0.39')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4821 Decimal('0.624499800') |
| 32482 | 4822 >>> ExtendedContext.sqrt(Decimal('100')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4823 Decimal('10') |
| 32482 | 4824 >>> ExtendedContext.sqrt(Decimal('1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4825 Decimal('1') |
| 32482 | 4826 >>> ExtendedContext.sqrt(Decimal('1.0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4827 Decimal('1.0') |
| 32482 | 4828 >>> ExtendedContext.sqrt(Decimal('1.00')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4829 Decimal('1.0') |
| 32482 | 4830 >>> ExtendedContext.sqrt(Decimal('7')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4831 Decimal('2.64575131') |
| 32482 | 4832 >>> ExtendedContext.sqrt(Decimal('10')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4833 Decimal('3.16227766') |
| 32482 | 4834 >>> ExtendedContext.prec |
|
32481
b835d5c61d86
* Make the tests independent of the default precision.
Raymond Hettinger <python@rcn.com>
parents:
32477
diff
changeset
|
4835 9 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4836 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4837 return a.sqrt(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4838 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4839 def subtract(self, a, b): |
|
35379
43211be0de41
bug [ 1266296 ] Mistakes in decimal.Context.subtract documentation
Georg Brandl <georg@python.org>
parents:
35113
diff
changeset
|
4840 """Return the difference between the two operands. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4841 |
| 32482 | 4842 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4843 Decimal('0.23') |
| 32482 | 4844 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4845 Decimal('0.00') |
| 32482 | 4846 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4847 Decimal('-0.77') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4848 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4849 return a.__sub__(b, context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4850 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4851 def to_eng_string(self, a): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4852 """Converts a number to a string, using scientific notation. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4853 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4854 The operation is not affected by the context. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4855 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4856 return a.to_eng_string(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4857 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4858 def to_sci_string(self, a): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4859 """Converts a number to a string, using scientific notation. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4860 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4861 The operation is not affected by the context. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4862 """ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4863 return a.__str__(context=self) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4864 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4865 def to_integral_exact(self, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4866 """Rounds to an integer. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4867 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4868 When the operand has a negative exponent, the result is the same |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4869 as using the quantize() operation using the given operand as the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4870 left-hand-operand, 1E+0 as the right-hand-operand, and the precision |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4871 of the operand as the precision setting; Inexact and Rounded flags |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4872 are allowed in this operation. The rounding mode is taken from the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4873 context. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4874 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4875 >>> ExtendedContext.to_integral_exact(Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4876 Decimal('2') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4877 >>> ExtendedContext.to_integral_exact(Decimal('100')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4878 Decimal('100') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4879 >>> ExtendedContext.to_integral_exact(Decimal('100.0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4880 Decimal('100') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4881 >>> ExtendedContext.to_integral_exact(Decimal('101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4882 Decimal('102') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4883 >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4884 Decimal('-102') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4885 >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4886 Decimal('1.0E+6') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4887 >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4888 Decimal('7.89E+77') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4889 >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4890 Decimal('-Infinity') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4891 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4892 return a.to_integral_exact(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4893 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4894 def to_integral_value(self, a): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4895 """Rounds to an integer. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4896 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4897 When the operand has a negative exponent, the result is the same |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4898 as using the quantize() operation using the given operand as the |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4899 left-hand-operand, 1E+0 as the right-hand-operand, and the precision |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4900 of the operand as the precision setting, except that no flags will |
|
41418
ae4ced28a839
General clean-up. Lot of margin corrections, comments, some typos.
Facundo Batista <facundobatista@gmail.com>
parents:
40770
diff
changeset
|
4901 be set. The rounding mode is taken from the context. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4902 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4903 >>> ExtendedContext.to_integral_value(Decimal('2.1')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4904 Decimal('2') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4905 >>> ExtendedContext.to_integral_value(Decimal('100')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4906 Decimal('100') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4907 >>> ExtendedContext.to_integral_value(Decimal('100.0')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4908 Decimal('100') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4909 >>> ExtendedContext.to_integral_value(Decimal('101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4910 Decimal('102') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4911 >>> ExtendedContext.to_integral_value(Decimal('-101.5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4912 Decimal('-102') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4913 >>> ExtendedContext.to_integral_value(Decimal('10E+5')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4914 Decimal('1.0E+6') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4915 >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4916 Decimal('7.89E+77') |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4917 >>> ExtendedContext.to_integral_value(Decimal('-Inf')) |
|
45321
33122ff83405
Fix decimal repr which should have used single quotes like other reprs.
Raymond Hettinger <python@rcn.com>
parents:
45293
diff
changeset
|
4918 Decimal('-Infinity') |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4919 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4920 return a.to_integral_value(context=self) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4921 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4922 # the method name changed, but we provide also the old one, for compatibility |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4923 to_integral = to_integral_value |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4924 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4925 class _WorkRep(object): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4926 __slots__ = ('sign','int','exp') |
| 33851 | 4927 # sign: 0 or 1 |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
4928 # int: int or long |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4929 # exp: None, int, or string |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4930 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4931 def __init__(self, value=None): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4932 if value is None: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4933 self.sign = None |
|
33519
139a4012bead
SF patch #1020845: Decimal performance enhancements
Raymond Hettinger <python@rcn.com>
parents:
33198
diff
changeset
|
4934 self.int = 0 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4935 self.exp = None |
| 33851 | 4936 elif isinstance(value, Decimal): |
| 4937 self.sign = value._sign | |
|
43993
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
parents:
43602
diff
changeset
|
4938 self.int = int(value._int) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4939 self.exp = value._exp |
| 33851 | 4940 else: |
| 4941 # assert isinstance(value, tuple) | |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4942 self.sign = value[0] |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4943 self.int = value[1] |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4944 self.exp = value[2] |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4945 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4946 def __repr__(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4947 return "(%r, %r, %r)" % (self.sign, self.int, self.exp) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4948 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4949 __str__ = __repr__ |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4950 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4951 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4952 |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4953 def _normalize(op1, op2, prec = 0): |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4954 """Normalizes op1, op2 to have the same exp and length of coefficient. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4955 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4956 Done during addition. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4957 """ |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4958 if op1.exp < op2.exp: |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4959 tmp = op2 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4960 other = op1 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4961 else: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4962 tmp = op1 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4963 other = op2 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4964 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4965 # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4966 # Then adding 10**exp to tmp has the same effect (after rounding) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4967 # as adding any positive quantity smaller than 10**exp; similarly |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4968 # for subtraction. So if other is smaller than 10**exp we replace |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4969 # it with 10**exp. This avoids tmp.exp - other.exp getting too large. |
|
44328
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4970 tmp_len = len(str(tmp.int)) |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4971 other_len = len(str(other.int)) |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4972 exp = tmp.exp + min(-1, tmp_len - prec - 2) |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4973 if other_len + other.exp - 1 < exp: |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4974 other.int = 1 |
|
09f74316d5fb
Removed the private _rounding_decision: it was not needed, and the code
Facundo Batista <facundobatista@gmail.com>
parents:
44148
diff
changeset
|
4975 other.exp = exp |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4976 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4977 tmp.int *= 10 ** (tmp.exp - other.exp) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4978 tmp.exp = other.exp |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4979 return op1, op2 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
4980 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4981 ##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4982 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4983 # This function from Tim Peters was taken from here: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4984 # http://mail.python.org/pipermail/python-list/1999-July/007758.html |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4985 # The correction being in the function definition is for speed, and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4986 # the whole function is not resolved with math.log because of avoiding |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4987 # the use of floats. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4988 def _nbits(n, correction = { |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4989 '0': 4, '1': 3, '2': 2, '3': 2, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4990 '4': 1, '5': 1, '6': 1, '7': 1, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4991 '8': 0, '9': 0, 'a': 0, 'b': 0, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4992 'c': 0, 'd': 0, 'e': 0, 'f': 0}): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4993 """Number of bits in binary representation of the positive integer n, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4994 or 0 if n == 0. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4995 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4996 if n < 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4997 raise ValueError("The argument to _nbits should be nonnegative.") |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4998 hex_n = "%x" % n |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
4999 return 4*len(hex_n) - correction[hex_n[0]] |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5000 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5001 def _sqrt_nearest(n, a): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5002 """Closest integer to the square root of the positive integer n. a is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5003 an initial approximation to the square root. Any positive integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5004 will do for a, but the closer a is to the square root of n the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5005 faster convergence will be. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5006 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5007 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5008 if n <= 0 or a <= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5009 raise ValueError("Both arguments to _sqrt_nearest should be positive.") |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5010 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5011 b=0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5012 while a != b: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5013 b, a = a, a--n//a>>1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5014 return a |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5015 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5016 def _rshift_nearest(x, shift): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5017 """Given an integer x and a nonnegative integer shift, return closest |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5018 integer to x / 2**shift; use round-to-even in case of a tie. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5019 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5020 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5021 b, q = 1L << shift, x >> shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5022 return q + (2*(x & (b-1)) + (q&1) > b) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5023 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5024 def _div_nearest(a, b): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5025 """Closest integer to a/b, a and b positive integers; rounds to even |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5026 in the case of a tie. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5027 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5028 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5029 q, r = divmod(a, b) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5030 return q + (2*r + (q&1) > b) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5031 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5032 def _ilog(x, M, L = 8): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5033 """Integer approximation to M*log(x/M), with absolute error boundable |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5034 in terms only of x/M. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5035 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5036 Given positive integers x and M, return an integer approximation to |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5037 M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5038 between the approximation and the exact result is at most 22. For |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5039 L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5040 both cases these are upper bounds on the error; it will usually be |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5041 much smaller.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5042 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5043 # The basic algorithm is the following: let log1p be the function |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5044 # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5045 # the reduction |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5046 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5047 # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5048 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5049 # repeatedly until the argument to log1p is small (< 2**-L in |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5050 # absolute value). For small y we can use the Taylor series |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5051 # expansion |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5052 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5053 # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5054 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5055 # truncating at T such that y**T is small enough. The whole |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5056 # computation is carried out in a form of fixed-point arithmetic, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5057 # with a real number z being represented by an integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5058 # approximation to z*M. To avoid loss of precision, the y below |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5059 # is actually an integer approximation to 2**R*y*M, where R is the |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5060 # number of reductions performed so far. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5061 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5062 y = x-M |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5063 # argument reduction; R = number of reductions performed |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5064 R = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5065 while (R <= L and long(abs(y)) << L-R >= M or |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5066 R > L and abs(y) >> R-L >= M): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5067 y = _div_nearest(long(M*y) << 1, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5068 M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5069 R += 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5070 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5071 # Taylor series with T terms |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5072 T = -int(-10*len(str(M))//(3*L)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5073 yshift = _rshift_nearest(y, R) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5074 w = _div_nearest(M, T) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5075 for k in xrange(T-1, 0, -1): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5076 w = _div_nearest(M, k) - _div_nearest(yshift*w, M) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5077 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5078 return _div_nearest(w*y, M) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5079 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5080 def _dlog10(c, e, p): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5081 """Given integers c, e and p with c > 0, p >= 0, compute an integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5082 approximation to 10**p * log10(c*10**e), with an absolute error of |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5083 at most 1. Assumes that c*10**e is not exactly 1.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5084 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5085 # increase precision by 2; compensate for this by dividing |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5086 # final result by 100 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5087 p += 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5088 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5089 # write c*10**e as d*10**f with either: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5090 # f >= 0 and 1 <= d <= 10, or |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5091 # f <= 0 and 0.1 <= d <= 1. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5092 # Thus for c*10**e close to 1, f = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5093 l = len(str(c)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5094 f = e+l - (e+l >= 1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5095 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5096 if p > 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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changeset
|
5097 M = 10**p |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5098 k = e+p-f |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5099 if k >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5100 c *= 10**k |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
5101 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5102 c = _div_nearest(c, 10**-k) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5103 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5104 log_d = _ilog(c, M) # error < 5 + 22 = 27 |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5105 log_10 = _log10_digits(p) # error < 1 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5106 log_d = _div_nearest(log_d*M, log_10) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
5107 log_tenpower = f*M # exact |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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|
5108 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5109 log_d = 0 # error < 2.31 |
| 48847 | 5110 log_tenpower = _div_nearest(f, 10**-p) # error < 0.5 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5111 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5112 return _div_nearest(log_tenpower+log_d, 100) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5113 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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parents:
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diff
changeset
|
5114 def _dlog(c, e, p): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5115 """Given integers c, e and p with c > 0, compute an integer |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5116 approximation to 10**p * log(c*10**e), with an absolute error of |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5117 at most 1. Assumes that c*10**e is not exactly 1.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5118 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5119 # Increase precision by 2. The precision increase is compensated |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5120 # for at the end with a division by 100. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5121 p += 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5122 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5123 # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5124 # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5125 # as 10**p * log(d) + 10**p*f * log(10). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5126 l = len(str(c)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5127 f = e+l - (e+l >= 1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5128 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5129 # compute approximation to 10**p*log(d), with error < 27 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5130 if p > 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5131 k = e+p-f |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5132 if k >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5133 c *= 10**k |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5134 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5135 c = _div_nearest(c, 10**-k) # error of <= 0.5 in c |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5136 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5137 # _ilog magnifies existing error in c by a factor of at most 10 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5138 log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5139 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5140 # p <= 0: just approximate the whole thing by 0; error < 2.31 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5141 log_d = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5142 |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5143 # compute approximation to f*10**p*log(10), with error < 11. |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5144 if f: |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5145 extra = len(str(abs(f)))-1 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5146 if p + extra >= 0: |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5147 # error in f * _log10_digits(p+extra) < |f| * 1 = |f| |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5148 # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5149 f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5150 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5151 f_log_ten = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5152 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5153 f_log_ten = 0 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5154 |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5155 # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5156 return _div_nearest(f_log_ten + log_d, 100) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5157 |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5158 class _Log10Memoize(object): |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5159 """Class to compute, store, and allow retrieval of, digits of the |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
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diff
changeset
|
5160 constant log(10) = 2.302585.... This constant is needed by |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
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diff
changeset
|
5161 Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
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changeset
|
5162 def __init__(self): |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
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diff
changeset
|
5163 self.digits = "23025850929940456840179914546843642076011014886" |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5164 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5165 def getdigits(self, p): |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5166 """Given an integer p >= 0, return floor(10**p)*log(10). |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5167 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5168 For example, self.getdigits(3) returns 2302. |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
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diff
changeset
|
5169 """ |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5170 # digits are stored as a string, for quick conversion to |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5171 # integer in the case that we've already computed enough |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5172 # digits; the stored digits should always be correct |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5173 # (truncated, not rounded to nearest). |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5174 if p < 0: |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5175 raise ValueError("p should be nonnegative") |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5176 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5177 if p >= len(self.digits): |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5178 # compute p+3, p+6, p+9, ... digits; continue until at |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5179 # least one of the extra digits is nonzero |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5180 extra = 3 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5181 while True: |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5182 # compute p+extra digits, correct to within 1ulp |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5183 M = 10**(p+extra+2) |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5184 digits = str(_div_nearest(_ilog(10*M, M), 100)) |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5185 if digits[-extra:] != '0'*extra: |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5186 break |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5187 extra += 3 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5188 # keep all reliable digits so far; remove trailing zeros |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5189 # and next nonzero digit |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5190 self.digits = digits.rstrip('0')[:-1] |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5191 return int(self.digits[:p+1]) |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5192 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
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parents:
43454
diff
changeset
|
5193 _log10_digits = _Log10Memoize().getdigits |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5194 |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5195 def _iexp(x, M, L=8): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5196 """Given integers x and M, M > 0, such that x/M is small in absolute |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5197 value, compute an integer approximation to M*exp(x/M). For 0 <= |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5198 x/M <= 2.4, the absolute error in the result is bounded by 60 (and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5199 is usually much smaller).""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5200 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5201 # Algorithm: to compute exp(z) for a real number z, first divide z |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5202 # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5203 # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5204 # series |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5205 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5206 # expm1(x) = x + x**2/2! + x**3/3! + ... |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5207 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5208 # Now use the identity |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5209 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5210 # expm1(2x) = expm1(x)*(expm1(x)+2) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5211 # |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5212 # R times to compute the sequence expm1(z/2**R), |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5213 # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5214 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5215 # Find R such that x/2**R/M <= 2**-L |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5216 R = _nbits((long(x)<<L)//M) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5217 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5218 # Taylor series. (2**L)**T > M |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5219 T = -int(-10*len(str(M))//(3*L)) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5220 y = _div_nearest(x, T) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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changeset
|
5221 Mshift = long(M)<<R |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
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diff
changeset
|
5222 for i in xrange(T-1, 0, -1): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5223 y = _div_nearest(x*(Mshift + y), Mshift * i) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5224 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5225 # Expansion |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5226 for k in xrange(R-1, -1, -1): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5227 Mshift = long(M)<<(k+2) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5228 y = _div_nearest(y*(y+Mshift), Mshift) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5229 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5230 return M+y |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5231 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5232 def _dexp(c, e, p): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5233 """Compute an approximation to exp(c*10**e), with p decimal places of |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5234 precision. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5235 |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5236 Returns integers d, f such that: |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5237 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5238 10**(p-1) <= d <= 10**p, and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5239 (d-1)*10**f < exp(c*10**e) < (d+1)*10**f |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5240 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5241 In other words, d*10**f is an approximation to exp(c*10**e) with p |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5242 digits of precision, and with an error in d of at most 1. This is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5243 almost, but not quite, the same as the error being < 1ulp: when d |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5244 = 10**(p-1) the error could be up to 10 ulp.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5245 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5246 # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5247 p += 2 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5248 |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5249 # compute log(10) with extra precision = adjusted exponent of c*10**e |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5250 extra = max(0, e + len(str(c)) - 1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5251 q = p + extra |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5252 |
|
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5253 # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5254 # rounding down |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5255 shift = e+q |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5256 if shift >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5257 cshift = c*10**shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5258 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5259 cshift = c//10**-shift |
|
43455
7943262e5fc4
Added a class to store the digits of log(10), so that they can be made
Facundo Batista <facundobatista@gmail.com>
parents:
43454
diff
changeset
|
5260 quot, rem = divmod(cshift, _log10_digits(q)) |
|
43360
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5261 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5262 # reduce remainder back to original precision |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5263 rem = _div_nearest(rem, 10**extra) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5264 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5265 # error in result of _iexp < 120; error after division < 0.62 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5266 return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5267 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5268 def _dpower(xc, xe, yc, ye, p): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5269 """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5270 y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5271 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5272 10**(p-1) <= c <= 10**p, and |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5273 (c-1)*10**e < x**y < (c+1)*10**e |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5274 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5275 in other words, c*10**e is an approximation to x**y with p digits |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5276 of precision, and with an error in c of at most 1. (This is |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5277 almost, but not quite, the same as the error being < 1ulp: when c |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5278 == 10**(p-1) we can only guarantee error < 10ulp.) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5279 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5280 We assume that: x is positive and not equal to 1, and y is nonzero. |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5281 """ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5282 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5283 # Find b such that 10**(b-1) <= |y| <= 10**b |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5284 b = len(str(abs(yc))) + ye |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5285 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5286 # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5287 lxc = _dlog(xc, xe, p+b+1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5288 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5289 # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5290 shift = ye-b |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5291 if shift >= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5292 pc = lxc*yc*10**shift |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5293 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5294 pc = _div_nearest(lxc*yc, 10**-shift) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5295 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5296 if pc == 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5297 # we prefer a result that isn't exactly 1; this makes it |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5298 # easier to compute a correctly rounded result in __pow__ |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5299 if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5300 coeff, exp = 10**(p-1)+1, 1-p |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5301 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5302 coeff, exp = 10**p-1, -p |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5303 else: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5304 coeff, exp = _dexp(pc, -(p+1), p+1) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5305 coeff = _div_nearest(coeff, 10) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5306 exp += 1 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5307 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5308 return coeff, exp |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5309 |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5310 def _log10_lb(c, correction = { |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5311 '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5312 '6': 23, '7': 16, '8': 10, '9': 5}): |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5313 """Compute a lower bound for 100*log10(c) for a positive integer c.""" |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5314 if c <= 0: |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5315 raise ValueError("The argument to _log10_lb should be nonnegative.") |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
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diff
changeset
|
5316 str_c = str(c) |
|
63f3154c731d
Merged the decimal-branch (revisions 54886 to 58140). Decimal is now
Facundo Batista <facundobatista@gmail.com>
parents:
42605
diff
changeset
|
5317 return 100*len(str_c) - correction[str_c[0]] |
|
63f3154c731d
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|
5318 |
|
41418
ae4ced28a839
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|
5319 ##### Helper Functions #################################################### |
|
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|
5320 |
|
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changeset
|
5321 def _convert_other(other, raiseit=False): |
|
33519
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SF patch #1020845: Decimal performance enhancements
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|
5322 """Convert other to Decimal. |
|
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SF patch #1020845: Decimal performance enhancements
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|
5323 |
|
139a4012bead
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|
5324 Verifies that it's ok to use in an implicit construction. |
|
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|
5325 """ |
|
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|
5326 if isinstance(other, Decimal): |
|
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SF patch #1020845: Decimal performance enhancements
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|
5327 return other |
|
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changeset
|
5328 if isinstance(other, (int, long)): |
|
139a4012bead
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changeset
|
5329 return Decimal(other) |
|
43360
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changeset
|
5330 if raiseit: |
|
63f3154c731d
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Facundo Batista <facundobatista@gmail.com>
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changeset
|
5331 raise TypeError("Unable to convert %s to Decimal" % other) |
|
34812
b016236dfbd9
* Fix decimal's handling of foreign types. Now returns NotImplemented
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|
5332 return NotImplemented |
|
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|
5333 |
|
41418
ae4ced28a839
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|
5334 ##### Setup Specific Contexts ############################################ |
|
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|
5335 |
|
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|
5336 # The default context prototype used by Context() |
|
32666
c13d911ae05b
* Rename "Signals" to "_signals" making it non-public.
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|
5337 # Is mutable, so that new contexts can have different default values |
|
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|
5338 |
|
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|
5339 DefaultContext = Context( |
|
32481
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* Make the tests independent of the default precision.
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|
5340 prec=28, rounding=ROUND_HALF_EVEN, |
|
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|
5341 traps=[DivisionByZero, Overflow, InvalidOperation], |
|
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|
5342 flags=[], |
|
32674
3479610fb288
Factor out two unnecessary global variables.
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|
5343 Emax=999999999, |
|
3479610fb288
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|
5344 Emin=-999999999, |
| 32496 | 5345 capitals=1 |
|
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|
5346 ) |
|
d2c1c7ae7cf4
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|
5347 |
|
d2c1c7ae7cf4
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|
5348 # Pre-made alternate contexts offered by the specification |
|
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|
5349 # Don't change these; the user should be able to select these |
|
d2c1c7ae7cf4
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parents:
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|
5350 # contexts and be able to reproduce results from other implementations |
|
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|
5351 # of the spec. |
|
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|
5352 |
| 32482 | 5353 BasicContext = Context( |
|
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|
5354 prec=9, rounding=ROUND_HALF_UP, |
|
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|
5355 traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], |
|
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|
5356 flags=[], |
|
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|
5357 ) |
|
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changeset
|
5358 |
| 32482 | 5359 ExtendedContext = Context( |
|
32481
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diff
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|
5360 prec=9, rounding=ROUND_HALF_EVEN, |
|
32576
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diff
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|
5361 traps=[], |
|
83cbc025bfc7
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|
5362 flags=[], |
|
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changeset
|
5363 ) |
|
d2c1c7ae7cf4
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diff
changeset
|
5364 |
|
d2c1c7ae7cf4
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|
5365 |
|
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|
5366 ##### crud for parsing strings ############################################# |
|
45505
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Remove duplicate 'import re' in decimal.py
Mark Dickinson <dickinsm@gmail.com>
parents:
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|
5367 # |
|
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|
5368 # Regular expression used for parsing numeric strings. Additional |
|
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Major change in the internal structure of the Decimal
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|
5369 # comments: |
|
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|
5370 # |
|
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changeset
|
5371 # 1. Uncomment the two '\s*' lines to allow leading and/or trailing |
|
a4a140486691
Major change in the internal structure of the Decimal
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changeset
|
5372 # whitespace. But note that the specification disallows whitespace in |
|
a4a140486691
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|
5373 # a numeric string. |
|
a4a140486691
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|
5374 # |
|
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changeset
|
5375 # 2. For finite numbers (not infinities and NaNs) the body of the |
|
a4a140486691
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changeset
|
5376 # number between the optional sign and the optional exponent must have |
|
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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diff
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|
5377 # at least one decimal digit, possibly after the decimal point. The |
|
a4a140486691
Major change in the internal structure of the Decimal
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parents:
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changeset
|
5378 # lookahead expression '(?=\d|\.\d)' checks this. |
|
a4a140486691
Major change in the internal structure of the Decimal
Facundo Batista <facundobatista@gmail.com>
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diff
changeset
|
5379 |
|
a4a140486691
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diff
changeset
|
5380 import re |
|
47872
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Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
5381 _parser = re.compile(r""" # A numeric string consists of: |
|
43993
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diff
changeset
|
5382 # \s* |
|
47872
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Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
5383 (?P<sign>[-+])? # an optional sign, followed by either... |
|
43993
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diff
changeset
|
5384 ( |
|
55519
8b48b282eba9
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diff
changeset
|
5385 (?=\d|\.\d) # ...a number (with at least one digit) |
|
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diff
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|
5386 (?P<int>\d*) # having a (possibly empty) integer part |
|
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diff
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|
5387 (\.(?P<frac>\d*))? # followed by an optional fractional part |
|
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changeset
|
5388 (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... |
|
43993
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diff
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|
5389 | |
|
47872
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diff
changeset
|
5390 Inf(inity)? # ...an infinity, or... |
|
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parents:
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|
5391 | |
|
47872
65af544da121
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Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
5392 (?P<signal>s)? # ...an (optionally signaling) |
|
65af544da121
Replace occurrences of '\d' with '[0-9]' in Decimal regex, to make sure
Mark Dickinson <dickinsm@gmail.com>
parents:
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|
5393 NaN # NaN |
|
55519
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Merged revisions 74281 via svnmerge from
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parents:
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diff
changeset
|
5394 (?P<diag>\d*) # with (possibly empty) diagnostic info. |
|
43993
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diff
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|
5395 ) |
|
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changeset
|
5396 # \s* |
|
44650
7b798548a4ad
Issue 1780: Allow leading and trailing whitespace in Decimal constructor,
Mark Dickinson <dickinsm@gmail.com>
parents:
44631
diff
changeset
|
5397 \Z |
|
55519
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diff
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|
5398 """, re.VERBOSE | re.IGNORECASE | re.UNICODE).match |
|
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diff
changeset
|
5399 |
|
44121
30f54977828b
Faster _fix function, and some reordering for a more elegant
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44120
diff
changeset
|
5400 _all_zeros = re.compile('0*$').match |
|
30f54977828b
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parents:
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diff
changeset
|
5401 _exact_half = re.compile('50*$').match |
|
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|
5402 |
|
bce4c40df7df
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diff
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|
5403 ##### PEP3101 support functions ############################################## |
|
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diff
changeset
|
5404 # The functions parse_format_specifier and format_align have little to do |
|
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diff
changeset
|
5405 # with the Decimal class, and could potentially be reused for other pure |
|
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diff
changeset
|
5406 # Python numeric classes that want to implement __format__ |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5407 # |
|
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Add __format__ method to Decimal, to support PEP 3101
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diff
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|
5408 # A format specifier for Decimal looks like: |
|
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|
5409 # |
|
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diff
changeset
|
5410 # [[fill]align][sign][0][minimumwidth][.precision][type] |
|
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|
5411 # |
|
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diff
changeset
|
5412 |
|
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diff
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|
5413 _parse_format_specifier_regex = re.compile(r"""\A |
|
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|
5414 (?: |
|
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diff
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|
5415 (?P<fill>.)? |
|
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diff
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|
5416 (?P<align>[<>=^]) |
|
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diff
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|
5417 )? |
|
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diff
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|
5418 (?P<sign>[-+ ])? |
|
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|
5419 (?P<zeropad>0)? |
|
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|
5420 (?P<minimumwidth>(?!0)\d+)? |
|
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|
5421 (?:\.(?P<precision>0|(?!0)\d+))? |
|
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|
5422 (?P<type>[eEfFgG%])? |
|
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|
5423 \Z |
|
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|
5424 """, re.VERBOSE) |
|
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|
5425 |
|
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|
5426 del re |
|
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changeset
|
5427 |
|
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changeset
|
5428 def _parse_format_specifier(format_spec): |
|
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changeset
|
5429 """Parse and validate a format specifier. |
|
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|
5430 |
|
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changeset
|
5431 Turns a standard numeric format specifier into a dict, with the |
|
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|
5432 following entries: |
|
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Add __format__ method to Decimal, to support PEP 3101
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diff
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|
5433 |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5434 fill: fill character to pad field to minimum width |
|
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|
5435 align: alignment type, either '<', '>', '=' or '^' |
|
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diff
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|
5436 sign: either '+', '-' or ' ' |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5437 minimumwidth: nonnegative integer giving minimum width |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5438 precision: nonnegative integer giving precision, or None |
|
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|
5439 type: one of the characters 'eEfFgG%', or None |
|
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|
5440 unicode: either True or False (always True for Python 3.x) |
|
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|
5441 |
|
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|
5442 """ |
|
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Add __format__ method to Decimal, to support PEP 3101
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diff
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|
5443 m = _parse_format_specifier_regex.match(format_spec) |
|
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|
5444 if m is None: |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5445 raise ValueError("Invalid format specifier: " + format_spec) |
|
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|
5446 |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5447 # get the dictionary |
|
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Add __format__ method to Decimal, to support PEP 3101
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|
5448 format_dict = m.groupdict() |
|
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|
5449 |
|
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|
5450 # defaults for fill and alignment |
|
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|
5451 fill = format_dict['fill'] |
|
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|
5452 align = format_dict['align'] |
|
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|
5453 if format_dict.pop('zeropad') is not None: |
|
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|
5454 # in the face of conflict, refuse the temptation to guess |
|
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|
5455 if fill is not None and fill != '0': |
|
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|
5456 raise ValueError("Fill character conflicts with '0'" |
|
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|
5457 " in format specifier: " + format_spec) |
|
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|
5458 if align is not None and align != '=': |
|
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|
5459 raise ValueError("Alignment conflicts with '0' in " |
|
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|
5460 "format specifier: " + format_spec) |
|
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|
5461 fill = '0' |
|
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|
5462 align = '=' |
|
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|
5463 format_dict['fill'] = fill or ' ' |
|
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|
5464 format_dict['align'] = align or '<' |
|
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|
5465 |
|
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|
5466 if format_dict['sign'] is None: |
|
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|
5467 format_dict['sign'] = '-' |
|
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|
5468 |
|
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|
5469 # turn minimumwidth and precision entries into integers. |
|
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|
5470 # minimumwidth defaults to 0; precision remains None if not given |
|
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|
5471 format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0') |
|
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|
5472 if format_dict['precision'] is not None: |
|
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|
5473 format_dict['precision'] = int(format_dict['precision']) |
|
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|
5474 |
|
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|
5475 # if format type is 'g' or 'G' then a precision of 0 makes little |
|
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|
5476 # sense; convert it to 1. Same if format type is unspecified. |
|
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|
5477 if format_dict['precision'] == 0: |
|
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|
5478 if format_dict['type'] is None or format_dict['type'] in 'gG': |
|
45566
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|
5479 format_dict['precision'] = 1 |
|
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|
5480 |
|
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|
5481 # record whether return type should be str or unicode |
|
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|
5482 format_dict['unicode'] = isinstance(format_spec, unicode) |
|
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|
5483 |
|
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|
5484 return format_dict |
|
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|
5485 |
|
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|
5486 def _format_align(body, spec_dict): |
|
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|
5487 """Given an unpadded, non-aligned numeric string, add padding and |
|
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|
5488 aligment to conform with the given format specifier dictionary (as |
|
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|
5489 output from parse_format_specifier). |
|
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|
5490 |
|
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diff
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|
5491 It's assumed that if body is negative then it starts with '-'. |
|
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|
5492 Any leading sign ('-' or '+') is stripped from the body before |
|
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|
5493 applying the alignment and padding rules, and replaced in the |
|
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|
5494 appropriate position. |
|
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|
5495 |
|
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|
5496 """ |
|
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|
5497 # figure out the sign; we only examine the first character, so if |
|
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|
5498 # body has leading whitespace the results may be surprising. |
|
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|
5499 if len(body) > 0 and body[0] in '-+': |
|
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|
5500 sign = body[0] |
|
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|
5501 body = body[1:] |
|
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|
5502 else: |
|
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|
5503 sign = '' |
|
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|
5504 |
|
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|
5505 if sign != '-': |
|
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|
5506 if spec_dict['sign'] in ' +': |
|
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|
5507 sign = spec_dict['sign'] |
|
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|
5508 else: |
|
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|
5509 sign = '' |
|
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|
5510 |
|
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|
5511 # how much extra space do we have to play with? |
|
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|
5512 minimumwidth = spec_dict['minimumwidth'] |
|
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|
5513 fill = spec_dict['fill'] |
|
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|
5514 padding = fill*(max(minimumwidth - (len(sign+body)), 0)) |
|
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|
5515 |
|
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|
5516 align = spec_dict['align'] |
|
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|
5517 if align == '<': |
|
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|
5518 result = sign + body + padding |
|
45566
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|
5519 elif align == '>': |
|
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|
5520 result = padding + sign + body |
|
45566
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|
5521 elif align == '=': |
|
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|
5522 result = sign + padding + body |
|
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|
5523 else: #align == '^' |
|
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|
5524 half = len(padding)//2 |
|
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|
5525 result = padding[:half] + sign + body + padding[half:] |
|
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|
5526 |
|
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|
5527 # make sure that result is unicode if necessary |
|
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|
5528 if spec_dict['unicode']: |
|
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|
5529 result = unicode(result) |
|
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|
5530 |
|
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|
5531 return result |
|
43993
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|
5532 |
|
41418
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|
5533 ##### Useful Constants (internal use only) ################################ |
|
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|
5534 |
|
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|
5535 # Reusable defaults |
|
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|
5536 _Infinity = Decimal('Inf') |
|
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|
5537 _NegativeInfinity = Decimal('-Inf') |
|
50471
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|
5538 _NaN = Decimal('NaN') |
|
50480
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5539 _Zero = Decimal(0) |
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5540 _One = Decimal(1) |
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5541 _NegativeOne = Decimal(-1) |
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5542 |
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5543 # _SignedInfinity[sign] is infinity w/ that sign |
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5544 _SignedInfinity = (_Infinity, _NegativeInfinity) |
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5545 |
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5547 |
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5548 if __name__ == '__main__': |
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5549 import doctest, sys |
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5550 doctest.testmod(sys.modules[__name__]) |