Mercurial > cpython-lru_cache-weakref
annotate Lib/decimal.py @ 78069:a8aa77458e12 3.2
Add c_size_t and c_ssize_t to the ctypes summary table.
| author | Antoine Pitrou <solipsis@pitrou.net> |
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| date | Thu, 12 Jul 2012 20:31:50 +0200 |
| parents | f5d5f3f4c081 |
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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 should be kept in sync with the latest updates of the |
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11 # IBM specification as it evolves. Those updates will be treated |
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12 # as bug fixes (deviation from the spec is a compatibility, usability |
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13 # bug) and will be backported. At this point the spec is stabilizing |
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14 # and the updates are becoming fewer, smaller, and less significant. |
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15 |
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16 """ |
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17 This is an implementation of decimal floating point arithmetic based on |
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18 the General Decimal Arithmetic Specification: |
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19 |
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20 http://speleotrove.com/decimal/decarith.html |
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21 |
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22 and IEEE standard 854-1987: |
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23 |
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24 www.cs.berkeley.edu/~ejr/projects/754/private/drafts/854-1987/dir.html |
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25 |
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26 Decimal floating point has finite precision with arbitrarily large bounds. |
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27 |
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28 The purpose of this module is to support arithmetic using familiar |
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29 "schoolhouse" rules and to avoid some of the tricky representation |
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30 issues associated with binary floating point. The package is especially |
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31 useful for financial applications or for contexts where users have |
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32 expectations that are at odds with binary floating point (for instance, |
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33 in binary floating point, 1.00 % 0.1 gives 0.09999999999999995 instead |
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34 of 0.0; Decimal('1.00') % Decimal('0.1') returns the expected |
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35 Decimal('0.00')). |
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36 |
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37 Here are some examples of using the decimal module: |
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38 |
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39 >>> from decimal import * |
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40 >>> setcontext(ExtendedContext) |
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41 >>> Decimal(0) |
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42 Decimal('0') |
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43 >>> Decimal('1') |
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44 Decimal('1') |
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45 >>> Decimal('-.0123') |
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46 Decimal('-0.0123') |
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47 >>> Decimal(123456) |
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48 Decimal('123456') |
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49 >>> Decimal('123.45e12345678901234567890') |
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50 Decimal('1.2345E+12345678901234567892') |
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51 >>> Decimal('1.33') + Decimal('1.27') |
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52 Decimal('2.60') |
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53 >>> Decimal('12.34') + Decimal('3.87') - Decimal('18.41') |
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54 Decimal('-2.20') |
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55 >>> dig = Decimal(1) |
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56 >>> print(dig / Decimal(3)) |
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57 0.333333333 |
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58 >>> getcontext().prec = 18 |
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59 >>> print(dig / Decimal(3)) |
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60 0.333333333333333333 |
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61 >>> print(dig.sqrt()) |
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62 1 |
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63 >>> print(Decimal(3).sqrt()) |
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64 1.73205080756887729 |
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65 >>> print(Decimal(3) ** 123) |
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66 4.85192780976896427E+58 |
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67 >>> inf = Decimal(1) / Decimal(0) |
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68 >>> print(inf) |
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69 Infinity |
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70 >>> neginf = Decimal(-1) / Decimal(0) |
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71 >>> print(neginf) |
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72 -Infinity |
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73 >>> print(neginf + inf) |
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74 NaN |
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75 >>> print(neginf * inf) |
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76 -Infinity |
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77 >>> print(dig / 0) |
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78 Infinity |
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79 >>> getcontext().traps[DivisionByZero] = 1 |
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80 >>> print(dig / 0) |
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81 Traceback (most recent call last): |
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82 ... |
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83 ... |
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84 ... |
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85 decimal.DivisionByZero: x / 0 |
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86 >>> c = Context() |
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87 >>> c.traps[InvalidOperation] = 0 |
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88 >>> print(c.flags[InvalidOperation]) |
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89 0 |
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90 >>> c.divide(Decimal(0), Decimal(0)) |
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91 Decimal('NaN') |
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92 >>> c.traps[InvalidOperation] = 1 |
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93 >>> print(c.flags[InvalidOperation]) |
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94 1 |
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96 >>> print(c.flags[InvalidOperation]) |
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97 0 |
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98 >>> print(c.divide(Decimal(0), Decimal(0))) |
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99 Traceback (most recent call last): |
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100 ... |
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101 ... |
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102 ... |
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103 decimal.InvalidOperation: 0 / 0 |
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104 >>> print(c.flags[InvalidOperation]) |
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105 1 |
| 32560 | 106 >>> c.flags[InvalidOperation] = 0 |
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107 >>> c.traps[InvalidOperation] = 0 |
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108 >>> print(c.divide(Decimal(0), Decimal(0))) |
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109 NaN |
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110 >>> print(c.flags[InvalidOperation]) |
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111 1 |
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112 >>> |
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113 """ |
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114 |
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115 __all__ = [ |
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116 # Two major classes |
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117 'Decimal', 'Context', |
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118 |
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119 # Contexts |
| 32482 | 120 'DefaultContext', 'BasicContext', 'ExtendedContext', |
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121 |
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122 # Exceptions |
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123 'DecimalException', 'Clamped', 'InvalidOperation', 'DivisionByZero', |
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124 'Inexact', 'Rounded', 'Subnormal', 'Overflow', 'Underflow', |
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125 |
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126 # Constants for use in setting up contexts |
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127 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', |
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128 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP', |
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129 |
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130 # Functions for manipulating contexts |
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131 'setcontext', 'getcontext', 'localcontext' |
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132 ] |
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133 |
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134 __version__ = '1.70' # Highest version of the spec this complies with |
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135 # See http://speleotrove.com/decimal/ |
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136 |
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137 import copy as _copy |
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138 import math as _math |
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139 import numbers as _numbers |
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140 |
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141 try: |
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142 from collections import namedtuple as _namedtuple |
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143 DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent') |
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144 except ImportError: |
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145 DecimalTuple = lambda *args: args |
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146 |
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147 # Rounding |
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148 ROUND_DOWN = 'ROUND_DOWN' |
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149 ROUND_HALF_UP = 'ROUND_HALF_UP' |
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150 ROUND_HALF_EVEN = 'ROUND_HALF_EVEN' |
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151 ROUND_CEILING = 'ROUND_CEILING' |
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152 ROUND_FLOOR = 'ROUND_FLOOR' |
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153 ROUND_UP = 'ROUND_UP' |
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154 ROUND_HALF_DOWN = 'ROUND_HALF_DOWN' |
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155 ROUND_05UP = 'ROUND_05UP' |
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156 |
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157 # Errors |
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158 |
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159 class DecimalException(ArithmeticError): |
| 32560 | 160 """Base exception class. |
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161 |
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162 Used exceptions derive from this. |
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163 If an exception derives from another exception besides this (such as |
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164 Underflow (Inexact, Rounded, Subnormal) that indicates that it is only |
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165 called if the others are present. This isn't actually used for |
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166 anything, though. |
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167 |
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168 handle -- Called when context._raise_error is called and the |
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169 trap_enabler is not set. First argument is self, second is the |
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170 context. More arguments can be given, those being after |
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171 the explanation in _raise_error (For example, |
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172 context._raise_error(NewError, '(-x)!', self._sign) would |
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173 call NewError().handle(context, self._sign).) |
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174 |
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175 To define a new exception, it should be sufficient to have it derive |
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176 from DecimalException. |
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177 """ |
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178 def handle(self, context, *args): |
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179 pass |
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180 |
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181 |
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182 class Clamped(DecimalException): |
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183 """Exponent of a 0 changed to fit bounds. |
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184 |
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185 This occurs and signals clamped if the exponent of a result has been |
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186 altered in order to fit the constraints of a specific concrete |
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187 representation. This may occur when the exponent of a zero result would |
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188 be outside the bounds of a representation, or when a large normal |
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189 number would have an encoded exponent that cannot be represented. In |
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190 this latter case, the exponent is reduced to fit and the corresponding |
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191 number of zero digits are appended to the coefficient ("fold-down"). |
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192 """ |
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193 |
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194 class InvalidOperation(DecimalException): |
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195 """An invalid operation was performed. |
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196 |
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197 Various bad things cause this: |
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198 |
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199 Something creates a signaling NaN |
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200 -INF + INF |
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201 0 * (+-)INF |
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202 (+-)INF / (+-)INF |
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203 x % 0 |
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204 (+-)INF % x |
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205 x._rescale( non-integer ) |
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206 sqrt(-x) , x > 0 |
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207 0 ** 0 |
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208 x ** (non-integer) |
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209 x ** (+-)INF |
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210 An operand is invalid |
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211 |
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212 The result of the operation after these is a quiet positive NaN, |
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213 except when the cause is a signaling NaN, in which case the result is |
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214 also a quiet NaN, but with the original sign, and an optional |
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215 diagnostic information. |
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216 """ |
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217 def handle(self, context, *args): |
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218 if args: |
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219 ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True) |
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220 return ans._fix_nan(context) |
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221 return _NaN |
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222 |
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223 class ConversionSyntax(InvalidOperation): |
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224 """Trying to convert badly formed string. |
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225 |
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226 This occurs and signals invalid-operation if an string is being |
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227 converted to a number and it does not conform to the numeric string |
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228 syntax. The result is [0,qNaN]. |
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229 """ |
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230 def handle(self, context, *args): |
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231 return _NaN |
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232 |
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233 class DivisionByZero(DecimalException, ZeroDivisionError): |
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234 """Division by 0. |
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235 |
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236 This occurs and signals division-by-zero if division of a finite number |
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237 by zero was attempted (during a divide-integer or divide operation, or a |
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238 power operation with negative right-hand operand), and the dividend was |
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239 not zero. |
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240 |
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241 The result of the operation is [sign,inf], where sign is the exclusive |
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242 or of the signs of the operands for divide, or is 1 for an odd power of |
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243 -0, for power. |
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244 """ |
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245 |
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246 def handle(self, context, sign, *args): |
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247 return _SignedInfinity[sign] |
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248 |
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249 class DivisionImpossible(InvalidOperation): |
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250 """Cannot perform the division adequately. |
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251 |
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252 This occurs and signals invalid-operation if the integer result of a |
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253 divide-integer or remainder operation had too many digits (would be |
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254 longer than precision). The result is [0,qNaN]. |
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255 """ |
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256 |
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257 def handle(self, context, *args): |
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258 return _NaN |
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259 |
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260 class DivisionUndefined(InvalidOperation, ZeroDivisionError): |
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261 """Undefined result of division. |
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262 |
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263 This occurs and signals invalid-operation if division by zero was |
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264 attempted (during a divide-integer, divide, or remainder operation), and |
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265 the dividend is also zero. The result is [0,qNaN]. |
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266 """ |
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267 |
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268 def handle(self, context, *args): |
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269 return _NaN |
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270 |
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271 class Inexact(DecimalException): |
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272 """Had to round, losing information. |
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273 |
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274 This occurs and signals inexact whenever the result of an operation is |
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275 not exact (that is, it needed to be rounded and any discarded digits |
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276 were non-zero), or if an overflow or underflow condition occurs. The |
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277 result in all cases is unchanged. |
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278 |
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279 The inexact signal may be tested (or trapped) to determine if a given |
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280 operation (or sequence of operations) was inexact. |
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281 """ |
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282 |
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283 class InvalidContext(InvalidOperation): |
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284 """Invalid context. Unknown rounding, for example. |
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285 |
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286 This occurs and signals invalid-operation if an invalid context was |
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287 detected during an operation. This can occur if contexts are not checked |
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288 on creation and either the precision exceeds the capability of the |
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289 underlying concrete representation or an unknown or unsupported rounding |
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290 was specified. These aspects of the context need only be checked when |
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291 the values are required to be used. The result is [0,qNaN]. |
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292 """ |
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293 |
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294 def handle(self, context, *args): |
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295 return _NaN |
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296 |
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297 class Rounded(DecimalException): |
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298 """Number got rounded (not necessarily changed during rounding). |
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299 |
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300 This occurs and signals rounded whenever the result of an operation is |
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301 rounded (that is, some zero or non-zero digits were discarded from the |
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302 coefficient), or if an overflow or underflow condition occurs. The |
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303 result in all cases is unchanged. |
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304 |
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305 The rounded signal may be tested (or trapped) to determine if a given |
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306 operation (or sequence of operations) caused a loss of precision. |
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307 """ |
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308 |
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309 class Subnormal(DecimalException): |
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310 """Exponent < Emin before rounding. |
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311 |
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312 This occurs and signals subnormal whenever the result of a conversion or |
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313 operation is subnormal (that is, its adjusted exponent is less than |
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314 Emin, before any rounding). The result in all cases is unchanged. |
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315 |
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316 The subnormal signal may be tested (or trapped) to determine if a given |
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317 or operation (or sequence of operations) yielded a subnormal result. |
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318 """ |
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319 |
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320 class Overflow(Inexact, Rounded): |
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321 """Numerical overflow. |
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322 |
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323 This occurs and signals overflow if the adjusted exponent of a result |
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324 (from a conversion or from an operation that is not an attempt to divide |
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325 by zero), after rounding, would be greater than the largest value that |
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326 can be handled by the implementation (the value Emax). |
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327 |
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328 The result depends on the rounding mode: |
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329 |
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330 For round-half-up and round-half-even (and for round-half-down and |
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331 round-up, if implemented), the result of the operation is [sign,inf], |
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332 where sign is the sign of the intermediate result. For round-down, the |
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333 result is the largest finite number that can be represented in the |
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334 current precision, with the sign of the intermediate result. For |
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335 round-ceiling, the result is the same as for round-down if the sign of |
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336 the intermediate result is 1, or is [0,inf] otherwise. For round-floor, |
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337 the result is the same as for round-down if the sign of the intermediate |
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338 result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded |
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339 will also be raised. |
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340 """ |
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341 |
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342 def handle(self, context, sign, *args): |
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343 if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, |
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344 ROUND_HALF_DOWN, ROUND_UP): |
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345 return _SignedInfinity[sign] |
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346 if sign == 0: |
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347 if context.rounding == ROUND_CEILING: |
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348 return _SignedInfinity[sign] |
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349 return _dec_from_triple(sign, '9'*context.prec, |
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350 context.Emax-context.prec+1) |
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351 if sign == 1: |
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352 if context.rounding == ROUND_FLOOR: |
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353 return _SignedInfinity[sign] |
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354 return _dec_from_triple(sign, '9'*context.prec, |
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355 context.Emax-context.prec+1) |
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356 |
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357 |
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358 class Underflow(Inexact, Rounded, Subnormal): |
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359 """Numerical underflow with result rounded to 0. |
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360 |
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361 This occurs and signals underflow if a result is inexact and the |
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362 adjusted exponent of the result would be smaller (more negative) than |
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363 the smallest value that can be handled by the implementation (the value |
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364 Emin). That is, the result is both inexact and subnormal. |
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365 |
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366 The result after an underflow will be a subnormal number rounded, if |
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367 necessary, so that its exponent is not less than Etiny. This may result |
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368 in 0 with the sign of the intermediate result and an exponent of Etiny. |
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369 |
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370 In all cases, Inexact, Rounded, and Subnormal will also be raised. |
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371 """ |
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372 |
| 32560 | 373 # List of public traps and flags |
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374 _signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, |
| 32560 | 375 Underflow, InvalidOperation, Subnormal] |
| 376 | |
| 377 # Map conditions (per the spec) to signals | |
| 378 _condition_map = {ConversionSyntax:InvalidOperation, | |
| 379 DivisionImpossible:InvalidOperation, | |
| 380 DivisionUndefined:InvalidOperation, | |
| 381 InvalidContext:InvalidOperation} | |
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382 |
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383 ##### Context Functions ################################################## |
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384 |
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385 # The getcontext() and setcontext() function manage access to a thread-local |
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386 # current context. Py2.4 offers direct support for thread locals. If that |
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387 # is not available, use threading.current_thread() which is slower but will |
| 34184 | 388 # work for older Pythons. If threads are not part of the build, create a |
| 389 # mock threading object with threading.local() returning the module namespace. | |
| 390 | |
| 391 try: | |
| 392 import threading | |
| 393 except ImportError: | |
| 394 # Python was compiled without threads; create a mock object instead | |
| 395 import sys | |
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396 class MockThreading(object): |
| 34184 | 397 def local(self, sys=sys): |
| 398 return sys.modules[__name__] | |
| 399 threading = MockThreading() | |
| 400 del sys, MockThreading | |
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401 |
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402 try: |
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403 threading.local |
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404 |
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405 except AttributeError: |
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406 |
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407 # To fix reloading, force it to create a new context |
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408 # Old contexts have different exceptions in their dicts, making problems. |
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409 if hasattr(threading.current_thread(), '__decimal_context__'): |
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410 del threading.current_thread().__decimal_context__ |
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411 |
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412 def setcontext(context): |
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413 """Set this thread's context to context.""" |
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414 if context in (DefaultContext, BasicContext, ExtendedContext): |
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415 context = context.copy() |
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416 context.clear_flags() |
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417 threading.current_thread().__decimal_context__ = context |
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418 |
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419 def getcontext(): |
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420 """Returns this thread's context. |
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421 |
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422 If this thread does not yet have a context, returns |
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423 a new context and sets this thread's context. |
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424 New contexts are copies of DefaultContext. |
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425 """ |
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426 try: |
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427 return threading.current_thread().__decimal_context__ |
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428 except AttributeError: |
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429 context = Context() |
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430 threading.current_thread().__decimal_context__ = context |
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431 return context |
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432 |
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433 else: |
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434 |
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435 local = threading.local() |
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436 if hasattr(local, '__decimal_context__'): |
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437 del local.__decimal_context__ |
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438 |
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439 def getcontext(_local=local): |
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440 """Returns this thread's context. |
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441 |
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442 If this thread does not yet have a context, returns |
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443 a new context and sets this thread's context. |
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444 New contexts are copies of DefaultContext. |
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445 """ |
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446 try: |
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447 return _local.__decimal_context__ |
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448 except AttributeError: |
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449 context = Context() |
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450 _local.__decimal_context__ = context |
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451 return context |
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452 |
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453 def setcontext(context, _local=local): |
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454 """Set this thread's context to context.""" |
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455 if context in (DefaultContext, BasicContext, ExtendedContext): |
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456 context = context.copy() |
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457 context.clear_flags() |
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458 _local.__decimal_context__ = context |
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459 |
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460 del threading, local # Don't contaminate the namespace |
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461 |
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462 def localcontext(ctx=None): |
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463 """Return a context manager for a copy of the supplied context |
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464 |
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465 Uses a copy of the current context if no context is specified |
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466 The returned context manager creates a local decimal context |
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467 in a with statement: |
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468 def sin(x): |
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469 with localcontext() as ctx: |
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470 ctx.prec += 2 |
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471 # Rest of sin calculation algorithm |
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472 # uses a precision 2 greater than normal |
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473 return +s # Convert result to normal precision |
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474 |
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475 def sin(x): |
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476 with localcontext(ExtendedContext): |
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477 # Rest of sin calculation algorithm |
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478 # uses the Extended Context from the |
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479 # General Decimal Arithmetic Specification |
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480 return +s # Convert result to normal context |
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481 |
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482 >>> setcontext(DefaultContext) |
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483 >>> print(getcontext().prec) |
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484 28 |
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485 >>> with localcontext(): |
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486 ... ctx = getcontext() |
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487 ... ctx.prec += 2 |
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488 ... print(ctx.prec) |
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489 ... |
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490 30 |
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491 >>> with localcontext(ExtendedContext): |
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492 ... print(getcontext().prec) |
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493 ... |
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494 9 |
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495 >>> print(getcontext().prec) |
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496 28 |
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497 """ |
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498 if ctx is None: ctx = getcontext() |
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499 return _ContextManager(ctx) |
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500 |
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501 |
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502 ##### Decimal class ####################################################### |
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503 |
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504 # Do not subclass Decimal from numbers.Real and do not register it as such |
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505 # (because Decimals are not interoperable with floats). See the notes in |
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506 # numbers.py for more detail. |
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507 |
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508 class Decimal(object): |
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509 """Floating point class for decimal arithmetic.""" |
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510 |
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511 __slots__ = ('_exp','_int','_sign', '_is_special') |
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512 # Generally, the value of the Decimal instance is given by |
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513 # (-1)**_sign * _int * 10**_exp |
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514 # Special values are signified by _is_special == True |
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515 |
| 33695 | 516 # We're immutable, so use __new__ not __init__ |
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517 def __new__(cls, value="0", context=None): |
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518 """Create a decimal point instance. |
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519 |
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520 >>> Decimal('3.14') # string input |
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521 Decimal('3.14') |
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522 >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) |
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523 Decimal('3.14') |
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524 >>> Decimal(314) # int |
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525 Decimal('314') |
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526 >>> Decimal(Decimal(314)) # another decimal instance |
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527 Decimal('314') |
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528 >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay |
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529 Decimal('3.14') |
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530 """ |
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531 |
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532 # Note that the coefficient, self._int, is actually stored as |
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533 # a string rather than as a tuple of digits. This speeds up |
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534 # the "digits to integer" and "integer to digits" conversions |
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535 # that are used in almost every arithmetic operation on |
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536 # Decimals. This is an internal detail: the as_tuple function |
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537 # and the Decimal constructor still deal with tuples of |
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538 # digits. |
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539 |
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540 self = object.__new__(cls) |
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541 |
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542 # From a string |
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543 # REs insist on real strings, so we can too. |
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544 if isinstance(value, str): |
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545 m = _parser(value.strip()) |
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546 if m is None: |
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547 if context is None: |
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548 context = getcontext() |
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549 return context._raise_error(ConversionSyntax, |
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550 "Invalid literal for Decimal: %r" % value) |
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551 |
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552 if m.group('sign') == "-": |
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553 self._sign = 1 |
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554 else: |
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555 self._sign = 0 |
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556 intpart = m.group('int') |
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557 if intpart is not None: |
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558 # finite number |
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559 fracpart = m.group('frac') or '' |
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560 exp = int(m.group('exp') or '0') |
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561 self._int = str(int(intpart+fracpart)) |
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562 self._exp = exp - len(fracpart) |
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563 self._is_special = False |
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564 else: |
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565 diag = m.group('diag') |
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566 if diag is not None: |
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567 # NaN |
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568 self._int = str(int(diag or '0')).lstrip('0') |
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569 if m.group('signal'): |
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570 self._exp = 'N' |
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571 else: |
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572 self._exp = 'n' |
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573 else: |
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574 # infinity |
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575 self._int = '0' |
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576 self._exp = 'F' |
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577 self._is_special = True |
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578 return self |
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579 |
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580 # From an integer |
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581 if isinstance(value, int): |
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582 if value >= 0: |
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583 self._sign = 0 |
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584 else: |
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585 self._sign = 1 |
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586 self._exp = 0 |
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587 self._int = str(abs(value)) |
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588 self._is_special = False |
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589 return self |
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590 |
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591 # From another decimal |
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592 if isinstance(value, Decimal): |
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593 self._exp = value._exp |
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594 self._sign = value._sign |
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595 self._int = value._int |
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596 self._is_special = value._is_special |
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597 return self |
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598 |
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599 # From an internal working value |
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600 if isinstance(value, _WorkRep): |
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601 self._sign = value.sign |
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602 self._int = str(value.int) |
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603 self._exp = int(value.exp) |
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604 self._is_special = False |
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605 return self |
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606 |
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607 # tuple/list conversion (possibly from as_tuple()) |
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608 if isinstance(value, (list,tuple)): |
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609 if len(value) != 3: |
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610 raise ValueError('Invalid tuple size in creation of Decimal ' |
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611 'from list or tuple. The list or tuple ' |
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612 'should have exactly three elements.') |
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613 # process sign. The isinstance test rejects floats |
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614 if not (isinstance(value[0], int) and value[0] in (0,1)): |
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615 raise ValueError("Invalid sign. The first value in the tuple " |
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616 "should be an integer; either 0 for a " |
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617 "positive number or 1 for a negative number.") |
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618 self._sign = value[0] |
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619 if value[2] == 'F': |
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620 # infinity: value[1] is ignored |
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621 self._int = '0' |
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622 self._exp = value[2] |
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623 self._is_special = True |
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624 else: |
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625 # process and validate the digits in value[1] |
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626 digits = [] |
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627 for digit in value[1]: |
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628 if isinstance(digit, int) and 0 <= digit <= 9: |
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629 # skip leading zeros |
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630 if digits or digit != 0: |
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631 digits.append(digit) |
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632 else: |
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633 raise ValueError("The second value in the tuple must " |
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634 "be composed of integers in the range " |
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635 "0 through 9.") |
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636 if value[2] in ('n', 'N'): |
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637 # NaN: digits form the diagnostic |
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638 self._int = ''.join(map(str, digits)) |
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639 self._exp = value[2] |
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640 self._is_special = True |
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641 elif isinstance(value[2], int): |
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642 # finite number: digits give the coefficient |
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643 self._int = ''.join(map(str, digits or [0])) |
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644 self._exp = value[2] |
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645 self._is_special = False |
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646 else: |
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647 raise ValueError("The third value in the tuple must " |
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648 "be an integer, or one of the " |
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649 "strings 'F', 'n', 'N'.") |
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650 return self |
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651 |
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652 if isinstance(value, float): |
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653 value = Decimal.from_float(value) |
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654 self._exp = value._exp |
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655 self._sign = value._sign |
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656 self._int = value._int |
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657 self._is_special = value._is_special |
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658 return self |
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659 |
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660 raise TypeError("Cannot convert %r to Decimal" % value) |
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661 |
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662 # @classmethod, but @decorator is not valid Python 2.3 syntax, so |
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663 # don't use it (see notes on Py2.3 compatibility at top of file) |
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664 def from_float(cls, f): |
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665 """Converts a float to a decimal number, exactly. |
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666 |
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667 Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). |
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668 Since 0.1 is not exactly representable in binary floating point, the |
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669 value is stored as the nearest representable value which is |
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670 0x1.999999999999ap-4. The exact equivalent of the value in decimal |
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671 is 0.1000000000000000055511151231257827021181583404541015625. |
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672 |
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673 >>> Decimal.from_float(0.1) |
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674 Decimal('0.1000000000000000055511151231257827021181583404541015625') |
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675 >>> Decimal.from_float(float('nan')) |
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676 Decimal('NaN') |
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677 >>> Decimal.from_float(float('inf')) |
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678 Decimal('Infinity') |
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679 >>> Decimal.from_float(-float('inf')) |
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680 Decimal('-Infinity') |
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681 >>> Decimal.from_float(-0.0) |
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682 Decimal('-0') |
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683 |
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684 """ |
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685 if isinstance(f, int): # handle integer inputs |
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686 return cls(f) |
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687 if _math.isinf(f) or _math.isnan(f): # raises TypeError if not a float |
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688 return cls(repr(f)) |
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689 if _math.copysign(1.0, f) == 1.0: |
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690 sign = 0 |
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691 else: |
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692 sign = 1 |
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693 n, d = abs(f).as_integer_ratio() |
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694 k = d.bit_length() - 1 |
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695 result = _dec_from_triple(sign, str(n*5**k), -k) |
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696 if cls is Decimal: |
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697 return result |
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698 else: |
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699 return cls(result) |
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700 from_float = classmethod(from_float) |
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701 |
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702 def _isnan(self): |
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703 """Returns whether the number is not actually one. |
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704 |
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705 0 if a number |
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706 1 if NaN |
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707 2 if sNaN |
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708 """ |
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709 if self._is_special: |
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710 exp = self._exp |
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711 if exp == 'n': |
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712 return 1 |
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713 elif exp == 'N': |
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714 return 2 |
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715 return 0 |
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716 |
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717 def _isinfinity(self): |
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718 """Returns whether the number is infinite |
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719 |
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720 0 if finite or not a number |
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721 1 if +INF |
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722 -1 if -INF |
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723 """ |
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724 if self._exp == 'F': |
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725 if self._sign: |
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726 return -1 |
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727 return 1 |
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728 return 0 |
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729 |
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730 def _check_nans(self, other=None, context=None): |
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731 """Returns whether the number is not actually one. |
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732 |
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733 if self, other are sNaN, signal |
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734 if self, other are NaN return nan |
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735 return 0 |
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736 |
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737 Done before operations. |
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738 """ |
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739 |
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741 if other is None: |
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743 else: |
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744 other_is_nan = other._isnan() |
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746 if self_is_nan or other_is_nan: |
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747 if context is None: |
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748 context = getcontext() |
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751 return context._raise_error(InvalidOperation, 'sNaN', |
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755 other) |
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756 if self_is_nan: |
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757 return self._fix_nan(context) |
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759 return other._fix_nan(context) |
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762 def _compare_check_nans(self, other, context): |
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763 """Version of _check_nans used for the signaling comparisons |
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764 compare_signal, __le__, __lt__, __ge__, __gt__. |
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766 Signal InvalidOperation if either self or other is a (quiet |
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767 or signaling) NaN. Signaling NaNs take precedence over quiet |
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768 NaNs. |
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769 |
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770 Return 0 if neither operand is a NaN. |
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771 |
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772 """ |
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773 if context is None: |
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774 context = getcontext() |
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776 if self._is_special or other._is_special: |
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777 if self.is_snan(): |
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778 return context._raise_error(InvalidOperation, |
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779 'comparison involving sNaN', |
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780 self) |
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781 elif other.is_snan(): |
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782 return context._raise_error(InvalidOperation, |
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783 'comparison involving sNaN', |
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784 other) |
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785 elif self.is_qnan(): |
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786 return context._raise_error(InvalidOperation, |
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787 'comparison involving NaN', |
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788 self) |
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790 return context._raise_error(InvalidOperation, |
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791 'comparison involving NaN', |
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792 other) |
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793 return 0 |
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794 |
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795 def __bool__(self): |
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796 """Return True if self is nonzero; otherwise return False. |
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798 NaNs and infinities are considered nonzero. |
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799 """ |
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800 return self._is_special or self._int != '0' |
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801 |
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802 def _cmp(self, other): |
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803 """Compare the two non-NaN decimal instances self and other. |
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804 |
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805 Returns -1 if self < other, 0 if self == other and 1 |
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806 if self > other. This routine is for internal use only.""" |
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807 |
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808 if self._is_special or other._is_special: |
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809 self_inf = self._isinfinity() |
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810 other_inf = other._isinfinity() |
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811 if self_inf == other_inf: |
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812 return 0 |
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813 elif self_inf < other_inf: |
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814 return -1 |
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815 else: |
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816 return 1 |
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817 |
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818 # check for zeros; Decimal('0') == Decimal('-0') |
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819 if not self: |
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820 if not other: |
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821 return 0 |
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822 else: |
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823 return -((-1)**other._sign) |
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824 if not other: |
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825 return (-1)**self._sign |
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827 # If different signs, neg one is less |
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828 if other._sign < self._sign: |
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829 return -1 |
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830 if self._sign < other._sign: |
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831 return 1 |
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832 |
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833 self_adjusted = self.adjusted() |
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834 other_adjusted = other.adjusted() |
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835 if self_adjusted == other_adjusted: |
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836 self_padded = self._int + '0'*(self._exp - other._exp) |
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837 other_padded = other._int + '0'*(other._exp - self._exp) |
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838 if self_padded == other_padded: |
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839 return 0 |
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840 elif self_padded < other_padded: |
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841 return -(-1)**self._sign |
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842 else: |
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843 return (-1)**self._sign |
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844 elif self_adjusted > other_adjusted: |
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845 return (-1)**self._sign |
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846 else: # self_adjusted < other_adjusted |
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847 return -((-1)**self._sign) |
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848 |
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849 # Note: The Decimal standard doesn't cover rich comparisons for |
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850 # Decimals. In particular, the specification is silent on the |
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851 # subject of what should happen for a comparison involving a NaN. |
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852 # We take the following approach: |
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853 # |
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854 # == comparisons involving a quiet NaN always return False |
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855 # != comparisons involving a quiet NaN always return True |
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856 # == or != comparisons involving a signaling NaN signal |
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857 # InvalidOperation, and return False or True as above if the |
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858 # InvalidOperation is not trapped. |
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859 # <, >, <= and >= comparisons involving a (quiet or signaling) |
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860 # NaN signal InvalidOperation, and return False if the |
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861 # InvalidOperation is not trapped. |
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862 # |
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863 # This behavior is designed to conform as closely as possible to |
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864 # that specified by IEEE 754. |
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865 |
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866 def __eq__(self, other, context=None): |
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867 self, other = _convert_for_comparison(self, other, equality_op=True) |
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868 if other is NotImplemented: |
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869 return other |
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870 if self._check_nans(other, context): |
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871 return False |
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872 return self._cmp(other) == 0 |
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* Add __eq__ and __ne__ so that things like list.index() work properly
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873 |
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874 def __ne__(self, other, context=None): |
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875 self, other = _convert_for_comparison(self, other, equality_op=True) |
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876 if other is NotImplemented: |
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877 return other |
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878 if self._check_nans(other, context): |
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879 return True |
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880 return self._cmp(other) != 0 |
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881 |
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882 |
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883 def __lt__(self, other, context=None): |
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884 self, other = _convert_for_comparison(self, other) |
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885 if other is NotImplemented: |
|
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886 return other |
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887 ans = self._compare_check_nans(other, context) |
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888 if ans: |
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889 return False |
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890 return self._cmp(other) < 0 |
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891 |
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892 def __le__(self, other, context=None): |
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893 self, other = _convert_for_comparison(self, other) |
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894 if other is NotImplemented: |
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|
895 return other |
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896 ans = self._compare_check_nans(other, context) |
|
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897 if ans: |
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|
898 return False |
|
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899 return self._cmp(other) <= 0 |
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900 |
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901 def __gt__(self, other, context=None): |
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902 self, other = _convert_for_comparison(self, other) |
|
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903 if other is NotImplemented: |
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|
904 return other |
|
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905 ans = self._compare_check_nans(other, context) |
|
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|
906 if ans: |
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|
907 return False |
|
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|
908 return self._cmp(other) > 0 |
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909 |
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|
910 def __ge__(self, other, context=None): |
|
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|
911 self, other = _convert_for_comparison(self, other) |
|
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912 if other is NotImplemented: |
|
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913 return other |
|
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914 ans = self._compare_check_nans(other, context) |
|
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915 if ans: |
|
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916 return False |
|
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917 return self._cmp(other) >= 0 |
|
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918 |
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919 def compare(self, other, context=None): |
|
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920 """Compares one to another. |
|
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921 |
|
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922 -1 => a < b |
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923 0 => a = b |
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924 1 => a > b |
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925 NaN => one is NaN |
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926 Like __cmp__, but returns Decimal instances. |
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927 """ |
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928 other = _convert_other(other, raiseit=True) |
|
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929 |
|
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930 # Compare(NaN, NaN) = NaN |
|
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931 if (self._is_special or other and other._is_special): |
|
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932 ans = self._check_nans(other, context) |
|
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933 if ans: |
|
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934 return ans |
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935 |
|
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936 return Decimal(self._cmp(other)) |
|
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937 |
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938 def __hash__(self): |
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939 """x.__hash__() <==> hash(x)""" |
|
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940 |
|
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|
941 # In order to make sure that the hash of a Decimal instance |
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|
942 # agrees with the hash of a numerically equal integer, float |
|
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|
943 # or Fraction, we follow the rules for numeric hashes outlined |
|
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|
944 # in the documentation. (See library docs, 'Built-in Types'). |
|
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|
945 if self._is_special: |
|
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|
946 if self.is_snan(): |
| 66346 | 947 raise TypeError('Cannot hash a signaling NaN value.') |
|
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948 elif self.is_nan(): |
|
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|
949 return _PyHASH_NAN |
|
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950 else: |
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|
951 if self._sign: |
|
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|
952 return -_PyHASH_INF |
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953 else: |
|
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|
954 return _PyHASH_INF |
|
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955 |
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|
956 if self._exp >= 0: |
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|
957 exp_hash = pow(10, self._exp, _PyHASH_MODULUS) |
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|
958 else: |
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|
959 exp_hash = pow(_PyHASH_10INV, -self._exp, _PyHASH_MODULUS) |
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|
960 hash_ = int(self._int) * exp_hash % _PyHASH_MODULUS |
|
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|
961 ans = hash_ if self >= 0 else -hash_ |
|
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|
962 return -2 if ans == -1 else ans |
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963 |
|
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964 def as_tuple(self): |
|
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965 """Represents the number as a triple tuple. |
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966 |
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967 To show the internals exactly as they are. |
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968 """ |
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969 return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp) |
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970 |
|
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|
971 def __repr__(self): |
|
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972 """Represents the number as an instance of Decimal.""" |
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973 # Invariant: eval(repr(d)) == d |
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974 return "Decimal('%s')" % str(self) |
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975 |
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976 def __str__(self, eng=False, context=None): |
|
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977 """Return string representation of the number in scientific notation. |
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|
978 |
|
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|
979 Captures all of the information in the underlying representation. |
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980 """ |
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981 |
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982 sign = ['', '-'][self._sign] |
|
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983 if self._is_special: |
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984 if self._exp == 'F': |
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985 return sign + 'Infinity' |
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986 elif self._exp == 'n': |
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987 return sign + 'NaN' + self._int |
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988 else: # self._exp == 'N' |
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989 return sign + 'sNaN' + self._int |
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990 |
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991 # number of digits of self._int to left of decimal point |
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992 leftdigits = self._exp + len(self._int) |
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993 |
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994 # dotplace is number of digits of self._int to the left of the |
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995 # decimal point in the mantissa of the output string (that is, |
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996 # after adjusting the exponent) |
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997 if self._exp <= 0 and leftdigits > -6: |
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998 # no exponent required |
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999 dotplace = leftdigits |
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1000 elif not eng: |
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1001 # usual scientific notation: 1 digit on left of the point |
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1002 dotplace = 1 |
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1003 elif self._int == '0': |
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1004 # engineering notation, zero |
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1005 dotplace = (leftdigits + 1) % 3 - 1 |
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1006 else: |
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|
1007 # engineering notation, nonzero |
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1008 dotplace = (leftdigits - 1) % 3 + 1 |
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|
1009 |
|
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1010 if dotplace <= 0: |
|
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|
1011 intpart = '0' |
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|
1012 fracpart = '.' + '0'*(-dotplace) + self._int |
|
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1013 elif dotplace >= len(self._int): |
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|
1014 intpart = self._int+'0'*(dotplace-len(self._int)) |
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1015 fracpart = '' |
|
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1016 else: |
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1017 intpart = self._int[:dotplace] |
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|
1018 fracpart = '.' + self._int[dotplace:] |
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|
1019 if leftdigits == dotplace: |
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|
1020 exp = '' |
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|
1021 else: |
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|
1022 if context is None: |
|
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|
1023 context = getcontext() |
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1024 exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) |
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|
1025 |
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1026 return sign + intpart + fracpart + exp |
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1027 |
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1028 def to_eng_string(self, context=None): |
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|
1029 """Convert to engineering-type string. |
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1030 |
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|
1031 Engineering notation has an exponent which is a multiple of 3, so there |
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1032 are up to 3 digits left of the decimal place. |
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|
1033 |
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1034 Same rules for when in exponential and when as a value as in __str__. |
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1035 """ |
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1036 return self.__str__(eng=True, context=context) |
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1037 |
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1038 def __neg__(self, context=None): |
|
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1039 """Returns a copy with the sign switched. |
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1040 |
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1041 Rounds, if it has reason. |
|
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1042 """ |
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1043 if self._is_special: |
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1044 ans = self._check_nans(context=context) |
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|
1045 if ans: |
|
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|
1046 return ans |
|
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1047 |
|
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|
1048 if context is None: |
|
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|
1049 context = getcontext() |
|
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|
1050 |
|
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|
1051 if not self and context.rounding != ROUND_FLOOR: |
|
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|
1052 # -Decimal('0') is Decimal('0'), not Decimal('-0'), except |
|
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|
1053 # in ROUND_FLOOR rounding mode. |
|
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1054 ans = self.copy_abs() |
|
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1055 else: |
|
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|
1056 ans = self.copy_negate() |
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|
1057 |
|
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|
1058 return ans._fix(context) |
|
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1059 |
|
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1060 def __pos__(self, context=None): |
|
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1061 """Returns a copy, unless it is a sNaN. |
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1062 |
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1063 Rounds the number (if more then precision digits) |
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1064 """ |
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1065 if self._is_special: |
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|
1066 ans = self._check_nans(context=context) |
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|
1067 if ans: |
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|
1068 return ans |
|
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1069 |
|
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|
1070 if context is None: |
|
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|
1071 context = getcontext() |
|
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|
1072 |
|
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|
1073 if not self and context.rounding != ROUND_FLOOR: |
|
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|
1074 # + (-0) = 0, except in ROUND_FLOOR rounding mode. |
|
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|
1075 ans = self.copy_abs() |
|
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|
1076 else: |
|
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|
1077 ans = Decimal(self) |
|
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1078 |
|
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|
1079 return ans._fix(context) |
|
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|
1080 |
|
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|
1081 def __abs__(self, round=True, context=None): |
|
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1082 """Returns the absolute value of self. |
|
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|
1083 |
|
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|
1084 If the keyword argument 'round' is false, do not round. The |
|
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|
1085 expression self.__abs__(round=False) is equivalent to |
|
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|
1086 self.copy_abs(). |
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1087 """ |
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|
1088 if not round: |
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|
1089 return self.copy_abs() |
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|
1090 |
|
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|
1091 if self._is_special: |
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1092 ans = self._check_nans(context=context) |
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1093 if ans: |
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|
1094 return ans |
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1095 |
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1096 if self._sign: |
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1097 ans = self.__neg__(context=context) |
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1098 else: |
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|
1099 ans = self.__pos__(context=context) |
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1100 |
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1101 return ans |
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1102 |
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1103 def __add__(self, other, context=None): |
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1104 """Returns self + other. |
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1105 |
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|
1106 -INF + INF (or the reverse) cause InvalidOperation errors. |
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1107 """ |
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1108 other = _convert_other(other) |
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1109 if other is NotImplemented: |
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1110 return other |
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1111 |
|
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1112 if context is None: |
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1113 context = getcontext() |
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1114 |
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|
1115 if self._is_special or other._is_special: |
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1116 ans = self._check_nans(other, context) |
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1117 if ans: |
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|
1118 return ans |
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1119 |
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1120 if self._isinfinity(): |
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1121 # If both INF, same sign => same as both, opposite => error. |
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1122 if self._sign != other._sign and other._isinfinity(): |
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1123 return context._raise_error(InvalidOperation, '-INF + INF') |
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1124 return Decimal(self) |
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1125 if other._isinfinity(): |
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1126 return Decimal(other) # Can't both be infinity here |
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1127 |
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1128 exp = min(self._exp, other._exp) |
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1129 negativezero = 0 |
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1130 if context.rounding == ROUND_FLOOR and self._sign != other._sign: |
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1131 # If the answer is 0, the sign should be negative, in this case. |
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1132 negativezero = 1 |
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1133 |
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1134 if not self and not other: |
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1135 sign = min(self._sign, other._sign) |
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1136 if negativezero: |
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1137 sign = 1 |
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1138 ans = _dec_from_triple(sign, '0', exp) |
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1139 ans = ans._fix(context) |
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1140 return ans |
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1141 if not self: |
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1142 exp = max(exp, other._exp - context.prec-1) |
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1143 ans = other._rescale(exp, context.rounding) |
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1144 ans = ans._fix(context) |
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1145 return ans |
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1146 if not other: |
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1147 exp = max(exp, self._exp - context.prec-1) |
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1148 ans = self._rescale(exp, context.rounding) |
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1149 ans = ans._fix(context) |
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1150 return ans |
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1151 |
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1152 op1 = _WorkRep(self) |
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1153 op2 = _WorkRep(other) |
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1154 op1, op2 = _normalize(op1, op2, context.prec) |
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1155 |
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1156 result = _WorkRep() |
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1157 if op1.sign != op2.sign: |
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1158 # Equal and opposite |
| 33851 | 1159 if op1.int == op2.int: |
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1160 ans = _dec_from_triple(negativezero, '0', exp) |
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1161 ans = ans._fix(context) |
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1162 return ans |
| 33851 | 1163 if op1.int < op2.int: |
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1164 op1, op2 = op2, op1 |
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1165 # OK, now abs(op1) > abs(op2) |
| 33851 | 1166 if op1.sign == 1: |
| 1167 result.sign = 1 | |
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1168 op1.sign, op2.sign = op2.sign, op1.sign |
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1169 else: |
| 33851 | 1170 result.sign = 0 |
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1171 # So we know the sign, and op1 > 0. |
| 33851 | 1172 elif op1.sign == 1: |
| 1173 result.sign = 1 | |
| 1174 op1.sign, op2.sign = (0, 0) | |
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1175 else: |
| 33851 | 1176 result.sign = 0 |
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1177 # Now, op1 > abs(op2) > 0 |
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1178 |
| 33851 | 1179 if op2.sign == 0: |
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1180 result.int = op1.int + op2.int |
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1181 else: |
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1182 result.int = op1.int - op2.int |
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1183 |
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1184 result.exp = op1.exp |
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1185 ans = Decimal(result) |
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1186 ans = ans._fix(context) |
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1187 return ans |
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1188 |
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1189 __radd__ = __add__ |
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1190 |
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1191 def __sub__(self, other, context=None): |
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1192 """Return self - other""" |
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1193 other = _convert_other(other) |
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1194 if other is NotImplemented: |
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1195 return other |
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1196 |
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1197 if self._is_special or other._is_special: |
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1198 ans = self._check_nans(other, context=context) |
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1199 if ans: |
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1200 return ans |
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1201 |
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1202 # self - other is computed as self + other.copy_negate() |
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1203 return self.__add__(other.copy_negate(), context=context) |
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1204 |
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1205 def __rsub__(self, other, context=None): |
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1206 """Return other - self""" |
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1207 other = _convert_other(other) |
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1208 if other is NotImplemented: |
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1209 return other |
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1210 |
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1211 return other.__sub__(self, context=context) |
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1212 |
|
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1213 def __mul__(self, other, context=None): |
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1214 """Return self * other. |
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1215 |
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1216 (+-) INF * 0 (or its reverse) raise InvalidOperation. |
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1217 """ |
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1218 other = _convert_other(other) |
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1219 if other is NotImplemented: |
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1220 return other |
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1221 |
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1222 if context is None: |
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1223 context = getcontext() |
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1224 |
|
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1225 resultsign = self._sign ^ other._sign |
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1226 |
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1227 if self._is_special or other._is_special: |
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1228 ans = self._check_nans(other, context) |
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1229 if ans: |
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1230 return ans |
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1231 |
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1232 if self._isinfinity(): |
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1233 if not other: |
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1234 return context._raise_error(InvalidOperation, '(+-)INF * 0') |
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1235 return _SignedInfinity[resultsign] |
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1236 |
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1237 if other._isinfinity(): |
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1238 if not self: |
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1239 return context._raise_error(InvalidOperation, '0 * (+-)INF') |
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1240 return _SignedInfinity[resultsign] |
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1241 |
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1242 resultexp = self._exp + other._exp |
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1243 |
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1244 # Special case for multiplying by zero |
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1245 if not self or not other: |
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1246 ans = _dec_from_triple(resultsign, '0', resultexp) |
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1247 # Fixing in case the exponent is out of bounds |
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1248 ans = ans._fix(context) |
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1249 return ans |
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1250 |
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1251 # Special case for multiplying by power of 10 |
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1252 if self._int == '1': |
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1253 ans = _dec_from_triple(resultsign, other._int, resultexp) |
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1254 ans = ans._fix(context) |
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1255 return ans |
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1256 if other._int == '1': |
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1257 ans = _dec_from_triple(resultsign, self._int, resultexp) |
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1258 ans = ans._fix(context) |
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1259 return ans |
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1260 |
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1261 op1 = _WorkRep(self) |
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1262 op2 = _WorkRep(other) |
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1263 |
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1264 ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) |
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1265 ans = ans._fix(context) |
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1266 |
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1267 return ans |
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1268 __rmul__ = __mul__ |
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1269 |
|
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1270 def __truediv__(self, other, context=None): |
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1271 """Return self / other.""" |
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1272 other = _convert_other(other) |
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1273 if other is NotImplemented: |
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1274 return NotImplemented |
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1275 |
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1276 if context is None: |
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1277 context = getcontext() |
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1278 |
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1279 sign = self._sign ^ other._sign |
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1280 |
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1281 if self._is_special or other._is_special: |
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1282 ans = self._check_nans(other, context) |
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1283 if ans: |
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1284 return ans |
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1285 |
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1286 if self._isinfinity() and other._isinfinity(): |
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1287 return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') |
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1288 |
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1289 if self._isinfinity(): |
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1290 return _SignedInfinity[sign] |
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1291 |
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1292 if other._isinfinity(): |
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1293 context._raise_error(Clamped, 'Division by infinity') |
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1294 return _dec_from_triple(sign, '0', context.Etiny()) |
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1295 |
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1296 # Special cases for zeroes |
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1297 if not other: |
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1298 if not self: |
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1299 return context._raise_error(DivisionUndefined, '0 / 0') |
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1300 return context._raise_error(DivisionByZero, 'x / 0', sign) |
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1301 |
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1302 if not self: |
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1303 exp = self._exp - other._exp |
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1304 coeff = 0 |
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1305 else: |
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1306 # OK, so neither = 0, INF or NaN |
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1307 shift = len(other._int) - len(self._int) + context.prec + 1 |
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1308 exp = self._exp - other._exp - shift |
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1309 op1 = _WorkRep(self) |
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1310 op2 = _WorkRep(other) |
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1311 if shift >= 0: |
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1312 coeff, remainder = divmod(op1.int * 10**shift, op2.int) |
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1313 else: |
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1314 coeff, remainder = divmod(op1.int, op2.int * 10**-shift) |
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1315 if remainder: |
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1316 # result is not exact; adjust to ensure correct rounding |
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1317 if coeff % 5 == 0: |
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1318 coeff += 1 |
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1319 else: |
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1320 # result is exact; get as close to ideal exponent as possible |
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1321 ideal_exp = self._exp - other._exp |
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1322 while exp < ideal_exp and coeff % 10 == 0: |
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1323 coeff //= 10 |
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1324 exp += 1 |
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1325 |
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1326 ans = _dec_from_triple(sign, str(coeff), exp) |
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1327 return ans._fix(context) |
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1328 |
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1329 def _divide(self, other, context): |
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1330 """Return (self // other, self % other), to context.prec precision. |
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1331 |
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1332 Assumes that neither self nor other is a NaN, that self is not |
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1333 infinite and that other is nonzero. |
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1334 """ |
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1335 sign = self._sign ^ other._sign |
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1336 if other._isinfinity(): |
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1337 ideal_exp = self._exp |
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1338 else: |
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1339 ideal_exp = min(self._exp, other._exp) |
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1340 |
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1341 expdiff = self.adjusted() - other.adjusted() |
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1342 if not self or other._isinfinity() or expdiff <= -2: |
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1343 return (_dec_from_triple(sign, '0', 0), |
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1344 self._rescale(ideal_exp, context.rounding)) |
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1345 if expdiff <= context.prec: |
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1346 op1 = _WorkRep(self) |
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1347 op2 = _WorkRep(other) |
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1348 if op1.exp >= op2.exp: |
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1349 op1.int *= 10**(op1.exp - op2.exp) |
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1350 else: |
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1351 op2.int *= 10**(op2.exp - op1.exp) |
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1352 q, r = divmod(op1.int, op2.int) |
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1353 if q < 10**context.prec: |
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1354 return (_dec_from_triple(sign, str(q), 0), |
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1355 _dec_from_triple(self._sign, str(r), ideal_exp)) |
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1356 |
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1357 # Here the quotient is too large to be representable |
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1358 ans = context._raise_error(DivisionImpossible, |
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1359 'quotient too large in //, % or divmod') |
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1360 return ans, ans |
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1361 |
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1362 def __rtruediv__(self, other, context=None): |
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1363 """Swaps self/other and returns __truediv__.""" |
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1364 other = _convert_other(other) |
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1365 if other is NotImplemented: |
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1366 return other |
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1367 return other.__truediv__(self, context=context) |
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1368 |
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1369 def __divmod__(self, other, context=None): |
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1370 """ |
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1371 Return (self // other, self % other) |
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1372 """ |
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1373 other = _convert_other(other) |
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1374 if other is NotImplemented: |
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1375 return other |
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1376 |
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1377 if context is None: |
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1378 context = getcontext() |
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1379 |
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1380 ans = self._check_nans(other, context) |
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1381 if ans: |
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1382 return (ans, ans) |
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1383 |
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1384 sign = self._sign ^ other._sign |
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1385 if self._isinfinity(): |
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1386 if other._isinfinity(): |
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1387 ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') |
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1388 return ans, ans |
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1389 else: |
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1390 return (_SignedInfinity[sign], |
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1391 context._raise_error(InvalidOperation, 'INF % x')) |
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1392 |
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1393 if not other: |
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1394 if not self: |
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1395 ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') |
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1396 return ans, ans |
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1397 else: |
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1398 return (context._raise_error(DivisionByZero, 'x // 0', sign), |
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1399 context._raise_error(InvalidOperation, 'x % 0')) |
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1400 |
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1401 quotient, remainder = self._divide(other, context) |
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1402 remainder = remainder._fix(context) |
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1403 return quotient, remainder |
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1404 |
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1405 def __rdivmod__(self, other, context=None): |
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1406 """Swaps self/other and returns __divmod__.""" |
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1407 other = _convert_other(other) |
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1408 if other is NotImplemented: |
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1409 return other |
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1410 return other.__divmod__(self, context=context) |
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1411 |
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1412 def __mod__(self, other, context=None): |
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1413 """ |
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1414 self % other |
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1415 """ |
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1416 other = _convert_other(other) |
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1417 if other is NotImplemented: |
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1418 return other |
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1419 |
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1420 if context is None: |
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1421 context = getcontext() |
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1422 |
|
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1423 ans = self._check_nans(other, context) |
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1424 if ans: |
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1425 return ans |
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1426 |
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1427 if self._isinfinity(): |
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1428 return context._raise_error(InvalidOperation, 'INF % x') |
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1429 elif not other: |
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1430 if self: |
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1431 return context._raise_error(InvalidOperation, 'x % 0') |
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1432 else: |
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1433 return context._raise_error(DivisionUndefined, '0 % 0') |
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1434 |
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1435 remainder = self._divide(other, context)[1] |
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1436 remainder = remainder._fix(context) |
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1437 return remainder |
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1438 |
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1439 def __rmod__(self, other, context=None): |
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1440 """Swaps self/other and returns __mod__.""" |
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1441 other = _convert_other(other) |
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1442 if other is NotImplemented: |
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1443 return other |
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1444 return other.__mod__(self, context=context) |
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1445 |
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1446 def remainder_near(self, other, context=None): |
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1447 """ |
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1448 Remainder nearest to 0- abs(remainder-near) <= other/2 |
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1449 """ |
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1450 if context is None: |
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1451 context = getcontext() |
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1452 |
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1453 other = _convert_other(other, raiseit=True) |
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1454 |
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1455 ans = self._check_nans(other, context) |
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1456 if ans: |
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1457 return ans |
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1458 |
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1459 # self == +/-infinity -> InvalidOperation |
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1460 if self._isinfinity(): |
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1461 return context._raise_error(InvalidOperation, |
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1462 'remainder_near(infinity, x)') |
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1463 |
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1464 # other == 0 -> either InvalidOperation or DivisionUndefined |
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1465 if not other: |
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1466 if self: |
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1467 return context._raise_error(InvalidOperation, |
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1468 'remainder_near(x, 0)') |
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1469 else: |
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1470 return context._raise_error(DivisionUndefined, |
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1471 'remainder_near(0, 0)') |
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1472 |
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1473 # other = +/-infinity -> remainder = self |
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1474 if other._isinfinity(): |
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1475 ans = Decimal(self) |
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1476 return ans._fix(context) |
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1477 |
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1478 # self = 0 -> remainder = self, with ideal exponent |
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1479 ideal_exponent = min(self._exp, other._exp) |
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1480 if not self: |
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1481 ans = _dec_from_triple(self._sign, '0', ideal_exponent) |
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1482 return ans._fix(context) |
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1483 |
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1484 # catch most cases of large or small quotient |
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1485 expdiff = self.adjusted() - other.adjusted() |
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1486 if expdiff >= context.prec + 1: |
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1487 # expdiff >= prec+1 => abs(self/other) > 10**prec |
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1488 return context._raise_error(DivisionImpossible) |
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1489 if expdiff <= -2: |
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1490 # expdiff <= -2 => abs(self/other) < 0.1 |
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1491 ans = self._rescale(ideal_exponent, context.rounding) |
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1492 return ans._fix(context) |
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1493 |
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1494 # adjust both arguments to have the same exponent, then divide |
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1495 op1 = _WorkRep(self) |
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1496 op2 = _WorkRep(other) |
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1497 if op1.exp >= op2.exp: |
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1498 op1.int *= 10**(op1.exp - op2.exp) |
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1499 else: |
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1500 op2.int *= 10**(op2.exp - op1.exp) |
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1501 q, r = divmod(op1.int, op2.int) |
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1502 # remainder is r*10**ideal_exponent; other is +/-op2.int * |
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1503 # 10**ideal_exponent. Apply correction to ensure that |
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1504 # abs(remainder) <= abs(other)/2 |
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1505 if 2*r + (q&1) > op2.int: |
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1506 r -= op2.int |
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1507 q += 1 |
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1508 |
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1509 if q >= 10**context.prec: |
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1510 return context._raise_error(DivisionImpossible) |
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1511 |
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1512 # result has same sign as self unless r is negative |
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1513 sign = self._sign |
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1514 if r < 0: |
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1515 sign = 1-sign |
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1516 r = -r |
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1517 |
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1518 ans = _dec_from_triple(sign, str(r), ideal_exponent) |
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1519 return ans._fix(context) |
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1520 |
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1521 def __floordiv__(self, other, context=None): |
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1522 """self // other""" |
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1523 other = _convert_other(other) |
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1524 if other is NotImplemented: |
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1525 return other |
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1526 |
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1527 if context is None: |
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1528 context = getcontext() |
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1529 |
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1530 ans = self._check_nans(other, context) |
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1531 if ans: |
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1532 return ans |
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1533 |
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1534 if self._isinfinity(): |
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1535 if other._isinfinity(): |
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1536 return context._raise_error(InvalidOperation, 'INF // INF') |
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1537 else: |
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1538 return _SignedInfinity[self._sign ^ other._sign] |
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1539 |
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1540 if not other: |
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1541 if self: |
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1542 return context._raise_error(DivisionByZero, 'x // 0', |
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1543 self._sign ^ other._sign) |
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1544 else: |
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1545 return context._raise_error(DivisionUndefined, '0 // 0') |
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1547 return self._divide(other, context)[0] |
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1548 |
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1549 def __rfloordiv__(self, other, context=None): |
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1550 """Swaps self/other and returns __floordiv__.""" |
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1551 other = _convert_other(other) |
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1552 if other is NotImplemented: |
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1553 return other |
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1554 return other.__floordiv__(self, context=context) |
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1555 |
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1556 def __float__(self): |
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1557 """Float representation.""" |
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1558 return float(str(self)) |
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1559 |
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1560 def __int__(self): |
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1561 """Converts self to an int, truncating if necessary.""" |
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1562 if self._is_special: |
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1563 if self._isnan(): |
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1564 raise ValueError("Cannot convert NaN to integer") |
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1565 elif self._isinfinity(): |
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1566 raise OverflowError("Cannot convert infinity to integer") |
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1567 s = (-1)**self._sign |
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1568 if self._exp >= 0: |
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1569 return s*int(self._int)*10**self._exp |
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1570 else: |
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1571 return s*int(self._int[:self._exp] or '0') |
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1573 __trunc__ = __int__ |
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1574 |
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1575 def real(self): |
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1576 return self |
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1577 real = property(real) |
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1578 |
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1579 def imag(self): |
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1580 return Decimal(0) |
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1581 imag = property(imag) |
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1582 |
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1583 def conjugate(self): |
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1584 return self |
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1585 |
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1586 def __complex__(self): |
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1587 return complex(float(self)) |
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1588 |
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1589 def _fix_nan(self, context): |
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1590 """Decapitate the payload of a NaN to fit the context""" |
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1591 payload = self._int |
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1592 |
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1593 # maximum length of payload is precision if clamp=0, |
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1594 # precision-1 if clamp=1. |
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1595 max_payload_len = context.prec - context.clamp |
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1596 if len(payload) > max_payload_len: |
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1597 payload = payload[len(payload)-max_payload_len:].lstrip('0') |
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1598 return _dec_from_triple(self._sign, payload, self._exp, True) |
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1599 return Decimal(self) |
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1600 |
| 33695 | 1601 def _fix(self, context): |
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1602 """Round if it is necessary to keep self within prec precision. |
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1603 |
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1604 Rounds and fixes the exponent. Does not raise on a sNaN. |
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1605 |
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1606 Arguments: |
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1607 self - Decimal instance |
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1608 context - context used. |
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1609 """ |
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1610 |
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1611 if self._is_special: |
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1612 if self._isnan(): |
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1613 # decapitate payload if necessary |
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1614 return self._fix_nan(context) |
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1615 else: |
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1616 # self is +/-Infinity; return unaltered |
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1617 return Decimal(self) |
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1618 |
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1619 # if self is zero then exponent should be between Etiny and |
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1620 # Emax if clamp==0, and between Etiny and Etop if clamp==1. |
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1621 Etiny = context.Etiny() |
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1622 Etop = context.Etop() |
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1623 if not self: |
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1624 exp_max = [context.Emax, Etop][context.clamp] |
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1625 new_exp = min(max(self._exp, Etiny), exp_max) |
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1626 if new_exp != self._exp: |
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1627 context._raise_error(Clamped) |
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1628 return _dec_from_triple(self._sign, '0', new_exp) |
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1629 else: |
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1630 return Decimal(self) |
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1631 |
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1632 # exp_min is the smallest allowable exponent of the result, |
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1633 # equal to max(self.adjusted()-context.prec+1, Etiny) |
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1634 exp_min = len(self._int) + self._exp - context.prec |
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1635 if exp_min > Etop: |
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1636 # overflow: exp_min > Etop iff self.adjusted() > Emax |
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1637 ans = context._raise_error(Overflow, 'above Emax', self._sign) |
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1638 context._raise_error(Inexact) |
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1639 context._raise_error(Rounded) |
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1640 return ans |
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1641 |
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1642 self_is_subnormal = exp_min < Etiny |
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1643 if self_is_subnormal: |
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1644 exp_min = Etiny |
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1645 |
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1646 # round if self has too many digits |
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1647 if self._exp < exp_min: |
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1648 digits = len(self._int) + self._exp - exp_min |
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1649 if digits < 0: |
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1650 self = _dec_from_triple(self._sign, '1', exp_min-1) |
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1651 digits = 0 |
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1652 rounding_method = self._pick_rounding_function[context.rounding] |
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1653 changed = rounding_method(self, digits) |
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1654 coeff = self._int[:digits] or '0' |
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1655 if changed > 0: |
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1656 coeff = str(int(coeff)+1) |
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1657 if len(coeff) > context.prec: |
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1658 coeff = coeff[:-1] |
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1659 exp_min += 1 |
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1660 |
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1661 # check whether the rounding pushed the exponent out of range |
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1662 if exp_min > Etop: |
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1663 ans = context._raise_error(Overflow, 'above Emax', self._sign) |
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1664 else: |
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1665 ans = _dec_from_triple(self._sign, coeff, exp_min) |
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1666 |
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1667 # raise the appropriate signals, taking care to respect |
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1668 # the precedence described in the specification |
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1669 if changed and self_is_subnormal: |
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1670 context._raise_error(Underflow) |
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1671 if self_is_subnormal: |
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1672 context._raise_error(Subnormal) |
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1673 if changed: |
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1674 context._raise_error(Inexact) |
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1675 context._raise_error(Rounded) |
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1676 if not ans: |
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1677 # raise Clamped on underflow to 0 |
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1678 context._raise_error(Clamped) |
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1679 return ans |
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1680 |
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1681 if self_is_subnormal: |
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1682 context._raise_error(Subnormal) |
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1683 |
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1684 # fold down if clamp == 1 and self has too few digits |
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1685 if context.clamp == 1 and self._exp > Etop: |
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1686 context._raise_error(Clamped) |
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1687 self_padded = self._int + '0'*(self._exp - Etop) |
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1688 return _dec_from_triple(self._sign, self_padded, Etop) |
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1689 |
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1690 # here self was representable to begin with; return unchanged |
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1691 return Decimal(self) |
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1692 |
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1693 # for each of the rounding functions below: |
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1694 # self is a finite, nonzero Decimal |
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1695 # prec is an integer satisfying 0 <= prec < len(self._int) |
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1696 # |
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1697 # each function returns either -1, 0, or 1, as follows: |
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1698 # 1 indicates that self should be rounded up (away from zero) |
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1699 # 0 indicates that self should be truncated, and that all the |
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1700 # digits to be truncated are zeros (so the value is unchanged) |
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1701 # -1 indicates that there are nonzero digits to be truncated |
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1702 |
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1703 def _round_down(self, prec): |
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1704 """Also known as round-towards-0, truncate.""" |
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1705 if _all_zeros(self._int, prec): |
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1706 return 0 |
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1707 else: |
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1708 return -1 |
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1709 |
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1710 def _round_up(self, prec): |
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1711 """Rounds away from 0.""" |
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1712 return -self._round_down(prec) |
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1713 |
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1714 def _round_half_up(self, prec): |
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1715 """Rounds 5 up (away from 0)""" |
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1716 if self._int[prec] in '56789': |
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1717 return 1 |
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1718 elif _all_zeros(self._int, prec): |
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1719 return 0 |
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1720 else: |
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1721 return -1 |
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|
1722 |
|
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|
1723 def _round_half_down(self, prec): |
|
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|
1724 """Round 5 down""" |
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1725 if _exact_half(self._int, prec): |
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|
1726 return -1 |
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1727 else: |
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1728 return self._round_half_up(prec) |
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|
1729 |
|
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|
1730 def _round_half_even(self, prec): |
|
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|
1731 """Round 5 to even, rest to nearest.""" |
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1732 if _exact_half(self._int, prec) and \ |
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1733 (prec == 0 or self._int[prec-1] in '02468'): |
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1734 return -1 |
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1735 else: |
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1736 return self._round_half_up(prec) |
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|
1737 |
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|
1738 def _round_ceiling(self, prec): |
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1739 """Rounds up (not away from 0 if negative.)""" |
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1740 if self._sign: |
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1741 return self._round_down(prec) |
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1742 else: |
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1743 return -self._round_down(prec) |
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1744 |
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1745 def _round_floor(self, prec): |
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1746 """Rounds down (not towards 0 if negative)""" |
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1747 if not self._sign: |
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1748 return self._round_down(prec) |
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1749 else: |
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1750 return -self._round_down(prec) |
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1751 |
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1752 def _round_05up(self, prec): |
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1753 """Round down unless digit prec-1 is 0 or 5.""" |
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1754 if prec and self._int[prec-1] not in '05': |
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1755 return self._round_down(prec) |
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1756 else: |
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1757 return -self._round_down(prec) |
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1758 |
|
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1759 _pick_rounding_function = dict( |
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1760 ROUND_DOWN = _round_down, |
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1761 ROUND_UP = _round_up, |
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1762 ROUND_HALF_UP = _round_half_up, |
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1763 ROUND_HALF_DOWN = _round_half_down, |
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1764 ROUND_HALF_EVEN = _round_half_even, |
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1765 ROUND_CEILING = _round_ceiling, |
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1766 ROUND_FLOOR = _round_floor, |
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1767 ROUND_05UP = _round_05up, |
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1768 ) |
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1769 |
|
46789
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1770 def __round__(self, n=None): |
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1771 """Round self to the nearest integer, or to a given precision. |
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1772 |
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1773 If only one argument is supplied, round a finite Decimal |
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1774 instance self to the nearest integer. If self is infinite or |
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1775 a NaN then a Python exception is raised. If self is finite |
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1776 and lies exactly halfway between two integers then it is |
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1777 rounded to the integer with even last digit. |
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1778 |
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1779 >>> round(Decimal('123.456')) |
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1780 123 |
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1781 >>> round(Decimal('-456.789')) |
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1782 -457 |
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1783 >>> round(Decimal('-3.0')) |
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1784 -3 |
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1785 >>> round(Decimal('2.5')) |
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1786 2 |
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1787 >>> round(Decimal('3.5')) |
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1788 4 |
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1789 >>> round(Decimal('Inf')) |
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1790 Traceback (most recent call last): |
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1791 ... |
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1792 OverflowError: cannot round an infinity |
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1793 >>> round(Decimal('NaN')) |
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1794 Traceback (most recent call last): |
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1795 ... |
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1796 ValueError: cannot round a NaN |
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1797 |
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1798 If a second argument n is supplied, self is rounded to n |
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1799 decimal places using the rounding mode for the current |
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1800 context. |
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1801 |
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1802 For an integer n, round(self, -n) is exactly equivalent to |
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1803 self.quantize(Decimal('1En')). |
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1804 |
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1805 >>> round(Decimal('123.456'), 0) |
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1806 Decimal('123') |
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1807 >>> round(Decimal('123.456'), 2) |
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1808 Decimal('123.46') |
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1809 >>> round(Decimal('123.456'), -2) |
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1810 Decimal('1E+2') |
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1811 >>> round(Decimal('-Infinity'), 37) |
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1812 Decimal('NaN') |
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1813 >>> round(Decimal('sNaN123'), 0) |
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1814 Decimal('NaN123') |
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1815 |
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1816 """ |
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1817 if n is not None: |
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1818 # two-argument form: use the equivalent quantize call |
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1819 if not isinstance(n, int): |
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1820 raise TypeError('Second argument to round should be integral') |
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1821 exp = _dec_from_triple(0, '1', -n) |
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1822 return self.quantize(exp) |
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1823 |
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1824 # one-argument form |
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1825 if self._is_special: |
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1826 if self.is_nan(): |
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1827 raise ValueError("cannot round a NaN") |
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1828 else: |
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1829 raise OverflowError("cannot round an infinity") |
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1830 return int(self._rescale(0, ROUND_HALF_EVEN)) |
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1831 |
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1832 def __floor__(self): |
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1833 """Return the floor of self, as an integer. |
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1834 |
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1835 For a finite Decimal instance self, return the greatest |
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1836 integer n such that n <= self. If self is infinite or a NaN |
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1837 then a Python exception is raised. |
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1838 |
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1839 """ |
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1840 if self._is_special: |
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1841 if self.is_nan(): |
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1842 raise ValueError("cannot round a NaN") |
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1843 else: |
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1844 raise OverflowError("cannot round an infinity") |
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1845 return int(self._rescale(0, ROUND_FLOOR)) |
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1846 |
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1847 def __ceil__(self): |
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1848 """Return the ceiling of self, as an integer. |
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1849 |
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1850 For a finite Decimal instance self, return the least integer n |
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1851 such that n >= self. If self is infinite or a NaN then a |
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1852 Python exception is raised. |
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1853 |
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1854 """ |
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1855 if self._is_special: |
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1856 if self.is_nan(): |
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1857 raise ValueError("cannot round a NaN") |
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1858 else: |
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1859 raise OverflowError("cannot round an infinity") |
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1860 return int(self._rescale(0, ROUND_CEILING)) |
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1861 |
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1862 def fma(self, other, third, context=None): |
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1863 """Fused multiply-add. |
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1864 |
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1865 Returns self*other+third with no rounding of the intermediate |
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1866 product self*other. |
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1867 |
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1868 self and other are multiplied together, with no rounding of |
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1869 the result. The third operand is then added to the result, |
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1870 and a single final rounding is performed. |
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1871 """ |
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1872 |
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1873 other = _convert_other(other, raiseit=True) |
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1874 |
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1875 # compute product; raise InvalidOperation if either operand is |
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1876 # a signaling NaN or if the product is zero times infinity. |
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1877 if self._is_special or other._is_special: |
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1878 if context is None: |
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1879 context = getcontext() |
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1880 if self._exp == 'N': |
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1881 return context._raise_error(InvalidOperation, 'sNaN', self) |
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1882 if other._exp == 'N': |
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1883 return context._raise_error(InvalidOperation, 'sNaN', other) |
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1884 if self._exp == 'n': |
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1885 product = self |
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1886 elif other._exp == 'n': |
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1887 product = other |
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1888 elif self._exp == 'F': |
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1889 if not other: |
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1890 return context._raise_error(InvalidOperation, |
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1891 'INF * 0 in fma') |
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1892 product = _SignedInfinity[self._sign ^ other._sign] |
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1893 elif other._exp == 'F': |
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1894 if not self: |
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1895 return context._raise_error(InvalidOperation, |
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1896 '0 * INF in fma') |
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1897 product = _SignedInfinity[self._sign ^ other._sign] |
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1898 else: |
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1899 product = _dec_from_triple(self._sign ^ other._sign, |
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1900 str(int(self._int) * int(other._int)), |
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1901 self._exp + other._exp) |
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1902 |
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1903 third = _convert_other(third, raiseit=True) |
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1904 return product.__add__(third, context) |
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1905 |
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1906 def _power_modulo(self, other, modulo, context=None): |
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1907 """Three argument version of __pow__""" |
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1908 |
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1909 # if can't convert other and modulo to Decimal, raise |
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1910 # TypeError; there's no point returning NotImplemented (no |
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1911 # equivalent of __rpow__ for three argument pow) |
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1912 other = _convert_other(other, raiseit=True) |
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1913 modulo = _convert_other(modulo, raiseit=True) |
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1914 |
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1915 if context is None: |
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1916 context = getcontext() |
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1917 |
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1918 # deal with NaNs: if there are any sNaNs then first one wins, |
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1919 # (i.e. behaviour for NaNs is identical to that of fma) |
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1920 self_is_nan = self._isnan() |
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1921 other_is_nan = other._isnan() |
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1922 modulo_is_nan = modulo._isnan() |
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1923 if self_is_nan or other_is_nan or modulo_is_nan: |
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1924 if self_is_nan == 2: |
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1925 return context._raise_error(InvalidOperation, 'sNaN', |
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1926 self) |
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1927 if other_is_nan == 2: |
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1928 return context._raise_error(InvalidOperation, 'sNaN', |
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1929 other) |
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1930 if modulo_is_nan == 2: |
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1931 return context._raise_error(InvalidOperation, 'sNaN', |
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1932 modulo) |
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1933 if self_is_nan: |
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1934 return self._fix_nan(context) |
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1935 if other_is_nan: |
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1936 return other._fix_nan(context) |
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1937 return modulo._fix_nan(context) |
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1938 |
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1939 # check inputs: we apply same restrictions as Python's pow() |
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1940 if not (self._isinteger() and |
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1941 other._isinteger() and |
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1942 modulo._isinteger()): |
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1943 return context._raise_error(InvalidOperation, |
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1944 'pow() 3rd argument not allowed ' |
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1945 'unless all arguments are integers') |
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1946 if other < 0: |
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1947 return context._raise_error(InvalidOperation, |
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1948 'pow() 2nd argument cannot be ' |
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1949 'negative when 3rd argument specified') |
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1950 if not modulo: |
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1951 return context._raise_error(InvalidOperation, |
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1952 'pow() 3rd argument cannot be 0') |
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1953 |
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1954 # additional restriction for decimal: the modulus must be less |
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1955 # than 10**prec in absolute value |
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1956 if modulo.adjusted() >= context.prec: |
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1957 return context._raise_error(InvalidOperation, |
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1958 'insufficient precision: pow() 3rd ' |
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1959 'argument must not have more than ' |
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1960 'precision digits') |
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1961 |
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1962 # define 0**0 == NaN, for consistency with two-argument pow |
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1963 # (even though it hurts!) |
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1964 if not other and not self: |
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1965 return context._raise_error(InvalidOperation, |
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1966 'at least one of pow() 1st argument ' |
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1967 'and 2nd argument must be nonzero ;' |
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1968 '0**0 is not defined') |
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1969 |
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1970 # compute sign of result |
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1971 if other._iseven(): |
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1972 sign = 0 |
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1973 else: |
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1974 sign = self._sign |
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1975 |
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1976 # convert modulo to a Python integer, and self and other to |
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1977 # Decimal integers (i.e. force their exponents to be >= 0) |
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1978 modulo = abs(int(modulo)) |
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1979 base = _WorkRep(self.to_integral_value()) |
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1980 exponent = _WorkRep(other.to_integral_value()) |
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1981 |
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1982 # compute result using integer pow() |
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1983 base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo |
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1984 for i in range(exponent.exp): |
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1985 base = pow(base, 10, modulo) |
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1986 base = pow(base, exponent.int, modulo) |
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1987 |
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1988 return _dec_from_triple(sign, str(base), 0) |
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1989 |
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1990 def _power_exact(self, other, p): |
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1991 """Attempt to compute self**other exactly. |
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1992 |
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1993 Given Decimals self and other and an integer p, attempt to |
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1994 compute an exact result for the power self**other, with p |
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1995 digits of precision. Return None if self**other is not |
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1996 exactly representable in p digits. |
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1997 |
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1998 Assumes that elimination of special cases has already been |
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1999 performed: self and other must both be nonspecial; self must |
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2000 be positive and not numerically equal to 1; other must be |
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2001 nonzero. For efficiency, other._exp should not be too large, |
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2002 so that 10**abs(other._exp) is a feasible calculation.""" |
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2003 |
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2004 # In the comments below, we write x for the value of self and |
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2005 # y for the value of other. Write x = xc*10**xe and y = |
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2006 # yc*10**ye. |
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2007 |
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2008 # The main purpose of this method is to identify the *failure* |
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2009 # of x**y to be exactly representable with as little effort as |
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2010 # possible. So we look for cheap and easy tests that |
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2011 # eliminate the possibility of x**y being exact. Only if all |
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2012 # these tests are passed do we go on to actually compute x**y. |
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2013 |
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2014 # Here's the main idea. First normalize both x and y. We |
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2015 # express y as a rational m/n, with m and n relatively prime |
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2016 # and n>0. Then for x**y to be exactly representable (at |
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2017 # *any* precision), xc must be the nth power of a positive |
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2018 # integer and xe must be divisible by n. If m is negative |
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2019 # then additionally xc must be a power of either 2 or 5, hence |
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2020 # a power of 2**n or 5**n. |
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2021 # |
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2022 # There's a limit to how small |y| can be: if y=m/n as above |
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2023 # then: |
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2024 # |
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2025 # (1) if xc != 1 then for the result to be representable we |
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2026 # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So |
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2027 # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= |
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2028 # 2**(1/|y|), hence xc**|y| < 2 and the result is not |
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2029 # representable. |
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2030 # |
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2031 # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if |
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2032 # |y| < 1/|xe| then the result is not representable. |
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2033 # |
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2034 # Note that since x is not equal to 1, at least one of (1) and |
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2035 # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < |
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2036 # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. |
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2037 # |
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2038 # There's also a limit to how large y can be, at least if it's |
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2039 # positive: the normalized result will have coefficient xc**y, |
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2040 # so if it's representable then xc**y < 10**p, and y < |
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2041 # p/log10(xc). Hence if y*log10(xc) >= p then the result is |
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2042 # not exactly representable. |
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2043 |
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2044 # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, |
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2045 # so |y| < 1/xe and the result is not representable. |
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2046 # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| |
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2047 # < 1/nbits(xc). |
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2048 |
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2049 x = _WorkRep(self) |
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2050 xc, xe = x.int, x.exp |
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2051 while xc % 10 == 0: |
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2052 xc //= 10 |
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2053 xe += 1 |
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2054 |
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2055 y = _WorkRep(other) |
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2056 yc, ye = y.int, y.exp |
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2057 while yc % 10 == 0: |
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2058 yc //= 10 |
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2059 ye += 1 |
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2060 |
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2061 # case where xc == 1: result is 10**(xe*y), with xe*y |
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2062 # required to be an integer |
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2063 if xc == 1: |
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2064 xe *= yc |
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2065 # result is now 10**(xe * 10**ye); xe * 10**ye must be integral |
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2066 while xe % 10 == 0: |
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2067 xe //= 10 |
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2068 ye += 1 |
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2069 if ye < 0: |
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2070 return None |
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2071 exponent = xe * 10**ye |
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2072 if y.sign == 1: |
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2073 exponent = -exponent |
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2074 # if other is a nonnegative integer, use ideal exponent |
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2075 if other._isinteger() and other._sign == 0: |
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2076 ideal_exponent = self._exp*int(other) |
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2077 zeros = min(exponent-ideal_exponent, p-1) |
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2078 else: |
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2079 zeros = 0 |
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2080 return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) |
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43400
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2081 |
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2082 # case where y is negative: xc must be either a power |
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2083 # of 2 or a power of 5. |
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2084 if y.sign == 1: |
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2085 last_digit = xc % 10 |
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2086 if last_digit in (2,4,6,8): |
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2087 # quick test for power of 2 |
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2088 if xc & -xc != xc: |
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2089 return None |
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2090 # now xc is a power of 2; e is its exponent |
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2091 e = _nbits(xc)-1 |
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2092 # find e*y and xe*y; both must be integers |
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2093 if ye >= 0: |
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2094 y_as_int = yc*10**ye |
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2095 e = e*y_as_int |
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2096 xe = xe*y_as_int |
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2097 else: |
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2098 ten_pow = 10**-ye |
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2099 e, remainder = divmod(e*yc, ten_pow) |
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2100 if remainder: |
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2101 return None |
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2102 xe, remainder = divmod(xe*yc, ten_pow) |
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2103 if remainder: |
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2104 return None |
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2105 |
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2106 if e*65 >= p*93: # 93/65 > log(10)/log(5) |
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2107 return None |
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2108 xc = 5**e |
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2109 |
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2110 elif last_digit == 5: |
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2111 # e >= log_5(xc) if xc is a power of 5; we have |
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2112 # equality all the way up to xc=5**2658 |
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2113 e = _nbits(xc)*28//65 |
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2114 xc, remainder = divmod(5**e, xc) |
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2115 if remainder: |
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2116 return None |
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2117 while xc % 5 == 0: |
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2118 xc //= 5 |
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2119 e -= 1 |
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2120 if ye >= 0: |
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2121 y_as_integer = yc*10**ye |
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2122 e = e*y_as_integer |
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2123 xe = xe*y_as_integer |
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2124 else: |
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2125 ten_pow = 10**-ye |
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2126 e, remainder = divmod(e*yc, ten_pow) |
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2127 if remainder: |
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2128 return None |
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2129 xe, remainder = divmod(xe*yc, ten_pow) |
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2130 if remainder: |
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2131 return None |
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2132 if e*3 >= p*10: # 10/3 > log(10)/log(2) |
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2133 return None |
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2134 xc = 2**e |
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2135 else: |
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2136 return None |
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2137 |
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2138 if xc >= 10**p: |
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2139 return None |
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2140 xe = -e-xe |
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2141 return _dec_from_triple(0, str(xc), xe) |
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2142 |
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2143 # now y is positive; find m and n such that y = m/n |
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2144 if ye >= 0: |
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2145 m, n = yc*10**ye, 1 |
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2146 else: |
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2147 if xe != 0 and len(str(abs(yc*xe))) <= -ye: |
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|
2148 return None |
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2149 xc_bits = _nbits(xc) |
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2150 if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: |
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2151 return None |
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|
2152 m, n = yc, 10**(-ye) |
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2153 while m % 2 == n % 2 == 0: |
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2154 m //= 2 |
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2155 n //= 2 |
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2156 while m % 5 == n % 5 == 0: |
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2157 m //= 5 |
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2158 n //= 5 |
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|
2159 |
|
1bac386c17cc
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2160 # compute nth root of xc*10**xe |
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2161 if n > 1: |
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2162 # if 1 < xc < 2**n then xc isn't an nth power |
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2163 if xc != 1 and xc_bits <= n: |
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2164 return None |
|
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|
2165 |
|
1bac386c17cc
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2166 xe, rem = divmod(xe, n) |
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2167 if rem != 0: |
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2168 return None |
|
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|
2169 |
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|
2170 # compute nth root of xc using Newton's method |
|
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2171 a = 1 << -(-_nbits(xc)//n) # initial estimate |
|
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2172 while True: |
|
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2173 q, r = divmod(xc, a**(n-1)) |
|
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|
2174 if a <= q: |
|
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|
2175 break |
|
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2176 else: |
|
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2177 a = (a*(n-1) + q)//n |
|
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2178 if not (a == q and r == 0): |
|
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|
2179 return None |
|
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2180 xc = a |
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|
2181 |
|
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2182 # now xc*10**xe is the nth root of the original xc*10**xe |
|
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2183 # compute mth power of xc*10**xe |
|
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|
2184 |
|
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2185 # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > |
|
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2186 # 10**p and the result is not representable. |
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2187 if xc > 1 and m > p*100//_log10_lb(xc): |
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|
2188 return None |
|
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2189 xc = xc**m |
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2190 xe *= m |
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2191 if xc > 10**p: |
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2192 return None |
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|
2193 |
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2194 # by this point the result *is* exactly representable |
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2195 # adjust the exponent to get as close as possible to the ideal |
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2196 # exponent, if necessary |
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2197 str_xc = str(xc) |
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2198 if other._isinteger() and other._sign == 0: |
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2199 ideal_exponent = self._exp*int(other) |
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2200 zeros = min(xe-ideal_exponent, p-len(str_xc)) |
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2201 else: |
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2202 zeros = 0 |
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2203 return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) |
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2204 |
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2205 def __pow__(self, other, modulo=None, context=None): |
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2206 """Return self ** other [ % modulo]. |
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2207 |
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2208 With two arguments, compute self**other. |
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2209 |
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2210 With three arguments, compute (self**other) % modulo. For the |
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2211 three argument form, the following restrictions on the |
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2212 arguments hold: |
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2213 |
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2214 - all three arguments must be integral |
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2215 - other must be nonnegative |
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2216 - either self or other (or both) must be nonzero |
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2217 - modulo must be nonzero and must have at most p digits, |
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2218 where p is the context precision. |
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2219 |
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2220 If any of these restrictions is violated the InvalidOperation |
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2221 flag is raised. |
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2222 |
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2223 The result of pow(self, other, modulo) is identical to the |
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2224 result that would be obtained by computing (self**other) % |
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2225 modulo with unbounded precision, but is computed more |
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2226 efficiently. It is always exact. |
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2227 """ |
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2228 |
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2229 if modulo is not None: |
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2230 return self._power_modulo(other, modulo, context) |
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2231 |
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2232 other = _convert_other(other) |
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2233 if other is NotImplemented: |
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2234 return other |
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2235 |
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2236 if context is None: |
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2237 context = getcontext() |
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2238 |
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2239 # either argument is a NaN => result is NaN |
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2240 ans = self._check_nans(other, context) |
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2241 if ans: |
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2242 return ans |
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2243 |
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2244 # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) |
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2245 if not other: |
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2246 if not self: |
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2247 return context._raise_error(InvalidOperation, '0 ** 0') |
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2248 else: |
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2249 return _One |
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2250 |
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2251 # result has sign 1 iff self._sign is 1 and other is an odd integer |
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2252 result_sign = 0 |
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2253 if self._sign == 1: |
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2254 if other._isinteger(): |
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2255 if not other._iseven(): |
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2256 result_sign = 1 |
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2257 else: |
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2258 # -ve**noninteger = NaN |
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2259 # (-0)**noninteger = 0**noninteger |
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2260 if self: |
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2261 return context._raise_error(InvalidOperation, |
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2262 'x ** y with x negative and y not an integer') |
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2263 # negate self, without doing any unwanted rounding |
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2264 self = self.copy_negate() |
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2265 |
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2266 # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity |
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2267 if not self: |
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2268 if other._sign == 0: |
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2269 return _dec_from_triple(result_sign, '0', 0) |
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2270 else: |
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2271 return _SignedInfinity[result_sign] |
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2272 |
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2273 # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 |
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2274 if self._isinfinity(): |
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2275 if other._sign == 0: |
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2276 return _SignedInfinity[result_sign] |
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2277 else: |
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2278 return _dec_from_triple(result_sign, '0', 0) |
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2279 |
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2280 # 1**other = 1, but the choice of exponent and the flags |
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2281 # depend on the exponent of self, and on whether other is a |
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2282 # positive integer, a negative integer, or neither |
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2283 if self == _One: |
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2284 if other._isinteger(): |
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2285 # exp = max(self._exp*max(int(other), 0), |
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2286 # 1-context.prec) but evaluating int(other) directly |
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2287 # is dangerous until we know other is small (other |
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2288 # could be 1e999999999) |
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2289 if other._sign == 1: |
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2290 multiplier = 0 |
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2291 elif other > context.prec: |
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2292 multiplier = context.prec |
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2293 else: |
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2294 multiplier = int(other) |
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2295 |
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2296 exp = self._exp * multiplier |
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2297 if exp < 1-context.prec: |
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2298 exp = 1-context.prec |
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2299 context._raise_error(Rounded) |
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2300 else: |
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2301 context._raise_error(Inexact) |
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2302 context._raise_error(Rounded) |
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2303 exp = 1-context.prec |
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2304 |
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2305 return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) |
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2306 |
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2307 # compute adjusted exponent of self |
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2308 self_adj = self.adjusted() |
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2309 |
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2310 # self ** infinity is infinity if self > 1, 0 if self < 1 |
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2311 # self ** -infinity is infinity if self < 1, 0 if self > 1 |
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2312 if other._isinfinity(): |
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2313 if (other._sign == 0) == (self_adj < 0): |
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2314 return _dec_from_triple(result_sign, '0', 0) |
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2315 else: |
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2316 return _SignedInfinity[result_sign] |
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2317 |
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2318 # from here on, the result always goes through the call |
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2319 # to _fix at the end of this function. |
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2320 ans = None |
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2321 exact = False |
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2322 |
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2323 # crude test to catch cases of extreme overflow/underflow. If |
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2324 # log10(self)*other >= 10**bound and bound >= len(str(Emax)) |
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2325 # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence |
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2326 # self**other >= 10**(Emax+1), so overflow occurs. The test |
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2327 # for underflow is similar. |
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2328 bound = self._log10_exp_bound() + other.adjusted() |
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2329 if (self_adj >= 0) == (other._sign == 0): |
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2330 # self > 1 and other +ve, or self < 1 and other -ve |
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2331 # possibility of overflow |
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2332 if bound >= len(str(context.Emax)): |
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2333 ans = _dec_from_triple(result_sign, '1', context.Emax+1) |
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2334 else: |
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2335 # self > 1 and other -ve, or self < 1 and other +ve |
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2336 # possibility of underflow to 0 |
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2337 Etiny = context.Etiny() |
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2338 if bound >= len(str(-Etiny)): |
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2339 ans = _dec_from_triple(result_sign, '1', Etiny-1) |
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2340 |
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2341 # try for an exact result with precision +1 |
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2342 if ans is None: |
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2343 ans = self._power_exact(other, context.prec + 1) |
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2344 if ans is not None: |
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2345 if result_sign == 1: |
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2346 ans = _dec_from_triple(1, ans._int, ans._exp) |
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2347 exact = True |
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2348 |
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2349 # usual case: inexact result, x**y computed directly as exp(y*log(x)) |
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2350 if ans is None: |
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2351 p = context.prec |
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2352 x = _WorkRep(self) |
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2353 xc, xe = x.int, x.exp |
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2354 y = _WorkRep(other) |
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2355 yc, ye = y.int, y.exp |
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2356 if y.sign == 1: |
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2357 yc = -yc |
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2358 |
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2359 # compute correctly rounded result: start with precision +3, |
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2360 # then increase precision until result is unambiguously roundable |
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2361 extra = 3 |
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2362 while True: |
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2363 coeff, exp = _dpower(xc, xe, yc, ye, p+extra) |
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2364 if coeff % (5*10**(len(str(coeff))-p-1)): |
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2365 break |
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2366 extra += 3 |
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2367 |
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2368 ans = _dec_from_triple(result_sign, str(coeff), exp) |
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2369 |
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2370 # unlike exp, ln and log10, the power function respects the |
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2371 # rounding mode; no need to switch to ROUND_HALF_EVEN here |
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2372 |
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2373 # There's a difficulty here when 'other' is not an integer and |
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2374 # the result is exact. In this case, the specification |
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2375 # requires that the Inexact flag be raised (in spite of |
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2376 # exactness), but since the result is exact _fix won't do this |
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2377 # for us. (Correspondingly, the Underflow signal should also |
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2378 # be raised for subnormal results.) We can't directly raise |
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2379 # these signals either before or after calling _fix, since |
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2380 # that would violate the precedence for signals. So we wrap |
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2381 # the ._fix call in a temporary context, and reraise |
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2382 # afterwards. |
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2383 if exact and not other._isinteger(): |
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2384 # pad with zeros up to length context.prec+1 if necessary; this |
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2385 # ensures that the Rounded signal will be raised. |
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2386 if len(ans._int) <= context.prec: |
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2387 expdiff = context.prec + 1 - len(ans._int) |
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2388 ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, |
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2389 ans._exp-expdiff) |
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2390 |
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2391 # create a copy of the current context, with cleared flags/traps |
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2392 newcontext = context.copy() |
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2393 newcontext.clear_flags() |
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2394 for exception in _signals: |
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2395 newcontext.traps[exception] = 0 |
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2396 |
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2397 # round in the new context |
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2398 ans = ans._fix(newcontext) |
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2399 |
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2400 # raise Inexact, and if necessary, Underflow |
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2401 newcontext._raise_error(Inexact) |
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2402 if newcontext.flags[Subnormal]: |
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2403 newcontext._raise_error(Underflow) |
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2404 |
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2405 # propagate signals to the original context; _fix could |
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2406 # have raised any of Overflow, Underflow, Subnormal, |
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2407 # Inexact, Rounded, Clamped. Overflow needs the correct |
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2408 # arguments. Note that the order of the exceptions is |
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2409 # important here. |
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2410 if newcontext.flags[Overflow]: |
|
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|
2411 context._raise_error(Overflow, 'above Emax', ans._sign) |
|
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|
2412 for exception in Underflow, Subnormal, Inexact, Rounded, Clamped: |
|
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|
2413 if newcontext.flags[exception]: |
|
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|
2414 context._raise_error(exception) |
|
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2415 |
|
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2416 else: |
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|
2417 ans = ans._fix(context) |
|
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2418 |
|
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|
2419 return ans |
|
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2420 |
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|
2421 def __rpow__(self, other, context=None): |
|
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|
2422 """Swaps self/other and returns __pow__.""" |
|
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|
2423 other = _convert_other(other) |
|
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|
2424 if other is NotImplemented: |
|
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* Fix decimal's handling of foreign types. Now returns NotImplemented
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|
2425 return other |
|
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|
2426 return other.__pow__(self, context=context) |
|
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2427 |
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|
2428 def normalize(self, context=None): |
|
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2429 """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" |
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2430 |
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2431 if context is None: |
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2432 context = getcontext() |
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2433 |
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2434 if self._is_special: |
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2435 ans = self._check_nans(context=context) |
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2436 if ans: |
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|
2437 return ans |
|
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2438 |
| 33695 | 2439 dup = self._fix(context) |
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2440 if dup._isinfinity(): |
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|
2441 return dup |
|
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2442 |
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2443 if not dup: |
|
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2444 return _dec_from_triple(dup._sign, '0', 0) |
|
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Mark Dickinson <dickinsm@gmail.com>
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|
2445 exp_max = [context.Emax, context.Etop()][context.clamp] |
|
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2446 end = len(dup._int) |
|
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2447 exp = dup._exp |
|
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2448 while dup._int[end-1] == '0' and exp < exp_max: |
|
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|
2449 exp += 1 |
|
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2450 end -= 1 |
|
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2451 return _dec_from_triple(dup._sign, dup._int[:end], exp) |
|
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2452 |
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|
2453 def quantize(self, exp, rounding=None, context=None, watchexp=True): |
|
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|
2454 """Quantize self so its exponent is the same as that of exp. |
|
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|
2455 |
|
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|
2456 Similar to self._rescale(exp._exp) but with error checking. |
|
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|
2457 """ |
|
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|
2458 exp = _convert_other(exp, raiseit=True) |
|
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|
2459 |
|
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|
2460 if context is None: |
|
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|
2461 context = getcontext() |
|
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|
2462 if rounding is None: |
|
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|
2463 rounding = context.rounding |
|
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|
2464 |
|
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|
2465 if self._is_special or exp._is_special: |
|
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|
2466 ans = self._check_nans(exp, context) |
|
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|
2467 if ans: |
|
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|
2468 return ans |
|
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diff
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|
2469 |
|
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|
2470 if exp._isinfinity() or self._isinfinity(): |
|
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|
2471 if exp._isinfinity() and self._isinfinity(): |
|
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|
2472 return Decimal(self) # if both are inf, it is OK |
|
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|
2473 return context._raise_error(InvalidOperation, |
|
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|
2474 'quantize with one INF') |
|
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|
2475 |
|
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|
2476 # if we're not watching exponents, do a simple rescale |
|
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|
2477 if not watchexp: |
|
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|
2478 ans = self._rescale(exp._exp, rounding) |
|
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|
2479 # raise Inexact and Rounded where appropriate |
|
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|
2480 if ans._exp > self._exp: |
|
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|
2481 context._raise_error(Rounded) |
|
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|
2482 if ans != self: |
|
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|
2483 context._raise_error(Inexact) |
|
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|
2484 return ans |
|
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|
2485 |
|
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|
2486 # exp._exp should be between Etiny and Emax |
|
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|
2487 if not (context.Etiny() <= exp._exp <= context.Emax): |
|
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|
2488 return context._raise_error(InvalidOperation, |
|
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|
2489 'target exponent out of bounds in quantize') |
|
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|
2490 |
|
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|
2491 if not self: |
|
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|
2492 ans = _dec_from_triple(self._sign, '0', exp._exp) |
|
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|
2493 return ans._fix(context) |
|
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|
2494 |
|
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|
2495 self_adjusted = self.adjusted() |
|
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|
2496 if self_adjusted > context.Emax: |
|
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|
2497 return context._raise_error(InvalidOperation, |
|
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|
2498 'exponent of quantize result too large for current context') |
|
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|
2499 if self_adjusted - exp._exp + 1 > context.prec: |
|
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|
2500 return context._raise_error(InvalidOperation, |
|
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|
2501 'quantize result has too many digits for current context') |
|
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|
2502 |
|
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|
2503 ans = self._rescale(exp._exp, rounding) |
|
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|
2504 if ans.adjusted() > context.Emax: |
|
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|
2505 return context._raise_error(InvalidOperation, |
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|
2506 'exponent of quantize result too large for current context') |
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|
2507 if len(ans._int) > context.prec: |
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|
2508 return context._raise_error(InvalidOperation, |
|
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|
2509 'quantize result has too many digits for current context') |
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2510 |
|
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|
2511 # raise appropriate flags |
|
61214
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|
2512 if ans and ans.adjusted() < context.Emin: |
|
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|
2513 context._raise_error(Subnormal) |
|
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2514 if ans._exp > self._exp: |
|
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|
2515 if ans != self: |
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2516 context._raise_error(Inexact) |
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2517 context._raise_error(Rounded) |
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2518 |
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2519 # call to fix takes care of any necessary folddown, and |
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2520 # signals Clamped if necessary |
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2521 ans = ans._fix(context) |
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2522 return ans |
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2523 |
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2524 def same_quantum(self, other): |
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2525 """Return True if self and other have the same exponent; otherwise |
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2526 return False. |
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2527 |
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2528 If either operand is a special value, the following rules are used: |
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2529 * return True if both operands are infinities |
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2530 * return True if both operands are NaNs |
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2531 * otherwise, return False. |
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2532 """ |
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2533 other = _convert_other(other, raiseit=True) |
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2534 if self._is_special or other._is_special: |
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2535 return (self.is_nan() and other.is_nan() or |
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2536 self.is_infinite() and other.is_infinite()) |
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2537 return self._exp == other._exp |
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2538 |
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2539 def _rescale(self, exp, rounding): |
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2540 """Rescale self so that the exponent is exp, either by padding with zeros |
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2541 or by truncating digits, using the given rounding mode. |
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2542 |
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2543 Specials are returned without change. This operation is |
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2544 quiet: it raises no flags, and uses no information from the |
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2545 context. |
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2546 |
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2547 exp = exp to scale to (an integer) |
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2548 rounding = rounding mode |
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2549 """ |
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2550 if self._is_special: |
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2551 return Decimal(self) |
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2552 if not self: |
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2553 return _dec_from_triple(self._sign, '0', exp) |
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2554 |
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2555 if self._exp >= exp: |
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2556 # pad answer with zeros if necessary |
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2557 return _dec_from_triple(self._sign, |
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2558 self._int + '0'*(self._exp - exp), exp) |
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2559 |
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2560 # too many digits; round and lose data. If self.adjusted() < |
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2561 # exp-1, replace self by 10**(exp-1) before rounding |
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2562 digits = len(self._int) + self._exp - exp |
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2563 if digits < 0: |
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2564 self = _dec_from_triple(self._sign, '1', exp-1) |
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2565 digits = 0 |
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2566 this_function = self._pick_rounding_function[rounding] |
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2567 changed = this_function(self, digits) |
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2568 coeff = self._int[:digits] or '0' |
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2569 if changed == 1: |
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2570 coeff = str(int(coeff)+1) |
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2571 return _dec_from_triple(self._sign, coeff, exp) |
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2572 |
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2573 def _round(self, places, rounding): |
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2574 """Round a nonzero, nonspecial Decimal to a fixed number of |
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2575 significant figures, using the given rounding mode. |
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2576 |
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2577 Infinities, NaNs and zeros are returned unaltered. |
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2578 |
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2579 This operation is quiet: it raises no flags, and uses no |
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2580 information from the context. |
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2581 |
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2582 """ |
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2583 if places <= 0: |
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2584 raise ValueError("argument should be at least 1 in _round") |
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2585 if self._is_special or not self: |
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2586 return Decimal(self) |
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2587 ans = self._rescale(self.adjusted()+1-places, rounding) |
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2588 # it can happen that the rescale alters the adjusted exponent; |
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2589 # for example when rounding 99.97 to 3 significant figures. |
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2590 # When this happens we end up with an extra 0 at the end of |
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2591 # the number; a second rescale fixes this. |
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2592 if ans.adjusted() != self.adjusted(): |
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2593 ans = ans._rescale(ans.adjusted()+1-places, rounding) |
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2594 return ans |
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2595 |
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2596 def to_integral_exact(self, rounding=None, context=None): |
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2597 """Rounds to a nearby integer. |
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2598 |
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2599 If no rounding mode is specified, take the rounding mode from |
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2600 the context. This method raises the Rounded and Inexact flags |
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2601 when appropriate. |
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2602 |
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2603 See also: to_integral_value, which does exactly the same as |
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2604 this method except that it doesn't raise Inexact or Rounded. |
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2605 """ |
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2606 if self._is_special: |
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2607 ans = self._check_nans(context=context) |
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2608 if ans: |
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2609 return ans |
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2610 return Decimal(self) |
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2611 if self._exp >= 0: |
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2612 return Decimal(self) |
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2613 if not self: |
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2614 return _dec_from_triple(self._sign, '0', 0) |
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2615 if context is None: |
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2616 context = getcontext() |
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2617 if rounding is None: |
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2618 rounding = context.rounding |
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2619 ans = self._rescale(0, rounding) |
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2620 if ans != self: |
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2621 context._raise_error(Inexact) |
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2622 context._raise_error(Rounded) |
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2623 return ans |
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2624 |
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2625 def to_integral_value(self, rounding=None, context=None): |
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2626 """Rounds to the nearest integer, without raising inexact, rounded.""" |
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2627 if context is None: |
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2628 context = getcontext() |
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2629 if rounding is None: |
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2630 rounding = context.rounding |
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2631 if self._is_special: |
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2632 ans = self._check_nans(context=context) |
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2633 if ans: |
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2634 return ans |
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2635 return Decimal(self) |
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2636 if self._exp >= 0: |
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2637 return Decimal(self) |
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2638 else: |
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2639 return self._rescale(0, rounding) |
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2640 |
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2641 # the method name changed, but we provide also the old one, for compatibility |
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2642 to_integral = to_integral_value |
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2643 |
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2644 def sqrt(self, context=None): |
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2645 """Return the square root of self.""" |
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2646 if context is None: |
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2647 context = getcontext() |
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2648 |
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2649 if self._is_special: |
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2650 ans = self._check_nans(context=context) |
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2651 if ans: |
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2652 return ans |
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2653 |
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2654 if self._isinfinity() and self._sign == 0: |
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2655 return Decimal(self) |
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2656 |
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2657 if not self: |
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2658 # exponent = self._exp // 2. sqrt(-0) = -0 |
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2659 ans = _dec_from_triple(self._sign, '0', self._exp // 2) |
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2660 return ans._fix(context) |
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2661 |
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2662 if self._sign == 1: |
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2663 return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') |
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2664 |
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2665 # At this point self represents a positive number. Let p be |
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2666 # the desired precision and express self in the form c*100**e |
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2667 # with c a positive real number and e an integer, c and e |
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2668 # being chosen so that 100**(p-1) <= c < 100**p. Then the |
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2669 # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) |
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2670 # <= sqrt(c) < 10**p, so the closest representable Decimal at |
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2671 # precision p is n*10**e where n = round_half_even(sqrt(c)), |
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2672 # the closest integer to sqrt(c) with the even integer chosen |
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2673 # in the case of a tie. |
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2674 # |
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2675 # To ensure correct rounding in all cases, we use the |
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2676 # following trick: we compute the square root to an extra |
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2677 # place (precision p+1 instead of precision p), rounding down. |
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2678 # Then, if the result is inexact and its last digit is 0 or 5, |
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2679 # we increase the last digit to 1 or 6 respectively; if it's |
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2680 # exact we leave the last digit alone. Now the final round to |
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2681 # p places (or fewer in the case of underflow) will round |
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2682 # correctly and raise the appropriate flags. |
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2683 |
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2684 # use an extra digit of precision |
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2685 prec = context.prec+1 |
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2686 |
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2687 # write argument in the form c*100**e where e = self._exp//2 |
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2688 # is the 'ideal' exponent, to be used if the square root is |
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2689 # exactly representable. l is the number of 'digits' of c in |
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2690 # base 100, so that 100**(l-1) <= c < 100**l. |
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2691 op = _WorkRep(self) |
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2692 e = op.exp >> 1 |
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2693 if op.exp & 1: |
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2694 c = op.int * 10 |
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2695 l = (len(self._int) >> 1) + 1 |
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2696 else: |
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2697 c = op.int |
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2698 l = len(self._int)+1 >> 1 |
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2699 |
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2700 # rescale so that c has exactly prec base 100 'digits' |
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2701 shift = prec-l |
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2702 if shift >= 0: |
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2703 c *= 100**shift |
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2704 exact = True |
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2705 else: |
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2706 c, remainder = divmod(c, 100**-shift) |
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2707 exact = not remainder |
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2708 e -= shift |
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2709 |
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2710 # find n = floor(sqrt(c)) using Newton's method |
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2711 n = 10**prec |
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2712 while True: |
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2713 q = c//n |
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2714 if n <= q: |
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2715 break |
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2716 else: |
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2717 n = n + q >> 1 |
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2718 exact = exact and n*n == c |
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2719 |
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2720 if exact: |
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2721 # result is exact; rescale to use ideal exponent e |
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2722 if shift >= 0: |
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2723 # assert n % 10**shift == 0 |
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2724 n //= 10**shift |
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2725 else: |
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2726 n *= 10**-shift |
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2727 e += shift |
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2728 else: |
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2729 # result is not exact; fix last digit as described above |
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2730 if n % 5 == 0: |
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2731 n += 1 |
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2732 |
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2733 ans = _dec_from_triple(0, str(n), e) |
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2734 |
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2735 # round, and fit to current context |
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2736 context = context._shallow_copy() |
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2737 rounding = context._set_rounding(ROUND_HALF_EVEN) |
| 33695 | 2738 ans = ans._fix(context) |
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2739 context.rounding = rounding |
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2740 |
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2741 return ans |
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2742 |
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2743 def max(self, other, context=None): |
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2744 """Returns the larger value. |
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2745 |
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2746 Like max(self, other) except if one is not a number, returns |
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2747 NaN (and signals if one is sNaN). Also rounds. |
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2748 """ |
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2749 other = _convert_other(other, raiseit=True) |
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2750 |
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2751 if context is None: |
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2752 context = getcontext() |
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2753 |
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2754 if self._is_special or other._is_special: |
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2755 # If one operand is a quiet NaN and the other is number, then the |
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2756 # number is always returned |
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2757 sn = self._isnan() |
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2758 on = other._isnan() |
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2759 if sn or on: |
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2760 if on == 1 and sn == 0: |
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2761 return self._fix(context) |
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2762 if sn == 1 and on == 0: |
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2763 return other._fix(context) |
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2764 return self._check_nans(other, context) |
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2765 |
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2766 c = self._cmp(other) |
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2767 if c == 0: |
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2768 # If both operands are finite and equal in numerical value |
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2769 # then an ordering is applied: |
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2770 # |
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2771 # If the signs differ then max returns the operand with the |
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2772 # positive sign and min returns the operand with the negative sign |
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2773 # |
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2774 # If the signs are the same then the exponent is used to select |
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2775 # the result. This is exactly the ordering used in compare_total. |
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2776 c = self.compare_total(other) |
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2777 |
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2778 if c == -1: |
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2779 ans = other |
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2780 else: |
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2781 ans = self |
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2782 |
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2783 return ans._fix(context) |
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2784 |
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2785 def min(self, other, context=None): |
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2786 """Returns the smaller value. |
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2787 |
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2788 Like min(self, other) except if one is not a number, returns |
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2789 NaN (and signals if one is sNaN). Also rounds. |
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2790 """ |
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2791 other = _convert_other(other, raiseit=True) |
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2792 |
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2793 if context is None: |
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2794 context = getcontext() |
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2795 |
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2796 if self._is_special or other._is_special: |
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2797 # If one operand is a quiet NaN and the other is number, then the |
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2798 # number is always returned |
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2799 sn = self._isnan() |
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2800 on = other._isnan() |
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2801 if sn or on: |
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2802 if on == 1 and sn == 0: |
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2803 return self._fix(context) |
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2804 if sn == 1 and on == 0: |
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2805 return other._fix(context) |
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2806 return self._check_nans(other, context) |
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2807 |
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2808 c = self._cmp(other) |
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2809 if c == 0: |
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2810 c = self.compare_total(other) |
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2811 |
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2812 if c == -1: |
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2813 ans = self |
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2814 else: |
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2815 ans = other |
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2816 |
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2817 return ans._fix(context) |
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2818 |
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2819 def _isinteger(self): |
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2820 """Returns whether self is an integer""" |
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2821 if self._is_special: |
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2822 return False |
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2823 if self._exp >= 0: |
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2824 return True |
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2825 rest = self._int[self._exp:] |
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2826 return rest == '0'*len(rest) |
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2827 |
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2828 def _iseven(self): |
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2829 """Returns True if self is even. Assumes self is an integer.""" |
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2830 if not self or self._exp > 0: |
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2831 return True |
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2832 return self._int[-1+self._exp] in '02468' |
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2833 |
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2834 def adjusted(self): |
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2835 """Return the adjusted exponent of self""" |
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2836 try: |
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2837 return self._exp + len(self._int) - 1 |
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2838 # If NaN or Infinity, self._exp is string |
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2839 except TypeError: |
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2840 return 0 |
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2841 |
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2842 def canonical(self, context=None): |
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2843 """Returns the same Decimal object. |
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2844 |
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2845 As we do not have different encodings for the same number, the |
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2846 received object already is in its canonical form. |
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2847 """ |
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2848 return self |
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2849 |
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2850 def compare_signal(self, other, context=None): |
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2851 """Compares self to the other operand numerically. |
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2852 |
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2853 It's pretty much like compare(), but all NaNs signal, with signaling |
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2854 NaNs taking precedence over quiet NaNs. |
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2855 """ |
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2856 other = _convert_other(other, raiseit = True) |
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2857 ans = self._compare_check_nans(other, context) |
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2858 if ans: |
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2859 return ans |
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2860 return self.compare(other, context=context) |
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2861 |
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2862 def compare_total(self, other): |
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2863 """Compares self to other using the abstract representations. |
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2864 |
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2865 This is not like the standard compare, which use their numerical |
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2866 value. Note that a total ordering is defined for all possible abstract |
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2867 representations. |
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2868 """ |
|
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2869 other = _convert_other(other, raiseit=True) |
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2870 |
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2871 # if one is negative and the other is positive, it's easy |
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2872 if self._sign and not other._sign: |
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2873 return _NegativeOne |
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2874 if not self._sign and other._sign: |
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2875 return _One |
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2876 sign = self._sign |
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2877 |
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2878 # let's handle both NaN types |
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2879 self_nan = self._isnan() |
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2880 other_nan = other._isnan() |
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2881 if self_nan or other_nan: |
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2882 if self_nan == other_nan: |
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2883 # compare payloads as though they're integers |
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2884 self_key = len(self._int), self._int |
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2885 other_key = len(other._int), other._int |
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2886 if self_key < other_key: |
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2887 if sign: |
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2888 return _One |
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2889 else: |
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2890 return _NegativeOne |
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2891 if self_key > other_key: |
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2892 if sign: |
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2893 return _NegativeOne |
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2894 else: |
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2895 return _One |
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2896 return _Zero |
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2897 |
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|
2898 if sign: |
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2899 if self_nan == 1: |
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2900 return _NegativeOne |
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43400
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2901 if other_nan == 1: |
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2902 return _One |
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2903 if self_nan == 2: |
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2904 return _NegativeOne |
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2905 if other_nan == 2: |
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2906 return _One |
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2907 else: |
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2908 if self_nan == 1: |
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2909 return _One |
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2910 if other_nan == 1: |
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2911 return _NegativeOne |
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2912 if self_nan == 2: |
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2913 return _One |
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2914 if other_nan == 2: |
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2915 return _NegativeOne |
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43400
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2916 |
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2917 if self < other: |
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2918 return _NegativeOne |
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2919 if self > other: |
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2920 return _One |
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2921 |
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2922 if self._exp < other._exp: |
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2923 if sign: |
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2924 return _One |
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43400
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2925 else: |
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2926 return _NegativeOne |
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2927 if self._exp > other._exp: |
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2928 if sign: |
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2929 return _NegativeOne |
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2930 else: |
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2931 return _One |
|
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2932 return _Zero |
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2933 |
|
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2934 |
|
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|
2935 def compare_total_mag(self, other): |
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2936 """Compares self to other using abstract repr., ignoring sign. |
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2937 |
|
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2938 Like compare_total, but with operand's sign ignored and assumed to be 0. |
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2939 """ |
|
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2940 other = _convert_other(other, raiseit=True) |
|
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2941 |
|
43400
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|
2942 s = self.copy_abs() |
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2943 o = other.copy_abs() |
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2944 return s.compare_total(o) |
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|
2945 |
|
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2946 def copy_abs(self): |
|
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|
2947 """Returns a copy with the sign set to 0. """ |
|
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2948 return _dec_from_triple(0, self._int, self._exp, self._is_special) |
|
43400
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|
2949 |
|
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2950 def copy_negate(self): |
|
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|
2951 """Returns a copy with the sign inverted.""" |
|
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|
2952 if self._sign: |
|
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2953 return _dec_from_triple(0, self._int, self._exp, self._is_special) |
|
43400
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2954 else: |
|
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2955 return _dec_from_triple(1, self._int, self._exp, self._is_special) |
|
43400
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|
2956 |
|
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|
2957 def copy_sign(self, other): |
|
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|
2958 """Returns self with the sign of other.""" |
|
58936
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2959 other = _convert_other(other, raiseit=True) |
|
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2960 return _dec_from_triple(other._sign, self._int, |
|
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|
2961 self._exp, self._is_special) |
|
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|
2962 |
|
1bac386c17cc
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|
2963 def exp(self, context=None): |
|
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|
2964 """Returns e ** self.""" |
|
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|
2965 |
|
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|
2966 if context is None: |
|
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|
2967 context = getcontext() |
|
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2968 |
|
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|
2969 # exp(NaN) = NaN |
|
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|
2970 ans = self._check_nans(context=context) |
|
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|
2971 if ans: |
|
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|
2972 return ans |
|
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|
2973 |
|
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|
2974 # exp(-Infinity) = 0 |
|
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|
2975 if self._isinfinity() == -1: |
|
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|
2976 return _Zero |
|
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2977 |
|
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|
2978 # exp(0) = 1 |
|
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2979 if not self: |
|
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|
2980 return _One |
|
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|
2981 |
|
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|
2982 # exp(Infinity) = Infinity |
|
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2983 if self._isinfinity() == 1: |
|
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|
2984 return Decimal(self) |
|
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2985 |
|
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2986 # the result is now guaranteed to be inexact (the true |
|
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2987 # mathematical result is transcendental). There's no need to |
|
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2988 # raise Rounded and Inexact here---they'll always be raised as |
|
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2989 # a result of the call to _fix. |
|
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|
2990 p = context.prec |
|
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|
2991 adj = self.adjusted() |
|
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2992 |
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2993 # we only need to do any computation for quite a small range |
|
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2994 # of adjusted exponents---for example, -29 <= adj <= 10 for |
|
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2995 # the default context. For smaller exponent the result is |
|
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2996 # indistinguishable from 1 at the given precision, while for |
|
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2997 # larger exponent the result either overflows or underflows. |
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2998 if self._sign == 0 and adj > len(str((context.Emax+1)*3)): |
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2999 # overflow |
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3000 ans = _dec_from_triple(0, '1', context.Emax+1) |
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3001 elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): |
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3002 # underflow to 0 |
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3003 ans = _dec_from_triple(0, '1', context.Etiny()-1) |
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3004 elif self._sign == 0 and adj < -p: |
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3005 # p+1 digits; final round will raise correct flags |
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3006 ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) |
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3007 elif self._sign == 1 and adj < -p-1: |
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3008 # p+1 digits; final round will raise correct flags |
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3009 ans = _dec_from_triple(0, '9'*(p+1), -p-1) |
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3010 # general case |
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3011 else: |
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3012 op = _WorkRep(self) |
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3013 c, e = op.int, op.exp |
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3014 if op.sign == 1: |
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3015 c = -c |
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3016 |
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3017 # compute correctly rounded result: increase precision by |
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3018 # 3 digits at a time until we get an unambiguously |
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3019 # roundable result |
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3020 extra = 3 |
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3021 while True: |
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3022 coeff, exp = _dexp(c, e, p+extra) |
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3023 if coeff % (5*10**(len(str(coeff))-p-1)): |
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3024 break |
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3025 extra += 3 |
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3026 |
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3027 ans = _dec_from_triple(0, str(coeff), exp) |
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3028 |
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3029 # at this stage, ans should round correctly with *any* |
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3030 # rounding mode, not just with ROUND_HALF_EVEN |
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3031 context = context._shallow_copy() |
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3032 rounding = context._set_rounding(ROUND_HALF_EVEN) |
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3033 ans = ans._fix(context) |
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3034 context.rounding = rounding |
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3035 |
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3036 return ans |
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3037 |
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3038 def is_canonical(self): |
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3039 """Return True if self is canonical; otherwise return False. |
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3040 |
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3041 Currently, the encoding of a Decimal instance is always |
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3042 canonical, so this method returns True for any Decimal. |
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3043 """ |
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3044 return True |
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3045 |
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3046 def is_finite(self): |
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3047 """Return True if self is finite; otherwise return False. |
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3048 |
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3049 A Decimal instance is considered finite if it is neither |
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3050 infinite nor a NaN. |
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3051 """ |
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3052 return not self._is_special |
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3053 |
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3054 def is_infinite(self): |
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3055 """Return True if self is infinite; otherwise return False.""" |
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3056 return self._exp == 'F' |
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3057 |
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3058 def is_nan(self): |
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3059 """Return True if self is a qNaN or sNaN; otherwise return False.""" |
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3060 return self._exp in ('n', 'N') |
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3061 |
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3062 def is_normal(self, context=None): |
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3063 """Return True if self is a normal number; otherwise return False.""" |
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3064 if self._is_special or not self: |
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3065 return False |
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3066 if context is None: |
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3067 context = getcontext() |
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3068 return context.Emin <= self.adjusted() |
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3069 |
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3070 def is_qnan(self): |
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3071 """Return True if self is a quiet NaN; otherwise return False.""" |
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3072 return self._exp == 'n' |
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3073 |
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3074 def is_signed(self): |
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3075 """Return True if self is negative; otherwise return False.""" |
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3076 return self._sign == 1 |
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3077 |
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3078 def is_snan(self): |
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3079 """Return True if self is a signaling NaN; otherwise return False.""" |
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3080 return self._exp == 'N' |
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3081 |
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3082 def is_subnormal(self, context=None): |
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3083 """Return True if self is subnormal; otherwise return False.""" |
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3084 if self._is_special or not self: |
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3085 return False |
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3086 if context is None: |
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3087 context = getcontext() |
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3088 return self.adjusted() < context.Emin |
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3089 |
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3090 def is_zero(self): |
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3091 """Return True if self is a zero; otherwise return False.""" |
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3092 return not self._is_special and self._int == '0' |
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3093 |
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3094 def _ln_exp_bound(self): |
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3095 """Compute a lower bound for the adjusted exponent of self.ln(). |
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3096 In other words, compute r such that self.ln() >= 10**r. Assumes |
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3097 that self is finite and positive and that self != 1. |
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3098 """ |
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3099 |
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3100 # for 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 |
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3101 adj = self._exp + len(self._int) - 1 |
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3102 if adj >= 1: |
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3103 # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) |
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3104 return len(str(adj*23//10)) - 1 |
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3105 if adj <= -2: |
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3106 # argument <= 0.1 |
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3107 return len(str((-1-adj)*23//10)) - 1 |
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3108 op = _WorkRep(self) |
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3109 c, e = op.int, op.exp |
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3110 if adj == 0: |
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3111 # 1 < self < 10 |
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3112 num = str(c-10**-e) |
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3113 den = str(c) |
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3114 return len(num) - len(den) - (num < den) |
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3115 # adj == -1, 0.1 <= self < 1 |
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3116 return e + len(str(10**-e - c)) - 1 |
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3117 |
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3118 |
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3119 def ln(self, context=None): |
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3120 """Returns the natural (base e) logarithm of self.""" |
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3121 |
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3122 if context is None: |
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3123 context = getcontext() |
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3124 |
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3125 # ln(NaN) = NaN |
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3126 ans = self._check_nans(context=context) |
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3127 if ans: |
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3128 return ans |
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3129 |
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3130 # ln(0.0) == -Infinity |
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3131 if not self: |
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3132 return _NegativeInfinity |
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3133 |
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3134 # ln(Infinity) = Infinity |
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3135 if self._isinfinity() == 1: |
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3136 return _Infinity |
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3137 |
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3138 # ln(1.0) == 0.0 |
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3139 if self == _One: |
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3140 return _Zero |
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3141 |
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3142 # ln(negative) raises InvalidOperation |
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3143 if self._sign == 1: |
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3144 return context._raise_error(InvalidOperation, |
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3145 'ln of a negative value') |
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3146 |
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3147 # result is irrational, so necessarily inexact |
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3148 op = _WorkRep(self) |
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3149 c, e = op.int, op.exp |
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3150 p = context.prec |
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3151 |
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3152 # correctly rounded result: repeatedly increase precision by 3 |
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3153 # until we get an unambiguously roundable result |
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3154 places = p - self._ln_exp_bound() + 2 # at least p+3 places |
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3155 while True: |
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3156 coeff = _dlog(c, e, places) |
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3157 # assert len(str(abs(coeff)))-p >= 1 |
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3158 if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
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3159 break |
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3160 places += 3 |
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3161 ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
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3162 |
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3163 context = context._shallow_copy() |
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3164 rounding = context._set_rounding(ROUND_HALF_EVEN) |
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3165 ans = ans._fix(context) |
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3166 context.rounding = rounding |
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3167 return ans |
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3168 |
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3169 def _log10_exp_bound(self): |
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3170 """Compute a lower bound for the adjusted exponent of self.log10(). |
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3171 In other words, find r such that self.log10() >= 10**r. |
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3172 Assumes that self is finite and positive and that self != 1. |
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3173 """ |
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3174 |
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3175 # For x >= 10 or x < 0.1 we only need a bound on the integer |
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3176 # part of log10(self), and this comes directly from the |
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3177 # exponent of x. For 0.1 <= x <= 10 we use the inequalities |
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3178 # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > |
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3179 # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 |
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3180 |
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3181 adj = self._exp + len(self._int) - 1 |
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3182 if adj >= 1: |
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3183 # self >= 10 |
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3184 return len(str(adj))-1 |
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3185 if adj <= -2: |
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3186 # self < 0.1 |
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3187 return len(str(-1-adj))-1 |
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3188 op = _WorkRep(self) |
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3189 c, e = op.int, op.exp |
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3190 if adj == 0: |
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3191 # 1 < self < 10 |
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3192 num = str(c-10**-e) |
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3193 den = str(231*c) |
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3194 return len(num) - len(den) - (num < den) + 2 |
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3195 # adj == -1, 0.1 <= self < 1 |
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3196 num = str(10**-e-c) |
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3197 return len(num) + e - (num < "231") - 1 |
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3198 |
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3199 def log10(self, context=None): |
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3200 """Returns the base 10 logarithm of self.""" |
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3201 |
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3202 if context is None: |
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3203 context = getcontext() |
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3204 |
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3205 # log10(NaN) = NaN |
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3206 ans = self._check_nans(context=context) |
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3207 if ans: |
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3208 return ans |
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3209 |
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3210 # log10(0.0) == -Infinity |
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3211 if not self: |
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3212 return _NegativeInfinity |
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3213 |
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3214 # log10(Infinity) = Infinity |
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3215 if self._isinfinity() == 1: |
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3216 return _Infinity |
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3217 |
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3218 # log10(negative or -Infinity) raises InvalidOperation |
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3219 if self._sign == 1: |
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3220 return context._raise_error(InvalidOperation, |
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3221 'log10 of a negative value') |
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3222 |
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3223 # log10(10**n) = n |
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3224 if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): |
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3225 # answer may need rounding |
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3226 ans = Decimal(self._exp + len(self._int) - 1) |
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3227 else: |
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3228 # result is irrational, so necessarily inexact |
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3229 op = _WorkRep(self) |
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3230 c, e = op.int, op.exp |
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3231 p = context.prec |
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3232 |
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3233 # correctly rounded result: repeatedly increase precision |
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3234 # until result is unambiguously roundable |
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3235 places = p-self._log10_exp_bound()+2 |
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3236 while True: |
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3237 coeff = _dlog10(c, e, places) |
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3238 # assert len(str(abs(coeff)))-p >= 1 |
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3239 if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
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3240 break |
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3241 places += 3 |
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3242 ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
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3243 |
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3244 context = context._shallow_copy() |
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3245 rounding = context._set_rounding(ROUND_HALF_EVEN) |
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3246 ans = ans._fix(context) |
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3247 context.rounding = rounding |
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3248 return ans |
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3249 |
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3250 def logb(self, context=None): |
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3251 """ Returns the exponent of the magnitude of self's MSD. |
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3252 |
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3253 The result is the integer which is the exponent of the magnitude |
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3254 of the most significant digit of self (as though it were truncated |
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3255 to a single digit while maintaining the value of that digit and |
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3256 without limiting the resulting exponent). |
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3257 """ |
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3258 # logb(NaN) = NaN |
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3259 ans = self._check_nans(context=context) |
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3260 if ans: |
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3261 return ans |
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3262 |
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3263 if context is None: |
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3264 context = getcontext() |
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3265 |
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3266 # logb(+/-Inf) = +Inf |
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3267 if self._isinfinity(): |
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3268 return _Infinity |
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3269 |
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3270 # logb(0) = -Inf, DivisionByZero |
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3271 if not self: |
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3272 return context._raise_error(DivisionByZero, 'logb(0)', 1) |
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3273 |
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3274 # otherwise, simply return the adjusted exponent of self, as a |
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3275 # Decimal. Note that no attempt is made to fit the result |
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3276 # into the current context. |
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3277 ans = Decimal(self.adjusted()) |
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3278 return ans._fix(context) |
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3279 |
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3280 def _islogical(self): |
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3281 """Return True if self is a logical operand. |
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3282 |
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44742
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3283 For being logical, it must be a finite number with a sign of 0, |
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3284 an exponent of 0, and a coefficient whose digits must all be |
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3285 either 0 or 1. |
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3286 """ |
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3287 if self._sign != 0 or self._exp != 0: |
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3288 return False |
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3289 for dig in self._int: |
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3290 if dig not in '01': |
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3291 return False |
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3292 return True |
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3293 |
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3294 def _fill_logical(self, context, opa, opb): |
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3295 dif = context.prec - len(opa) |
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3296 if dif > 0: |
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3297 opa = '0'*dif + opa |
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3298 elif dif < 0: |
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3299 opa = opa[-context.prec:] |
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3300 dif = context.prec - len(opb) |
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3301 if dif > 0: |
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3302 opb = '0'*dif + opb |
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3303 elif dif < 0: |
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3304 opb = opb[-context.prec:] |
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3305 return opa, opb |
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3306 |
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3307 def logical_and(self, other, context=None): |
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3308 """Applies an 'and' operation between self and other's digits.""" |
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3309 if context is None: |
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3310 context = getcontext() |
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3311 |
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3312 other = _convert_other(other, raiseit=True) |
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3313 |
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3314 if not self._islogical() or not other._islogical(): |
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3315 return context._raise_error(InvalidOperation) |
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3316 |
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3317 # fill to context.prec |
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3318 (opa, opb) = self._fill_logical(context, self._int, other._int) |
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3319 |
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|
3320 # make the operation, and clean starting zeroes |
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3321 result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) |
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3322 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
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3323 |
|
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3324 def logical_invert(self, context=None): |
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3325 """Invert all its digits.""" |
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3326 if context is None: |
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3327 context = getcontext() |
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3328 return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), |
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|
3329 context) |
|
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3330 |
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3331 def logical_or(self, other, context=None): |
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3332 """Applies an 'or' operation between self and other's digits.""" |
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3333 if context is None: |
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3334 context = getcontext() |
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3335 |
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3336 other = _convert_other(other, raiseit=True) |
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3337 |
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3338 if not self._islogical() or not other._islogical(): |
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3339 return context._raise_error(InvalidOperation) |
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3340 |
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3341 # fill to context.prec |
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3342 (opa, opb) = self._fill_logical(context, self._int, other._int) |
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3343 |
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3344 # make the operation, and clean starting zeroes |
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3345 result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)]) |
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3346 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
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3347 |
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|
3348 def logical_xor(self, other, context=None): |
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3349 """Applies an 'xor' operation between self and other's digits.""" |
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3350 if context is None: |
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3351 context = getcontext() |
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3352 |
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3353 other = _convert_other(other, raiseit=True) |
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3354 |
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3355 if not self._islogical() or not other._islogical(): |
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3356 return context._raise_error(InvalidOperation) |
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3357 |
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3358 # fill to context.prec |
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3359 (opa, opb) = self._fill_logical(context, self._int, other._int) |
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3360 |
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3361 # make the operation, and clean starting zeroes |
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3362 result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)]) |
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3363 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
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3364 |
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3365 def max_mag(self, other, context=None): |
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3366 """Compares the values numerically with their sign ignored.""" |
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3367 other = _convert_other(other, raiseit=True) |
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3368 |
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3369 if context is None: |
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3370 context = getcontext() |
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3371 |
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3372 if self._is_special or other._is_special: |
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3373 # If one operand is a quiet NaN and the other is number, then the |
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3374 # number is always returned |
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3375 sn = self._isnan() |
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3376 on = other._isnan() |
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3377 if sn or on: |
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3378 if on == 1 and sn == 0: |
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3379 return self._fix(context) |
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3380 if sn == 1 and on == 0: |
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3381 return other._fix(context) |
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3382 return self._check_nans(other, context) |
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3383 |
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3384 c = self.copy_abs()._cmp(other.copy_abs()) |
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3385 if c == 0: |
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3386 c = self.compare_total(other) |
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3387 |
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3388 if c == -1: |
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3389 ans = other |
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3390 else: |
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3391 ans = self |
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3392 |
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3393 return ans._fix(context) |
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3394 |
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3395 def min_mag(self, other, context=None): |
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3396 """Compares the values numerically with their sign ignored.""" |
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3397 other = _convert_other(other, raiseit=True) |
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3398 |
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3399 if context is None: |
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3400 context = getcontext() |
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3401 |
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3402 if self._is_special or other._is_special: |
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3403 # If one operand is a quiet NaN and the other is number, then the |
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3404 # number is always returned |
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3405 sn = self._isnan() |
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3406 on = other._isnan() |
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3407 if sn or on: |
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3408 if on == 1 and sn == 0: |
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3409 return self._fix(context) |
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3410 if sn == 1 and on == 0: |
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3411 return other._fix(context) |
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3412 return self._check_nans(other, context) |
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3413 |
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3414 c = self.copy_abs()._cmp(other.copy_abs()) |
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3415 if c == 0: |
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3416 c = self.compare_total(other) |
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3417 |
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3418 if c == -1: |
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3419 ans = self |
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3420 else: |
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3421 ans = other |
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3422 |
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3423 return ans._fix(context) |
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3424 |
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3425 def next_minus(self, context=None): |
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3426 """Returns the largest representable number smaller than itself.""" |
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3427 if context is None: |
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3428 context = getcontext() |
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3429 |
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3430 ans = self._check_nans(context=context) |
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3431 if ans: |
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3432 return ans |
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3433 |
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3434 if self._isinfinity() == -1: |
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3435 return _NegativeInfinity |
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3436 if self._isinfinity() == 1: |
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3437 return _dec_from_triple(0, '9'*context.prec, context.Etop()) |
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3438 |
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3439 context = context.copy() |
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3440 context._set_rounding(ROUND_FLOOR) |
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3441 context._ignore_all_flags() |
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3442 new_self = self._fix(context) |
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3443 if new_self != self: |
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3444 return new_self |
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3445 return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), |
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3446 context) |
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3447 |
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3448 def next_plus(self, context=None): |
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3449 """Returns the smallest representable number larger than itself.""" |
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3450 if context is None: |
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3451 context = getcontext() |
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3452 |
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3453 ans = self._check_nans(context=context) |
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3454 if ans: |
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3455 return ans |
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3456 |
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3457 if self._isinfinity() == 1: |
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3458 return _Infinity |
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3459 if self._isinfinity() == -1: |
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3460 return _dec_from_triple(1, '9'*context.prec, context.Etop()) |
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3461 |
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3462 context = context.copy() |
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3463 context._set_rounding(ROUND_CEILING) |
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3464 context._ignore_all_flags() |
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3465 new_self = self._fix(context) |
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3466 if new_self != self: |
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3467 return new_self |
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3468 return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), |
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3469 context) |
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3470 |
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3471 def next_toward(self, other, context=None): |
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3472 """Returns the number closest to self, in the direction towards other. |
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3473 |
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3474 The result is the closest representable number to self |
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3475 (excluding self) that is in the direction towards other, |
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3476 unless both have the same value. If the two operands are |
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3477 numerically equal, then the result is a copy of self with the |
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3478 sign set to be the same as the sign of other. |
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3479 """ |
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3480 other = _convert_other(other, raiseit=True) |
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3481 |
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3482 if context is None: |
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3483 context = getcontext() |
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3484 |
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3485 ans = self._check_nans(other, context) |
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3486 if ans: |
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3487 return ans |
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3488 |
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45244
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3489 comparison = self._cmp(other) |
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3490 if comparison == 0: |
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44025
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3491 return self.copy_sign(other) |
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3492 |
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3493 if comparison == -1: |
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3494 ans = self.next_plus(context) |
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3495 else: # comparison == 1 |
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3496 ans = self.next_minus(context) |
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3497 |
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3498 # decide which flags to raise using value of ans |
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3499 if ans._isinfinity(): |
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3500 context._raise_error(Overflow, |
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3501 'Infinite result from next_toward', |
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3502 ans._sign) |
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3503 context._raise_error(Inexact) |
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3504 context._raise_error(Rounded) |
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3505 elif ans.adjusted() < context.Emin: |
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3506 context._raise_error(Underflow) |
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3507 context._raise_error(Subnormal) |
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3508 context._raise_error(Inexact) |
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3509 context._raise_error(Rounded) |
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3510 # if precision == 1 then we don't raise Clamped for a |
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3511 # result 0E-Etiny. |
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3512 if not ans: |
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3513 context._raise_error(Clamped) |
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3514 |
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3515 return ans |
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3516 |
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3517 def number_class(self, context=None): |
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3518 """Returns an indication of the class of self. |
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3519 |
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3520 The class is one of the following strings: |
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3521 sNaN |
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3522 NaN |
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3523 -Infinity |
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3524 -Normal |
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3525 -Subnormal |
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3526 -Zero |
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3527 +Zero |
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3528 +Subnormal |
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3529 +Normal |
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3530 +Infinity |
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3531 """ |
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3532 if self.is_snan(): |
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3533 return "sNaN" |
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3534 if self.is_qnan(): |
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3535 return "NaN" |
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3536 inf = self._isinfinity() |
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3537 if inf == 1: |
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3538 return "+Infinity" |
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3539 if inf == -1: |
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3540 return "-Infinity" |
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3541 if self.is_zero(): |
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3542 if self._sign: |
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3543 return "-Zero" |
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3544 else: |
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3545 return "+Zero" |
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3546 if context is None: |
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3547 context = getcontext() |
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3548 if self.is_subnormal(context=context): |
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3549 if self._sign: |
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3550 return "-Subnormal" |
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3551 else: |
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3552 return "+Subnormal" |
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3553 # just a normal, regular, boring number, :) |
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3554 if self._sign: |
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3555 return "-Normal" |
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3556 else: |
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3557 return "+Normal" |
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3558 |
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3559 def radix(self): |
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3560 """Just returns 10, as this is Decimal, :)""" |
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3561 return Decimal(10) |
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3562 |
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3563 def rotate(self, other, context=None): |
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3564 """Returns a rotated copy of self, value-of-other times.""" |
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3565 if context is None: |
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3566 context = getcontext() |
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3567 |
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3568 other = _convert_other(other, raiseit=True) |
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3569 |
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3570 ans = self._check_nans(other, context) |
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3571 if ans: |
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3572 return ans |
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3573 |
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3574 if other._exp != 0: |
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3575 return context._raise_error(InvalidOperation) |
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3576 if not (-context.prec <= int(other) <= context.prec): |
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3577 return context._raise_error(InvalidOperation) |
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3578 |
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3579 if self._isinfinity(): |
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3580 return Decimal(self) |
|
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3581 |
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|
3582 # get values, pad if necessary |
|
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|
3583 torot = int(other) |
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3584 rotdig = self._int |
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|
3585 topad = context.prec - len(rotdig) |
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3586 if topad > 0: |
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3587 rotdig = '0'*topad + rotdig |
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3588 elif topad < 0: |
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3589 rotdig = rotdig[-topad:] |
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3590 |
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|
3591 # let's rotate! |
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3592 rotated = rotdig[torot:] + rotdig[:torot] |
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3593 return _dec_from_triple(self._sign, |
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3594 rotated.lstrip('0') or '0', self._exp) |
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3595 |
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3596 def scaleb(self, other, context=None): |
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3597 """Returns self operand after adding the second value to its exp.""" |
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3598 if context is None: |
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3599 context = getcontext() |
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3600 |
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3601 other = _convert_other(other, raiseit=True) |
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3602 |
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3603 ans = self._check_nans(other, context) |
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3604 if ans: |
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3605 return ans |
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3606 |
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3607 if other._exp != 0: |
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3608 return context._raise_error(InvalidOperation) |
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3609 liminf = -2 * (context.Emax + context.prec) |
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|
3610 limsup = 2 * (context.Emax + context.prec) |
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3611 if not (liminf <= int(other) <= limsup): |
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3612 return context._raise_error(InvalidOperation) |
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3613 |
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3614 if self._isinfinity(): |
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3615 return Decimal(self) |
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3616 |
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3617 d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) |
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3618 d = d._fix(context) |
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3619 return d |
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3620 |
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3621 def shift(self, other, context=None): |
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3622 """Returns a shifted copy of self, value-of-other times.""" |
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3623 if context is None: |
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3624 context = getcontext() |
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3625 |
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3626 other = _convert_other(other, raiseit=True) |
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3627 |
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3628 ans = self._check_nans(other, context) |
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3629 if ans: |
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3630 return ans |
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3631 |
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3632 if other._exp != 0: |
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3633 return context._raise_error(InvalidOperation) |
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3634 if not (-context.prec <= int(other) <= context.prec): |
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3635 return context._raise_error(InvalidOperation) |
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3636 |
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3637 if self._isinfinity(): |
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3638 return Decimal(self) |
|
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3639 |
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|
3640 # get values, pad if necessary |
|
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3641 torot = int(other) |
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3642 rotdig = self._int |
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3643 topad = context.prec - len(rotdig) |
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3644 if topad > 0: |
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3645 rotdig = '0'*topad + rotdig |
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3646 elif topad < 0: |
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3647 rotdig = rotdig[-topad:] |
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3648 |
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|
3649 # let's shift! |
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3650 if torot < 0: |
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3651 shifted = rotdig[:torot] |
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3652 else: |
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3653 shifted = rotdig + '0'*torot |
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3654 shifted = shifted[-context.prec:] |
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3655 |
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3656 return _dec_from_triple(self._sign, |
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3657 shifted.lstrip('0') or '0', self._exp) |
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3658 |
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3659 # Support for pickling, copy, and deepcopy |
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3660 def __reduce__(self): |
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3661 return (self.__class__, (str(self),)) |
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3662 |
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3663 def __copy__(self): |
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3664 if type(self) is Decimal: |
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3665 return self # I'm immutable; therefore I am my own clone |
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3666 return self.__class__(str(self)) |
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3667 |
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3668 def __deepcopy__(self, memo): |
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3669 if type(self) is Decimal: |
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3670 return self # My components are also immutable |
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3671 return self.__class__(str(self)) |
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3672 |
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3673 # PEP 3101 support. the _localeconv keyword argument should be |
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3674 # considered private: it's provided for ease of testing only. |
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3675 def __format__(self, specifier, context=None, _localeconv=None): |
|
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3676 """Format a Decimal instance according to the given specifier. |
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3677 |
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3678 The specifier should be a standard format specifier, with the |
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3679 form described in PEP 3101. Formatting types 'e', 'E', 'f', |
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3680 'F', 'g', 'G', 'n' and '%' are supported. If the formatting |
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3681 type is omitted it defaults to 'g' or 'G', depending on the |
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3682 value of context.capitals. |
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3683 """ |
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3684 |
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3685 # Note: PEP 3101 says that if the type is not present then |
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3686 # there should be at least one digit after the decimal point. |
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3687 # We take the liberty of ignoring this requirement for |
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3688 # Decimal---it's presumably there to make sure that |
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3689 # format(float, '') behaves similarly to str(float). |
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3690 if context is None: |
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3691 context = getcontext() |
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3692 |
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3693 spec = _parse_format_specifier(specifier, _localeconv=_localeconv) |
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3694 |
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3695 # special values don't care about the type or precision |
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3696 if self._is_special: |
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3697 sign = _format_sign(self._sign, spec) |
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3698 body = str(self.copy_abs()) |
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3699 return _format_align(sign, body, spec) |
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3700 |
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3701 # a type of None defaults to 'g' or 'G', depending on context |
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3702 if spec['type'] is None: |
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3703 spec['type'] = ['g', 'G'][context.capitals] |
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3704 |
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3705 # if type is '%', adjust exponent of self accordingly |
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3706 if spec['type'] == '%': |
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3707 self = _dec_from_triple(self._sign, self._int, self._exp+2) |
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3708 |
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3709 # round if necessary, taking rounding mode from the context |
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3710 rounding = context.rounding |
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3711 precision = spec['precision'] |
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3712 if precision is not None: |
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3713 if spec['type'] in 'eE': |
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3714 self = self._round(precision+1, rounding) |
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3715 elif spec['type'] in 'fF%': |
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3716 self = self._rescale(-precision, rounding) |
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3717 elif spec['type'] in 'gG' and len(self._int) > precision: |
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3718 self = self._round(precision, rounding) |
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3719 # special case: zeros with a positive exponent can't be |
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3720 # represented in fixed point; rescale them to 0e0. |
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3721 if not self and self._exp > 0 and spec['type'] in 'fF%': |
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3722 self = self._rescale(0, rounding) |
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3723 |
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3724 # figure out placement of the decimal point |
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3725 leftdigits = self._exp + len(self._int) |
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3726 if spec['type'] in 'eE': |
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3727 if not self and precision is not None: |
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3728 dotplace = 1 - precision |
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3729 else: |
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3730 dotplace = 1 |
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3731 elif spec['type'] in 'fF%': |
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3732 dotplace = leftdigits |
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3733 elif spec['type'] in 'gG': |
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3734 if self._exp <= 0 and leftdigits > -6: |
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3735 dotplace = leftdigits |
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3736 else: |
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3737 dotplace = 1 |
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3738 |
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3739 # find digits before and after decimal point, and get exponent |
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3740 if dotplace < 0: |
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3741 intpart = '0' |
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3742 fracpart = '0'*(-dotplace) + self._int |
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3743 elif dotplace > len(self._int): |
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3744 intpart = self._int + '0'*(dotplace-len(self._int)) |
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3745 fracpart = '' |
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3746 else: |
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3747 intpart = self._int[:dotplace] or '0' |
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3748 fracpart = self._int[dotplace:] |
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3749 exp = leftdigits-dotplace |
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3750 |
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3751 # done with the decimal-specific stuff; hand over the rest |
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3752 # of the formatting to the _format_number function |
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3753 return _format_number(self._sign, intpart, fracpart, exp, spec) |
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3754 |
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3755 def _dec_from_triple(sign, coefficient, exponent, special=False): |
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3756 """Create a decimal instance directly, without any validation, |
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3757 normalization (e.g. removal of leading zeros) or argument |
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3758 conversion. |
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3759 |
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3760 This function is for *internal use only*. |
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3761 """ |
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3762 |
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3763 self = object.__new__(Decimal) |
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3764 self._sign = sign |
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3765 self._int = coefficient |
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3766 self._exp = exponent |
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3767 self._is_special = special |
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3768 |
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3769 return self |
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3770 |
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3771 # Register Decimal as a kind of Number (an abstract base class). |
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3772 # However, do not register it as Real (because Decimals are not |
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3773 # interoperable with floats). |
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3774 _numbers.Number.register(Decimal) |
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3775 |
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3776 |
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3777 ##### Context class ####################################################### |
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3778 |
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3779 class _ContextManager(object): |
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3780 """Context manager class to support localcontext(). |
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3781 |
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3782 Sets a copy of the supplied context in __enter__() and restores |
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3783 the previous decimal context in __exit__() |
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3784 """ |
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3785 def __init__(self, new_context): |
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3786 self.new_context = new_context.copy() |
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3787 def __enter__(self): |
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3788 self.saved_context = getcontext() |
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3789 setcontext(self.new_context) |
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3790 return self.new_context |
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3791 def __exit__(self, t, v, tb): |
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3792 setcontext(self.saved_context) |
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3793 |
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3794 class Context(object): |
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3795 """Contains the context for a Decimal instance. |
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3796 |
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3797 Contains: |
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3798 prec - precision (for use in rounding, division, square roots..) |
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3799 rounding - rounding type (how you round) |
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3800 traps - If traps[exception] = 1, then the exception is |
|
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3801 raised when it is caused. Otherwise, a value is |
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3802 substituted in. |
|
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Context flags get set, not incremented.
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3803 flags - When an exception is caused, flags[exception] is set. |
|
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3804 (Whether or not the trap_enabler is set) |
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3805 Should be reset by user of Decimal instance. |
|
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3806 Emin - Minimum exponent |
|
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3807 Emax - Maximum exponent |
|
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|
3808 capitals - If 1, 1*10^1 is printed as 1E+1. |
|
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|
3809 If 0, printed as 1e1 |
|
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|
3810 clamp - If 1, change exponents if too high (Default 0) |
|
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|
3811 """ |
| 32482 | 3812 |
|
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3813 def __init__(self, prec=None, rounding=None, |
|
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|
3814 traps=None, flags=None, |
|
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|
3815 Emin=None, Emax=None, |
|
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|
3816 capitals=None, clamp=None, |
|
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|
3817 _ignored_flags=None): |
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3818 # Set defaults; for everything except flags and _ignored_flags, |
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3819 # inherit from DefaultContext. |
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3820 try: |
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3821 dc = DefaultContext |
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3822 except NameError: |
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3823 pass |
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3824 |
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|
3825 self.prec = prec if prec is not None else dc.prec |
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3826 self.rounding = rounding if rounding is not None else dc.rounding |
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3827 self.Emin = Emin if Emin is not None else dc.Emin |
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|
3828 self.Emax = Emax if Emax is not None else dc.Emax |
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|
3829 self.capitals = capitals if capitals is not None else dc.capitals |
|
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3830 self.clamp = clamp if clamp is not None else dc.clamp |
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3831 |
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|
3832 if _ignored_flags is None: |
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3833 self._ignored_flags = [] |
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3834 else: |
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3835 self._ignored_flags = _ignored_flags |
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3836 |
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3837 if traps is None: |
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|
3838 self.traps = dc.traps.copy() |
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3839 elif not isinstance(traps, dict): |
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3840 self.traps = dict((s, int(s in traps)) for s in _signals) |
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3841 else: |
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3842 self.traps = traps |
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3843 |
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3844 if flags is None: |
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|
3845 self.flags = dict.fromkeys(_signals, 0) |
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3846 elif not isinstance(flags, dict): |
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3847 self.flags = dict((s, int(s in flags)) for s in _signals) |
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3848 else: |
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3849 self.flags = flags |
|
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3850 |
|
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|
3851 def __repr__(self): |
|
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|
3852 """Show the current context.""" |
|
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|
3853 s = [] |
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|
3854 s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' |
|
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|
3855 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, ' |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3856 'clamp=%(clamp)d' |
|
41554
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Guido van Rossum <guido@python.org>
parents:
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diff
changeset
|
3857 % vars(self)) |
|
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Guido van Rossum <guido@python.org>
parents:
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diff
changeset
|
3858 names = [f.__name__ for f, v in self.flags.items() if v] |
|
06145fbc7ab9
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Guido van Rossum <guido@python.org>
parents:
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diff
changeset
|
3859 s.append('flags=[' + ', '.join(names) + ']') |
|
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Guido van Rossum <guido@python.org>
parents:
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diff
changeset
|
3860 names = [t.__name__ for t, v in self.traps.items() if v] |
|
06145fbc7ab9
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Guido van Rossum <guido@python.org>
parents:
41464
diff
changeset
|
3861 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
|
3862 return ', '.join(s) + ')' |
|
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Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3863 |
|
32477
bc586db9945a
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Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3864 def clear_flags(self): |
|
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Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3865 """Reset all flags to zero""" |
|
bc586db9945a
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Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3866 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
|
3867 self.flags[flag] = 0 |
|
32477
bc586db9945a
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Raymond Hettinger <python@rcn.com>
parents:
32456
diff
changeset
|
3868 |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3869 def _shallow_copy(self): |
|
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3870 """Returns a shallow copy from self.""" |
|
44329
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Christian Heimes <christian@cheimes.de>
parents:
44256
diff
changeset
|
3871 nc = Context(self.prec, self.rounding, self.traps, |
|
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Christian Heimes <christian@cheimes.de>
parents:
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diff
changeset
|
3872 self.flags, self.Emin, self.Emax, |
|
61864
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3873 self.capitals, self.clamp, self._ignored_flags) |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
3874 return nc |
|
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* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
32980
diff
changeset
|
3875 |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3876 def copy(self): |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
3877 """Returns a deep copy from self.""" |
|
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Guido van Rossum <guido@python.org>
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|
3878 nc = Context(self.prec, self.rounding, self.traps.copy(), |
|
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parents:
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changeset
|
3879 self.flags.copy(), self.Emin, self.Emax, |
|
61864
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3880 self.capitals, self.clamp, self._ignored_flags) |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3881 return nc |
| 32482 | 3882 __copy__ = copy |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3883 |
|
61864
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3884 # _clamp is provided for backwards compatibility with third-party |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3885 # code. May be removed in Python >= 3.3. |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3886 def _get_clamp(self): |
|
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#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3887 "_clamp mirrors the clamp attribute. Its use is deprecated." |
|
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#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3888 import warnings |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3889 warnings.warn('Use of the _clamp attribute is deprecated. ' |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3890 'Please use clamp instead.', |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3891 DeprecationWarning) |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3892 return self.clamp |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3893 |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3894 def _set_clamp(self, clamp): |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3895 "_clamp mirrors the clamp attribute. Its use is deprecated." |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3896 import warnings |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3897 warnings.warn('Use of the _clamp attribute is deprecated. ' |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3898 'Please use clamp instead.', |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3899 DeprecationWarning) |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3900 self.clamp = clamp |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3901 |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3902 # don't bother with _del_clamp; no sane 3rd party code should |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3903 # be deleting the _clamp attribute |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3904 _clamp = property(_get_clamp, _set_clamp) |
|
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
61745
diff
changeset
|
3905 |
| 32560 | 3906 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
|
3907 """Handles an error |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3908 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3909 If the flag is in _ignored_flags, returns the default response. |
|
45092
faa88ff4cce4
Context flags get set, not incremented.
Raymond Hettinger <python@rcn.com>
parents:
44943
diff
changeset
|
3910 Otherwise, it sets the flag, then, if the corresponding |
|
61746
49d7de9d7b1a
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Stefan Krah <stefan@bytereef.org>
parents:
61214
diff
changeset
|
3911 trap_enabler is set, it reraises the exception. Otherwise, it returns |
|
45092
faa88ff4cce4
Context flags get set, not incremented.
Raymond Hettinger <python@rcn.com>
parents:
44943
diff
changeset
|
3912 the default value after setting the flag. |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3913 """ |
| 32560 | 3914 error = _condition_map.get(condition, condition) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3915 if error in self._ignored_flags: |
|
41554
06145fbc7ab9
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Guido van Rossum <guido@python.org>
parents:
41464
diff
changeset
|
3916 # Don't touch the flag |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3917 return error().handle(self, *args) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3918 |
|
45092
faa88ff4cce4
Context flags get set, not incremented.
Raymond Hettinger <python@rcn.com>
parents:
44943
diff
changeset
|
3919 self.flags[error] = 1 |
|
32576
83cbc025bfc7
Improve Context construction and representation:
Raymond Hettinger <python@rcn.com>
parents:
32561
diff
changeset
|
3920 if not self.traps[error]: |
|
41554
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Guido van Rossum <guido@python.org>
parents:
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changeset
|
3921 # The errors define how to handle themselves. |
| 32560 | 3922 return condition().handle(self, *args) |
|
32451
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3923 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3924 # Errors should only be risked on copies of the context |
|
41554
06145fbc7ab9
Merged revisions 53952-54987 via svnmerge from
Guido van Rossum <guido@python.org>
parents:
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diff
changeset
|
3925 # self._ignored_flags = [] |
|
43020
907a45df1295
Raise statement normalization in Lib/.
Collin Winter <collinw@gmail.com>
parents:
42629
diff
changeset
|
3926 raise error(explanation) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3927 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3928 def _ignore_all_flags(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3929 """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
|
3930 return self._ignore_flags(*_signals) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3931 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3932 def _ignore_flags(self, *flags): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3933 """Ignore the flags, if they are raised""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3934 # 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
|
3935 # alone. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3936 self._ignored_flags = (self._ignored_flags + list(flags)) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3937 return list(flags) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3938 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3939 def _regard_flags(self, *flags): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3940 """Stop ignoring the flags, if they are raised""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3941 if flags and isinstance(flags[0], (tuple,list)): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3942 flags = flags[0] |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3943 for flag in flags: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3944 self._ignored_flags.remove(flag) |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3945 |
|
48475
f4e7ef4329a9
Manual forward port of 64962 - use PyObject_HashNotImplemented as a tp_hash level indicator that the default hash implementation has not been inherited
Nick Coghlan <ncoghlan@gmail.com>
parents:
48412
diff
changeset
|
3946 # We inherit object.__hash__, so we must deny this explicitly |
|
f4e7ef4329a9
Manual forward port of 64962 - use PyObject_HashNotImplemented as a tp_hash level indicator that the default hash implementation has not been inherited
Nick Coghlan <ncoghlan@gmail.com>
parents:
48412
diff
changeset
|
3947 __hash__ = None |
| 32560 | 3948 |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3949 def Etiny(self): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3950 """Returns Etiny (= Emin - prec + 1)""" |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3951 return int(self.Emin - self.prec + 1) |
|
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Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
3952 |
|
d2c1c7ae7cf4
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Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3953 def Etop(self): |
| 32496 | 3954 """Returns maximum exponent (= Emax - prec + 1)""" |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3955 return int(self.Emax - self.prec + 1) |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3956 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3957 def _set_rounding(self, type): |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3958 """Sets the rounding type. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
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parents:
diff
changeset
|
3959 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3960 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
|
3961 rounding type. Often used like: |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3962 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3963 context = context.copy() |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3964 # so you don't change the calling context |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3965 # if an error occurs in the middle. |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3966 rounding = context._set_rounding(ROUND_UP) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3967 val = self.__sub__(other, context=context) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3968 context._set_rounding(rounding) |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3969 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3970 This will make it round up for that operation. |
|
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3971 """ |
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3972 rounding = self.rounding |
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3973 self.rounding= type |
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3974 return rounding |
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3975 |
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3976 def create_decimal(self, num='0'): |
|
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3977 """Creates a new Decimal instance but using self as context. |
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3978 |
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3979 This method implements the to-number operation of the |
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3980 IBM Decimal specification.""" |
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3981 |
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3982 if isinstance(num, str) and num != num.strip(): |
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3983 return self._raise_error(ConversionSyntax, |
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3984 "no trailing or leading whitespace is " |
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3985 "permitted.") |
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3986 |
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3987 d = Decimal(num, context=self) |
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3988 if d._isnan() and len(d._int) > self.prec - self.clamp: |
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3989 return self._raise_error(ConversionSyntax, |
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3990 "diagnostic info too long in NaN") |
| 33695 | 3991 return d._fix(self) |
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3992 |
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50499
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3993 def create_decimal_from_float(self, f): |
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3994 """Creates a new Decimal instance from a float but rounding using self |
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3995 as the context. |
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3996 |
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3997 >>> context = Context(prec=5, rounding=ROUND_DOWN) |
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3998 >>> context.create_decimal_from_float(3.1415926535897932) |
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3999 Decimal('3.1415') |
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4000 >>> context = Context(prec=5, traps=[Inexact]) |
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4001 >>> context.create_decimal_from_float(3.1415926535897932) |
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4002 Traceback (most recent call last): |
|
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4003 ... |
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4004 decimal.Inexact: None |
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4005 |
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4006 """ |
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4007 d = Decimal.from_float(f) # An exact conversion |
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4008 return d._fix(self) # Apply the context rounding |
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4009 |
|
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4010 # Methods |
|
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4011 def abs(self, a): |
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4012 """Returns the absolute value of the operand. |
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4013 |
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4014 If the operand is negative, the result is the same as using the minus |
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4015 operation on the operand. Otherwise, the result is the same as using |
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4016 the plus operation on the operand. |
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4017 |
| 32482 | 4018 >>> ExtendedContext.abs(Decimal('2.1')) |
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4019 Decimal('2.1') |
| 32482 | 4020 >>> ExtendedContext.abs(Decimal('-100')) |
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4021 Decimal('100') |
| 32482 | 4022 >>> ExtendedContext.abs(Decimal('101.5')) |
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4023 Decimal('101.5') |
| 32482 | 4024 >>> ExtendedContext.abs(Decimal('-101.5')) |
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4025 Decimal('101.5') |
|
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4026 >>> ExtendedContext.abs(-1) |
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4027 Decimal('1') |
|
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4028 """ |
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4029 a = _convert_other(a, raiseit=True) |
|
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4030 return a.__abs__(context=self) |
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4031 |
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4032 def add(self, a, b): |
|
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4033 """Return the sum of the two operands. |
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4034 |
| 32482 | 4035 >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) |
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4036 Decimal('19.00') |
| 32482 | 4037 >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) |
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4038 Decimal('1.02E+4') |
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4039 >>> ExtendedContext.add(1, Decimal(2)) |
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4040 Decimal('3') |
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4041 >>> ExtendedContext.add(Decimal(8), 5) |
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4042 Decimal('13') |
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4043 >>> ExtendedContext.add(5, 5) |
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4044 Decimal('10') |
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4045 """ |
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4046 a = _convert_other(a, raiseit=True) |
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4047 r = a.__add__(b, context=self) |
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4048 if r is NotImplemented: |
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4049 raise TypeError("Unable to convert %s to Decimal" % b) |
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4050 else: |
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4051 return r |
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4052 |
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4053 def _apply(self, a): |
| 33695 | 4054 return str(a._fix(self)) |
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4055 |
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4056 def canonical(self, a): |
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4057 """Returns the same Decimal object. |
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4058 |
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4059 As we do not have different encodings for the same number, the |
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4060 received object already is in its canonical form. |
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4061 |
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4062 >>> ExtendedContext.canonical(Decimal('2.50')) |
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4063 Decimal('2.50') |
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4064 """ |
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4065 return a.canonical(context=self) |
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4066 |
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4067 def compare(self, a, b): |
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4068 """Compares values numerically. |
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4069 |
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4070 If the signs of the operands differ, a value representing each operand |
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4071 ('-1' if the operand is less than zero, '0' if the operand is zero or |
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4072 negative zero, or '1' if the operand is greater than zero) is used in |
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4073 place of that operand for the comparison instead of the actual |
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4074 operand. |
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4075 |
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4076 The comparison is then effected by subtracting the second operand from |
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4077 the first and then returning a value according to the result of the |
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4078 subtraction: '-1' if the result is less than zero, '0' if the result is |
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4079 zero or negative zero, or '1' if the result is greater than zero. |
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4080 |
| 32482 | 4081 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) |
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4082 Decimal('-1') |
| 32482 | 4083 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) |
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4084 Decimal('0') |
| 32482 | 4085 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) |
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4086 Decimal('0') |
| 32482 | 4087 >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) |
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4088 Decimal('1') |
| 32482 | 4089 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) |
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4090 Decimal('1') |
| 32482 | 4091 >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) |
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4092 Decimal('-1') |
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4093 >>> ExtendedContext.compare(1, 2) |
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4094 Decimal('-1') |
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4095 >>> ExtendedContext.compare(Decimal(1), 2) |
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4096 Decimal('-1') |
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4097 >>> ExtendedContext.compare(1, Decimal(2)) |
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4098 Decimal('-1') |
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4099 """ |
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4100 a = _convert_other(a, raiseit=True) |
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4101 return a.compare(b, context=self) |
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4102 |
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4103 def compare_signal(self, a, b): |
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4104 """Compares the values of the two operands numerically. |
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4105 |
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4106 It's pretty much like compare(), but all NaNs signal, with signaling |
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4107 NaNs taking precedence over quiet NaNs. |
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4108 |
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4109 >>> c = ExtendedContext |
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4110 >>> c.compare_signal(Decimal('2.1'), Decimal('3')) |
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4111 Decimal('-1') |
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4112 >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) |
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4113 Decimal('0') |
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4114 >>> c.flags[InvalidOperation] = 0 |
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4115 >>> print(c.flags[InvalidOperation]) |
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4116 0 |
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4117 >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) |
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4118 Decimal('NaN') |
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4119 >>> print(c.flags[InvalidOperation]) |
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4120 1 |
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4121 >>> c.flags[InvalidOperation] = 0 |
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4122 >>> print(c.flags[InvalidOperation]) |
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4123 0 |
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4124 >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) |
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4125 Decimal('NaN') |
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4126 >>> print(c.flags[InvalidOperation]) |
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4127 1 |
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4128 >>> c.compare_signal(-1, 2) |
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4129 Decimal('-1') |
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4130 >>> c.compare_signal(Decimal(-1), 2) |
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4131 Decimal('-1') |
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4132 >>> c.compare_signal(-1, Decimal(2)) |
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4133 Decimal('-1') |
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4134 """ |
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4135 a = _convert_other(a, raiseit=True) |
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4136 return a.compare_signal(b, context=self) |
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4137 |
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4138 def compare_total(self, a, b): |
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4139 """Compares two operands using their abstract representation. |
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4140 |
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4141 This is not like the standard compare, which use their numerical |
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4142 value. Note that a total ordering is defined for all possible abstract |
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4143 representations. |
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4144 |
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4145 >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) |
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4146 Decimal('-1') |
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4147 >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) |
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4148 Decimal('-1') |
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4149 >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) |
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4150 Decimal('-1') |
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4151 >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) |
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4152 Decimal('0') |
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4153 >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) |
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4154 Decimal('1') |
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4155 >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) |
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4156 Decimal('-1') |
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4157 >>> ExtendedContext.compare_total(1, 2) |
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4158 Decimal('-1') |
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4159 >>> ExtendedContext.compare_total(Decimal(1), 2) |
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4160 Decimal('-1') |
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4161 >>> ExtendedContext.compare_total(1, Decimal(2)) |
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4162 Decimal('-1') |
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4163 """ |
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4164 a = _convert_other(a, raiseit=True) |
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4165 return a.compare_total(b) |
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4166 |
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4167 def compare_total_mag(self, a, b): |
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4168 """Compares two operands using their abstract representation ignoring sign. |
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4169 |
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4170 Like compare_total, but with operand's sign ignored and assumed to be 0. |
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4171 """ |
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4172 a = _convert_other(a, raiseit=True) |
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4173 return a.compare_total_mag(b) |
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4174 |
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4175 def copy_abs(self, a): |
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4176 """Returns a copy of the operand with the sign set to 0. |
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4177 |
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4178 >>> ExtendedContext.copy_abs(Decimal('2.1')) |
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4179 Decimal('2.1') |
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4180 >>> ExtendedContext.copy_abs(Decimal('-100')) |
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4181 Decimal('100') |
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4182 >>> ExtendedContext.copy_abs(-1) |
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4183 Decimal('1') |
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4184 """ |
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4185 a = _convert_other(a, raiseit=True) |
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4186 return a.copy_abs() |
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4187 |
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4188 def copy_decimal(self, a): |
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4189 """Returns a copy of the decimal object. |
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4190 |
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4191 >>> ExtendedContext.copy_decimal(Decimal('2.1')) |
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4192 Decimal('2.1') |
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4193 >>> ExtendedContext.copy_decimal(Decimal('-1.00')) |
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4194 Decimal('-1.00') |
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4195 >>> ExtendedContext.copy_decimal(1) |
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4196 Decimal('1') |
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4197 """ |
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4198 a = _convert_other(a, raiseit=True) |
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4199 return Decimal(a) |
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4200 |
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4201 def copy_negate(self, a): |
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4202 """Returns a copy of the operand with the sign inverted. |
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4203 |
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4204 >>> ExtendedContext.copy_negate(Decimal('101.5')) |
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4205 Decimal('-101.5') |
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4206 >>> ExtendedContext.copy_negate(Decimal('-101.5')) |
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4207 Decimal('101.5') |
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4208 >>> ExtendedContext.copy_negate(1) |
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4209 Decimal('-1') |
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4210 """ |
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4211 a = _convert_other(a, raiseit=True) |
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4212 return a.copy_negate() |
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4213 |
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4214 def copy_sign(self, a, b): |
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4215 """Copies the second operand's sign to the first one. |
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4216 |
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4217 In detail, it returns a copy of the first operand with the sign |
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4218 equal to the sign of the second operand. |
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4219 |
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4220 >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) |
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4221 Decimal('1.50') |
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4222 >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) |
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4223 Decimal('1.50') |
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4224 >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) |
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4225 Decimal('-1.50') |
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4226 >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) |
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4227 Decimal('-1.50') |
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4228 >>> ExtendedContext.copy_sign(1, -2) |
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4229 Decimal('-1') |
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4230 >>> ExtendedContext.copy_sign(Decimal(1), -2) |
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4231 Decimal('-1') |
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4232 >>> ExtendedContext.copy_sign(1, Decimal(-2)) |
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4233 Decimal('-1') |
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4234 """ |
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4235 a = _convert_other(a, raiseit=True) |
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4236 return a.copy_sign(b) |
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4237 |
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4238 def divide(self, a, b): |
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4239 """Decimal division in a specified context. |
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4240 |
| 32482 | 4241 >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) |
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4242 Decimal('0.333333333') |
| 32482 | 4243 >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) |
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4244 Decimal('0.666666667') |
| 32482 | 4245 >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) |
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4246 Decimal('2.5') |
| 32482 | 4247 >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) |
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4248 Decimal('0.1') |
| 32482 | 4249 >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) |
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4250 Decimal('1') |
| 32482 | 4251 >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) |
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4252 Decimal('4.00') |
| 32482 | 4253 >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) |
|
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4254 Decimal('1.20') |
| 32482 | 4255 >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) |
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4256 Decimal('10') |
| 32482 | 4257 >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) |
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4258 Decimal('1000') |
| 32482 | 4259 >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) |
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4260 Decimal('1.20E+6') |
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4261 >>> ExtendedContext.divide(5, 5) |
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4262 Decimal('1') |
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4263 >>> ExtendedContext.divide(Decimal(5), 5) |
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4264 Decimal('1') |
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4265 >>> ExtendedContext.divide(5, Decimal(5)) |
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4266 Decimal('1') |
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4267 """ |
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4268 a = _convert_other(a, raiseit=True) |
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4269 r = a.__truediv__(b, context=self) |
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4270 if r is NotImplemented: |
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4271 raise TypeError("Unable to convert %s to Decimal" % b) |
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4272 else: |
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4273 return r |
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4274 |
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4275 def divide_int(self, a, b): |
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4276 """Divides two numbers and returns the integer part of the result. |
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4277 |
| 32482 | 4278 >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) |
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4279 Decimal('0') |
| 32482 | 4280 >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) |
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4281 Decimal('3') |
| 32482 | 4282 >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) |
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4283 Decimal('3') |
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4284 >>> ExtendedContext.divide_int(10, 3) |
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4285 Decimal('3') |
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4286 >>> ExtendedContext.divide_int(Decimal(10), 3) |
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4287 Decimal('3') |
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4288 >>> ExtendedContext.divide_int(10, Decimal(3)) |
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4289 Decimal('3') |
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4290 """ |
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4291 a = _convert_other(a, raiseit=True) |
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4292 r = a.__floordiv__(b, context=self) |
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4293 if r is NotImplemented: |
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4294 raise TypeError("Unable to convert %s to Decimal" % b) |
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4295 else: |
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4296 return r |
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4297 |
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4298 def divmod(self, a, b): |
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4299 """Return (a // b, a % b). |
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4300 |
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4301 >>> ExtendedContext.divmod(Decimal(8), Decimal(3)) |
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4302 (Decimal('2'), Decimal('2')) |
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4303 >>> ExtendedContext.divmod(Decimal(8), Decimal(4)) |
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4304 (Decimal('2'), Decimal('0')) |
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4305 >>> ExtendedContext.divmod(8, 4) |
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4306 (Decimal('2'), Decimal('0')) |
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4307 >>> ExtendedContext.divmod(Decimal(8), 4) |
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4308 (Decimal('2'), Decimal('0')) |
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4309 >>> ExtendedContext.divmod(8, Decimal(4)) |
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4310 (Decimal('2'), Decimal('0')) |
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4311 """ |
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4312 a = _convert_other(a, raiseit=True) |
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4313 r = a.__divmod__(b, context=self) |
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4314 if r is NotImplemented: |
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4315 raise TypeError("Unable to convert %s to Decimal" % b) |
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4316 else: |
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4317 return r |
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4318 |
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4319 def exp(self, a): |
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4320 """Returns e ** a. |
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4321 |
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4322 >>> c = ExtendedContext.copy() |
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4323 >>> c.Emin = -999 |
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4324 >>> c.Emax = 999 |
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4325 >>> c.exp(Decimal('-Infinity')) |
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4326 Decimal('0') |
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4327 >>> c.exp(Decimal('-1')) |
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4328 Decimal('0.367879441') |
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4329 >>> c.exp(Decimal('0')) |
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4330 Decimal('1') |
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4331 >>> c.exp(Decimal('1')) |
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4332 Decimal('2.71828183') |
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4333 >>> c.exp(Decimal('0.693147181')) |
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4334 Decimal('2.00000000') |
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4335 >>> c.exp(Decimal('+Infinity')) |
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4336 Decimal('Infinity') |
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4337 >>> c.exp(10) |
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4338 Decimal('22026.4658') |
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4339 """ |
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4340 a =_convert_other(a, raiseit=True) |
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4341 return a.exp(context=self) |
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4342 |
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4343 def fma(self, a, b, c): |
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4344 """Returns a multiplied by b, plus c. |
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4345 |
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4346 The first two operands are multiplied together, using multiply, |
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4347 the third operand is then added to the result of that |
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4348 multiplication, using add, all with only one final rounding. |
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4349 |
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4350 >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) |
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4351 Decimal('22') |
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4352 >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) |
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4353 Decimal('-8') |
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4354 >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) |
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4355 Decimal('1.38435736E+12') |
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4356 >>> ExtendedContext.fma(1, 3, 4) |
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4357 Decimal('7') |
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4358 >>> ExtendedContext.fma(1, Decimal(3), 4) |
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4359 Decimal('7') |
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4360 >>> ExtendedContext.fma(1, 3, Decimal(4)) |
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4361 Decimal('7') |
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4362 """ |
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4363 a = _convert_other(a, raiseit=True) |
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4364 return a.fma(b, c, context=self) |
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4365 |
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4366 def is_canonical(self, a): |
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4367 """Return True if the operand is canonical; otherwise return False. |
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4368 |
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4369 Currently, the encoding of a Decimal instance is always |
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4370 canonical, so this method returns True for any Decimal. |
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4371 |
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4372 >>> ExtendedContext.is_canonical(Decimal('2.50')) |
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4373 True |
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4374 """ |
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4375 return a.is_canonical() |
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4376 |
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4377 def is_finite(self, a): |
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4378 """Return True if the operand is finite; otherwise return False. |
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4379 |
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4380 A Decimal instance is considered finite if it is neither |
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4381 infinite nor a NaN. |
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4382 |
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4383 >>> ExtendedContext.is_finite(Decimal('2.50')) |
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4384 True |
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4385 >>> ExtendedContext.is_finite(Decimal('-0.3')) |
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4386 True |
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4387 >>> ExtendedContext.is_finite(Decimal('0')) |
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4388 True |
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4389 >>> ExtendedContext.is_finite(Decimal('Inf')) |
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4390 False |
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4391 >>> ExtendedContext.is_finite(Decimal('NaN')) |
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4392 False |
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4393 >>> ExtendedContext.is_finite(1) |
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4394 True |
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4395 """ |
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4396 a = _convert_other(a, raiseit=True) |
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4397 return a.is_finite() |
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4398 |
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4399 def is_infinite(self, a): |
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4400 """Return True if the operand is infinite; otherwise return False. |
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4401 |
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4402 >>> ExtendedContext.is_infinite(Decimal('2.50')) |
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4403 False |
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4404 >>> ExtendedContext.is_infinite(Decimal('-Inf')) |
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4405 True |
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4406 >>> ExtendedContext.is_infinite(Decimal('NaN')) |
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4407 False |
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4408 >>> ExtendedContext.is_infinite(1) |
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4409 False |
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4410 """ |
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4411 a = _convert_other(a, raiseit=True) |
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4412 return a.is_infinite() |
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4413 |
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4414 def is_nan(self, a): |
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4415 """Return True if the operand is a qNaN or sNaN; |
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4416 otherwise return False. |
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4417 |
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4418 >>> ExtendedContext.is_nan(Decimal('2.50')) |
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4419 False |
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4420 >>> ExtendedContext.is_nan(Decimal('NaN')) |
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4421 True |
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4422 >>> ExtendedContext.is_nan(Decimal('-sNaN')) |
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4423 True |
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4424 >>> ExtendedContext.is_nan(1) |
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4425 False |
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4426 """ |
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4427 a = _convert_other(a, raiseit=True) |
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4428 return a.is_nan() |
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4429 |
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4430 def is_normal(self, a): |
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4431 """Return True if the operand is a normal number; |
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4432 otherwise return False. |
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4433 |
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4434 >>> c = ExtendedContext.copy() |
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4435 >>> c.Emin = -999 |
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4436 >>> c.Emax = 999 |
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4437 >>> c.is_normal(Decimal('2.50')) |
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4438 True |
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4439 >>> c.is_normal(Decimal('0.1E-999')) |
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4440 False |
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4441 >>> c.is_normal(Decimal('0.00')) |
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4442 False |
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4443 >>> c.is_normal(Decimal('-Inf')) |
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4444 False |
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4445 >>> c.is_normal(Decimal('NaN')) |
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4446 False |
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4447 >>> c.is_normal(1) |
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4448 True |
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4449 """ |
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4450 a = _convert_other(a, raiseit=True) |
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4451 return a.is_normal(context=self) |
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4452 |
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4453 def is_qnan(self, a): |
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4454 """Return True if the operand is a quiet NaN; otherwise return False. |
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4455 |
|
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4456 >>> ExtendedContext.is_qnan(Decimal('2.50')) |
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4457 False |
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4458 >>> ExtendedContext.is_qnan(Decimal('NaN')) |
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4459 True |
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4460 >>> ExtendedContext.is_qnan(Decimal('sNaN')) |
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4461 False |
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4462 >>> ExtendedContext.is_qnan(1) |
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4463 False |
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4464 """ |
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4465 a = _convert_other(a, raiseit=True) |
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4466 return a.is_qnan() |
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4467 |
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4468 def is_signed(self, a): |
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4469 """Return True if the operand is negative; otherwise return False. |
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4470 |
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4471 >>> ExtendedContext.is_signed(Decimal('2.50')) |
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4472 False |
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4473 >>> ExtendedContext.is_signed(Decimal('-12')) |
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4474 True |
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4475 >>> ExtendedContext.is_signed(Decimal('-0')) |
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4476 True |
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4477 >>> ExtendedContext.is_signed(8) |
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4478 False |
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4479 >>> ExtendedContext.is_signed(-8) |
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4480 True |
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4481 """ |
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4482 a = _convert_other(a, raiseit=True) |
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4483 return a.is_signed() |
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4484 |
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4485 def is_snan(self, a): |
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4486 """Return True if the operand is a signaling NaN; |
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4487 otherwise return False. |
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4488 |
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4489 >>> ExtendedContext.is_snan(Decimal('2.50')) |
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4490 False |
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4491 >>> ExtendedContext.is_snan(Decimal('NaN')) |
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4492 False |
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4493 >>> ExtendedContext.is_snan(Decimal('sNaN')) |
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4494 True |
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4495 >>> ExtendedContext.is_snan(1) |
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4496 False |
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4497 """ |
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4498 a = _convert_other(a, raiseit=True) |
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4499 return a.is_snan() |
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4500 |
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4501 def is_subnormal(self, a): |
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4502 """Return True if the operand is subnormal; otherwise return False. |
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4503 |
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4504 >>> c = ExtendedContext.copy() |
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4505 >>> c.Emin = -999 |
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4506 >>> c.Emax = 999 |
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4507 >>> c.is_subnormal(Decimal('2.50')) |
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4508 False |
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4509 >>> c.is_subnormal(Decimal('0.1E-999')) |
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4510 True |
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4511 >>> c.is_subnormal(Decimal('0.00')) |
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4512 False |
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4513 >>> c.is_subnormal(Decimal('-Inf')) |
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4514 False |
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4515 >>> c.is_subnormal(Decimal('NaN')) |
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4516 False |
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4517 >>> c.is_subnormal(1) |
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4518 False |
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4519 """ |
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4520 a = _convert_other(a, raiseit=True) |
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4521 return a.is_subnormal(context=self) |
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4522 |
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4523 def is_zero(self, a): |
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4524 """Return True if the operand is a zero; otherwise return False. |
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4525 |
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4526 >>> ExtendedContext.is_zero(Decimal('0')) |
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4527 True |
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4528 >>> ExtendedContext.is_zero(Decimal('2.50')) |
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4529 False |
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4530 >>> ExtendedContext.is_zero(Decimal('-0E+2')) |
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4531 True |
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4532 >>> ExtendedContext.is_zero(1) |
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4533 False |
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4534 >>> ExtendedContext.is_zero(0) |
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4535 True |
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4536 """ |
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4537 a = _convert_other(a, raiseit=True) |
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4538 return a.is_zero() |
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4539 |
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4540 def ln(self, a): |
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4541 """Returns the natural (base e) logarithm of the operand. |
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4542 |
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4543 >>> c = ExtendedContext.copy() |
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4544 >>> c.Emin = -999 |
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4545 >>> c.Emax = 999 |
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4546 >>> c.ln(Decimal('0')) |
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4547 Decimal('-Infinity') |
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4548 >>> c.ln(Decimal('1.000')) |
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4549 Decimal('0') |
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4550 >>> c.ln(Decimal('2.71828183')) |
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4551 Decimal('1.00000000') |
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4552 >>> c.ln(Decimal('10')) |
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4553 Decimal('2.30258509') |
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4554 >>> c.ln(Decimal('+Infinity')) |
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4555 Decimal('Infinity') |
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4556 >>> c.ln(1) |
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4557 Decimal('0') |
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4558 """ |
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4559 a = _convert_other(a, raiseit=True) |
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4560 return a.ln(context=self) |
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4561 |
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4562 def log10(self, a): |
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4563 """Returns the base 10 logarithm of the operand. |
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4564 |
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4565 >>> c = ExtendedContext.copy() |
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4566 >>> c.Emin = -999 |
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4567 >>> c.Emax = 999 |
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4568 >>> c.log10(Decimal('0')) |
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4569 Decimal('-Infinity') |
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4570 >>> c.log10(Decimal('0.001')) |
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4571 Decimal('-3') |
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4572 >>> c.log10(Decimal('1.000')) |
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4573 Decimal('0') |
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4574 >>> c.log10(Decimal('2')) |
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4575 Decimal('0.301029996') |
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4576 >>> c.log10(Decimal('10')) |
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4577 Decimal('1') |
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4578 >>> c.log10(Decimal('70')) |
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4579 Decimal('1.84509804') |
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4580 >>> c.log10(Decimal('+Infinity')) |
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4581 Decimal('Infinity') |
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4582 >>> c.log10(0) |
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4583 Decimal('-Infinity') |
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4584 >>> c.log10(1) |
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4585 Decimal('0') |
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4586 """ |
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4587 a = _convert_other(a, raiseit=True) |
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4588 return a.log10(context=self) |
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4589 |
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4590 def logb(self, a): |
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4591 """ Returns the exponent of the magnitude of the operand's MSD. |
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4592 |
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4593 The result is the integer which is the exponent of the magnitude |
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4594 of the most significant digit of the operand (as though the |
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4595 operand were truncated to a single digit while maintaining the |
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4596 value of that digit and without limiting the resulting exponent). |
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4597 |
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4598 >>> ExtendedContext.logb(Decimal('250')) |
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4599 Decimal('2') |
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4600 >>> ExtendedContext.logb(Decimal('2.50')) |
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4601 Decimal('0') |
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4602 >>> ExtendedContext.logb(Decimal('0.03')) |
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4603 Decimal('-2') |
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4604 >>> ExtendedContext.logb(Decimal('0')) |
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4605 Decimal('-Infinity') |
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4606 >>> ExtendedContext.logb(1) |
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4607 Decimal('0') |
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4608 >>> ExtendedContext.logb(10) |
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4609 Decimal('1') |
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4610 >>> ExtendedContext.logb(100) |
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4611 Decimal('2') |
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4612 """ |
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4613 a = _convert_other(a, raiseit=True) |
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4614 return a.logb(context=self) |
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4615 |
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4616 def logical_and(self, a, b): |
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4617 """Applies the logical operation 'and' between each operand's digits. |
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4618 |
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4619 The operands must be both logical numbers. |
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4620 |
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4621 >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) |
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4622 Decimal('0') |
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4623 >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) |
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4624 Decimal('0') |
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4625 >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) |
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4626 Decimal('0') |
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4627 >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) |
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4628 Decimal('1') |
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4629 >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) |
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4630 Decimal('1000') |
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4631 >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) |
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4632 Decimal('10') |
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4633 >>> ExtendedContext.logical_and(110, 1101) |
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4634 Decimal('100') |
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4635 >>> ExtendedContext.logical_and(Decimal(110), 1101) |
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4636 Decimal('100') |
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4637 >>> ExtendedContext.logical_and(110, Decimal(1101)) |
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4638 Decimal('100') |
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4639 """ |
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4640 a = _convert_other(a, raiseit=True) |
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4641 return a.logical_and(b, context=self) |
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4642 |
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4643 def logical_invert(self, a): |
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4644 """Invert all the digits in the operand. |
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4645 |
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4646 The operand must be a logical number. |
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4648 >>> ExtendedContext.logical_invert(Decimal('0')) |
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4649 Decimal('111111111') |
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4650 >>> ExtendedContext.logical_invert(Decimal('1')) |
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4651 Decimal('111111110') |
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4652 >>> ExtendedContext.logical_invert(Decimal('111111111')) |
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4653 Decimal('0') |
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4654 >>> ExtendedContext.logical_invert(Decimal('101010101')) |
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4655 Decimal('10101010') |
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4656 >>> ExtendedContext.logical_invert(1101) |
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4657 Decimal('111110010') |
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4658 """ |
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4659 a = _convert_other(a, raiseit=True) |
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4660 return a.logical_invert(context=self) |
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4661 |
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4662 def logical_or(self, a, b): |
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4663 """Applies the logical operation 'or' between each operand's digits. |
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4664 |
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4665 The operands must be both logical numbers. |
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4667 >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) |
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4668 Decimal('0') |
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4669 >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) |
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4670 Decimal('1') |
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4671 >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) |
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4672 Decimal('1') |
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4673 >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) |
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4674 Decimal('1') |
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4675 >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) |
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4676 Decimal('1110') |
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4677 >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) |
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4678 Decimal('1110') |
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4679 >>> ExtendedContext.logical_or(110, 1101) |
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4680 Decimal('1111') |
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4681 >>> ExtendedContext.logical_or(Decimal(110), 1101) |
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4682 Decimal('1111') |
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4683 >>> ExtendedContext.logical_or(110, Decimal(1101)) |
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4684 Decimal('1111') |
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4685 """ |
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4686 a = _convert_other(a, raiseit=True) |
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4687 return a.logical_or(b, context=self) |
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4688 |
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4689 def logical_xor(self, a, b): |
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4690 """Applies the logical operation 'xor' between each operand's digits. |
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4691 |
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4692 The operands must be both logical numbers. |
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4693 |
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4694 >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) |
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4695 Decimal('0') |
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4696 >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) |
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4697 Decimal('1') |
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4698 >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) |
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4699 Decimal('1') |
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4700 >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) |
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4701 Decimal('0') |
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4702 >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) |
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4703 Decimal('110') |
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4704 >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) |
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4705 Decimal('1101') |
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4706 >>> ExtendedContext.logical_xor(110, 1101) |
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4707 Decimal('1011') |
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4708 >>> ExtendedContext.logical_xor(Decimal(110), 1101) |
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4709 Decimal('1011') |
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4710 >>> ExtendedContext.logical_xor(110, Decimal(1101)) |
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4711 Decimal('1011') |
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4712 """ |
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4713 a = _convert_other(a, raiseit=True) |
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4714 return a.logical_xor(b, context=self) |
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4715 |
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4716 def max(self, a, b): |
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4717 """max compares two values numerically and returns the maximum. |
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4718 |
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4719 If either operand is a NaN then the general rules apply. |
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4720 Otherwise, the operands are compared as though by the compare |
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4721 operation. If they are numerically equal then the left-hand operand |
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4722 is chosen as the result. Otherwise the maximum (closer to positive |
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4723 infinity) of the two operands is chosen as the result. |
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4724 |
| 32482 | 4725 >>> ExtendedContext.max(Decimal('3'), Decimal('2')) |
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4726 Decimal('3') |
| 32482 | 4727 >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) |
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4728 Decimal('3') |
| 32482 | 4729 >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) |
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4730 Decimal('1') |
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4731 >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) |
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4732 Decimal('7') |
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4733 >>> ExtendedContext.max(1, 2) |
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4734 Decimal('2') |
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4735 >>> ExtendedContext.max(Decimal(1), 2) |
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4736 Decimal('2') |
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4737 >>> ExtendedContext.max(1, Decimal(2)) |
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4738 Decimal('2') |
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4739 """ |
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4740 a = _convert_other(a, raiseit=True) |
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4741 return a.max(b, context=self) |
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4742 |
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4743 def max_mag(self, a, b): |
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4744 """Compares the values numerically with their sign ignored. |
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4745 |
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4746 >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN')) |
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4747 Decimal('7') |
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4748 >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10')) |
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4749 Decimal('-10') |
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4750 >>> ExtendedContext.max_mag(1, -2) |
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4751 Decimal('-2') |
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4752 >>> ExtendedContext.max_mag(Decimal(1), -2) |
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4753 Decimal('-2') |
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4754 >>> ExtendedContext.max_mag(1, Decimal(-2)) |
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4755 Decimal('-2') |
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4756 """ |
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4757 a = _convert_other(a, raiseit=True) |
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4758 return a.max_mag(b, context=self) |
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4759 |
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4760 def min(self, a, b): |
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4761 """min compares two values numerically and returns the minimum. |
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4762 |
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4763 If either operand is a NaN then the general rules apply. |
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4764 Otherwise, the operands are compared as though by the compare |
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4765 operation. If they are numerically equal then the left-hand operand |
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4766 is chosen as the result. Otherwise the minimum (closer to negative |
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4767 infinity) of the two operands is chosen as the result. |
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4768 |
| 32482 | 4769 >>> ExtendedContext.min(Decimal('3'), Decimal('2')) |
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4770 Decimal('2') |
| 32482 | 4771 >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) |
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4772 Decimal('-10') |
| 32482 | 4773 >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) |
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4774 Decimal('1.0') |
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4775 >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) |
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4776 Decimal('7') |
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4777 >>> ExtendedContext.min(1, 2) |
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4778 Decimal('1') |
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4779 >>> ExtendedContext.min(Decimal(1), 2) |
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4780 Decimal('1') |
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4781 >>> ExtendedContext.min(1, Decimal(29)) |
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4782 Decimal('1') |
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4783 """ |
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4784 a = _convert_other(a, raiseit=True) |
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4785 return a.min(b, context=self) |
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4786 |
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4787 def min_mag(self, a, b): |
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4788 """Compares the values numerically with their sign ignored. |
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4789 |
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4790 >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2')) |
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4791 Decimal('-2') |
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4792 >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN')) |
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4793 Decimal('-3') |
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4794 >>> ExtendedContext.min_mag(1, -2) |
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4795 Decimal('1') |
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4796 >>> ExtendedContext.min_mag(Decimal(1), -2) |
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4797 Decimal('1') |
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4798 >>> ExtendedContext.min_mag(1, Decimal(-2)) |
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4799 Decimal('1') |
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4800 """ |
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4801 a = _convert_other(a, raiseit=True) |
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4802 return a.min_mag(b, context=self) |
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4803 |
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4804 def minus(self, a): |
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4805 """Minus corresponds to unary prefix minus in Python. |
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4806 |
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4807 The operation is evaluated using the same rules as subtract; the |
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4808 operation minus(a) is calculated as subtract('0', a) where the '0' |
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4809 has the same exponent as the operand. |
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4810 |
| 32482 | 4811 >>> ExtendedContext.minus(Decimal('1.3')) |
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4812 Decimal('-1.3') |
| 32482 | 4813 >>> ExtendedContext.minus(Decimal('-1.3')) |
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4814 Decimal('1.3') |
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4815 >>> ExtendedContext.minus(1) |
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4816 Decimal('-1') |
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4817 """ |
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4818 a = _convert_other(a, raiseit=True) |
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4819 return a.__neg__(context=self) |
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4820 |
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4821 def multiply(self, a, b): |
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4822 """multiply multiplies two operands. |
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4823 |
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4824 If either operand is a special value then the general rules apply. |
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4825 Otherwise, the operands are multiplied together |
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4826 ('long multiplication'), resulting in a number which may be as long as |
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4827 the sum of the lengths of the two operands. |
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4828 |
| 32482 | 4829 >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) |
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4830 Decimal('3.60') |
| 32482 | 4831 >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) |
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4832 Decimal('21') |
| 32482 | 4833 >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) |
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4834 Decimal('0.72') |
| 32482 | 4835 >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) |
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4836 Decimal('-0.0') |
| 32482 | 4837 >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) |
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4838 Decimal('4.28135971E+11') |
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4839 >>> ExtendedContext.multiply(7, 7) |
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4840 Decimal('49') |
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4841 >>> ExtendedContext.multiply(Decimal(7), 7) |
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4842 Decimal('49') |
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4843 >>> ExtendedContext.multiply(7, Decimal(7)) |
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4844 Decimal('49') |
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4845 """ |
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4846 a = _convert_other(a, raiseit=True) |
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4847 r = a.__mul__(b, context=self) |
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4848 if r is NotImplemented: |
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4849 raise TypeError("Unable to convert %s to Decimal" % b) |
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4850 else: |
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4851 return r |
|
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4852 |
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4853 def next_minus(self, a): |
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4854 """Returns the largest representable number smaller than a. |
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4855 |
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4856 >>> c = ExtendedContext.copy() |
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4857 >>> c.Emin = -999 |
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4858 >>> c.Emax = 999 |
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4859 >>> ExtendedContext.next_minus(Decimal('1')) |
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4860 Decimal('0.999999999') |
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4861 >>> c.next_minus(Decimal('1E-1007')) |
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4862 Decimal('0E-1007') |
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4863 >>> ExtendedContext.next_minus(Decimal('-1.00000003')) |
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4864 Decimal('-1.00000004') |
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4865 >>> c.next_minus(Decimal('Infinity')) |
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4866 Decimal('9.99999999E+999') |
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4867 >>> c.next_minus(1) |
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4868 Decimal('0.999999999') |
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4869 """ |
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4870 a = _convert_other(a, raiseit=True) |
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4871 return a.next_minus(context=self) |
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4872 |
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4873 def next_plus(self, a): |
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4874 """Returns the smallest representable number larger than a. |
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4875 |
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4876 >>> c = ExtendedContext.copy() |
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4877 >>> c.Emin = -999 |
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4878 >>> c.Emax = 999 |
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4879 >>> ExtendedContext.next_plus(Decimal('1')) |
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4880 Decimal('1.00000001') |
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4881 >>> c.next_plus(Decimal('-1E-1007')) |
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4882 Decimal('-0E-1007') |
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4883 >>> ExtendedContext.next_plus(Decimal('-1.00000003')) |
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4884 Decimal('-1.00000002') |
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4885 >>> c.next_plus(Decimal('-Infinity')) |
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4886 Decimal('-9.99999999E+999') |
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4887 >>> c.next_plus(1) |
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4888 Decimal('1.00000001') |
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4889 """ |
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4890 a = _convert_other(a, raiseit=True) |
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4891 return a.next_plus(context=self) |
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4892 |
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4893 def next_toward(self, a, b): |
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4894 """Returns the number closest to a, in direction towards b. |
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4895 |
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4896 The result is the closest representable number from the first |
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4897 operand (but not the first operand) that is in the direction |
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4898 towards the second operand, unless the operands have the same |
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4899 value. |
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4900 |
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4901 >>> c = ExtendedContext.copy() |
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4902 >>> c.Emin = -999 |
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4903 >>> c.Emax = 999 |
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4904 >>> c.next_toward(Decimal('1'), Decimal('2')) |
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4905 Decimal('1.00000001') |
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4906 >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) |
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4907 Decimal('-0E-1007') |
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4908 >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) |
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4909 Decimal('-1.00000002') |
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4910 >>> c.next_toward(Decimal('1'), Decimal('0')) |
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4911 Decimal('0.999999999') |
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4912 >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) |
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4913 Decimal('0E-1007') |
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4914 >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) |
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4915 Decimal('-1.00000004') |
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4916 >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) |
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4917 Decimal('-0.00') |
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4918 >>> c.next_toward(0, 1) |
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4919 Decimal('1E-1007') |
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4920 >>> c.next_toward(Decimal(0), 1) |
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4921 Decimal('1E-1007') |
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4922 >>> c.next_toward(0, Decimal(1)) |
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4923 Decimal('1E-1007') |
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4924 """ |
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4925 a = _convert_other(a, raiseit=True) |
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4926 return a.next_toward(b, context=self) |
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4927 |
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4928 def normalize(self, a): |
| 32496 | 4929 """normalize reduces an operand to its simplest form. |
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4930 |
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4931 Essentially a plus operation with all trailing zeros removed from the |
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4932 result. |
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4933 |
| 32482 | 4934 >>> ExtendedContext.normalize(Decimal('2.1')) |
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4935 Decimal('2.1') |
| 32482 | 4936 >>> ExtendedContext.normalize(Decimal('-2.0')) |
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4937 Decimal('-2') |
| 32482 | 4938 >>> ExtendedContext.normalize(Decimal('1.200')) |
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4939 Decimal('1.2') |
| 32482 | 4940 >>> ExtendedContext.normalize(Decimal('-120')) |
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4941 Decimal('-1.2E+2') |
| 32482 | 4942 >>> ExtendedContext.normalize(Decimal('120.00')) |
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4943 Decimal('1.2E+2') |
| 32482 | 4944 >>> ExtendedContext.normalize(Decimal('0.00')) |
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4945 Decimal('0') |
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4946 >>> ExtendedContext.normalize(6) |
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4947 Decimal('6') |
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4948 """ |
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4949 a = _convert_other(a, raiseit=True) |
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4950 return a.normalize(context=self) |
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4951 |
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4952 def number_class(self, a): |
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4953 """Returns an indication of the class of the operand. |
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4954 |
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4955 The class is one of the following strings: |
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4956 -sNaN |
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4957 -NaN |
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4958 -Infinity |
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4959 -Normal |
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4960 -Subnormal |
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4961 -Zero |
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4962 +Zero |
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4963 +Subnormal |
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4964 +Normal |
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4965 +Infinity |
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4966 |
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4967 >>> c = Context(ExtendedContext) |
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4968 >>> c.Emin = -999 |
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4969 >>> c.Emax = 999 |
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4970 >>> c.number_class(Decimal('Infinity')) |
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4971 '+Infinity' |
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4972 >>> c.number_class(Decimal('1E-10')) |
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4973 '+Normal' |
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4974 >>> c.number_class(Decimal('2.50')) |
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4975 '+Normal' |
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4976 >>> c.number_class(Decimal('0.1E-999')) |
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4977 '+Subnormal' |
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4978 >>> c.number_class(Decimal('0')) |
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4979 '+Zero' |
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4980 >>> c.number_class(Decimal('-0')) |
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4981 '-Zero' |
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4982 >>> c.number_class(Decimal('-0.1E-999')) |
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4983 '-Subnormal' |
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4984 >>> c.number_class(Decimal('-1E-10')) |
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4985 '-Normal' |
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4986 >>> c.number_class(Decimal('-2.50')) |
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4987 '-Normal' |
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4988 >>> c.number_class(Decimal('-Infinity')) |
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4989 '-Infinity' |
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4990 >>> c.number_class(Decimal('NaN')) |
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4991 'NaN' |
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4992 >>> c.number_class(Decimal('-NaN')) |
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4993 'NaN' |
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4994 >>> c.number_class(Decimal('sNaN')) |
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4995 'sNaN' |
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4996 >>> c.number_class(123) |
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4997 '+Normal' |
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43400
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4998 """ |
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4999 a = _convert_other(a, raiseit=True) |
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5000 return a.number_class(context=self) |
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5001 |
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5002 def plus(self, a): |
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5003 """Plus corresponds to unary prefix plus in Python. |
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5004 |
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5005 The operation is evaluated using the same rules as add; the |
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5006 operation plus(a) is calculated as add('0', a) where the '0' |
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5007 has the same exponent as the operand. |
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5008 |
| 32482 | 5009 >>> ExtendedContext.plus(Decimal('1.3')) |
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5010 Decimal('1.3') |
| 32482 | 5011 >>> ExtendedContext.plus(Decimal('-1.3')) |
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5012 Decimal('-1.3') |
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5013 >>> ExtendedContext.plus(-1) |
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5014 Decimal('-1') |
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5015 """ |
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5016 a = _convert_other(a, raiseit=True) |
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5017 return a.__pos__(context=self) |
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5018 |
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5019 def power(self, a, b, modulo=None): |
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5020 """Raises a to the power of b, to modulo if given. |
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5021 |
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5022 With two arguments, compute a**b. If a is negative then b |
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5023 must be integral. The result will be inexact unless b is |
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5024 integral and the result is finite and can be expressed exactly |
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5025 in 'precision' digits. |
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5026 |
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5027 With three arguments, compute (a**b) % modulo. For the |
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5028 three argument form, the following restrictions on the |
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5029 arguments hold: |
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5030 |
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5031 - all three arguments must be integral |
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5032 - b must be nonnegative |
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5033 - at least one of a or b must be nonzero |
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5034 - modulo must be nonzero and have at most 'precision' digits |
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5035 |
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5036 The result of pow(a, b, modulo) is identical to the result |
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5037 that would be obtained by computing (a**b) % modulo with |
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5038 unbounded precision, but is computed more efficiently. It is |
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5039 always exact. |
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5040 |
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5041 >>> c = ExtendedContext.copy() |
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5042 >>> c.Emin = -999 |
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5043 >>> c.Emax = 999 |
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5044 >>> c.power(Decimal('2'), Decimal('3')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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|
5045 Decimal('8') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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changeset
|
5046 >>> c.power(Decimal('-2'), Decimal('3')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5047 Decimal('-8') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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diff
changeset
|
5048 >>> c.power(Decimal('2'), Decimal('-3')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5049 Decimal('0.125') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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diff
changeset
|
5050 >>> c.power(Decimal('1.7'), Decimal('8')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5051 Decimal('69.7575744') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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diff
changeset
|
5052 >>> c.power(Decimal('10'), Decimal('0.301029996')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5053 Decimal('2.00000000') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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diff
changeset
|
5054 >>> c.power(Decimal('Infinity'), Decimal('-1')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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diff
changeset
|
5055 Decimal('0') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5056 >>> c.power(Decimal('Infinity'), Decimal('0')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5057 Decimal('1') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5058 >>> c.power(Decimal('Infinity'), Decimal('1')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5059 Decimal('Infinity') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5060 >>> c.power(Decimal('-Infinity'), Decimal('-1')) |
|
45333
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5061 Decimal('-0') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5062 >>> c.power(Decimal('-Infinity'), Decimal('0')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5063 Decimal('1') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5064 >>> c.power(Decimal('-Infinity'), Decimal('1')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5065 Decimal('-Infinity') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5066 >>> c.power(Decimal('-Infinity'), Decimal('2')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5067 Decimal('Infinity') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5068 >>> c.power(Decimal('0'), Decimal('0')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5069 Decimal('NaN') |
|
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Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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|
5070 |
|
1bac386c17cc
Merged revisions 58095-58132,58136-58148,58151-58197 via svnmerge from
Thomas Wouters <thomas@python.org>
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changeset
|
5071 >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
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changeset
|
5072 Decimal('11') |
|
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Thomas Wouters <thomas@python.org>
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changeset
|
5073 >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5074 Decimal('-11') |
|
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Thomas Wouters <thomas@python.org>
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changeset
|
5075 >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5076 Decimal('1') |
|
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Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5077 >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) |
|
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Merged revisions 60481,60485,60489-60492,60494-60496,60498-60499,60501-60503,60505-60506,60508-60509,60523-60524,60532,60543,60545,60547-60548,60552,60554,60556-60559,60561-60562,60569,60571-60572,60574,60576-60583,60585-60586,60589,60591,60594-60595,60597-60598,60600-60601,60606-60612,60615,60617,60619-60621,60623-60625,60627-60629,60631,60633,60635,60647,60650,60652,60654,60656,60658-60659,60664-60666,60668-60670,60672,60676,60678,60680-60683,60685-60686,60688,60690,60692-60694,60697-60700,60705-60706,60708,60711,60714,60720,60724-60730,60732,60736,60742,60744,60746,60748,60750-60766,60769-60786 via svnmerge from
Christian Heimes <christian@cheimes.de>
parents:
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changeset
|
5078 Decimal('11') |
|
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Thomas Wouters <thomas@python.org>
parents:
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diff
changeset
|
5079 >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) |
|
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5080 Decimal('11729830') |
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5081 >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) |
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5082 Decimal('-0') |
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5083 >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) |
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5084 Decimal('1') |
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5085 >>> ExtendedContext.power(7, 7) |
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5086 Decimal('823543') |
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5087 >>> ExtendedContext.power(Decimal(7), 7) |
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5088 Decimal('823543') |
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5089 >>> ExtendedContext.power(7, Decimal(7), 2) |
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5090 Decimal('1') |
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5091 """ |
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5092 a = _convert_other(a, raiseit=True) |
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5093 r = a.__pow__(b, modulo, context=self) |
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5094 if r is NotImplemented: |
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5095 raise TypeError("Unable to convert %s to Decimal" % b) |
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5096 else: |
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5097 return r |
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5098 |
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5099 def quantize(self, a, b): |
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5100 """Returns a value equal to 'a' (rounded), having the exponent of 'b'. |
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5101 |
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5102 The coefficient of the result is derived from that of the left-hand |
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5103 operand. It may be rounded using the current rounding setting (if the |
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5104 exponent is being increased), multiplied by a positive power of ten (if |
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5105 the exponent is being decreased), or is unchanged (if the exponent is |
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5106 already equal to that of the right-hand operand). |
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5107 |
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5108 Unlike other operations, if the length of the coefficient after the |
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5109 quantize operation would be greater than precision then an Invalid |
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5110 operation condition is raised. This guarantees that, unless there is |
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5111 an error condition, the exponent of the result of a quantize is always |
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5112 equal to that of the right-hand operand. |
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5113 |
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5114 Also unlike other operations, quantize will never raise Underflow, even |
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5115 if the result is subnormal and inexact. |
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5116 |
| 32482 | 5117 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) |
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5118 Decimal('2.170') |
| 32482 | 5119 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) |
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5120 Decimal('2.17') |
| 32482 | 5121 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) |
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5122 Decimal('2.2') |
| 32482 | 5123 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) |
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5124 Decimal('2') |
| 32482 | 5125 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) |
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5126 Decimal('0E+1') |
| 32482 | 5127 >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) |
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5128 Decimal('-Infinity') |
| 32482 | 5129 >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) |
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5130 Decimal('NaN') |
| 32482 | 5131 >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) |
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5132 Decimal('-0') |
| 32482 | 5133 >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) |
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5134 Decimal('-0E+5') |
| 32482 | 5135 >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) |
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|
5136 Decimal('NaN') |
| 32482 | 5137 >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) |
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5138 Decimal('NaN') |
| 32482 | 5139 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) |
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5140 Decimal('217.0') |
| 32482 | 5141 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) |
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5142 Decimal('217') |
| 32482 | 5143 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) |
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5144 Decimal('2.2E+2') |
| 32482 | 5145 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) |
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5146 Decimal('2E+2') |
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5147 >>> ExtendedContext.quantize(1, 2) |
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5148 Decimal('1') |
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5149 >>> ExtendedContext.quantize(Decimal(1), 2) |
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5150 Decimal('1') |
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5151 >>> ExtendedContext.quantize(1, Decimal(2)) |
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5152 Decimal('1') |
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5153 """ |
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5154 a = _convert_other(a, raiseit=True) |
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5155 return a.quantize(b, context=self) |
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5156 |
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5157 def radix(self): |
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5158 """Just returns 10, as this is Decimal, :) |
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5159 |
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5160 >>> ExtendedContext.radix() |
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5161 Decimal('10') |
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5162 """ |
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5163 return Decimal(10) |
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5164 |
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5165 def remainder(self, a, b): |
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5166 """Returns the remainder from integer division. |
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5167 |
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5168 The result is the residue of the dividend after the operation of |
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5169 calculating integer division as described for divide-integer, rounded |
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5170 to precision digits if necessary. The sign of the result, if |
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5171 non-zero, is the same as that of the original dividend. |
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5172 |
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5173 This operation will fail under the same conditions as integer division |
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5174 (that is, if integer division on the same two operands would fail, the |
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5175 remainder cannot be calculated). |
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5176 |
| 32482 | 5177 >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) |
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5178 Decimal('2.1') |
| 32482 | 5179 >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) |
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5180 Decimal('1') |
| 32482 | 5181 >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) |
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5182 Decimal('-1') |
| 32482 | 5183 >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) |
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5184 Decimal('0.2') |
| 32482 | 5185 >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) |
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5186 Decimal('0.1') |
| 32482 | 5187 >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) |
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5188 Decimal('1.0') |
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5189 >>> ExtendedContext.remainder(22, 6) |
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5190 Decimal('4') |
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5191 >>> ExtendedContext.remainder(Decimal(22), 6) |
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5192 Decimal('4') |
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5193 >>> ExtendedContext.remainder(22, Decimal(6)) |
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5194 Decimal('4') |
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5195 """ |
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5196 a = _convert_other(a, raiseit=True) |
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5197 r = a.__mod__(b, context=self) |
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5198 if r is NotImplemented: |
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5199 raise TypeError("Unable to convert %s to Decimal" % b) |
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5200 else: |
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5201 return r |
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5202 |
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5203 def remainder_near(self, a, b): |
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5204 """Returns to be "a - b * n", where n is the integer nearest the exact |
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5205 value of "x / b" (if two integers are equally near then the even one |
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5206 is chosen). If the result is equal to 0 then its sign will be the |
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5207 sign of a. |
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5208 |
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5209 This operation will fail under the same conditions as integer division |
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5210 (that is, if integer division on the same two operands would fail, the |
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5211 remainder cannot be calculated). |
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5212 |
| 32482 | 5213 >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) |
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5214 Decimal('-0.9') |
| 32482 | 5215 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) |
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5216 Decimal('-2') |
| 32482 | 5217 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) |
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5218 Decimal('1') |
| 32482 | 5219 >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) |
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5220 Decimal('-1') |
| 32482 | 5221 >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) |
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5222 Decimal('0.2') |
| 32482 | 5223 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) |
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5224 Decimal('0.1') |
| 32482 | 5225 >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) |
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5226 Decimal('-0.3') |
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5227 >>> ExtendedContext.remainder_near(3, 11) |
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5228 Decimal('3') |
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5229 >>> ExtendedContext.remainder_near(Decimal(3), 11) |
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5230 Decimal('3') |
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5231 >>> ExtendedContext.remainder_near(3, Decimal(11)) |
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5232 Decimal('3') |
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5233 """ |
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5234 a = _convert_other(a, raiseit=True) |
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5235 return a.remainder_near(b, context=self) |
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5236 |
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5237 def rotate(self, a, b): |
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5238 """Returns a rotated copy of a, b times. |
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5239 |
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5240 The coefficient of the result is a rotated copy of the digits in |
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5241 the coefficient of the first operand. The number of places of |
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5242 rotation is taken from the absolute value of the second operand, |
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5243 with the rotation being to the left if the second operand is |
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5244 positive or to the right otherwise. |
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5245 |
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5246 >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) |
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5247 Decimal('400000003') |
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5248 >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) |
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5249 Decimal('12') |
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5250 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) |
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5251 Decimal('891234567') |
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5252 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) |
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5253 Decimal('123456789') |
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5254 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) |
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5255 Decimal('345678912') |
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5256 >>> ExtendedContext.rotate(1333333, 1) |
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5257 Decimal('13333330') |
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5258 >>> ExtendedContext.rotate(Decimal(1333333), 1) |
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5259 Decimal('13333330') |
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5260 >>> ExtendedContext.rotate(1333333, Decimal(1)) |
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5261 Decimal('13333330') |
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5262 """ |
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5263 a = _convert_other(a, raiseit=True) |
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5264 return a.rotate(b, context=self) |
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5265 |
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5266 def same_quantum(self, a, b): |
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5267 """Returns True if the two operands have the same exponent. |
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5268 |
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5269 The result is never affected by either the sign or the coefficient of |
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5270 either operand. |
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5271 |
| 32482 | 5272 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) |
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5273 False |
| 32482 | 5274 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) |
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5275 True |
| 32482 | 5276 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) |
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5277 False |
| 32482 | 5278 >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) |
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5279 True |
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5280 >>> ExtendedContext.same_quantum(10000, -1) |
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5281 True |
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5282 >>> ExtendedContext.same_quantum(Decimal(10000), -1) |
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5283 True |
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5284 >>> ExtendedContext.same_quantum(10000, Decimal(-1)) |
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5285 True |
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5286 """ |
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5287 a = _convert_other(a, raiseit=True) |
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5288 return a.same_quantum(b) |
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5289 |
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5290 def scaleb (self, a, b): |
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5291 """Returns the first operand after adding the second value its exp. |
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5292 |
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5293 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) |
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5294 Decimal('0.0750') |
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5295 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) |
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5296 Decimal('7.50') |
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5297 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) |
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5298 Decimal('7.50E+3') |
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5299 >>> ExtendedContext.scaleb(1, 4) |
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5300 Decimal('1E+4') |
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5301 >>> ExtendedContext.scaleb(Decimal(1), 4) |
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5302 Decimal('1E+4') |
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5303 >>> ExtendedContext.scaleb(1, Decimal(4)) |
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5304 Decimal('1E+4') |
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5305 """ |
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5306 a = _convert_other(a, raiseit=True) |
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5307 return a.scaleb(b, context=self) |
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5308 |
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5309 def shift(self, a, b): |
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5310 """Returns a shifted copy of a, b times. |
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5311 |
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5312 The coefficient of the result is a shifted copy of the digits |
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5313 in the coefficient of the first operand. The number of places |
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5314 to shift is taken from the absolute value of the second operand, |
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5315 with the shift being to the left if the second operand is |
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5316 positive or to the right otherwise. Digits shifted into the |
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5317 coefficient are zeros. |
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5318 |
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5319 >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) |
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5320 Decimal('400000000') |
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5321 >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) |
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5322 Decimal('0') |
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5323 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) |
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5324 Decimal('1234567') |
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5325 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) |
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5326 Decimal('123456789') |
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5327 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) |
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5328 Decimal('345678900') |
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5329 >>> ExtendedContext.shift(88888888, 2) |
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5330 Decimal('888888800') |
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5331 >>> ExtendedContext.shift(Decimal(88888888), 2) |
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5332 Decimal('888888800') |
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5333 >>> ExtendedContext.shift(88888888, Decimal(2)) |
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5334 Decimal('888888800') |
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5335 """ |
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5336 a = _convert_other(a, raiseit=True) |
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5337 return a.shift(b, context=self) |
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5338 |
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5339 def sqrt(self, a): |
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5340 """Square root of a non-negative number to context precision. |
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5341 |
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5342 If the result must be inexact, it is rounded using the round-half-even |
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5343 algorithm. |
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5344 |
| 32482 | 5345 >>> ExtendedContext.sqrt(Decimal('0')) |
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5346 Decimal('0') |
| 32482 | 5347 >>> ExtendedContext.sqrt(Decimal('-0')) |
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5348 Decimal('-0') |
| 32482 | 5349 >>> ExtendedContext.sqrt(Decimal('0.39')) |
|
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5350 Decimal('0.624499800') |
| 32482 | 5351 >>> ExtendedContext.sqrt(Decimal('100')) |
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5352 Decimal('10') |
| 32482 | 5353 >>> ExtendedContext.sqrt(Decimal('1')) |
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5354 Decimal('1') |
| 32482 | 5355 >>> ExtendedContext.sqrt(Decimal('1.0')) |
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5356 Decimal('1.0') |
| 32482 | 5357 >>> ExtendedContext.sqrt(Decimal('1.00')) |
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5358 Decimal('1.0') |
| 32482 | 5359 >>> ExtendedContext.sqrt(Decimal('7')) |
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5360 Decimal('2.64575131') |
| 32482 | 5361 >>> ExtendedContext.sqrt(Decimal('10')) |
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5362 Decimal('3.16227766') |
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5363 >>> ExtendedContext.sqrt(2) |
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5364 Decimal('1.41421356') |
| 32482 | 5365 >>> ExtendedContext.prec |
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5366 9 |
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5367 """ |
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5368 a = _convert_other(a, raiseit=True) |
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5369 return a.sqrt(context=self) |
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5370 |
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5371 def subtract(self, a, b): |
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5372 """Return the difference between the two operands. |
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5373 |
| 32482 | 5374 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) |
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5375 Decimal('0.23') |
| 32482 | 5376 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) |
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5377 Decimal('0.00') |
| 32482 | 5378 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) |
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5379 Decimal('-0.77') |
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5380 >>> ExtendedContext.subtract(8, 5) |
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5381 Decimal('3') |
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5382 >>> ExtendedContext.subtract(Decimal(8), 5) |
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5383 Decimal('3') |
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5384 >>> ExtendedContext.subtract(8, Decimal(5)) |
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5385 Decimal('3') |
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5386 """ |
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5387 a = _convert_other(a, raiseit=True) |
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5388 r = a.__sub__(b, context=self) |
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5389 if r is NotImplemented: |
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5390 raise TypeError("Unable to convert %s to Decimal" % b) |
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5391 else: |
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5392 return r |
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5393 |
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5394 def to_eng_string(self, a): |
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5395 """Converts a number to a string, using scientific notation. |
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5396 |
|
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5397 The operation is not affected by the context. |
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5398 """ |
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5399 a = _convert_other(a, raiseit=True) |
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5400 return a.to_eng_string(context=self) |
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5401 |
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5402 def to_sci_string(self, a): |
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5403 """Converts a number to a string, using scientific notation. |
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5404 |
|
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5405 The operation is not affected by the context. |
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5406 """ |
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5407 a = _convert_other(a, raiseit=True) |
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5408 return a.__str__(context=self) |
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5409 |
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5410 def to_integral_exact(self, a): |
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5411 """Rounds to an integer. |
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5412 |
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5413 When the operand has a negative exponent, the result is the same |
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5414 as using the quantize() operation using the given operand as the |
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5415 left-hand-operand, 1E+0 as the right-hand-operand, and the precision |
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5416 of the operand as the precision setting; Inexact and Rounded flags |
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5417 are allowed in this operation. The rounding mode is taken from the |
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5418 context. |
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5419 |
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5420 >>> ExtendedContext.to_integral_exact(Decimal('2.1')) |
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5421 Decimal('2') |
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5422 >>> ExtendedContext.to_integral_exact(Decimal('100')) |
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5423 Decimal('100') |
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5424 >>> ExtendedContext.to_integral_exact(Decimal('100.0')) |
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5425 Decimal('100') |
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5426 >>> ExtendedContext.to_integral_exact(Decimal('101.5')) |
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5427 Decimal('102') |
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5428 >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) |
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5429 Decimal('-102') |
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5430 >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) |
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5431 Decimal('1.0E+6') |
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5432 >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) |
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5433 Decimal('7.89E+77') |
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5434 >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) |
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5435 Decimal('-Infinity') |
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5436 """ |
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5437 a = _convert_other(a, raiseit=True) |
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5438 return a.to_integral_exact(context=self) |
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5439 |
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5440 def to_integral_value(self, a): |
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5441 """Rounds to an integer. |
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5442 |
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5443 When the operand has a negative exponent, the result is the same |
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5444 as using the quantize() operation using the given operand as the |
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5445 left-hand-operand, 1E+0 as the right-hand-operand, and the precision |
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5446 of the operand as the precision setting, except that no flags will |
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5447 be set. The rounding mode is taken from the context. |
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5449 >>> ExtendedContext.to_integral_value(Decimal('2.1')) |
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5450 Decimal('2') |
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5451 >>> ExtendedContext.to_integral_value(Decimal('100')) |
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5452 Decimal('100') |
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5453 >>> ExtendedContext.to_integral_value(Decimal('100.0')) |
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5454 Decimal('100') |
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5455 >>> ExtendedContext.to_integral_value(Decimal('101.5')) |
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5456 Decimal('102') |
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5457 >>> ExtendedContext.to_integral_value(Decimal('-101.5')) |
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5458 Decimal('-102') |
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5459 >>> ExtendedContext.to_integral_value(Decimal('10E+5')) |
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5460 Decimal('1.0E+6') |
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5461 >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) |
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5462 Decimal('7.89E+77') |
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5463 >>> ExtendedContext.to_integral_value(Decimal('-Inf')) |
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5464 Decimal('-Infinity') |
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5465 """ |
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5466 a = _convert_other(a, raiseit=True) |
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5467 return a.to_integral_value(context=self) |
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5468 |
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5469 # the method name changed, but we provide also the old one, for compatibility |
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5470 to_integral = to_integral_value |
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5471 |
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5472 class _WorkRep(object): |
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5473 __slots__ = ('sign','int','exp') |
| 33851 | 5474 # sign: 0 or 1 |
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5475 # int: int |
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5476 # exp: None, int, or string |
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5477 |
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5478 def __init__(self, value=None): |
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5479 if value is None: |
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5480 self.sign = None |
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5481 self.int = 0 |
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5482 self.exp = None |
| 33851 | 5483 elif isinstance(value, Decimal): |
| 5484 self.sign = value._sign | |
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5485 self.int = int(value._int) |
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5486 self.exp = value._exp |
| 33851 | 5487 else: |
| 5488 # assert isinstance(value, tuple) | |
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5489 self.sign = value[0] |
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5490 self.int = value[1] |
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5491 self.exp = value[2] |
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5492 |
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5493 def __repr__(self): |
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5494 return "(%r, %r, %r)" % (self.sign, self.int, self.exp) |
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5495 |
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5496 __str__ = __repr__ |
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5497 |
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5498 |
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5499 |
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5500 def _normalize(op1, op2, prec = 0): |
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5501 """Normalizes op1, op2 to have the same exp and length of coefficient. |
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5502 |
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5503 Done during addition. |
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5504 """ |
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5505 if op1.exp < op2.exp: |
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5506 tmp = op2 |
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5507 other = op1 |
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5508 else: |
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5509 tmp = op1 |
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5510 other = op2 |
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5511 |
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5512 # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). |
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5513 # Then adding 10**exp to tmp has the same effect (after rounding) |
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5514 # as adding any positive quantity smaller than 10**exp; similarly |
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5515 # for subtraction. So if other is smaller than 10**exp we replace |
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5516 # it with 10**exp. This avoids tmp.exp - other.exp getting too large. |
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5517 tmp_len = len(str(tmp.int)) |
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5518 other_len = len(str(other.int)) |
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5519 exp = tmp.exp + min(-1, tmp_len - prec - 2) |
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5520 if other_len + other.exp - 1 < exp: |
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5521 other.int = 1 |
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5522 other.exp = exp |
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5523 |
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5524 tmp.int *= 10 ** (tmp.exp - other.exp) |
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5525 tmp.exp = other.exp |
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5526 return op1, op2 |
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5527 |
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5528 ##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### |
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5529 |
|
66506
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5530 _nbits = int.bit_length |
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5531 |
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5532 def _sqrt_nearest(n, a): |
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5533 """Closest integer to the square root of the positive integer n. a is |
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5534 an initial approximation to the square root. Any positive integer |
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5535 will do for a, but the closer a is to the square root of n the |
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5536 faster convergence will be. |
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5537 |
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5538 """ |
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5539 if n <= 0 or a <= 0: |
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5540 raise ValueError("Both arguments to _sqrt_nearest should be positive.") |
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5541 |
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5542 b=0 |
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5543 while a != b: |
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5544 b, a = a, a--n//a>>1 |
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5545 return a |
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5546 |
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5547 def _rshift_nearest(x, shift): |
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5548 """Given an integer x and a nonnegative integer shift, return closest |
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5549 integer to x / 2**shift; use round-to-even in case of a tie. |
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5550 |
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5551 """ |
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5552 b, q = 1 << shift, x >> shift |
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5553 return q + (2*(x & (b-1)) + (q&1) > b) |
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5554 |
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5555 def _div_nearest(a, b): |
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5556 """Closest integer to a/b, a and b positive integers; rounds to even |
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5557 in the case of a tie. |
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5558 |
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5559 """ |
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5560 q, r = divmod(a, b) |
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5561 return q + (2*r + (q&1) > b) |
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5562 |
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5563 def _ilog(x, M, L = 8): |
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5564 """Integer approximation to M*log(x/M), with absolute error boundable |
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5565 in terms only of x/M. |
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5566 |
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5567 Given positive integers x and M, return an integer approximation to |
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5568 M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference |
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5569 between the approximation and the exact result is at most 22. For |
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5570 L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In |
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5571 both cases these are upper bounds on the error; it will usually be |
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5572 much smaller.""" |
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5573 |
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5574 # The basic algorithm is the following: let log1p be the function |
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5575 # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use |
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5576 # the reduction |
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5577 # |
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5578 # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) |
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5579 # |
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5580 # repeatedly until the argument to log1p is small (< 2**-L in |
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5581 # absolute value). For small y we can use the Taylor series |
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5582 # expansion |
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5583 # |
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5584 # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T |
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5585 # |
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5586 # truncating at T such that y**T is small enough. The whole |
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5587 # computation is carried out in a form of fixed-point arithmetic, |
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5588 # with a real number z being represented by an integer |
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5589 # approximation to z*M. To avoid loss of precision, the y below |
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5590 # is actually an integer approximation to 2**R*y*M, where R is the |
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5591 # number of reductions performed so far. |
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5592 |
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5593 y = x-M |
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5594 # argument reduction; R = number of reductions performed |
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5595 R = 0 |
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5596 while (R <= L and abs(y) << L-R >= M or |
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5597 R > L and abs(y) >> R-L >= M): |
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5598 y = _div_nearest((M*y) << 1, |
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5599 M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) |
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5600 R += 1 |
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5601 |
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5602 # Taylor series with T terms |
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5603 T = -int(-10*len(str(M))//(3*L)) |
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5604 yshift = _rshift_nearest(y, R) |
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5605 w = _div_nearest(M, T) |
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5606 for k in range(T-1, 0, -1): |
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5607 w = _div_nearest(M, k) - _div_nearest(yshift*w, M) |
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5608 |
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5609 return _div_nearest(w*y, M) |
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5610 |
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5611 def _dlog10(c, e, p): |
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5612 """Given integers c, e and p with c > 0, p >= 0, compute an integer |
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5613 approximation to 10**p * log10(c*10**e), with an absolute error of |
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5614 at most 1. Assumes that c*10**e is not exactly 1.""" |
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5615 |
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5616 # increase precision by 2; compensate for this by dividing |
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5617 # final result by 100 |
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5618 p += 2 |
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5619 |
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5620 # write c*10**e as d*10**f with either: |
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5621 # f >= 0 and 1 <= d <= 10, or |
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5622 # f <= 0 and 0.1 <= d <= 1. |
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5623 # Thus for c*10**e close to 1, f = 0 |
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5624 l = len(str(c)) |
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5625 f = e+l - (e+l >= 1) |
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5626 |
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5627 if p > 0: |
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5628 M = 10**p |
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5629 k = e+p-f |
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5630 if k >= 0: |
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5631 c *= 10**k |
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5632 else: |
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5633 c = _div_nearest(c, 10**-k) |
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5634 |
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5635 log_d = _ilog(c, M) # error < 5 + 22 = 27 |
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5636 log_10 = _log10_digits(p) # error < 1 |
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5637 log_d = _div_nearest(log_d*M, log_10) |
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5638 log_tenpower = f*M # exact |
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5639 else: |
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5640 log_d = 0 # error < 2.31 |
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5641 log_tenpower = _div_nearest(f, 10**-p) # error < 0.5 |
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43400
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5642 |
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5643 return _div_nearest(log_tenpower+log_d, 100) |
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5644 |
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5645 def _dlog(c, e, p): |
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5646 """Given integers c, e and p with c > 0, compute an integer |
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5647 approximation to 10**p * log(c*10**e), with an absolute error of |
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5648 at most 1. Assumes that c*10**e is not exactly 1.""" |
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5649 |
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5650 # Increase precision by 2. The precision increase is compensated |
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5651 # for at the end with a division by 100. |
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5652 p += 2 |
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5653 |
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5654 # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, |
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5655 # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) |
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5656 # as 10**p * log(d) + 10**p*f * log(10). |
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5657 l = len(str(c)) |
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5658 f = e+l - (e+l >= 1) |
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5659 |
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5660 # compute approximation to 10**p*log(d), with error < 27 |
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5661 if p > 0: |
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5662 k = e+p-f |
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5663 if k >= 0: |
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5664 c *= 10**k |
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5665 else: |
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5666 c = _div_nearest(c, 10**-k) # error of <= 0.5 in c |
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5667 |
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5668 # _ilog magnifies existing error in c by a factor of at most 10 |
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5669 log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 |
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5670 else: |
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5671 # p <= 0: just approximate the whole thing by 0; error < 2.31 |
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5672 log_d = 0 |
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5673 |
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43734
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5674 # compute approximation to f*10**p*log(10), with error < 11. |
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43400
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5675 if f: |
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5676 extra = len(str(abs(f)))-1 |
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5677 if p + extra >= 0: |
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5678 # error in f * _log10_digits(p+extra) < |f| * 1 = |f| |
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5679 # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 |
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5680 f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) |
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43400
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5681 else: |
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5682 f_log_ten = 0 |
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5683 else: |
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5684 f_log_ten = 0 |
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5685 |
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5686 # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 |
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43400
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5687 return _div_nearest(f_log_ten + log_d, 100) |
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5688 |
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5689 class _Log10Memoize(object): |
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5690 """Class to compute, store, and allow retrieval of, digits of the |
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5691 constant log(10) = 2.302585.... This constant is needed by |
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5692 Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" |
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5693 def __init__(self): |
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5694 self.digits = "23025850929940456840179914546843642076011014886" |
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5695 |
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5696 def getdigits(self, p): |
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5697 """Given an integer p >= 0, return floor(10**p)*log(10). |
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5698 |
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5699 For example, self.getdigits(3) returns 2302. |
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5700 """ |
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5701 # digits are stored as a string, for quick conversion to |
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5702 # integer in the case that we've already computed enough |
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5703 # digits; the stored digits should always be correct |
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5704 # (truncated, not rounded to nearest). |
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5705 if p < 0: |
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5706 raise ValueError("p should be nonnegative") |
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5707 |
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5708 if p >= len(self.digits): |
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5709 # compute p+3, p+6, p+9, ... digits; continue until at |
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5710 # least one of the extra digits is nonzero |
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5711 extra = 3 |
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5712 while True: |
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5713 # compute p+extra digits, correct to within 1ulp |
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5714 M = 10**(p+extra+2) |
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5715 digits = str(_div_nearest(_ilog(10*M, M), 100)) |
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5716 if digits[-extra:] != '0'*extra: |
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5717 break |
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5718 extra += 3 |
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5719 # keep all reliable digits so far; remove trailing zeros |
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5720 # and next nonzero digit |
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5721 self.digits = digits.rstrip('0')[:-1] |
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5722 return int(self.digits[:p+1]) |
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5723 |
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5724 _log10_digits = _Log10Memoize().getdigits |
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5725 |
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43400
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5726 def _iexp(x, M, L=8): |
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5727 """Given integers x and M, M > 0, such that x/M is small in absolute |
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5728 value, compute an integer approximation to M*exp(x/M). For 0 <= |
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5729 x/M <= 2.4, the absolute error in the result is bounded by 60 (and |
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5730 is usually much smaller).""" |
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5731 |
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5732 # Algorithm: to compute exp(z) for a real number z, first divide z |
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5733 # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then |
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5734 # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor |
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5735 # series |
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5736 # |
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5737 # expm1(x) = x + x**2/2! + x**3/3! + ... |
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5738 # |
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5739 # Now use the identity |
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5740 # |
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5741 # expm1(2x) = expm1(x)*(expm1(x)+2) |
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5742 # |
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5743 # R times to compute the sequence expm1(z/2**R), |
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5744 # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). |
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5745 |
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5746 # Find R such that x/2**R/M <= 2**-L |
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5747 R = _nbits((x<<L)//M) |
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5748 |
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5749 # Taylor series. (2**L)**T > M |
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5750 T = -int(-10*len(str(M))//(3*L)) |
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5751 y = _div_nearest(x, T) |
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5752 Mshift = M<<R |
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5753 for i in range(T-1, 0, -1): |
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5754 y = _div_nearest(x*(Mshift + y), Mshift * i) |
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5755 |
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5756 # Expansion |
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5757 for k in range(R-1, -1, -1): |
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5758 Mshift = M<<(k+2) |
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5759 y = _div_nearest(y*(y+Mshift), Mshift) |
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5760 |
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5761 return M+y |
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5762 |
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5763 def _dexp(c, e, p): |
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5764 """Compute an approximation to exp(c*10**e), with p decimal places of |
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5765 precision. |
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5766 |
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5767 Returns integers d, f such that: |
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5768 |
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5769 10**(p-1) <= d <= 10**p, and |
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5770 (d-1)*10**f < exp(c*10**e) < (d+1)*10**f |
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5771 |
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5772 In other words, d*10**f is an approximation to exp(c*10**e) with p |
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5773 digits of precision, and with an error in d of at most 1. This is |
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5774 almost, but not quite, the same as the error being < 1ulp: when d |
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5775 = 10**(p-1) the error could be up to 10 ulp.""" |
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5776 |
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5777 # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision |
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5778 p += 2 |
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5779 |
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5780 # compute log(10) with extra precision = adjusted exponent of c*10**e |
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5781 extra = max(0, e + len(str(c)) - 1) |
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5782 q = p + extra |
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5783 |
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5784 # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), |
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5785 # rounding down |
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5786 shift = e+q |
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5787 if shift >= 0: |
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5788 cshift = c*10**shift |
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5789 else: |
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5790 cshift = c//10**-shift |
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5791 quot, rem = divmod(cshift, _log10_digits(q)) |
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5792 |
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5793 # reduce remainder back to original precision |
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5794 rem = _div_nearest(rem, 10**extra) |
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5795 |
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5796 # error in result of _iexp < 120; error after division < 0.62 |
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5797 return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 |
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5798 |
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5799 def _dpower(xc, xe, yc, ye, p): |
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5800 """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and |
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5801 y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: |
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5802 |
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5803 10**(p-1) <= c <= 10**p, and |
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5804 (c-1)*10**e < x**y < (c+1)*10**e |
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5805 |
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5806 in other words, c*10**e is an approximation to x**y with p digits |
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5807 of precision, and with an error in c of at most 1. (This is |
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5808 almost, but not quite, the same as the error being < 1ulp: when c |
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5809 == 10**(p-1) we can only guarantee error < 10ulp.) |
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5810 |
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5811 We assume that: x is positive and not equal to 1, and y is nonzero. |
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5812 """ |
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5813 |
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5814 # Find b such that 10**(b-1) <= |y| <= 10**b |
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5815 b = len(str(abs(yc))) + ye |
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5816 |
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5817 # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point |
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5818 lxc = _dlog(xc, xe, p+b+1) |
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5819 |
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5820 # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) |
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5821 shift = ye-b |
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5822 if shift >= 0: |
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5823 pc = lxc*yc*10**shift |
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5824 else: |
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5825 pc = _div_nearest(lxc*yc, 10**-shift) |
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5826 |
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5827 if pc == 0: |
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5828 # we prefer a result that isn't exactly 1; this makes it |
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5829 # easier to compute a correctly rounded result in __pow__ |
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5830 if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: |
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5831 coeff, exp = 10**(p-1)+1, 1-p |
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5832 else: |
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5833 coeff, exp = 10**p-1, -p |
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5834 else: |
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5835 coeff, exp = _dexp(pc, -(p+1), p+1) |
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5836 coeff = _div_nearest(coeff, 10) |
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5837 exp += 1 |
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5838 |
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5839 return coeff, exp |
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5840 |
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5841 def _log10_lb(c, correction = { |
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5842 '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, |
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5843 '6': 23, '7': 16, '8': 10, '9': 5}): |
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5844 """Compute a lower bound for 100*log10(c) for a positive integer c.""" |
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5845 if c <= 0: |
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5846 raise ValueError("The argument to _log10_lb should be nonnegative.") |
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5847 str_c = str(c) |
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5848 return 100*len(str_c) - correction[str_c[0]] |
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5849 |
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5850 ##### Helper Functions #################################################### |
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5851 |
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5852 def _convert_other(other, raiseit=False, allow_float=False): |
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5853 """Convert other to Decimal. |
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5854 |
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5855 Verifies that it's ok to use in an implicit construction. |
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5856 If allow_float is true, allow conversion from float; this |
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5857 is used in the comparison methods (__eq__ and friends). |
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5858 |
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5859 """ |
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5860 if isinstance(other, Decimal): |
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5861 return other |
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5862 if isinstance(other, int): |
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5863 return Decimal(other) |
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5864 if allow_float and isinstance(other, float): |
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5865 return Decimal.from_float(other) |
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5866 |
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5867 if raiseit: |
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5868 raise TypeError("Unable to convert %s to Decimal" % other) |
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5869 return NotImplemented |
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5870 |
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5871 def _convert_for_comparison(self, other, equality_op=False): |
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5872 """Given a Decimal instance self and a Python object other, return |
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5873 a pair (s, o) of Decimal instances such that "s op o" is |
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5874 equivalent to "self op other" for any of the 6 comparison |
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5875 operators "op". |
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5876 |
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5877 """ |
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5878 if isinstance(other, Decimal): |
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5879 return self, other |
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5880 |
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5881 # Comparison with a Rational instance (also includes integers): |
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5882 # self op n/d <=> self*d op n (for n and d integers, d positive). |
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5883 # A NaN or infinity can be left unchanged without affecting the |
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5884 # comparison result. |
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5885 if isinstance(other, _numbers.Rational): |
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5886 if not self._is_special: |
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5887 self = _dec_from_triple(self._sign, |
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|
5888 str(int(self._int) * other.denominator), |
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|
5889 self._exp) |
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5890 return self, Decimal(other.numerator) |
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5891 |
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5892 # Comparisons with float and complex types. == and != comparisons |
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5893 # with complex numbers should succeed, returning either True or False |
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5894 # as appropriate. Other comparisons return NotImplemented. |
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|
5895 if equality_op and isinstance(other, _numbers.Complex) and other.imag == 0: |
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5896 other = other.real |
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5897 if isinstance(other, float): |
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|
5898 return self, Decimal.from_float(other) |
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5899 return NotImplemented, NotImplemented |
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5900 |
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5901 |
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5902 ##### Setup Specific Contexts ############################################ |
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5903 |
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|
5904 # The default context prototype used by Context() |
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5905 # Is mutable, so that new contexts can have different default values |
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5906 |
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|
5907 DefaultContext = Context( |
|
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5908 prec=28, rounding=ROUND_HALF_EVEN, |
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5909 traps=[DivisionByZero, Overflow, InvalidOperation], |
|
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|
5910 flags=[], |
|
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|
5911 Emax=999999999, |
|
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|
5912 Emin=-999999999, |
|
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|
5913 capitals=1, |
|
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|
5914 clamp=0 |
|
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|
5915 ) |
|
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|
5916 |
|
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|
5917 # Pre-made alternate contexts offered by the specification |
|
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|
5918 # Don't change these; the user should be able to select these |
|
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|
5919 # contexts and be able to reproduce results from other implementations |
|
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|
5920 # of the spec. |
|
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|
5921 |
| 32482 | 5922 BasicContext = Context( |
|
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5923 prec=9, rounding=ROUND_HALF_UP, |
|
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|
5924 traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], |
|
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|
5925 flags=[], |
|
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|
5926 ) |
|
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5927 |
| 32482 | 5928 ExtendedContext = Context( |
|
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|
5929 prec=9, rounding=ROUND_HALF_EVEN, |
|
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|
5930 traps=[], |
|
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|
5931 flags=[], |
|
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5932 ) |
|
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5933 |
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5934 |
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5935 ##### crud for parsing strings ############################################# |
|
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5936 # |
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5937 # Regular expression used for parsing numeric strings. Additional |
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5938 # comments: |
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5939 # |
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5940 # 1. Uncomment the two '\s*' lines to allow leading and/or trailing |
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5941 # whitespace. But note that the specification disallows whitespace in |
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5942 # a numeric string. |
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5943 # |
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5944 # 2. For finite numbers (not infinities and NaNs) the body of the |
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5945 # number between the optional sign and the optional exponent must have |
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5946 # at least one decimal digit, possibly after the decimal point. The |
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5947 # lookahead expression '(?=\d|\.\d)' checks this. |
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5948 |
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5949 import re |
|
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5950 _parser = re.compile(r""" # A numeric string consists of: |
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5951 # \s* |
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5952 (?P<sign>[-+])? # an optional sign, followed by either... |
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5953 ( |
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5954 (?=\d|\.\d) # ...a number (with at least one digit) |
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5955 (?P<int>\d*) # having a (possibly empty) integer part |
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5956 (\.(?P<frac>\d*))? # followed by an optional fractional part |
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5957 (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... |
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5958 | |
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5959 Inf(inity)? # ...an infinity, or... |
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5960 | |
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5961 (?P<signal>s)? # ...an (optionally signaling) |
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5962 NaN # NaN |
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5963 (?P<diag>\d*) # with (possibly empty) diagnostic info. |
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5964 ) |
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5965 # \s* |
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5966 \Z |
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5967 """, re.VERBOSE | re.IGNORECASE).match |
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5969 _all_zeros = re.compile('0*$').match |
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5970 _exact_half = re.compile('50*$').match |
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5971 |
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5972 ##### PEP3101 support functions ############################################## |
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5973 # The functions in this section have little to do with the Decimal |
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5974 # class, and could potentially be reused or adapted for other pure |
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5975 # Python numeric classes that want to implement __format__ |
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5976 # |
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5977 # A format specifier for Decimal looks like: |
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5978 # |
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5979 # [[fill]align][sign][#][0][minimumwidth][,][.precision][type] |
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5980 |
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5981 _parse_format_specifier_regex = re.compile(r"""\A |
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5982 (?: |
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5983 (?P<fill>.)? |
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5984 (?P<align>[<>=^]) |
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5985 )? |
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5986 (?P<sign>[-+ ])? |
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5987 (?P<alt>\#)? |
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5988 (?P<zeropad>0)? |
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5989 (?P<minimumwidth>(?!0)\d+)? |
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5990 (?P<thousands_sep>,)? |
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5991 (?:\.(?P<precision>0|(?!0)\d+))? |
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5992 (?P<type>[eEfFgGn%])? |
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5993 \Z |
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5994 """, re.VERBOSE) |
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5995 |
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5996 del re |
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5997 |
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5998 # The locale module is only needed for the 'n' format specifier. The |
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5999 # rest of the PEP 3101 code functions quite happily without it, so we |
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6000 # don't care too much if locale isn't present. |
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6001 try: |
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6002 import locale as _locale |
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6003 except ImportError: |
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6004 pass |
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6005 |
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6006 def _parse_format_specifier(format_spec, _localeconv=None): |
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6007 """Parse and validate a format specifier. |
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6008 |
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6009 Turns a standard numeric format specifier into a dict, with the |
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6010 following entries: |
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6011 |
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6012 fill: fill character to pad field to minimum width |
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6013 align: alignment type, either '<', '>', '=' or '^' |
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6014 sign: either '+', '-' or ' ' |
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6015 minimumwidth: nonnegative integer giving minimum width |
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6016 zeropad: boolean, indicating whether to pad with zeros |
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6017 thousands_sep: string to use as thousands separator, or '' |
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6018 grouping: grouping for thousands separators, in format |
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6019 used by localeconv |
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6020 decimal_point: string to use for decimal point |
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6021 precision: nonnegative integer giving precision, or None |
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6022 type: one of the characters 'eEfFgG%', or None |
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6023 |
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6024 """ |
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6025 m = _parse_format_specifier_regex.match(format_spec) |
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6026 if m is None: |
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6027 raise ValueError("Invalid format specifier: " + format_spec) |
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6028 |
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6029 # get the dictionary |
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6030 format_dict = m.groupdict() |
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6032 # zeropad; defaults for fill and alignment. If zero padding |
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6033 # is requested, the fill and align fields should be absent. |
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6034 fill = format_dict['fill'] |
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6035 align = format_dict['align'] |
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6036 format_dict['zeropad'] = (format_dict['zeropad'] is not None) |
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6037 if format_dict['zeropad']: |
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6038 if fill is not None: |
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6039 raise ValueError("Fill character conflicts with '0'" |
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6040 " in format specifier: " + format_spec) |
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6041 if align is not None: |
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6042 raise ValueError("Alignment conflicts with '0' in " |
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6043 "format specifier: " + format_spec) |
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6044 format_dict['fill'] = fill or ' ' |
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6045 # PEP 3101 originally specified that the default alignment should |
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6046 # be left; it was later agreed that right-aligned makes more sense |
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6047 # for numeric types. See http://bugs.python.org/issue6857. |
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6048 format_dict['align'] = align or '>' |
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6049 |
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6050 # default sign handling: '-' for negative, '' for positive |
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6051 if format_dict['sign'] is None: |
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6052 format_dict['sign'] = '-' |
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6053 |
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6054 # minimumwidth defaults to 0; precision remains None if not given |
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6055 format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0') |
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6056 if format_dict['precision'] is not None: |
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6057 format_dict['precision'] = int(format_dict['precision']) |
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6058 |
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6059 # if format type is 'g' or 'G' then a precision of 0 makes little |
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6060 # sense; convert it to 1. Same if format type is unspecified. |
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6061 if format_dict['precision'] == 0: |
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6062 if format_dict['type'] is None or format_dict['type'] in 'gG': |
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6063 format_dict['precision'] = 1 |
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6064 |
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6065 # determine thousands separator, grouping, and decimal separator, and |
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6066 # add appropriate entries to format_dict |
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6067 if format_dict['type'] == 'n': |
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6068 # apart from separators, 'n' behaves just like 'g' |
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6069 format_dict['type'] = 'g' |
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6070 if _localeconv is None: |
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6071 _localeconv = _locale.localeconv() |
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6072 if format_dict['thousands_sep'] is not None: |
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6073 raise ValueError("Explicit thousands separator conflicts with " |
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6074 "'n' type in format specifier: " + format_spec) |
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6075 format_dict['thousands_sep'] = _localeconv['thousands_sep'] |
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6076 format_dict['grouping'] = _localeconv['grouping'] |
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6077 format_dict['decimal_point'] = _localeconv['decimal_point'] |
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6078 else: |
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6079 if format_dict['thousands_sep'] is None: |
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6080 format_dict['thousands_sep'] = '' |
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6081 format_dict['grouping'] = [3, 0] |
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6082 format_dict['decimal_point'] = '.' |
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6083 |
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6084 return format_dict |
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6085 |
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6086 def _format_align(sign, body, spec): |
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6087 """Given an unpadded, non-aligned numeric string 'body' and sign |
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6088 string 'sign', add padding and alignment conforming to the given |
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6089 format specifier dictionary 'spec' (as produced by |
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6090 parse_format_specifier). |
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6091 |
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6092 """ |
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6093 # how much extra space do we have to play with? |
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6094 minimumwidth = spec['minimumwidth'] |
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6095 fill = spec['fill'] |
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6096 padding = fill*(minimumwidth - len(sign) - len(body)) |
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6097 |
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6098 align = spec['align'] |
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6099 if align == '<': |
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6100 result = sign + body + padding |
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6101 elif align == '>': |
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6102 result = padding + sign + body |
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6103 elif align == '=': |
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6104 result = sign + padding + body |
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6105 elif align == '^': |
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6106 half = len(padding)//2 |
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6107 result = padding[:half] + sign + body + padding[half:] |
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6108 else: |
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6109 raise ValueError('Unrecognised alignment field') |
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6110 |
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6111 return result |
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6112 |
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6113 def _group_lengths(grouping): |
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6114 """Convert a localeconv-style grouping into a (possibly infinite) |
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6115 iterable of integers representing group lengths. |
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6116 |
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6117 """ |
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6118 # The result from localeconv()['grouping'], and the input to this |
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6119 # function, should be a list of integers in one of the |
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6120 # following three forms: |
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6121 # |
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6122 # (1) an empty list, or |
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6123 # (2) nonempty list of positive integers + [0] |
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6124 # (3) list of positive integers + [locale.CHAR_MAX], or |
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6125 |
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6126 from itertools import chain, repeat |
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6127 if not grouping: |
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6128 return [] |
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6129 elif grouping[-1] == 0 and len(grouping) >= 2: |
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6130 return chain(grouping[:-1], repeat(grouping[-2])) |
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6131 elif grouping[-1] == _locale.CHAR_MAX: |
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6132 return grouping[:-1] |
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6133 else: |
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6134 raise ValueError('unrecognised format for grouping') |
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6135 |
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6136 def _insert_thousands_sep(digits, spec, min_width=1): |
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6137 """Insert thousands separators into a digit string. |
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6138 |
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6139 spec is a dictionary whose keys should include 'thousands_sep' and |
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6140 'grouping'; typically it's the result of parsing the format |
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6141 specifier using _parse_format_specifier. |
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6142 |
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6143 The min_width keyword argument gives the minimum length of the |
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6144 result, which will be padded on the left with zeros if necessary. |
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6145 |
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6146 If necessary, the zero padding adds an extra '0' on the left to |
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6147 avoid a leading thousands separator. For example, inserting |
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6148 commas every three digits in '123456', with min_width=8, gives |
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6149 '0,123,456', even though that has length 9. |
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6150 |
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6151 """ |
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6152 |
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6153 sep = spec['thousands_sep'] |
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6154 grouping = spec['grouping'] |
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6155 |
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6156 groups = [] |
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6157 for l in _group_lengths(grouping): |
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6158 if l <= 0: |
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6159 raise ValueError("group length should be positive") |
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6160 # max(..., 1) forces at least 1 digit to the left of a separator |
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6161 l = min(max(len(digits), min_width, 1), l) |
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6162 groups.append('0'*(l - len(digits)) + digits[-l:]) |
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6163 digits = digits[:-l] |
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6164 min_width -= l |
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6165 if not digits and min_width <= 0: |
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6166 break |
|
52201
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6167 min_width -= len(sep) |
|
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6168 else: |
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6169 l = max(len(digits), min_width, 1) |
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6170 groups.append('0'*(l - len(digits)) + digits[-l:]) |
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6171 return sep.join(reversed(groups)) |
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6172 |
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6173 def _format_sign(is_negative, spec): |
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6174 """Determine sign character.""" |
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6175 |
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6176 if is_negative: |
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6177 return '-' |
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6178 elif spec['sign'] in ' +': |
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6179 return spec['sign'] |
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6180 else: |
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6181 return '' |
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|
6182 |
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6183 def _format_number(is_negative, intpart, fracpart, exp, spec): |
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6184 """Format a number, given the following data: |
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6185 |
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6186 is_negative: true if the number is negative, else false |
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6187 intpart: string of digits that must appear before the decimal point |
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6188 fracpart: string of digits that must come after the point |
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6189 exp: exponent, as an integer |
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6190 spec: dictionary resulting from parsing the format specifier |
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6191 |
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6192 This function uses the information in spec to: |
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6193 insert separators (decimal separator and thousands separators) |
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6194 format the sign |
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6195 format the exponent |
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6196 add trailing '%' for the '%' type |
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6197 zero-pad if necessary |
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6198 fill and align if necessary |
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6199 """ |
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6200 |
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6201 sign = _format_sign(is_negative, spec) |
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6202 |
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66444
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Issue #7094: Add alternate ('#') flag to __format__ methods for float, complex and Decimal. Allows greater control over when decimal points appear. Added to make transitioning from %-formatting easier. '#g' still has a problem with Decimal which I'll fix soon.
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6203 if fracpart or spec['alt']: |
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6204 fracpart = spec['decimal_point'] + fracpart |
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6205 |
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6206 if exp != 0 or spec['type'] in 'eE': |
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6207 echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']] |
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6208 fracpart += "{0}{1:+}".format(echar, exp) |
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6209 if spec['type'] == '%': |
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6210 fracpart += '%' |
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6211 |
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6212 if spec['zeropad']: |
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6213 min_width = spec['minimumwidth'] - len(fracpart) - len(sign) |
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6214 else: |
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6215 min_width = 0 |
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6216 intpart = _insert_thousands_sep(intpart, spec, min_width) |
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6218 return _format_align(sign, intpart+fracpart, spec) |
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6221 ##### Useful Constants (internal use only) ################################ |
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6223 # Reusable defaults |
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6224 _Infinity = Decimal('Inf') |
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6225 _NegativeInfinity = Decimal('-Inf') |
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6226 _NaN = Decimal('NaN') |
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6227 _Zero = Decimal(0) |
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6228 _One = Decimal(1) |
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6229 _NegativeOne = Decimal(-1) |
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6231 # _SignedInfinity[sign] is infinity w/ that sign |
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6232 _SignedInfinity = (_Infinity, _NegativeInfinity) |
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6234 # Constants related to the hash implementation; hash(x) is based |
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6235 # on the reduction of x modulo _PyHASH_MODULUS |
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6236 import sys |
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6237 _PyHASH_MODULUS = sys.hash_info.modulus |
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6238 # hash values to use for positive and negative infinities, and nans |
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6239 _PyHASH_INF = sys.hash_info.inf |
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6240 _PyHASH_NAN = sys.hash_info.nan |
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6241 del sys |
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6243 # _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS |
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6244 _PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS) |
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6247 if __name__ == '__main__': |
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6248 import doctest, decimal |
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6249 doctest.testmod(decimal) |