Mercurial > cpython-lru_cache-weakref
annotate Lib/decimal.py @ 79691:05c8928362ee
Merge __next__ method link fixes with 3.3.
| author | Ezio Melotti <ezio.melotti@gmail.com> |
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| date | Fri, 12 Oct 2012 13:46:37 +0300 |
| parents | 52aaa9295cc4 |
| children | 29becac5dd9b 7ada0faded9b |
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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('123.45e12345678') |
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50 Decimal('1.2345E+12345680') |
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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 'FloatOperation', |
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126 |
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127 # Constants for use in setting up contexts |
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128 'ROUND_DOWN', 'ROUND_HALF_UP', 'ROUND_HALF_EVEN', 'ROUND_CEILING', |
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129 'ROUND_FLOOR', 'ROUND_UP', 'ROUND_HALF_DOWN', 'ROUND_05UP', |
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130 |
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131 # Functions for manipulating contexts |
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132 'setcontext', 'getcontext', 'localcontext', |
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133 |
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134 # Limits for the C version for compatibility |
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135 'MAX_PREC', 'MAX_EMAX', 'MIN_EMIN', 'MIN_ETINY', |
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136 |
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137 # C version: compile time choice that enables the thread local context |
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138 'HAVE_THREADS' |
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139 ] |
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140 |
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141 __version__ = '1.70' # Highest version of the spec this complies with |
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142 # See http://speleotrove.com/decimal/ |
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143 |
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144 import copy as _copy |
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145 import math as _math |
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146 import numbers as _numbers |
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147 import sys |
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148 |
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149 try: |
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150 from collections import namedtuple as _namedtuple |
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151 DecimalTuple = _namedtuple('DecimalTuple', 'sign digits exponent') |
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152 except ImportError: |
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153 DecimalTuple = lambda *args: args |
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154 |
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155 # Rounding |
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156 ROUND_DOWN = 'ROUND_DOWN' |
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157 ROUND_HALF_UP = 'ROUND_HALF_UP' |
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158 ROUND_HALF_EVEN = 'ROUND_HALF_EVEN' |
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159 ROUND_CEILING = 'ROUND_CEILING' |
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160 ROUND_FLOOR = 'ROUND_FLOOR' |
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161 ROUND_UP = 'ROUND_UP' |
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162 ROUND_HALF_DOWN = 'ROUND_HALF_DOWN' |
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163 ROUND_05UP = 'ROUND_05UP' |
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164 |
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165 # Compatibility with the C version |
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166 HAVE_THREADS = True |
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167 if sys.maxsize == 2**63-1: |
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168 MAX_PREC = 999999999999999999 |
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169 MAX_EMAX = 999999999999999999 |
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170 MIN_EMIN = -999999999999999999 |
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171 else: |
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172 MAX_PREC = 425000000 |
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173 MAX_EMAX = 425000000 |
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174 MIN_EMIN = -425000000 |
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175 |
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176 MIN_ETINY = MIN_EMIN - (MAX_PREC-1) |
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177 |
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178 # Errors |
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179 |
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180 class DecimalException(ArithmeticError): |
| 32560 | 181 """Base exception class. |
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182 |
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183 Used exceptions derive from this. |
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184 If an exception derives from another exception besides this (such as |
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185 Underflow (Inexact, Rounded, Subnormal) that indicates that it is only |
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186 called if the others are present. This isn't actually used for |
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187 anything, though. |
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188 |
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189 handle -- Called when context._raise_error is called and the |
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190 trap_enabler is not set. First argument is self, second is the |
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191 context. More arguments can be given, those being after |
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192 the explanation in _raise_error (For example, |
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193 context._raise_error(NewError, '(-x)!', self._sign) would |
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194 call NewError().handle(context, self._sign).) |
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195 |
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196 To define a new exception, it should be sufficient to have it derive |
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197 from DecimalException. |
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198 """ |
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199 def handle(self, context, *args): |
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200 pass |
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201 |
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202 |
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203 class Clamped(DecimalException): |
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204 """Exponent of a 0 changed to fit bounds. |
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205 |
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206 This occurs and signals clamped if the exponent of a result has been |
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207 altered in order to fit the constraints of a specific concrete |
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208 representation. This may occur when the exponent of a zero result would |
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209 be outside the bounds of a representation, or when a large normal |
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210 number would have an encoded exponent that cannot be represented. In |
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211 this latter case, the exponent is reduced to fit and the corresponding |
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212 number of zero digits are appended to the coefficient ("fold-down"). |
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213 """ |
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214 |
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215 class InvalidOperation(DecimalException): |
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216 """An invalid operation was performed. |
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217 |
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218 Various bad things cause this: |
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219 |
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220 Something creates a signaling NaN |
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221 -INF + INF |
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222 0 * (+-)INF |
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223 (+-)INF / (+-)INF |
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224 x % 0 |
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225 (+-)INF % x |
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226 x._rescale( non-integer ) |
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227 sqrt(-x) , x > 0 |
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228 0 ** 0 |
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229 x ** (non-integer) |
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230 x ** (+-)INF |
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231 An operand is invalid |
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232 |
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233 The result of the operation after these is a quiet positive NaN, |
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234 except when the cause is a signaling NaN, in which case the result is |
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235 also a quiet NaN, but with the original sign, and an optional |
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236 diagnostic information. |
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237 """ |
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238 def handle(self, context, *args): |
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239 if args: |
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240 ans = _dec_from_triple(args[0]._sign, args[0]._int, 'n', True) |
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241 return ans._fix_nan(context) |
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242 return _NaN |
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243 |
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244 class ConversionSyntax(InvalidOperation): |
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245 """Trying to convert badly formed string. |
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246 |
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247 This occurs and signals invalid-operation if an string is being |
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248 converted to a number and it does not conform to the numeric string |
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249 syntax. The result is [0,qNaN]. |
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250 """ |
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251 def handle(self, context, *args): |
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252 return _NaN |
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253 |
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254 class DivisionByZero(DecimalException, ZeroDivisionError): |
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255 """Division by 0. |
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256 |
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257 This occurs and signals division-by-zero if division of a finite number |
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258 by zero was attempted (during a divide-integer or divide operation, or a |
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259 power operation with negative right-hand operand), and the dividend was |
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260 not zero. |
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261 |
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262 The result of the operation is [sign,inf], where sign is the exclusive |
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263 or of the signs of the operands for divide, or is 1 for an odd power of |
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264 -0, for power. |
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265 """ |
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266 |
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267 def handle(self, context, sign, *args): |
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268 return _SignedInfinity[sign] |
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269 |
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270 class DivisionImpossible(InvalidOperation): |
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271 """Cannot perform the division adequately. |
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272 |
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273 This occurs and signals invalid-operation if the integer result of a |
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274 divide-integer or remainder operation had too many digits (would be |
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275 longer than precision). The result is [0,qNaN]. |
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276 """ |
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277 |
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278 def handle(self, context, *args): |
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279 return _NaN |
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280 |
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281 class DivisionUndefined(InvalidOperation, ZeroDivisionError): |
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282 """Undefined result of division. |
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283 |
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284 This occurs and signals invalid-operation if division by zero was |
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285 attempted (during a divide-integer, divide, or remainder operation), and |
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286 the dividend is also zero. The result is [0,qNaN]. |
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287 """ |
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288 |
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289 def handle(self, context, *args): |
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290 return _NaN |
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291 |
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292 class Inexact(DecimalException): |
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293 """Had to round, losing information. |
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294 |
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295 This occurs and signals inexact whenever the result of an operation is |
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296 not exact (that is, it needed to be rounded and any discarded digits |
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297 were non-zero), or if an overflow or underflow condition occurs. The |
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298 result in all cases is unchanged. |
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299 |
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300 The inexact signal may be tested (or trapped) to determine if a given |
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301 operation (or sequence of operations) was inexact. |
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302 """ |
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303 |
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304 class InvalidContext(InvalidOperation): |
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305 """Invalid context. Unknown rounding, for example. |
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306 |
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307 This occurs and signals invalid-operation if an invalid context was |
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308 detected during an operation. This can occur if contexts are not checked |
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309 on creation and either the precision exceeds the capability of the |
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310 underlying concrete representation or an unknown or unsupported rounding |
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311 was specified. These aspects of the context need only be checked when |
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312 the values are required to be used. The result is [0,qNaN]. |
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313 """ |
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314 |
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315 def handle(self, context, *args): |
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316 return _NaN |
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317 |
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318 class Rounded(DecimalException): |
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319 """Number got rounded (not necessarily changed during rounding). |
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320 |
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321 This occurs and signals rounded whenever the result of an operation is |
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322 rounded (that is, some zero or non-zero digits were discarded from the |
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323 coefficient), or if an overflow or underflow condition occurs. The |
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324 result in all cases is unchanged. |
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325 |
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326 The rounded signal may be tested (or trapped) to determine if a given |
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327 operation (or sequence of operations) caused a loss of precision. |
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328 """ |
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329 |
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330 class Subnormal(DecimalException): |
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331 """Exponent < Emin before rounding. |
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332 |
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333 This occurs and signals subnormal whenever the result of a conversion or |
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334 operation is subnormal (that is, its adjusted exponent is less than |
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335 Emin, before any rounding). The result in all cases is unchanged. |
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336 |
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337 The subnormal signal may be tested (or trapped) to determine if a given |
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338 or operation (or sequence of operations) yielded a subnormal result. |
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339 """ |
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340 |
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341 class Overflow(Inexact, Rounded): |
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342 """Numerical overflow. |
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343 |
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344 This occurs and signals overflow if the adjusted exponent of a result |
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345 (from a conversion or from an operation that is not an attempt to divide |
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346 by zero), after rounding, would be greater than the largest value that |
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347 can be handled by the implementation (the value Emax). |
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348 |
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349 The result depends on the rounding mode: |
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350 |
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351 For round-half-up and round-half-even (and for round-half-down and |
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352 round-up, if implemented), the result of the operation is [sign,inf], |
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353 where sign is the sign of the intermediate result. For round-down, the |
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354 result is the largest finite number that can be represented in the |
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355 current precision, with the sign of the intermediate result. For |
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356 round-ceiling, the result is the same as for round-down if the sign of |
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357 the intermediate result is 1, or is [0,inf] otherwise. For round-floor, |
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358 the result is the same as for round-down if the sign of the intermediate |
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359 result is 0, or is [1,inf] otherwise. In all cases, Inexact and Rounded |
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360 will also be raised. |
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361 """ |
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362 |
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363 def handle(self, context, sign, *args): |
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364 if context.rounding in (ROUND_HALF_UP, ROUND_HALF_EVEN, |
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365 ROUND_HALF_DOWN, ROUND_UP): |
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366 return _SignedInfinity[sign] |
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367 if sign == 0: |
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368 if context.rounding == ROUND_CEILING: |
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369 return _SignedInfinity[sign] |
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370 return _dec_from_triple(sign, '9'*context.prec, |
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371 context.Emax-context.prec+1) |
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372 if sign == 1: |
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373 if context.rounding == ROUND_FLOOR: |
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374 return _SignedInfinity[sign] |
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375 return _dec_from_triple(sign, '9'*context.prec, |
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376 context.Emax-context.prec+1) |
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377 |
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378 |
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379 class Underflow(Inexact, Rounded, Subnormal): |
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380 """Numerical underflow with result rounded to 0. |
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381 |
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382 This occurs and signals underflow if a result is inexact and the |
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383 adjusted exponent of the result would be smaller (more negative) than |
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384 the smallest value that can be handled by the implementation (the value |
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385 Emin). That is, the result is both inexact and subnormal. |
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386 |
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387 The result after an underflow will be a subnormal number rounded, if |
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388 necessary, so that its exponent is not less than Etiny. This may result |
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389 in 0 with the sign of the intermediate result and an exponent of Etiny. |
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390 |
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391 In all cases, Inexact, Rounded, and Subnormal will also be raised. |
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392 """ |
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393 |
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394 class FloatOperation(DecimalException, TypeError): |
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395 """Enable stricter semantics for mixing floats and Decimals. |
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396 |
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397 If the signal is not trapped (default), mixing floats and Decimals is |
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398 permitted in the Decimal() constructor, context.create_decimal() and |
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399 all comparison operators. Both conversion and comparisons are exact. |
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400 Any occurrence of a mixed operation is silently recorded by setting |
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401 FloatOperation in the context flags. Explicit conversions with |
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402 Decimal.from_float() or context.create_decimal_from_float() do not |
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403 set the flag. |
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404 |
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405 Otherwise (the signal is trapped), only equality comparisons and explicit |
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406 conversions are silent. All other mixed operations raise FloatOperation. |
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407 """ |
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408 |
| 32560 | 409 # List of public traps and flags |
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410 _signals = [Clamped, DivisionByZero, Inexact, Overflow, Rounded, |
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411 Underflow, InvalidOperation, Subnormal, FloatOperation] |
| 32560 | 412 |
| 413 # Map conditions (per the spec) to signals | |
| 414 _condition_map = {ConversionSyntax:InvalidOperation, | |
| 415 DivisionImpossible:InvalidOperation, | |
| 416 DivisionUndefined:InvalidOperation, | |
| 417 InvalidContext:InvalidOperation} | |
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418 |
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419 # Valid rounding modes |
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420 _rounding_modes = (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_CEILING, |
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421 ROUND_FLOOR, ROUND_UP, ROUND_HALF_DOWN, ROUND_05UP) |
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422 |
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423 ##### Context Functions ################################################## |
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424 |
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425 # The getcontext() and setcontext() function manage access to a thread-local |
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426 # current context. Py2.4 offers direct support for thread locals. If that |
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427 # is not available, use threading.current_thread() which is slower but will |
| 34184 | 428 # work for older Pythons. If threads are not part of the build, create a |
| 429 # mock threading object with threading.local() returning the module namespace. | |
| 430 | |
| 431 try: | |
| 432 import threading | |
| 433 except ImportError: | |
| 434 # Python was compiled without threads; create a mock object instead | |
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435 class MockThreading(object): |
| 34184 | 436 def local(self, sys=sys): |
| 437 return sys.modules[__name__] | |
| 438 threading = MockThreading() | |
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439 del MockThreading |
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440 |
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441 try: |
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442 threading.local |
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443 |
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444 except AttributeError: |
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445 |
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446 # To fix reloading, force it to create a new context |
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447 # Old contexts have different exceptions in their dicts, making problems. |
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448 if hasattr(threading.current_thread(), '__decimal_context__'): |
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449 del threading.current_thread().__decimal_context__ |
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450 |
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451 def setcontext(context): |
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452 """Set this thread's context to context.""" |
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453 if context in (DefaultContext, BasicContext, ExtendedContext): |
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454 context = context.copy() |
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455 context.clear_flags() |
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456 threading.current_thread().__decimal_context__ = context |
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457 |
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458 def getcontext(): |
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459 """Returns this thread's context. |
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460 |
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461 If this thread does not yet have a context, returns |
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462 a new context and sets this thread's context. |
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463 New contexts are copies of DefaultContext. |
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464 """ |
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465 try: |
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466 return threading.current_thread().__decimal_context__ |
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467 except AttributeError: |
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468 context = Context() |
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469 threading.current_thread().__decimal_context__ = context |
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470 return context |
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471 |
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472 else: |
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473 |
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474 local = threading.local() |
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475 if hasattr(local, '__decimal_context__'): |
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476 del local.__decimal_context__ |
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477 |
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478 def getcontext(_local=local): |
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479 """Returns this thread's context. |
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480 |
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481 If this thread does not yet have a context, returns |
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482 a new context and sets this thread's context. |
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483 New contexts are copies of DefaultContext. |
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484 """ |
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485 try: |
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486 return _local.__decimal_context__ |
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487 except AttributeError: |
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488 context = Context() |
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489 _local.__decimal_context__ = context |
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490 return context |
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491 |
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492 def setcontext(context, _local=local): |
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493 """Set this thread's context to context.""" |
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494 if context in (DefaultContext, BasicContext, ExtendedContext): |
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495 context = context.copy() |
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496 context.clear_flags() |
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497 _local.__decimal_context__ = context |
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498 |
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499 del threading, local # Don't contaminate the namespace |
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500 |
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501 def localcontext(ctx=None): |
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502 """Return a context manager for a copy of the supplied context |
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503 |
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504 Uses a copy of the current context if no context is specified |
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505 The returned context manager creates a local decimal context |
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506 in a with statement: |
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507 def sin(x): |
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508 with localcontext() as ctx: |
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509 ctx.prec += 2 |
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510 # Rest of sin calculation algorithm |
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511 # uses a precision 2 greater than normal |
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512 return +s # Convert result to normal precision |
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513 |
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514 def sin(x): |
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515 with localcontext(ExtendedContext): |
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516 # Rest of sin calculation algorithm |
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517 # uses the Extended Context from the |
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518 # General Decimal Arithmetic Specification |
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519 return +s # Convert result to normal context |
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520 |
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521 >>> setcontext(DefaultContext) |
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522 >>> print(getcontext().prec) |
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523 28 |
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524 >>> with localcontext(): |
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525 ... ctx = getcontext() |
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526 ... ctx.prec += 2 |
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527 ... print(ctx.prec) |
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528 ... |
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529 30 |
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530 >>> with localcontext(ExtendedContext): |
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531 ... print(getcontext().prec) |
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532 ... |
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533 9 |
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534 >>> print(getcontext().prec) |
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535 28 |
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536 """ |
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537 if ctx is None: ctx = getcontext() |
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538 return _ContextManager(ctx) |
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539 |
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540 |
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541 ##### Decimal class ####################################################### |
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542 |
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543 # Do not subclass Decimal from numbers.Real and do not register it as such |
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544 # (because Decimals are not interoperable with floats). See the notes in |
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545 # numbers.py for more detail. |
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546 |
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547 class Decimal(object): |
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548 """Floating point class for decimal arithmetic.""" |
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549 |
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550 __slots__ = ('_exp','_int','_sign', '_is_special') |
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551 # Generally, the value of the Decimal instance is given by |
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552 # (-1)**_sign * _int * 10**_exp |
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553 # Special values are signified by _is_special == True |
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554 |
| 33695 | 555 # We're immutable, so use __new__ not __init__ |
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556 def __new__(cls, value="0", context=None): |
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557 """Create a decimal point instance. |
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558 |
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559 >>> Decimal('3.14') # string input |
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560 Decimal('3.14') |
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561 >>> Decimal((0, (3, 1, 4), -2)) # tuple (sign, digit_tuple, exponent) |
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562 Decimal('3.14') |
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563 >>> Decimal(314) # int |
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564 Decimal('314') |
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565 >>> Decimal(Decimal(314)) # another decimal instance |
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566 Decimal('314') |
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567 >>> Decimal(' 3.14 \\n') # leading and trailing whitespace okay |
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568 Decimal('3.14') |
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569 """ |
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570 |
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571 # Note that the coefficient, self._int, is actually stored as |
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572 # a string rather than as a tuple of digits. This speeds up |
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573 # the "digits to integer" and "integer to digits" conversions |
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574 # that are used in almost every arithmetic operation on |
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575 # Decimals. This is an internal detail: the as_tuple function |
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576 # and the Decimal constructor still deal with tuples of |
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577 # digits. |
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578 |
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579 self = object.__new__(cls) |
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580 |
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581 # From a string |
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582 # REs insist on real strings, so we can too. |
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583 if isinstance(value, str): |
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584 m = _parser(value.strip()) |
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585 if m is None: |
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586 if context is None: |
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587 context = getcontext() |
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588 return context._raise_error(ConversionSyntax, |
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589 "Invalid literal for Decimal: %r" % value) |
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590 |
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591 if m.group('sign') == "-": |
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592 self._sign = 1 |
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593 else: |
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594 self._sign = 0 |
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595 intpart = m.group('int') |
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596 if intpart is not None: |
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597 # finite number |
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598 fracpart = m.group('frac') or '' |
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599 exp = int(m.group('exp') or '0') |
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600 self._int = str(int(intpart+fracpart)) |
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601 self._exp = exp - len(fracpart) |
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602 self._is_special = False |
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603 else: |
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604 diag = m.group('diag') |
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605 if diag is not None: |
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606 # NaN |
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607 self._int = str(int(diag or '0')).lstrip('0') |
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608 if m.group('signal'): |
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609 self._exp = 'N' |
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610 else: |
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611 self._exp = 'n' |
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612 else: |
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613 # infinity |
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614 self._int = '0' |
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615 self._exp = 'F' |
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616 self._is_special = True |
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617 return self |
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618 |
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619 # From an integer |
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620 if isinstance(value, int): |
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621 if value >= 0: |
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622 self._sign = 0 |
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623 else: |
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624 self._sign = 1 |
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625 self._exp = 0 |
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626 self._int = str(abs(value)) |
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627 self._is_special = False |
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628 return self |
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629 |
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630 # From another decimal |
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631 if isinstance(value, Decimal): |
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632 self._exp = value._exp |
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633 self._sign = value._sign |
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634 self._int = value._int |
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635 self._is_special = value._is_special |
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636 return self |
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637 |
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638 # From an internal working value |
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639 if isinstance(value, _WorkRep): |
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640 self._sign = value.sign |
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641 self._int = str(value.int) |
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642 self._exp = int(value.exp) |
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643 self._is_special = False |
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644 return self |
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645 |
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646 # tuple/list conversion (possibly from as_tuple()) |
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647 if isinstance(value, (list,tuple)): |
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648 if len(value) != 3: |
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649 raise ValueError('Invalid tuple size in creation of Decimal ' |
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650 'from list or tuple. The list or tuple ' |
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651 'should have exactly three elements.') |
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652 # process sign. The isinstance test rejects floats |
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653 if not (isinstance(value[0], int) and value[0] in (0,1)): |
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654 raise ValueError("Invalid sign. The first value in the tuple " |
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655 "should be an integer; either 0 for a " |
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656 "positive number or 1 for a negative number.") |
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657 self._sign = value[0] |
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658 if value[2] == 'F': |
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659 # infinity: value[1] is ignored |
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660 self._int = '0' |
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661 self._exp = value[2] |
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662 self._is_special = True |
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663 else: |
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664 # process and validate the digits in value[1] |
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665 digits = [] |
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666 for digit in value[1]: |
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667 if isinstance(digit, int) and 0 <= digit <= 9: |
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668 # skip leading zeros |
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669 if digits or digit != 0: |
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670 digits.append(digit) |
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671 else: |
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672 raise ValueError("The second value in the tuple must " |
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673 "be composed of integers in the range " |
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674 "0 through 9.") |
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675 if value[2] in ('n', 'N'): |
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676 # NaN: digits form the diagnostic |
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677 self._int = ''.join(map(str, digits)) |
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678 self._exp = value[2] |
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679 self._is_special = True |
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680 elif isinstance(value[2], int): |
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681 # finite number: digits give the coefficient |
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682 self._int = ''.join(map(str, digits or [0])) |
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683 self._exp = value[2] |
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684 self._is_special = False |
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685 else: |
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686 raise ValueError("The third value in the tuple must " |
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687 "be an integer, or one of the " |
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688 "strings 'F', 'n', 'N'.") |
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689 return self |
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690 |
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691 if isinstance(value, float): |
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692 if context is None: |
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693 context = getcontext() |
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694 context._raise_error(FloatOperation, |
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695 "strict semantics for mixing floats and Decimals are " |
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696 "enabled") |
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697 value = Decimal.from_float(value) |
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698 self._exp = value._exp |
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699 self._sign = value._sign |
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700 self._int = value._int |
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701 self._is_special = value._is_special |
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702 return self |
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703 |
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704 raise TypeError("Cannot convert %r to Decimal" % value) |
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705 |
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706 # @classmethod, but @decorator is not valid Python 2.3 syntax, so |
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707 # don't use it (see notes on Py2.3 compatibility at top of file) |
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708 def from_float(cls, f): |
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709 """Converts a float to a decimal number, exactly. |
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710 |
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711 Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). |
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712 Since 0.1 is not exactly representable in binary floating point, the |
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713 value is stored as the nearest representable value which is |
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714 0x1.999999999999ap-4. The exact equivalent of the value in decimal |
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715 is 0.1000000000000000055511151231257827021181583404541015625. |
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716 |
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717 >>> Decimal.from_float(0.1) |
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718 Decimal('0.1000000000000000055511151231257827021181583404541015625') |
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719 >>> Decimal.from_float(float('nan')) |
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720 Decimal('NaN') |
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721 >>> Decimal.from_float(float('inf')) |
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722 Decimal('Infinity') |
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723 >>> Decimal.from_float(-float('inf')) |
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724 Decimal('-Infinity') |
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725 >>> Decimal.from_float(-0.0) |
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726 Decimal('-0') |
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727 |
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728 """ |
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729 if isinstance(f, int): # handle integer inputs |
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730 return cls(f) |
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731 if not isinstance(f, float): |
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732 raise TypeError("argument must be int or float.") |
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733 if _math.isinf(f) or _math.isnan(f): |
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734 return cls(repr(f)) |
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735 if _math.copysign(1.0, f) == 1.0: |
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736 sign = 0 |
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737 else: |
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738 sign = 1 |
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739 n, d = abs(f).as_integer_ratio() |
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740 k = d.bit_length() - 1 |
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741 result = _dec_from_triple(sign, str(n*5**k), -k) |
|
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742 if cls is Decimal: |
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743 return result |
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744 else: |
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|
745 return cls(result) |
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746 from_float = classmethod(from_float) |
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747 |
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748 def _isnan(self): |
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749 """Returns whether the number is not actually one. |
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750 |
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751 0 if a number |
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752 1 if NaN |
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753 2 if sNaN |
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754 """ |
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755 if self._is_special: |
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756 exp = self._exp |
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757 if exp == 'n': |
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758 return 1 |
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759 elif exp == 'N': |
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760 return 2 |
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761 return 0 |
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762 |
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763 def _isinfinity(self): |
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764 """Returns whether the number is infinite |
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765 |
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766 0 if finite or not a number |
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767 1 if +INF |
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768 -1 if -INF |
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769 """ |
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770 if self._exp == 'F': |
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771 if self._sign: |
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772 return -1 |
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773 return 1 |
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774 return 0 |
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775 |
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776 def _check_nans(self, other=None, context=None): |
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777 """Returns whether the number is not actually one. |
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778 |
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779 if self, other are sNaN, signal |
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780 if self, other are NaN return nan |
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781 return 0 |
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782 |
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783 Done before operations. |
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784 """ |
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785 |
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786 self_is_nan = self._isnan() |
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787 if other is None: |
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788 other_is_nan = False |
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789 else: |
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790 other_is_nan = other._isnan() |
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791 |
|
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|
792 if self_is_nan or other_is_nan: |
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793 if context is None: |
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794 context = getcontext() |
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|
795 |
|
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796 if self_is_nan == 2: |
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797 return context._raise_error(InvalidOperation, 'sNaN', |
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798 self) |
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799 if other_is_nan == 2: |
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800 return context._raise_error(InvalidOperation, 'sNaN', |
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|
801 other) |
|
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|
802 if self_is_nan: |
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803 return self._fix_nan(context) |
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804 |
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805 return other._fix_nan(context) |
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806 return 0 |
|
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807 |
|
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808 def _compare_check_nans(self, other, context): |
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809 """Version of _check_nans used for the signaling comparisons |
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810 compare_signal, __le__, __lt__, __ge__, __gt__. |
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811 |
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812 Signal InvalidOperation if either self or other is a (quiet |
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813 or signaling) NaN. Signaling NaNs take precedence over quiet |
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814 NaNs. |
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815 |
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816 Return 0 if neither operand is a NaN. |
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817 |
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818 """ |
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819 if context is None: |
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820 context = getcontext() |
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821 |
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822 if self._is_special or other._is_special: |
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823 if self.is_snan(): |
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824 return context._raise_error(InvalidOperation, |
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825 'comparison involving sNaN', |
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826 self) |
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827 elif other.is_snan(): |
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828 return context._raise_error(InvalidOperation, |
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829 'comparison involving sNaN', |
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830 other) |
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831 elif self.is_qnan(): |
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832 return context._raise_error(InvalidOperation, |
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833 'comparison involving NaN', |
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834 self) |
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835 elif other.is_qnan(): |
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836 return context._raise_error(InvalidOperation, |
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837 'comparison involving NaN', |
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838 other) |
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839 return 0 |
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840 |
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841 def __bool__(self): |
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842 """Return True if self is nonzero; otherwise return False. |
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843 |
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844 NaNs and infinities are considered nonzero. |
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845 """ |
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846 return self._is_special or self._int != '0' |
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847 |
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848 def _cmp(self, other): |
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849 """Compare the two non-NaN decimal instances self and other. |
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850 |
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851 Returns -1 if self < other, 0 if self == other and 1 |
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852 if self > other. This routine is for internal use only.""" |
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853 |
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854 if self._is_special or other._is_special: |
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855 self_inf = self._isinfinity() |
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856 other_inf = other._isinfinity() |
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857 if self_inf == other_inf: |
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858 return 0 |
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859 elif self_inf < other_inf: |
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860 return -1 |
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861 else: |
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862 return 1 |
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863 |
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864 # check for zeros; Decimal('0') == Decimal('-0') |
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865 if not self: |
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866 if not other: |
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867 return 0 |
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868 else: |
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869 return -((-1)**other._sign) |
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870 if not other: |
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871 return (-1)**self._sign |
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872 |
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873 # If different signs, neg one is less |
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874 if other._sign < self._sign: |
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875 return -1 |
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876 if self._sign < other._sign: |
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877 return 1 |
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878 |
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879 self_adjusted = self.adjusted() |
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880 other_adjusted = other.adjusted() |
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881 if self_adjusted == other_adjusted: |
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882 self_padded = self._int + '0'*(self._exp - other._exp) |
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883 other_padded = other._int + '0'*(other._exp - self._exp) |
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884 if self_padded == other_padded: |
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885 return 0 |
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886 elif self_padded < other_padded: |
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887 return -(-1)**self._sign |
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888 else: |
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889 return (-1)**self._sign |
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890 elif self_adjusted > other_adjusted: |
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891 return (-1)**self._sign |
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892 else: # self_adjusted < other_adjusted |
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893 return -((-1)**self._sign) |
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894 |
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895 # Note: The Decimal standard doesn't cover rich comparisons for |
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896 # Decimals. In particular, the specification is silent on the |
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897 # subject of what should happen for a comparison involving a NaN. |
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898 # We take the following approach: |
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899 # |
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900 # == comparisons involving a quiet NaN always return False |
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901 # != comparisons involving a quiet NaN always return True |
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902 # == or != comparisons involving a signaling NaN signal |
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903 # InvalidOperation, and return False or True as above if the |
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904 # InvalidOperation is not trapped. |
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905 # <, >, <= and >= comparisons involving a (quiet or signaling) |
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906 # NaN signal InvalidOperation, and return False if the |
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907 # InvalidOperation is not trapped. |
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908 # |
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909 # This behavior is designed to conform as closely as possible to |
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910 # that specified by IEEE 754. |
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911 |
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912 def __eq__(self, other, context=None): |
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913 self, other = _convert_for_comparison(self, other, equality_op=True) |
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914 if other is NotImplemented: |
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915 return other |
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916 if self._check_nans(other, context): |
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917 return False |
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918 return self._cmp(other) == 0 |
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919 |
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920 def __ne__(self, other, context=None): |
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921 self, other = _convert_for_comparison(self, other, equality_op=True) |
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922 if other is NotImplemented: |
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923 return other |
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924 if self._check_nans(other, context): |
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925 return True |
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926 return self._cmp(other) != 0 |
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927 |
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928 |
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929 def __lt__(self, other, context=None): |
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930 self, other = _convert_for_comparison(self, other) |
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931 if other is NotImplemented: |
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932 return other |
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933 ans = self._compare_check_nans(other, context) |
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934 if ans: |
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935 return False |
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936 return self._cmp(other) < 0 |
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937 |
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938 def __le__(self, other, context=None): |
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939 self, other = _convert_for_comparison(self, other) |
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940 if other is NotImplemented: |
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941 return other |
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942 ans = self._compare_check_nans(other, context) |
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943 if ans: |
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944 return False |
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945 return self._cmp(other) <= 0 |
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946 |
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947 def __gt__(self, other, context=None): |
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948 self, other = _convert_for_comparison(self, other) |
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949 if other is NotImplemented: |
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950 return other |
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951 ans = self._compare_check_nans(other, context) |
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952 if ans: |
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953 return False |
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954 return self._cmp(other) > 0 |
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955 |
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956 def __ge__(self, other, context=None): |
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957 self, other = _convert_for_comparison(self, other) |
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958 if other is NotImplemented: |
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959 return other |
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960 ans = self._compare_check_nans(other, context) |
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961 if ans: |
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962 return False |
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963 return self._cmp(other) >= 0 |
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964 |
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965 def compare(self, other, context=None): |
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966 """Compares one to another. |
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967 |
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968 -1 => a < b |
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969 0 => a = b |
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970 1 => a > b |
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971 NaN => one is NaN |
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972 Like __cmp__, but returns Decimal instances. |
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973 """ |
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974 other = _convert_other(other, raiseit=True) |
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975 |
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976 # Compare(NaN, NaN) = NaN |
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977 if (self._is_special or other and other._is_special): |
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978 ans = self._check_nans(other, context) |
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979 if ans: |
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980 return ans |
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981 |
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982 return Decimal(self._cmp(other)) |
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983 |
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984 def __hash__(self): |
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985 """x.__hash__() <==> hash(x)""" |
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986 |
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987 # In order to make sure that the hash of a Decimal instance |
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988 # agrees with the hash of a numerically equal integer, float |
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989 # or Fraction, we follow the rules for numeric hashes outlined |
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990 # in the documentation. (See library docs, 'Built-in Types'). |
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991 if self._is_special: |
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992 if self.is_snan(): |
| 66346 | 993 raise TypeError('Cannot hash a signaling NaN value.') |
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994 elif self.is_nan(): |
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995 return _PyHASH_NAN |
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996 else: |
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997 if self._sign: |
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998 return -_PyHASH_INF |
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999 else: |
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1000 return _PyHASH_INF |
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1001 |
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1002 if self._exp >= 0: |
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1003 exp_hash = pow(10, self._exp, _PyHASH_MODULUS) |
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1004 else: |
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1005 exp_hash = pow(_PyHASH_10INV, -self._exp, _PyHASH_MODULUS) |
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1006 hash_ = int(self._int) * exp_hash % _PyHASH_MODULUS |
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1007 ans = hash_ if self >= 0 else -hash_ |
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1008 return -2 if ans == -1 else ans |
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1009 |
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1010 def as_tuple(self): |
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1011 """Represents the number as a triple tuple. |
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1012 |
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1013 To show the internals exactly as they are. |
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1014 """ |
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1015 return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp) |
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1016 |
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1017 def __repr__(self): |
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1018 """Represents the number as an instance of Decimal.""" |
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1019 # Invariant: eval(repr(d)) == d |
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1020 return "Decimal('%s')" % str(self) |
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1021 |
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1022 def __str__(self, eng=False, context=None): |
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1023 """Return string representation of the number in scientific notation. |
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1024 |
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1025 Captures all of the information in the underlying representation. |
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1026 """ |
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1027 |
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1028 sign = ['', '-'][self._sign] |
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1029 if self._is_special: |
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1030 if self._exp == 'F': |
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1031 return sign + 'Infinity' |
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1032 elif self._exp == 'n': |
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1033 return sign + 'NaN' + self._int |
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1034 else: # self._exp == 'N' |
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1035 return sign + 'sNaN' + self._int |
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1036 |
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1037 # number of digits of self._int to left of decimal point |
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1038 leftdigits = self._exp + len(self._int) |
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1039 |
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1040 # dotplace is number of digits of self._int to the left of the |
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1041 # decimal point in the mantissa of the output string (that is, |
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1042 # after adjusting the exponent) |
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1043 if self._exp <= 0 and leftdigits > -6: |
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1044 # no exponent required |
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1045 dotplace = leftdigits |
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1046 elif not eng: |
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1047 # usual scientific notation: 1 digit on left of the point |
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1048 dotplace = 1 |
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1049 elif self._int == '0': |
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1050 # engineering notation, zero |
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1051 dotplace = (leftdigits + 1) % 3 - 1 |
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1052 else: |
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1053 # engineering notation, nonzero |
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1054 dotplace = (leftdigits - 1) % 3 + 1 |
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1055 |
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1056 if dotplace <= 0: |
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1057 intpart = '0' |
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1058 fracpart = '.' + '0'*(-dotplace) + self._int |
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1059 elif dotplace >= len(self._int): |
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1060 intpart = self._int+'0'*(dotplace-len(self._int)) |
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1061 fracpart = '' |
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1062 else: |
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1063 intpart = self._int[:dotplace] |
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1064 fracpart = '.' + self._int[dotplace:] |
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1065 if leftdigits == dotplace: |
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1066 exp = '' |
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1067 else: |
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1068 if context is None: |
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1069 context = getcontext() |
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1070 exp = ['e', 'E'][context.capitals] + "%+d" % (leftdigits-dotplace) |
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1071 |
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1072 return sign + intpart + fracpart + exp |
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1073 |
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1074 def to_eng_string(self, context=None): |
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1075 """Convert to engineering-type string. |
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1076 |
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1077 Engineering notation has an exponent which is a multiple of 3, so there |
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1078 are up to 3 digits left of the decimal place. |
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1079 |
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1080 Same rules for when in exponential and when as a value as in __str__. |
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1081 """ |
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1082 return self.__str__(eng=True, context=context) |
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1083 |
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1084 def __neg__(self, context=None): |
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1085 """Returns a copy with the sign switched. |
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1086 |
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1087 Rounds, if it has reason. |
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1088 """ |
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1089 if self._is_special: |
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1090 ans = self._check_nans(context=context) |
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1091 if ans: |
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1092 return ans |
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1093 |
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1094 if context is None: |
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1095 context = getcontext() |
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1096 |
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1097 if not self and context.rounding != ROUND_FLOOR: |
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1098 # -Decimal('0') is Decimal('0'), not Decimal('-0'), except |
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1099 # in ROUND_FLOOR rounding mode. |
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1100 ans = self.copy_abs() |
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1101 else: |
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1102 ans = self.copy_negate() |
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1103 |
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1104 return ans._fix(context) |
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1105 |
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1106 def __pos__(self, context=None): |
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1107 """Returns a copy, unless it is a sNaN. |
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1108 |
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1109 Rounds the number (if more then precision digits) |
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1110 """ |
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1111 if self._is_special: |
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1112 ans = self._check_nans(context=context) |
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1113 if ans: |
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1114 return ans |
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1115 |
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1116 if context is None: |
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1117 context = getcontext() |
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1118 |
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1119 if not self and context.rounding != ROUND_FLOOR: |
|
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Issue 11131: Fix sign of zero result on decimal.Decimal plus and minus operations in ROUND_FLOOR rounding mode.
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|
1120 # + (-0) = 0, except in ROUND_FLOOR rounding mode. |
|
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1121 ans = self.copy_abs() |
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1122 else: |
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|
1123 ans = Decimal(self) |
|
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1124 |
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|
1125 return ans._fix(context) |
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1126 |
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|
1127 def __abs__(self, round=True, context=None): |
|
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1128 """Returns the absolute value of self. |
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1129 |
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|
1130 If the keyword argument 'round' is false, do not round. The |
|
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|
1131 expression self.__abs__(round=False) is equivalent to |
|
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1132 self.copy_abs(). |
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1133 """ |
|
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|
1134 if not round: |
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1135 return self.copy_abs() |
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1136 |
|
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1137 if self._is_special: |
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1138 ans = self._check_nans(context=context) |
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1139 if ans: |
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1140 return ans |
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1141 |
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1142 if self._sign: |
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1143 ans = self.__neg__(context=context) |
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1144 else: |
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1145 ans = self.__pos__(context=context) |
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1146 |
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1147 return ans |
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1148 |
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1149 def __add__(self, other, context=None): |
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1150 """Returns self + other. |
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1151 |
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1152 -INF + INF (or the reverse) cause InvalidOperation errors. |
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1153 """ |
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1154 other = _convert_other(other) |
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1155 if other is NotImplemented: |
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1156 return other |
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1157 |
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1158 if context is None: |
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1159 context = getcontext() |
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1160 |
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1161 if self._is_special or other._is_special: |
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1162 ans = self._check_nans(other, context) |
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1163 if ans: |
|
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1164 return ans |
|
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|
1165 |
|
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1166 if self._isinfinity(): |
|
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1167 # If both INF, same sign => same as both, opposite => error. |
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1168 if self._sign != other._sign and other._isinfinity(): |
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1169 return context._raise_error(InvalidOperation, '-INF + INF') |
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1170 return Decimal(self) |
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1171 if other._isinfinity(): |
|
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1172 return Decimal(other) # Can't both be infinity here |
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1173 |
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1174 exp = min(self._exp, other._exp) |
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1175 negativezero = 0 |
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1176 if context.rounding == ROUND_FLOOR and self._sign != other._sign: |
|
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1177 # If the answer is 0, the sign should be negative, in this case. |
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1178 negativezero = 1 |
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1179 |
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1180 if not self and not other: |
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1181 sign = min(self._sign, other._sign) |
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1182 if negativezero: |
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1183 sign = 1 |
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1184 ans = _dec_from_triple(sign, '0', exp) |
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1185 ans = ans._fix(context) |
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|
1186 return ans |
|
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1187 if not self: |
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1188 exp = max(exp, other._exp - context.prec-1) |
|
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1189 ans = other._rescale(exp, context.rounding) |
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1190 ans = ans._fix(context) |
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1191 return ans |
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1192 if not other: |
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|
1193 exp = max(exp, self._exp - context.prec-1) |
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|
1194 ans = self._rescale(exp, context.rounding) |
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|
1195 ans = ans._fix(context) |
|
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1196 return ans |
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1197 |
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1198 op1 = _WorkRep(self) |
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1199 op2 = _WorkRep(other) |
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|
1200 op1, op2 = _normalize(op1, op2, context.prec) |
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1201 |
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1202 result = _WorkRep() |
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1203 if op1.sign != op2.sign: |
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|
1204 # Equal and opposite |
| 33851 | 1205 if op1.int == op2.int: |
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|
1206 ans = _dec_from_triple(negativezero, '0', exp) |
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1207 ans = ans._fix(context) |
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1208 return ans |
| 33851 | 1209 if op1.int < op2.int: |
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1210 op1, op2 = op2, op1 |
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1211 # OK, now abs(op1) > abs(op2) |
| 33851 | 1212 if op1.sign == 1: |
| 1213 result.sign = 1 | |
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1214 op1.sign, op2.sign = op2.sign, op1.sign |
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1215 else: |
| 33851 | 1216 result.sign = 0 |
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|
1217 # So we know the sign, and op1 > 0. |
| 33851 | 1218 elif op1.sign == 1: |
| 1219 result.sign = 1 | |
| 1220 op1.sign, op2.sign = (0, 0) | |
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1221 else: |
| 33851 | 1222 result.sign = 0 |
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1223 # Now, op1 > abs(op2) > 0 |
|
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1224 |
| 33851 | 1225 if op2.sign == 0: |
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1226 result.int = op1.int + op2.int |
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1227 else: |
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1228 result.int = op1.int - op2.int |
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1229 |
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1230 result.exp = op1.exp |
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1231 ans = Decimal(result) |
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1232 ans = ans._fix(context) |
|
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1233 return ans |
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1234 |
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1235 __radd__ = __add__ |
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1236 |
|
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1237 def __sub__(self, other, context=None): |
|
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|
1238 """Return self - other""" |
|
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|
1239 other = _convert_other(other) |
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1240 if other is NotImplemented: |
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1241 return other |
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|
1242 |
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|
1243 if self._is_special or other._is_special: |
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|
1244 ans = self._check_nans(other, context=context) |
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|
1245 if ans: |
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|
1246 return ans |
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1247 |
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|
1248 # self - other is computed as self + other.copy_negate() |
|
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|
1249 return self.__add__(other.copy_negate(), context=context) |
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1250 |
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1251 def __rsub__(self, other, context=None): |
|
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1252 """Return other - self""" |
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1253 other = _convert_other(other) |
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1254 if other is NotImplemented: |
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1255 return other |
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1256 |
|
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|
1257 return other.__sub__(self, context=context) |
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|
1258 |
|
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1259 def __mul__(self, other, context=None): |
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1260 """Return self * other. |
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1261 |
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1262 (+-) INF * 0 (or its reverse) raise InvalidOperation. |
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1263 """ |
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1264 other = _convert_other(other) |
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1265 if other is NotImplemented: |
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1266 return other |
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1267 |
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1268 if context is None: |
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1269 context = getcontext() |
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1270 |
|
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1271 resultsign = self._sign ^ other._sign |
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1272 |
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1273 if self._is_special or other._is_special: |
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1274 ans = self._check_nans(other, context) |
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1275 if ans: |
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1276 return ans |
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1277 |
|
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1278 if self._isinfinity(): |
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1279 if not other: |
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1280 return context._raise_error(InvalidOperation, '(+-)INF * 0') |
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1281 return _SignedInfinity[resultsign] |
|
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1282 |
|
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1283 if other._isinfinity(): |
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1284 if not self: |
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1285 return context._raise_error(InvalidOperation, '0 * (+-)INF') |
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1286 return _SignedInfinity[resultsign] |
|
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1287 |
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1288 resultexp = self._exp + other._exp |
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1289 |
|
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1290 # Special case for multiplying by zero |
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|
1291 if not self or not other: |
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1292 ans = _dec_from_triple(resultsign, '0', resultexp) |
|
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1293 # Fixing in case the exponent is out of bounds |
|
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1294 ans = ans._fix(context) |
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1295 return ans |
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1296 |
|
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|
1297 # Special case for multiplying by power of 10 |
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1298 if self._int == '1': |
|
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1299 ans = _dec_from_triple(resultsign, other._int, resultexp) |
|
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1300 ans = ans._fix(context) |
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1301 return ans |
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1302 if other._int == '1': |
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1303 ans = _dec_from_triple(resultsign, self._int, resultexp) |
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1304 ans = ans._fix(context) |
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1305 return ans |
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1306 |
|
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|
1307 op1 = _WorkRep(self) |
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1308 op2 = _WorkRep(other) |
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|
1309 |
|
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1310 ans = _dec_from_triple(resultsign, str(op1.int * op2.int), resultexp) |
|
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1311 ans = ans._fix(context) |
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1312 |
|
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1313 return ans |
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1314 __rmul__ = __mul__ |
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1315 |
|
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|
1316 def __truediv__(self, other, context=None): |
|
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1317 """Return self / other.""" |
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1318 other = _convert_other(other) |
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1319 if other is NotImplemented: |
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1320 return NotImplemented |
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1321 |
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1322 if context is None: |
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1323 context = getcontext() |
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1324 |
|
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1325 sign = self._sign ^ other._sign |
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1326 |
|
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1327 if self._is_special or other._is_special: |
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|
1328 ans = self._check_nans(other, context) |
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1329 if ans: |
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|
1330 return ans |
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1331 |
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1332 if self._isinfinity() and other._isinfinity(): |
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1333 return context._raise_error(InvalidOperation, '(+-)INF/(+-)INF') |
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1334 |
|
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1335 if self._isinfinity(): |
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1336 return _SignedInfinity[sign] |
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1337 |
|
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|
1338 if other._isinfinity(): |
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|
1339 context._raise_error(Clamped, 'Division by infinity') |
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1340 return _dec_from_triple(sign, '0', context.Etiny()) |
|
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|
1341 |
|
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|
1342 # Special cases for zeroes |
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|
1343 if not other: |
|
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1344 if not self: |
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|
1345 return context._raise_error(DivisionUndefined, '0 / 0') |
|
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|
1346 return context._raise_error(DivisionByZero, 'x / 0', sign) |
|
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1347 |
|
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1348 if not self: |
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|
1349 exp = self._exp - other._exp |
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|
1350 coeff = 0 |
|
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|
1351 else: |
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1352 # OK, so neither = 0, INF or NaN |
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1353 shift = len(other._int) - len(self._int) + context.prec + 1 |
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1354 exp = self._exp - other._exp - shift |
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1355 op1 = _WorkRep(self) |
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1356 op2 = _WorkRep(other) |
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1357 if shift >= 0: |
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1358 coeff, remainder = divmod(op1.int * 10**shift, op2.int) |
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1359 else: |
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1360 coeff, remainder = divmod(op1.int, op2.int * 10**-shift) |
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1361 if remainder: |
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1362 # result is not exact; adjust to ensure correct rounding |
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1363 if coeff % 5 == 0: |
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1364 coeff += 1 |
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1365 else: |
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1366 # result is exact; get as close to ideal exponent as possible |
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1367 ideal_exp = self._exp - other._exp |
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1368 while exp < ideal_exp and coeff % 10 == 0: |
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1369 coeff //= 10 |
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1370 exp += 1 |
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1371 |
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1372 ans = _dec_from_triple(sign, str(coeff), exp) |
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1373 return ans._fix(context) |
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1374 |
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1375 def _divide(self, other, context): |
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1376 """Return (self // other, self % other), to context.prec precision. |
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1377 |
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1378 Assumes that neither self nor other is a NaN, that self is not |
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1379 infinite and that other is nonzero. |
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1380 """ |
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1381 sign = self._sign ^ other._sign |
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1382 if other._isinfinity(): |
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1383 ideal_exp = self._exp |
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1384 else: |
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1385 ideal_exp = min(self._exp, other._exp) |
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1386 |
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1387 expdiff = self.adjusted() - other.adjusted() |
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1388 if not self or other._isinfinity() or expdiff <= -2: |
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1389 return (_dec_from_triple(sign, '0', 0), |
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1390 self._rescale(ideal_exp, context.rounding)) |
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1391 if expdiff <= context.prec: |
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1392 op1 = _WorkRep(self) |
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1393 op2 = _WorkRep(other) |
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1394 if op1.exp >= op2.exp: |
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1395 op1.int *= 10**(op1.exp - op2.exp) |
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1396 else: |
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1397 op2.int *= 10**(op2.exp - op1.exp) |
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1398 q, r = divmod(op1.int, op2.int) |
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1399 if q < 10**context.prec: |
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1400 return (_dec_from_triple(sign, str(q), 0), |
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1401 _dec_from_triple(self._sign, str(r), ideal_exp)) |
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1402 |
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1403 # Here the quotient is too large to be representable |
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1404 ans = context._raise_error(DivisionImpossible, |
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1405 'quotient too large in //, % or divmod') |
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1406 return ans, ans |
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1407 |
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1408 def __rtruediv__(self, other, context=None): |
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1409 """Swaps self/other and returns __truediv__.""" |
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1410 other = _convert_other(other) |
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1411 if other is NotImplemented: |
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1412 return other |
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1413 return other.__truediv__(self, context=context) |
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1414 |
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1415 def __divmod__(self, other, context=None): |
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1416 """ |
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1417 Return (self // other, self % other) |
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1418 """ |
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1419 other = _convert_other(other) |
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1420 if other is NotImplemented: |
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1421 return other |
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1422 |
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1423 if context is None: |
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1424 context = getcontext() |
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1425 |
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1426 ans = self._check_nans(other, context) |
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1427 if ans: |
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1428 return (ans, ans) |
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1429 |
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1430 sign = self._sign ^ other._sign |
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1431 if self._isinfinity(): |
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1432 if other._isinfinity(): |
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1433 ans = context._raise_error(InvalidOperation, 'divmod(INF, INF)') |
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1434 return ans, ans |
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1435 else: |
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1436 return (_SignedInfinity[sign], |
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1437 context._raise_error(InvalidOperation, 'INF % x')) |
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1438 |
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1439 if not other: |
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1440 if not self: |
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1441 ans = context._raise_error(DivisionUndefined, 'divmod(0, 0)') |
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1442 return ans, ans |
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1443 else: |
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1444 return (context._raise_error(DivisionByZero, 'x // 0', sign), |
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1445 context._raise_error(InvalidOperation, 'x % 0')) |
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1446 |
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1447 quotient, remainder = self._divide(other, context) |
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1448 remainder = remainder._fix(context) |
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1449 return quotient, remainder |
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1450 |
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1451 def __rdivmod__(self, other, context=None): |
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1452 """Swaps self/other and returns __divmod__.""" |
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1453 other = _convert_other(other) |
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1454 if other is NotImplemented: |
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1455 return other |
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1456 return other.__divmod__(self, context=context) |
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1457 |
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1458 def __mod__(self, other, context=None): |
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1459 """ |
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1460 self % other |
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1461 """ |
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1462 other = _convert_other(other) |
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1463 if other is NotImplemented: |
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1464 return other |
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1465 |
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1466 if context is None: |
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1467 context = getcontext() |
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1468 |
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1469 ans = self._check_nans(other, context) |
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1470 if ans: |
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1471 return ans |
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1472 |
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1473 if self._isinfinity(): |
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1474 return context._raise_error(InvalidOperation, 'INF % x') |
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1475 elif not other: |
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1476 if self: |
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1477 return context._raise_error(InvalidOperation, 'x % 0') |
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1478 else: |
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1479 return context._raise_error(DivisionUndefined, '0 % 0') |
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1480 |
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1481 remainder = self._divide(other, context)[1] |
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1482 remainder = remainder._fix(context) |
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1483 return remainder |
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1484 |
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1485 def __rmod__(self, other, context=None): |
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1486 """Swaps self/other and returns __mod__.""" |
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1487 other = _convert_other(other) |
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1488 if other is NotImplemented: |
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1489 return other |
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1490 return other.__mod__(self, context=context) |
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1491 |
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1492 def remainder_near(self, other, context=None): |
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1493 """ |
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1494 Remainder nearest to 0- abs(remainder-near) <= other/2 |
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1495 """ |
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1496 if context is None: |
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1497 context = getcontext() |
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1498 |
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1499 other = _convert_other(other, raiseit=True) |
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1500 |
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1501 ans = self._check_nans(other, context) |
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1502 if ans: |
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1503 return ans |
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1504 |
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1505 # self == +/-infinity -> InvalidOperation |
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1506 if self._isinfinity(): |
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1507 return context._raise_error(InvalidOperation, |
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1508 'remainder_near(infinity, x)') |
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1509 |
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1510 # other == 0 -> either InvalidOperation or DivisionUndefined |
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1511 if not other: |
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1512 if self: |
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1513 return context._raise_error(InvalidOperation, |
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1514 'remainder_near(x, 0)') |
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1515 else: |
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1516 return context._raise_error(DivisionUndefined, |
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1517 'remainder_near(0, 0)') |
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1518 |
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1519 # other = +/-infinity -> remainder = self |
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1520 if other._isinfinity(): |
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1521 ans = Decimal(self) |
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1522 return ans._fix(context) |
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1523 |
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1524 # self = 0 -> remainder = self, with ideal exponent |
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1525 ideal_exponent = min(self._exp, other._exp) |
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1526 if not self: |
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1527 ans = _dec_from_triple(self._sign, '0', ideal_exponent) |
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1528 return ans._fix(context) |
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1529 |
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1530 # catch most cases of large or small quotient |
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1531 expdiff = self.adjusted() - other.adjusted() |
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1532 if expdiff >= context.prec + 1: |
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1533 # expdiff >= prec+1 => abs(self/other) > 10**prec |
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1534 return context._raise_error(DivisionImpossible) |
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1535 if expdiff <= -2: |
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1536 # expdiff <= -2 => abs(self/other) < 0.1 |
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1537 ans = self._rescale(ideal_exponent, context.rounding) |
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1538 return ans._fix(context) |
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1539 |
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1540 # adjust both arguments to have the same exponent, then divide |
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1541 op1 = _WorkRep(self) |
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1542 op2 = _WorkRep(other) |
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1543 if op1.exp >= op2.exp: |
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1544 op1.int *= 10**(op1.exp - op2.exp) |
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1545 else: |
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1546 op2.int *= 10**(op2.exp - op1.exp) |
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1547 q, r = divmod(op1.int, op2.int) |
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1548 # remainder is r*10**ideal_exponent; other is +/-op2.int * |
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1549 # 10**ideal_exponent. Apply correction to ensure that |
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1550 # abs(remainder) <= abs(other)/2 |
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1551 if 2*r + (q&1) > op2.int: |
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1552 r -= op2.int |
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1553 q += 1 |
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1554 |
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1555 if q >= 10**context.prec: |
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1556 return context._raise_error(DivisionImpossible) |
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1557 |
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1558 # result has same sign as self unless r is negative |
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1559 sign = self._sign |
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1560 if r < 0: |
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1561 sign = 1-sign |
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1562 r = -r |
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1563 |
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1564 ans = _dec_from_triple(sign, str(r), ideal_exponent) |
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1565 return ans._fix(context) |
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1566 |
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1567 def __floordiv__(self, other, context=None): |
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1568 """self // other""" |
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1569 other = _convert_other(other) |
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1570 if other is NotImplemented: |
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1571 return other |
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1572 |
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1573 if context is None: |
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1574 context = getcontext() |
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1575 |
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1576 ans = self._check_nans(other, context) |
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1577 if ans: |
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1578 return ans |
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1579 |
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1580 if self._isinfinity(): |
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1581 if other._isinfinity(): |
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1582 return context._raise_error(InvalidOperation, 'INF // INF') |
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1583 else: |
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1584 return _SignedInfinity[self._sign ^ other._sign] |
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1585 |
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1586 if not other: |
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1587 if self: |
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1588 return context._raise_error(DivisionByZero, 'x // 0', |
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1589 self._sign ^ other._sign) |
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1590 else: |
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1591 return context._raise_error(DivisionUndefined, '0 // 0') |
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1592 |
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1593 return self._divide(other, context)[0] |
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1594 |
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1595 def __rfloordiv__(self, other, context=None): |
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1596 """Swaps self/other and returns __floordiv__.""" |
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1597 other = _convert_other(other) |
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1598 if other is NotImplemented: |
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1599 return other |
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1600 return other.__floordiv__(self, context=context) |
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1601 |
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1602 def __float__(self): |
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1603 """Float representation.""" |
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1604 if self._isnan(): |
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1605 if self.is_snan(): |
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1606 raise ValueError("Cannot convert signaling NaN to float") |
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1607 s = "-nan" if self._sign else "nan" |
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1608 else: |
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1609 s = str(self) |
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1610 return float(s) |
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1611 |
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1612 def __int__(self): |
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1613 """Converts self to an int, truncating if necessary.""" |
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1614 if self._is_special: |
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1615 if self._isnan(): |
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1616 raise ValueError("Cannot convert NaN to integer") |
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1617 elif self._isinfinity(): |
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1618 raise OverflowError("Cannot convert infinity to integer") |
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1619 s = (-1)**self._sign |
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1620 if self._exp >= 0: |
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1621 return s*int(self._int)*10**self._exp |
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1622 else: |
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1623 return s*int(self._int[:self._exp] or '0') |
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1625 __trunc__ = __int__ |
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1627 def real(self): |
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1628 return self |
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1629 real = property(real) |
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1631 def imag(self): |
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1632 return Decimal(0) |
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1633 imag = property(imag) |
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1634 |
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1635 def conjugate(self): |
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1636 return self |
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1637 |
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1638 def __complex__(self): |
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1639 return complex(float(self)) |
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1640 |
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1641 def _fix_nan(self, context): |
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1642 """Decapitate the payload of a NaN to fit the context""" |
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1643 payload = self._int |
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1644 |
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1645 # maximum length of payload is precision if clamp=0, |
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1646 # precision-1 if clamp=1. |
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1647 max_payload_len = context.prec - context.clamp |
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1648 if len(payload) > max_payload_len: |
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1649 payload = payload[len(payload)-max_payload_len:].lstrip('0') |
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1650 return _dec_from_triple(self._sign, payload, self._exp, True) |
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1651 return Decimal(self) |
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1652 |
| 33695 | 1653 def _fix(self, context): |
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1654 """Round if it is necessary to keep self within prec precision. |
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1655 |
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1656 Rounds and fixes the exponent. Does not raise on a sNaN. |
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1657 |
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1658 Arguments: |
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1659 self - Decimal instance |
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1660 context - context used. |
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1661 """ |
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1662 |
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1663 if self._is_special: |
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1664 if self._isnan(): |
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1665 # decapitate payload if necessary |
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1666 return self._fix_nan(context) |
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1667 else: |
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1668 # self is +/-Infinity; return unaltered |
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1669 return Decimal(self) |
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1670 |
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1671 # if self is zero then exponent should be between Etiny and |
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1672 # Emax if clamp==0, and between Etiny and Etop if clamp==1. |
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1673 Etiny = context.Etiny() |
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1674 Etop = context.Etop() |
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1675 if not self: |
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1676 exp_max = [context.Emax, Etop][context.clamp] |
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1677 new_exp = min(max(self._exp, Etiny), exp_max) |
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1678 if new_exp != self._exp: |
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1679 context._raise_error(Clamped) |
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1680 return _dec_from_triple(self._sign, '0', new_exp) |
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1681 else: |
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1682 return Decimal(self) |
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1683 |
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1684 # exp_min is the smallest allowable exponent of the result, |
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1685 # equal to max(self.adjusted()-context.prec+1, Etiny) |
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1686 exp_min = len(self._int) + self._exp - context.prec |
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1687 if exp_min > Etop: |
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1688 # overflow: exp_min > Etop iff self.adjusted() > Emax |
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1689 ans = context._raise_error(Overflow, 'above Emax', self._sign) |
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1690 context._raise_error(Inexact) |
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1691 context._raise_error(Rounded) |
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1692 return ans |
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1693 |
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1694 self_is_subnormal = exp_min < Etiny |
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1695 if self_is_subnormal: |
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1696 exp_min = Etiny |
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1697 |
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1698 # round if self has too many digits |
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1699 if self._exp < exp_min: |
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1700 digits = len(self._int) + self._exp - exp_min |
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1701 if digits < 0: |
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1702 self = _dec_from_triple(self._sign, '1', exp_min-1) |
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1703 digits = 0 |
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1704 rounding_method = self._pick_rounding_function[context.rounding] |
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1705 changed = rounding_method(self, digits) |
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1706 coeff = self._int[:digits] or '0' |
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1707 if changed > 0: |
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1708 coeff = str(int(coeff)+1) |
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1709 if len(coeff) > context.prec: |
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1710 coeff = coeff[:-1] |
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1711 exp_min += 1 |
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1712 |
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1713 # check whether the rounding pushed the exponent out of range |
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1714 if exp_min > Etop: |
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1715 ans = context._raise_error(Overflow, 'above Emax', self._sign) |
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1716 else: |
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1717 ans = _dec_from_triple(self._sign, coeff, exp_min) |
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1718 |
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1719 # raise the appropriate signals, taking care to respect |
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1720 # the precedence described in the specification |
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1721 if changed and self_is_subnormal: |
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1722 context._raise_error(Underflow) |
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1723 if self_is_subnormal: |
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1724 context._raise_error(Subnormal) |
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1725 if changed: |
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1726 context._raise_error(Inexact) |
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1727 context._raise_error(Rounded) |
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1728 if not ans: |
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1729 # raise Clamped on underflow to 0 |
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1730 context._raise_error(Clamped) |
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1731 return ans |
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1732 |
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1733 if self_is_subnormal: |
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1734 context._raise_error(Subnormal) |
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1735 |
|
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1736 # fold down if clamp == 1 and self has too few digits |
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1737 if context.clamp == 1 and self._exp > Etop: |
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1738 context._raise_error(Clamped) |
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1739 self_padded = self._int + '0'*(self._exp - Etop) |
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1740 return _dec_from_triple(self._sign, self_padded, Etop) |
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1741 |
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1742 # here self was representable to begin with; return unchanged |
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1743 return Decimal(self) |
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1744 |
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1745 # for each of the rounding functions below: |
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1746 # self is a finite, nonzero Decimal |
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1747 # prec is an integer satisfying 0 <= prec < len(self._int) |
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1748 # |
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1749 # each function returns either -1, 0, or 1, as follows: |
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1750 # 1 indicates that self should be rounded up (away from zero) |
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1751 # 0 indicates that self should be truncated, and that all the |
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1752 # digits to be truncated are zeros (so the value is unchanged) |
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1753 # -1 indicates that there are nonzero digits to be truncated |
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1754 |
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1755 def _round_down(self, prec): |
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1756 """Also known as round-towards-0, truncate.""" |
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1757 if _all_zeros(self._int, prec): |
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1758 return 0 |
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1759 else: |
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1760 return -1 |
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1761 |
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1762 def _round_up(self, prec): |
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1763 """Rounds away from 0.""" |
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1764 return -self._round_down(prec) |
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1765 |
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1766 def _round_half_up(self, prec): |
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1767 """Rounds 5 up (away from 0)""" |
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1768 if self._int[prec] in '56789': |
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1769 return 1 |
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1770 elif _all_zeros(self._int, prec): |
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1771 return 0 |
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1772 else: |
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1773 return -1 |
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1774 |
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1775 def _round_half_down(self, prec): |
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1776 """Round 5 down""" |
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1777 if _exact_half(self._int, prec): |
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1778 return -1 |
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1779 else: |
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1780 return self._round_half_up(prec) |
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1781 |
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1782 def _round_half_even(self, prec): |
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1783 """Round 5 to even, rest to nearest.""" |
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1784 if _exact_half(self._int, prec) and \ |
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1785 (prec == 0 or self._int[prec-1] in '02468'): |
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1786 return -1 |
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1787 else: |
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1788 return self._round_half_up(prec) |
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1789 |
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1790 def _round_ceiling(self, prec): |
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1791 """Rounds up (not away from 0 if negative.)""" |
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1792 if self._sign: |
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1793 return self._round_down(prec) |
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1794 else: |
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1795 return -self._round_down(prec) |
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1796 |
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1797 def _round_floor(self, prec): |
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1798 """Rounds down (not towards 0 if negative)""" |
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1799 if not self._sign: |
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1800 return self._round_down(prec) |
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1801 else: |
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1802 return -self._round_down(prec) |
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1803 |
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1804 def _round_05up(self, prec): |
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1805 """Round down unless digit prec-1 is 0 or 5.""" |
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1806 if prec and self._int[prec-1] not in '05': |
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1807 return self._round_down(prec) |
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1808 else: |
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1809 return -self._round_down(prec) |
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1810 |
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1811 _pick_rounding_function = dict( |
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1812 ROUND_DOWN = _round_down, |
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1813 ROUND_UP = _round_up, |
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1814 ROUND_HALF_UP = _round_half_up, |
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1815 ROUND_HALF_DOWN = _round_half_down, |
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1816 ROUND_HALF_EVEN = _round_half_even, |
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1817 ROUND_CEILING = _round_ceiling, |
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1818 ROUND_FLOOR = _round_floor, |
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1819 ROUND_05UP = _round_05up, |
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1820 ) |
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1821 |
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1822 def __round__(self, n=None): |
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1823 """Round self to the nearest integer, or to a given precision. |
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1824 |
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1825 If only one argument is supplied, round a finite Decimal |
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1826 instance self to the nearest integer. If self is infinite or |
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1827 a NaN then a Python exception is raised. If self is finite |
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1828 and lies exactly halfway between two integers then it is |
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1829 rounded to the integer with even last digit. |
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1830 |
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1831 >>> round(Decimal('123.456')) |
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1832 123 |
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1833 >>> round(Decimal('-456.789')) |
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1834 -457 |
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1835 >>> round(Decimal('-3.0')) |
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1836 -3 |
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1837 >>> round(Decimal('2.5')) |
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1838 2 |
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1839 >>> round(Decimal('3.5')) |
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1840 4 |
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1841 >>> round(Decimal('Inf')) |
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1842 Traceback (most recent call last): |
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1843 ... |
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1844 OverflowError: cannot round an infinity |
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1845 >>> round(Decimal('NaN')) |
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1846 Traceback (most recent call last): |
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1847 ... |
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1848 ValueError: cannot round a NaN |
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1849 |
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1850 If a second argument n is supplied, self is rounded to n |
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1851 decimal places using the rounding mode for the current |
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1852 context. |
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1853 |
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1854 For an integer n, round(self, -n) is exactly equivalent to |
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1855 self.quantize(Decimal('1En')). |
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1856 |
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1857 >>> round(Decimal('123.456'), 0) |
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1858 Decimal('123') |
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1859 >>> round(Decimal('123.456'), 2) |
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1860 Decimal('123.46') |
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1861 >>> round(Decimal('123.456'), -2) |
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1862 Decimal('1E+2') |
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1863 >>> round(Decimal('-Infinity'), 37) |
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1864 Decimal('NaN') |
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1865 >>> round(Decimal('sNaN123'), 0) |
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1866 Decimal('NaN123') |
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1867 |
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1868 """ |
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1869 if n is not None: |
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1870 # two-argument form: use the equivalent quantize call |
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1871 if not isinstance(n, int): |
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1872 raise TypeError('Second argument to round should be integral') |
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1873 exp = _dec_from_triple(0, '1', -n) |
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1874 return self.quantize(exp) |
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1875 |
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1876 # one-argument form |
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1877 if self._is_special: |
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1878 if self.is_nan(): |
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1879 raise ValueError("cannot round a NaN") |
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1880 else: |
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1881 raise OverflowError("cannot round an infinity") |
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1882 return int(self._rescale(0, ROUND_HALF_EVEN)) |
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1883 |
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1884 def __floor__(self): |
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1885 """Return the floor of self, as an integer. |
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1886 |
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1887 For a finite Decimal instance self, return the greatest |
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1888 integer n such that n <= self. If self is infinite or a NaN |
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1889 then a Python exception is raised. |
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1890 |
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1891 """ |
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1892 if self._is_special: |
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1893 if self.is_nan(): |
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1894 raise ValueError("cannot round a NaN") |
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1895 else: |
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1896 raise OverflowError("cannot round an infinity") |
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1897 return int(self._rescale(0, ROUND_FLOOR)) |
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1898 |
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1899 def __ceil__(self): |
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1900 """Return the ceiling of self, as an integer. |
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1901 |
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1902 For a finite Decimal instance self, return the least integer n |
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1903 such that n >= self. If self is infinite or a NaN then a |
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1904 Python exception is raised. |
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1905 |
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1906 """ |
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1907 if self._is_special: |
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1908 if self.is_nan(): |
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1909 raise ValueError("cannot round a NaN") |
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1910 else: |
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1911 raise OverflowError("cannot round an infinity") |
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1912 return int(self._rescale(0, ROUND_CEILING)) |
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1913 |
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1914 def fma(self, other, third, context=None): |
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1915 """Fused multiply-add. |
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1916 |
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1917 Returns self*other+third with no rounding of the intermediate |
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1918 product self*other. |
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1919 |
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1920 self and other are multiplied together, with no rounding of |
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1921 the result. The third operand is then added to the result, |
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1922 and a single final rounding is performed. |
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1923 """ |
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1925 other = _convert_other(other, raiseit=True) |
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1926 third = _convert_other(third, raiseit=True) |
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1927 |
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1928 # compute product; raise InvalidOperation if either operand is |
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1929 # a signaling NaN or if the product is zero times infinity. |
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1930 if self._is_special or other._is_special: |
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1931 if context is None: |
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1932 context = getcontext() |
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1933 if self._exp == 'N': |
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1934 return context._raise_error(InvalidOperation, 'sNaN', self) |
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1935 if other._exp == 'N': |
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1936 return context._raise_error(InvalidOperation, 'sNaN', other) |
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1937 if self._exp == 'n': |
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1938 product = self |
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1939 elif other._exp == 'n': |
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1940 product = other |
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1941 elif self._exp == 'F': |
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1942 if not other: |
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1943 return context._raise_error(InvalidOperation, |
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1944 'INF * 0 in fma') |
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1945 product = _SignedInfinity[self._sign ^ other._sign] |
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1946 elif other._exp == 'F': |
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1947 if not self: |
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1948 return context._raise_error(InvalidOperation, |
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1949 '0 * INF in fma') |
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1950 product = _SignedInfinity[self._sign ^ other._sign] |
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1951 else: |
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1952 product = _dec_from_triple(self._sign ^ other._sign, |
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1953 str(int(self._int) * int(other._int)), |
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1954 self._exp + other._exp) |
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1955 |
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1956 return product.__add__(third, context) |
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1957 |
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1958 def _power_modulo(self, other, modulo, context=None): |
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1959 """Three argument version of __pow__""" |
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1960 |
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1961 other = _convert_other(other) |
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1962 if other is NotImplemented: |
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1963 return other |
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1964 modulo = _convert_other(modulo) |
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1965 if modulo is NotImplemented: |
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1966 return modulo |
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1967 |
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1968 if context is None: |
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1969 context = getcontext() |
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1970 |
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1971 # deal with NaNs: if there are any sNaNs then first one wins, |
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1972 # (i.e. behaviour for NaNs is identical to that of fma) |
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1973 self_is_nan = self._isnan() |
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1974 other_is_nan = other._isnan() |
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1975 modulo_is_nan = modulo._isnan() |
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1976 if self_is_nan or other_is_nan or modulo_is_nan: |
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1977 if self_is_nan == 2: |
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1978 return context._raise_error(InvalidOperation, 'sNaN', |
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1979 self) |
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1980 if other_is_nan == 2: |
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1981 return context._raise_error(InvalidOperation, 'sNaN', |
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1982 other) |
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1983 if modulo_is_nan == 2: |
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1984 return context._raise_error(InvalidOperation, 'sNaN', |
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1985 modulo) |
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1986 if self_is_nan: |
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1987 return self._fix_nan(context) |
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1988 if other_is_nan: |
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1989 return other._fix_nan(context) |
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1990 return modulo._fix_nan(context) |
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1991 |
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1992 # check inputs: we apply same restrictions as Python's pow() |
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1993 if not (self._isinteger() and |
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1994 other._isinteger() and |
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1995 modulo._isinteger()): |
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1996 return context._raise_error(InvalidOperation, |
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1997 'pow() 3rd argument not allowed ' |
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1998 'unless all arguments are integers') |
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1999 if other < 0: |
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2000 return context._raise_error(InvalidOperation, |
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2001 'pow() 2nd argument cannot be ' |
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2002 'negative when 3rd argument specified') |
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2003 if not modulo: |
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2004 return context._raise_error(InvalidOperation, |
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2005 'pow() 3rd argument cannot be 0') |
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2006 |
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2007 # additional restriction for decimal: the modulus must be less |
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2008 # than 10**prec in absolute value |
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2009 if modulo.adjusted() >= context.prec: |
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2010 return context._raise_error(InvalidOperation, |
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2011 'insufficient precision: pow() 3rd ' |
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2012 'argument must not have more than ' |
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2013 'precision digits') |
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2014 |
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2015 # define 0**0 == NaN, for consistency with two-argument pow |
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2016 # (even though it hurts!) |
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2017 if not other and not self: |
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2018 return context._raise_error(InvalidOperation, |
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2019 'at least one of pow() 1st argument ' |
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2020 'and 2nd argument must be nonzero ;' |
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2021 '0**0 is not defined') |
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2022 |
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2023 # compute sign of result |
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2024 if other._iseven(): |
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2025 sign = 0 |
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2026 else: |
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2027 sign = self._sign |
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2028 |
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2029 # convert modulo to a Python integer, and self and other to |
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2030 # Decimal integers (i.e. force their exponents to be >= 0) |
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2031 modulo = abs(int(modulo)) |
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2032 base = _WorkRep(self.to_integral_value()) |
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2033 exponent = _WorkRep(other.to_integral_value()) |
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2034 |
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2035 # compute result using integer pow() |
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2036 base = (base.int % modulo * pow(10, base.exp, modulo)) % modulo |
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2037 for i in range(exponent.exp): |
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2038 base = pow(base, 10, modulo) |
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2039 base = pow(base, exponent.int, modulo) |
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2040 |
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2041 return _dec_from_triple(sign, str(base), 0) |
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2042 |
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2043 def _power_exact(self, other, p): |
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2044 """Attempt to compute self**other exactly. |
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2045 |
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2046 Given Decimals self and other and an integer p, attempt to |
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2047 compute an exact result for the power self**other, with p |
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2048 digits of precision. Return None if self**other is not |
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2049 exactly representable in p digits. |
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2050 |
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2051 Assumes that elimination of special cases has already been |
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2052 performed: self and other must both be nonspecial; self must |
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2053 be positive and not numerically equal to 1; other must be |
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2054 nonzero. For efficiency, other._exp should not be too large, |
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2055 so that 10**abs(other._exp) is a feasible calculation.""" |
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2056 |
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2057 # In the comments below, we write x for the value of self and y for the |
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2058 # value of other. Write x = xc*10**xe and abs(y) = yc*10**ye, with xc |
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2059 # and yc positive integers not divisible by 10. |
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2060 |
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2061 # The main purpose of this method is to identify the *failure* |
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2062 # of x**y to be exactly representable with as little effort as |
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2063 # possible. So we look for cheap and easy tests that |
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2064 # eliminate the possibility of x**y being exact. Only if all |
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2065 # these tests are passed do we go on to actually compute x**y. |
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2066 |
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2067 # Here's the main idea. Express y as a rational number m/n, with m and |
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2068 # n relatively prime and n>0. Then for x**y to be exactly |
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2069 # representable (at *any* precision), xc must be the nth power of a |
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2070 # positive integer and xe must be divisible by n. If y is negative |
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2071 # then additionally xc must be a power of either 2 or 5, hence a power |
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2072 # of 2**n or 5**n. |
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2073 # |
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2074 # There's a limit to how small |y| can be: if y=m/n as above |
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2075 # then: |
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2076 # |
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2077 # (1) if xc != 1 then for the result to be representable we |
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2078 # need xc**(1/n) >= 2, and hence also xc**|y| >= 2. So |
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2079 # if |y| <= 1/nbits(xc) then xc < 2**nbits(xc) <= |
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2080 # 2**(1/|y|), hence xc**|y| < 2 and the result is not |
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2081 # representable. |
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2082 # |
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2083 # (2) if xe != 0, |xe|*(1/n) >= 1, so |xe|*|y| >= 1. Hence if |
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2084 # |y| < 1/|xe| then the result is not representable. |
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2085 # |
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2086 # Note that since x is not equal to 1, at least one of (1) and |
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2087 # (2) must apply. Now |y| < 1/nbits(xc) iff |yc|*nbits(xc) < |
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2088 # 10**-ye iff len(str(|yc|*nbits(xc)) <= -ye. |
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2089 # |
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2090 # There's also a limit to how large y can be, at least if it's |
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2091 # positive: the normalized result will have coefficient xc**y, |
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2092 # so if it's representable then xc**y < 10**p, and y < |
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2093 # p/log10(xc). Hence if y*log10(xc) >= p then the result is |
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2094 # not exactly representable. |
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2095 |
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2096 # if len(str(abs(yc*xe)) <= -ye then abs(yc*xe) < 10**-ye, |
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2097 # so |y| < 1/xe and the result is not representable. |
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2098 # Similarly, len(str(abs(yc)*xc_bits)) <= -ye implies |y| |
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2099 # < 1/nbits(xc). |
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2100 |
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2101 x = _WorkRep(self) |
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2102 xc, xe = x.int, x.exp |
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2103 while xc % 10 == 0: |
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2104 xc //= 10 |
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2105 xe += 1 |
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2106 |
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2107 y = _WorkRep(other) |
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2108 yc, ye = y.int, y.exp |
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2109 while yc % 10 == 0: |
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2110 yc //= 10 |
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2111 ye += 1 |
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2112 |
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2113 # case where xc == 1: result is 10**(xe*y), with xe*y |
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2114 # required to be an integer |
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2115 if xc == 1: |
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2116 xe *= yc |
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2117 # result is now 10**(xe * 10**ye); xe * 10**ye must be integral |
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2118 while xe % 10 == 0: |
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2119 xe //= 10 |
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2120 ye += 1 |
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2121 if ye < 0: |
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2122 return None |
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2123 exponent = xe * 10**ye |
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2124 if y.sign == 1: |
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2125 exponent = -exponent |
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2126 # if other is a nonnegative integer, use ideal exponent |
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2127 if other._isinteger() and other._sign == 0: |
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2128 ideal_exponent = self._exp*int(other) |
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2129 zeros = min(exponent-ideal_exponent, p-1) |
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2130 else: |
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2131 zeros = 0 |
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2132 return _dec_from_triple(0, '1' + '0'*zeros, exponent-zeros) |
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2133 |
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2134 # case where y is negative: xc must be either a power |
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2135 # of 2 or a power of 5. |
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2136 if y.sign == 1: |
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2137 last_digit = xc % 10 |
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2138 if last_digit in (2,4,6,8): |
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2139 # quick test for power of 2 |
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2140 if xc & -xc != xc: |
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2141 return None |
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2142 # now xc is a power of 2; e is its exponent |
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2143 e = _nbits(xc)-1 |
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2144 |
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2145 # We now have: |
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2146 # |
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2147 # x = 2**e * 10**xe, e > 0, and y < 0. |
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2148 # |
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2149 # The exact result is: |
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2150 # |
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2151 # x**y = 5**(-e*y) * 10**(e*y + xe*y) |
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2152 # |
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2153 # provided that both e*y and xe*y are integers. Note that if |
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2154 # 5**(-e*y) >= 10**p, then the result can't be expressed |
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2155 # exactly with p digits of precision. |
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2156 # |
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2157 # Using the above, we can guard against large values of ye. |
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2158 # 93/65 is an upper bound for log(10)/log(5), so if |
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2159 # |
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2160 # ye >= len(str(93*p//65)) |
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2161 # |
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2162 # then |
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2163 # |
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2164 # -e*y >= -y >= 10**ye > 93*p/65 > p*log(10)/log(5), |
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2165 # |
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2166 # so 5**(-e*y) >= 10**p, and the coefficient of the result |
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2167 # can't be expressed in p digits. |
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2168 |
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2169 # emax >= largest e such that 5**e < 10**p. |
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2170 emax = p*93//65 |
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2171 if ye >= len(str(emax)): |
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2172 return None |
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2173 |
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2174 # Find -e*y and -xe*y; both must be integers |
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2175 e = _decimal_lshift_exact(e * yc, ye) |
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2176 xe = _decimal_lshift_exact(xe * yc, ye) |
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2177 if e is None or xe is None: |
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2178 return None |
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2179 |
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2180 if e > emax: |
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2181 return None |
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2182 xc = 5**e |
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2183 |
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2184 elif last_digit == 5: |
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2185 # e >= log_5(xc) if xc is a power of 5; we have |
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2186 # equality all the way up to xc=5**2658 |
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2187 e = _nbits(xc)*28//65 |
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2188 xc, remainder = divmod(5**e, xc) |
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2189 if remainder: |
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2190 return None |
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2191 while xc % 5 == 0: |
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2192 xc //= 5 |
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2193 e -= 1 |
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2194 |
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2195 # Guard against large values of ye, using the same logic as in |
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2196 # the 'xc is a power of 2' branch. 10/3 is an upper bound for |
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2197 # log(10)/log(2). |
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2198 emax = p*10//3 |
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2199 if ye >= len(str(emax)): |
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2200 return None |
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2201 |
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2202 e = _decimal_lshift_exact(e * yc, ye) |
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2203 xe = _decimal_lshift_exact(xe * yc, ye) |
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2204 if e is None or xe is None: |
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2205 return None |
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2206 |
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2207 if e > emax: |
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2208 return None |
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2209 xc = 2**e |
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2210 else: |
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2211 return None |
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2212 |
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2213 if xc >= 10**p: |
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2214 return None |
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2215 xe = -e-xe |
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2216 return _dec_from_triple(0, str(xc), xe) |
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2217 |
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2218 # now y is positive; find m and n such that y = m/n |
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2219 if ye >= 0: |
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2220 m, n = yc*10**ye, 1 |
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2221 else: |
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2222 if xe != 0 and len(str(abs(yc*xe))) <= -ye: |
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2223 return None |
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2224 xc_bits = _nbits(xc) |
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2225 if xc != 1 and len(str(abs(yc)*xc_bits)) <= -ye: |
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2226 return None |
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2227 m, n = yc, 10**(-ye) |
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2228 while m % 2 == n % 2 == 0: |
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2229 m //= 2 |
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2230 n //= 2 |
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2231 while m % 5 == n % 5 == 0: |
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2232 m //= 5 |
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2233 n //= 5 |
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2234 |
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2235 # compute nth root of xc*10**xe |
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2236 if n > 1: |
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2237 # if 1 < xc < 2**n then xc isn't an nth power |
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2238 if xc != 1 and xc_bits <= n: |
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2239 return None |
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2240 |
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2241 xe, rem = divmod(xe, n) |
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2242 if rem != 0: |
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2243 return None |
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2244 |
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2245 # compute nth root of xc using Newton's method |
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2246 a = 1 << -(-_nbits(xc)//n) # initial estimate |
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2247 while True: |
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2248 q, r = divmod(xc, a**(n-1)) |
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2249 if a <= q: |
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2250 break |
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2251 else: |
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2252 a = (a*(n-1) + q)//n |
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2253 if not (a == q and r == 0): |
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2254 return None |
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2255 xc = a |
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2256 |
|
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2257 # now xc*10**xe is the nth root of the original xc*10**xe |
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2258 # compute mth power of xc*10**xe |
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2259 |
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2260 # if m > p*100//_log10_lb(xc) then m > p/log10(xc), hence xc**m > |
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2261 # 10**p and the result is not representable. |
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2262 if xc > 1 and m > p*100//_log10_lb(xc): |
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2263 return None |
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2264 xc = xc**m |
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2265 xe *= m |
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2266 if xc > 10**p: |
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2267 return None |
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2268 |
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2269 # by this point the result *is* exactly representable |
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2270 # adjust the exponent to get as close as possible to the ideal |
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2271 # exponent, if necessary |
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2272 str_xc = str(xc) |
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2273 if other._isinteger() and other._sign == 0: |
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2274 ideal_exponent = self._exp*int(other) |
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2275 zeros = min(xe-ideal_exponent, p-len(str_xc)) |
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2276 else: |
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2277 zeros = 0 |
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2278 return _dec_from_triple(0, str_xc+'0'*zeros, xe-zeros) |
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2279 |
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2280 def __pow__(self, other, modulo=None, context=None): |
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2281 """Return self ** other [ % modulo]. |
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2282 |
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2283 With two arguments, compute self**other. |
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2284 |
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2285 With three arguments, compute (self**other) % modulo. For the |
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2286 three argument form, the following restrictions on the |
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2287 arguments hold: |
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2288 |
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2289 - all three arguments must be integral |
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2290 - other must be nonnegative |
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2291 - either self or other (or both) must be nonzero |
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2292 - modulo must be nonzero and must have at most p digits, |
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2293 where p is the context precision. |
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2294 |
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2295 If any of these restrictions is violated the InvalidOperation |
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2296 flag is raised. |
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2297 |
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2298 The result of pow(self, other, modulo) is identical to the |
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2299 result that would be obtained by computing (self**other) % |
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2300 modulo with unbounded precision, but is computed more |
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2301 efficiently. It is always exact. |
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2302 """ |
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2303 |
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2304 if modulo is not None: |
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2305 return self._power_modulo(other, modulo, context) |
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2306 |
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2307 other = _convert_other(other) |
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2308 if other is NotImplemented: |
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2309 return other |
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2310 |
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2311 if context is None: |
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2312 context = getcontext() |
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2313 |
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2314 # either argument is a NaN => result is NaN |
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2315 ans = self._check_nans(other, context) |
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2316 if ans: |
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2317 return ans |
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2318 |
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2319 # 0**0 = NaN (!), x**0 = 1 for nonzero x (including +/-Infinity) |
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2320 if not other: |
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2321 if not self: |
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2322 return context._raise_error(InvalidOperation, '0 ** 0') |
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2323 else: |
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2324 return _One |
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2325 |
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2326 # result has sign 1 iff self._sign is 1 and other is an odd integer |
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2327 result_sign = 0 |
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2328 if self._sign == 1: |
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2329 if other._isinteger(): |
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2330 if not other._iseven(): |
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2331 result_sign = 1 |
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2332 else: |
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2333 # -ve**noninteger = NaN |
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2334 # (-0)**noninteger = 0**noninteger |
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2335 if self: |
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2336 return context._raise_error(InvalidOperation, |
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2337 'x ** y with x negative and y not an integer') |
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2338 # negate self, without doing any unwanted rounding |
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2339 self = self.copy_negate() |
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2340 |
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2341 # 0**(+ve or Inf)= 0; 0**(-ve or -Inf) = Infinity |
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2342 if not self: |
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2343 if other._sign == 0: |
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2344 return _dec_from_triple(result_sign, '0', 0) |
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2345 else: |
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2346 return _SignedInfinity[result_sign] |
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2347 |
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2348 # Inf**(+ve or Inf) = Inf; Inf**(-ve or -Inf) = 0 |
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2349 if self._isinfinity(): |
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2350 if other._sign == 0: |
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2351 return _SignedInfinity[result_sign] |
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2352 else: |
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2353 return _dec_from_triple(result_sign, '0', 0) |
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2354 |
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2355 # 1**other = 1, but the choice of exponent and the flags |
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2356 # depend on the exponent of self, and on whether other is a |
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2357 # positive integer, a negative integer, or neither |
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2358 if self == _One: |
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2359 if other._isinteger(): |
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2360 # exp = max(self._exp*max(int(other), 0), |
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2361 # 1-context.prec) but evaluating int(other) directly |
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2362 # is dangerous until we know other is small (other |
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2363 # could be 1e999999999) |
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2364 if other._sign == 1: |
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2365 multiplier = 0 |
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2366 elif other > context.prec: |
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2367 multiplier = context.prec |
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2368 else: |
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2369 multiplier = int(other) |
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2370 |
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2371 exp = self._exp * multiplier |
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2372 if exp < 1-context.prec: |
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2373 exp = 1-context.prec |
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2374 context._raise_error(Rounded) |
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2375 else: |
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2376 context._raise_error(Inexact) |
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2377 context._raise_error(Rounded) |
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2378 exp = 1-context.prec |
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2379 |
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2380 return _dec_from_triple(result_sign, '1'+'0'*-exp, exp) |
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2381 |
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2382 # compute adjusted exponent of self |
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2383 self_adj = self.adjusted() |
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2384 |
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2385 # self ** infinity is infinity if self > 1, 0 if self < 1 |
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2386 # self ** -infinity is infinity if self < 1, 0 if self > 1 |
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2387 if other._isinfinity(): |
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2388 if (other._sign == 0) == (self_adj < 0): |
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2389 return _dec_from_triple(result_sign, '0', 0) |
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2390 else: |
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2391 return _SignedInfinity[result_sign] |
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2392 |
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2393 # from here on, the result always goes through the call |
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2394 # to _fix at the end of this function. |
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2395 ans = None |
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2396 exact = False |
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2397 |
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2398 # crude test to catch cases of extreme overflow/underflow. If |
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2399 # log10(self)*other >= 10**bound and bound >= len(str(Emax)) |
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2400 # then 10**bound >= 10**len(str(Emax)) >= Emax+1 and hence |
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2401 # self**other >= 10**(Emax+1), so overflow occurs. The test |
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2402 # for underflow is similar. |
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2403 bound = self._log10_exp_bound() + other.adjusted() |
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2404 if (self_adj >= 0) == (other._sign == 0): |
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2405 # self > 1 and other +ve, or self < 1 and other -ve |
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2406 # possibility of overflow |
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2407 if bound >= len(str(context.Emax)): |
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2408 ans = _dec_from_triple(result_sign, '1', context.Emax+1) |
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2409 else: |
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2410 # self > 1 and other -ve, or self < 1 and other +ve |
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2411 # possibility of underflow to 0 |
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2412 Etiny = context.Etiny() |
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2413 if bound >= len(str(-Etiny)): |
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2414 ans = _dec_from_triple(result_sign, '1', Etiny-1) |
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2415 |
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2416 # try for an exact result with precision +1 |
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2417 if ans is None: |
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2418 ans = self._power_exact(other, context.prec + 1) |
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2419 if ans is not None: |
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2420 if result_sign == 1: |
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2421 ans = _dec_from_triple(1, ans._int, ans._exp) |
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2422 exact = True |
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2423 |
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2424 # usual case: inexact result, x**y computed directly as exp(y*log(x)) |
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2425 if ans is None: |
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2426 p = context.prec |
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2427 x = _WorkRep(self) |
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2428 xc, xe = x.int, x.exp |
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2429 y = _WorkRep(other) |
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2430 yc, ye = y.int, y.exp |
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2431 if y.sign == 1: |
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2432 yc = -yc |
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2433 |
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2434 # compute correctly rounded result: start with precision +3, |
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2435 # then increase precision until result is unambiguously roundable |
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2436 extra = 3 |
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2437 while True: |
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2438 coeff, exp = _dpower(xc, xe, yc, ye, p+extra) |
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2439 if coeff % (5*10**(len(str(coeff))-p-1)): |
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2440 break |
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2441 extra += 3 |
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2442 |
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2443 ans = _dec_from_triple(result_sign, str(coeff), exp) |
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2444 |
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2445 # unlike exp, ln and log10, the power function respects the |
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2446 # rounding mode; no need to switch to ROUND_HALF_EVEN here |
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2447 |
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2448 # There's a difficulty here when 'other' is not an integer and |
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2449 # the result is exact. In this case, the specification |
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2450 # requires that the Inexact flag be raised (in spite of |
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2451 # exactness), but since the result is exact _fix won't do this |
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2452 # for us. (Correspondingly, the Underflow signal should also |
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2453 # be raised for subnormal results.) We can't directly raise |
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2454 # these signals either before or after calling _fix, since |
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2455 # that would violate the precedence for signals. So we wrap |
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2456 # the ._fix call in a temporary context, and reraise |
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2457 # afterwards. |
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2458 if exact and not other._isinteger(): |
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2459 # pad with zeros up to length context.prec+1 if necessary; this |
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2460 # ensures that the Rounded signal will be raised. |
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2461 if len(ans._int) <= context.prec: |
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2462 expdiff = context.prec + 1 - len(ans._int) |
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2463 ans = _dec_from_triple(ans._sign, ans._int+'0'*expdiff, |
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2464 ans._exp-expdiff) |
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2465 |
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2466 # create a copy of the current context, with cleared flags/traps |
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2467 newcontext = context.copy() |
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2468 newcontext.clear_flags() |
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2469 for exception in _signals: |
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2470 newcontext.traps[exception] = 0 |
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2471 |
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2472 # round in the new context |
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2473 ans = ans._fix(newcontext) |
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2474 |
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2475 # raise Inexact, and if necessary, Underflow |
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2476 newcontext._raise_error(Inexact) |
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2477 if newcontext.flags[Subnormal]: |
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2478 newcontext._raise_error(Underflow) |
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2479 |
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2480 # propagate signals to the original context; _fix could |
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2481 # have raised any of Overflow, Underflow, Subnormal, |
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2482 # Inexact, Rounded, Clamped. Overflow needs the correct |
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2483 # arguments. Note that the order of the exceptions is |
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2484 # important here. |
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2485 if newcontext.flags[Overflow]: |
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2486 context._raise_error(Overflow, 'above Emax', ans._sign) |
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2487 for exception in Underflow, Subnormal, Inexact, Rounded, Clamped: |
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2488 if newcontext.flags[exception]: |
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2489 context._raise_error(exception) |
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2490 |
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2491 else: |
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2492 ans = ans._fix(context) |
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2493 |
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2494 return ans |
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2495 |
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2496 def __rpow__(self, other, context=None): |
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2497 """Swaps self/other and returns __pow__.""" |
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2498 other = _convert_other(other) |
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2499 if other is NotImplemented: |
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2500 return other |
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2501 return other.__pow__(self, context=context) |
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2502 |
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2503 def normalize(self, context=None): |
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2504 """Normalize- strip trailing 0s, change anything equal to 0 to 0e0""" |
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2505 |
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2506 if context is None: |
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2507 context = getcontext() |
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2508 |
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2509 if self._is_special: |
|
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|
2510 ans = self._check_nans(context=context) |
|
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|
2511 if ans: |
|
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diff
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|
2512 return ans |
|
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|
2513 |
| 33695 | 2514 dup = self._fix(context) |
|
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|
2515 if dup._isinfinity(): |
|
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|
2516 return dup |
|
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|
2517 |
|
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|
2518 if not dup: |
|
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|
2519 return _dec_from_triple(dup._sign, '0', 0) |
|
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Mark Dickinson <dickinsm@gmail.com>
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diff
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|
2520 exp_max = [context.Emax, context.Etop()][context.clamp] |
|
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|
2521 end = len(dup._int) |
|
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|
2522 exp = dup._exp |
|
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|
2523 while dup._int[end-1] == '0' and exp < exp_max: |
|
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|
2524 exp += 1 |
|
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|
2525 end -= 1 |
|
44025
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2526 return _dec_from_triple(dup._sign, dup._int[:end], exp) |
|
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2527 |
|
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|
2528 def quantize(self, exp, rounding=None, context=None, watchexp=True): |
|
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|
2529 """Quantize self so its exponent is the same as that of exp. |
|
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|
2530 |
|
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|
2531 Similar to self._rescale(exp._exp) but with error checking. |
|
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2532 """ |
|
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|
2533 exp = _convert_other(exp, raiseit=True) |
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2534 |
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|
2535 if context is None: |
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|
2536 context = getcontext() |
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|
2537 if rounding is None: |
|
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|
2538 rounding = context.rounding |
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|
2539 |
|
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|
2540 if self._is_special or exp._is_special: |
|
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|
2541 ans = self._check_nans(exp, context) |
|
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|
2542 if ans: |
|
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Raymond Hettinger <python@rcn.com>
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|
2543 return ans |
|
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Raymond Hettinger <python@rcn.com>
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diff
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|
2544 |
|
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Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
2545 if exp._isinfinity() or self._isinfinity(): |
|
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Raymond Hettinger <python@rcn.com>
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diff
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|
2546 if exp._isinfinity() and self._isinfinity(): |
|
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|
2547 return Decimal(self) # if both are inf, it is OK |
|
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diff
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|
2548 return context._raise_error(InvalidOperation, |
|
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|
2549 'quantize with one INF') |
|
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|
2550 |
|
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|
2551 # if we're not watching exponents, do a simple rescale |
|
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|
2552 if not watchexp: |
|
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|
2553 ans = self._rescale(exp._exp, rounding) |
|
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|
2554 # raise Inexact and Rounded where appropriate |
|
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|
2555 if ans._exp > self._exp: |
|
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|
2556 context._raise_error(Rounded) |
|
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|
2557 if ans != self: |
|
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|
2558 context._raise_error(Inexact) |
|
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|
2559 return ans |
|
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|
2560 |
|
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|
2561 # exp._exp should be between Etiny and Emax |
|
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|
2562 if not (context.Etiny() <= exp._exp <= context.Emax): |
|
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|
2563 return context._raise_error(InvalidOperation, |
|
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|
2564 'target exponent out of bounds in quantize') |
|
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|
2565 |
|
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|
2566 if not self: |
|
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|
2567 ans = _dec_from_triple(self._sign, '0', exp._exp) |
|
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|
2568 return ans._fix(context) |
|
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|
2569 |
|
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|
2570 self_adjusted = self.adjusted() |
|
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|
2571 if self_adjusted > context.Emax: |
|
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|
2572 return context._raise_error(InvalidOperation, |
|
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|
2573 'exponent of quantize result too large for current context') |
|
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|
2574 if self_adjusted - exp._exp + 1 > context.prec: |
|
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|
2575 return context._raise_error(InvalidOperation, |
|
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|
2576 'quantize result has too many digits for current context') |
|
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|
2577 |
|
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|
2578 ans = self._rescale(exp._exp, rounding) |
|
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|
2579 if ans.adjusted() > context.Emax: |
|
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|
2580 return context._raise_error(InvalidOperation, |
|
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|
2581 'exponent of quantize result too large for current context') |
|
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|
2582 if len(ans._int) > context.prec: |
|
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|
2583 return context._raise_error(InvalidOperation, |
|
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|
2584 'quantize result has too many digits for current context') |
|
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|
2585 |
|
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|
2586 # raise appropriate flags |
|
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|
2587 if ans and ans.adjusted() < context.Emin: |
|
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|
2588 context._raise_error(Subnormal) |
|
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|
2589 if ans._exp > self._exp: |
|
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|
2590 if ans != self: |
|
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|
2591 context._raise_error(Inexact) |
|
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|
2592 context._raise_error(Rounded) |
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|
2593 |
|
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|
2594 # call to fix takes care of any necessary folddown, and |
|
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|
2595 # signals Clamped if necessary |
|
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|
2596 ans = ans._fix(context) |
|
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|
2597 return ans |
|
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2598 |
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|
2599 def same_quantum(self, other): |
|
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|
2600 """Return True if self and other have the same exponent; otherwise |
|
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|
2601 return False. |
|
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2602 |
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|
2603 If either operand is a special value, the following rules are used: |
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2604 * return True if both operands are infinities |
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|
2605 * return True if both operands are NaNs |
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|
2606 * otherwise, return False. |
|
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2607 """ |
|
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|
2608 other = _convert_other(other, raiseit=True) |
|
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|
2609 if self._is_special or other._is_special: |
|
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2610 return (self.is_nan() and other.is_nan() or |
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2611 self.is_infinite() and other.is_infinite()) |
|
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2612 return self._exp == other._exp |
|
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2614 def _rescale(self, exp, rounding): |
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2615 """Rescale self so that the exponent is exp, either by padding with zeros |
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2616 or by truncating digits, using the given rounding mode. |
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2617 |
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2618 Specials are returned without change. This operation is |
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2619 quiet: it raises no flags, and uses no information from the |
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2620 context. |
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2621 |
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2622 exp = exp to scale to (an integer) |
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2623 rounding = rounding mode |
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2624 """ |
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2625 if self._is_special: |
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2626 return Decimal(self) |
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2627 if not self: |
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2628 return _dec_from_triple(self._sign, '0', exp) |
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2629 |
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2630 if self._exp >= exp: |
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2631 # pad answer with zeros if necessary |
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2632 return _dec_from_triple(self._sign, |
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2633 self._int + '0'*(self._exp - exp), exp) |
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2634 |
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2635 # too many digits; round and lose data. If self.adjusted() < |
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2636 # exp-1, replace self by 10**(exp-1) before rounding |
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2637 digits = len(self._int) + self._exp - exp |
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2638 if digits < 0: |
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2639 self = _dec_from_triple(self._sign, '1', exp-1) |
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2640 digits = 0 |
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2641 this_function = self._pick_rounding_function[rounding] |
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2642 changed = this_function(self, digits) |
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2643 coeff = self._int[:digits] or '0' |
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2644 if changed == 1: |
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2645 coeff = str(int(coeff)+1) |
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2646 return _dec_from_triple(self._sign, coeff, exp) |
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2647 |
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2648 def _round(self, places, rounding): |
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2649 """Round a nonzero, nonspecial Decimal to a fixed number of |
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2650 significant figures, using the given rounding mode. |
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2651 |
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2652 Infinities, NaNs and zeros are returned unaltered. |
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2653 |
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2654 This operation is quiet: it raises no flags, and uses no |
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2655 information from the context. |
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2656 |
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2657 """ |
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2658 if places <= 0: |
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2659 raise ValueError("argument should be at least 1 in _round") |
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2660 if self._is_special or not self: |
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2661 return Decimal(self) |
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2662 ans = self._rescale(self.adjusted()+1-places, rounding) |
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2663 # it can happen that the rescale alters the adjusted exponent; |
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2664 # for example when rounding 99.97 to 3 significant figures. |
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2665 # When this happens we end up with an extra 0 at the end of |
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2666 # the number; a second rescale fixes this. |
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2667 if ans.adjusted() != self.adjusted(): |
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2668 ans = ans._rescale(ans.adjusted()+1-places, rounding) |
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2669 return ans |
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2670 |
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2671 def to_integral_exact(self, rounding=None, context=None): |
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2672 """Rounds to a nearby integer. |
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2673 |
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2674 If no rounding mode is specified, take the rounding mode from |
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2675 the context. This method raises the Rounded and Inexact flags |
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2676 when appropriate. |
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2677 |
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2678 See also: to_integral_value, which does exactly the same as |
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2679 this method except that it doesn't raise Inexact or Rounded. |
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2680 """ |
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2681 if self._is_special: |
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2682 ans = self._check_nans(context=context) |
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2683 if ans: |
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2684 return ans |
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2685 return Decimal(self) |
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2686 if self._exp >= 0: |
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2687 return Decimal(self) |
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2688 if not self: |
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2689 return _dec_from_triple(self._sign, '0', 0) |
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2690 if context is None: |
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2691 context = getcontext() |
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2692 if rounding is None: |
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2693 rounding = context.rounding |
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2694 ans = self._rescale(0, rounding) |
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2695 if ans != self: |
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2696 context._raise_error(Inexact) |
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2697 context._raise_error(Rounded) |
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2698 return ans |
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2699 |
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2700 def to_integral_value(self, rounding=None, context=None): |
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2701 """Rounds to the nearest integer, without raising inexact, rounded.""" |
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2702 if context is None: |
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2703 context = getcontext() |
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2704 if rounding is None: |
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2705 rounding = context.rounding |
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2706 if self._is_special: |
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2707 ans = self._check_nans(context=context) |
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2708 if ans: |
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2709 return ans |
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2710 return Decimal(self) |
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2711 if self._exp >= 0: |
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2712 return Decimal(self) |
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2713 else: |
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2714 return self._rescale(0, rounding) |
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2715 |
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2716 # the method name changed, but we provide also the old one, for compatibility |
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2717 to_integral = to_integral_value |
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2718 |
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2719 def sqrt(self, context=None): |
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2720 """Return the square root of self.""" |
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2721 if context is None: |
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2722 context = getcontext() |
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2723 |
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33519
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2724 if self._is_special: |
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2725 ans = self._check_nans(context=context) |
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2726 if ans: |
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2727 return ans |
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2728 |
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2729 if self._isinfinity() and self._sign == 0: |
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2730 return Decimal(self) |
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2731 |
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2732 if not self: |
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2733 # exponent = self._exp // 2. sqrt(-0) = -0 |
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2734 ans = _dec_from_triple(self._sign, '0', self._exp // 2) |
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2735 return ans._fix(context) |
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2736 |
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2737 if self._sign == 1: |
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2738 return context._raise_error(InvalidOperation, 'sqrt(-x), x > 0') |
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2739 |
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2740 # At this point self represents a positive number. Let p be |
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2741 # the desired precision and express self in the form c*100**e |
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2742 # with c a positive real number and e an integer, c and e |
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2743 # being chosen so that 100**(p-1) <= c < 100**p. Then the |
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2744 # (exact) square root of self is sqrt(c)*10**e, and 10**(p-1) |
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2745 # <= sqrt(c) < 10**p, so the closest representable Decimal at |
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2746 # precision p is n*10**e where n = round_half_even(sqrt(c)), |
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2747 # the closest integer to sqrt(c) with the even integer chosen |
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2748 # in the case of a tie. |
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2749 # |
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2750 # To ensure correct rounding in all cases, we use the |
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2751 # following trick: we compute the square root to an extra |
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2752 # place (precision p+1 instead of precision p), rounding down. |
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2753 # Then, if the result is inexact and its last digit is 0 or 5, |
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2754 # we increase the last digit to 1 or 6 respectively; if it's |
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2755 # exact we leave the last digit alone. Now the final round to |
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2756 # p places (or fewer in the case of underflow) will round |
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2757 # correctly and raise the appropriate flags. |
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2758 |
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2759 # use an extra digit of precision |
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2760 prec = context.prec+1 |
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2761 |
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2762 # write argument in the form c*100**e where e = self._exp//2 |
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2763 # is the 'ideal' exponent, to be used if the square root is |
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2764 # exactly representable. l is the number of 'digits' of c in |
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2765 # base 100, so that 100**(l-1) <= c < 100**l. |
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2766 op = _WorkRep(self) |
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2767 e = op.exp >> 1 |
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2768 if op.exp & 1: |
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2769 c = op.int * 10 |
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2770 l = (len(self._int) >> 1) + 1 |
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2771 else: |
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2772 c = op.int |
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2773 l = len(self._int)+1 >> 1 |
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2774 |
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2775 # rescale so that c has exactly prec base 100 'digits' |
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2776 shift = prec-l |
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2777 if shift >= 0: |
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2778 c *= 100**shift |
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2779 exact = True |
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2780 else: |
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2781 c, remainder = divmod(c, 100**-shift) |
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2782 exact = not remainder |
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2783 e -= shift |
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2784 |
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2785 # find n = floor(sqrt(c)) using Newton's method |
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2786 n = 10**prec |
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2787 while True: |
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2788 q = c//n |
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2789 if n <= q: |
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2790 break |
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2791 else: |
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2792 n = n + q >> 1 |
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2793 exact = exact and n*n == c |
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2794 |
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2795 if exact: |
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2796 # result is exact; rescale to use ideal exponent e |
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2797 if shift >= 0: |
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2798 # assert n % 10**shift == 0 |
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2799 n //= 10**shift |
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2800 else: |
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2801 n *= 10**-shift |
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2802 e += shift |
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2803 else: |
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2804 # result is not exact; fix last digit as described above |
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2805 if n % 5 == 0: |
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2806 n += 1 |
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2807 |
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2808 ans = _dec_from_triple(0, str(n), e) |
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2809 |
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2810 # round, and fit to current context |
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2811 context = context._shallow_copy() |
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2812 rounding = context._set_rounding(ROUND_HALF_EVEN) |
| 33695 | 2813 ans = ans._fix(context) |
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2814 context.rounding = rounding |
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2815 |
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2816 return ans |
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2817 |
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2818 def max(self, other, context=None): |
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2819 """Returns the larger value. |
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2820 |
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2821 Like max(self, other) except if one is not a number, returns |
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2822 NaN (and signals if one is sNaN). Also rounds. |
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2823 """ |
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2824 other = _convert_other(other, raiseit=True) |
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2825 |
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2826 if context is None: |
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2827 context = getcontext() |
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2828 |
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2829 if self._is_special or other._is_special: |
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2830 # If one operand is a quiet NaN and the other is number, then the |
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2831 # number is always returned |
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2832 sn = self._isnan() |
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2833 on = other._isnan() |
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2834 if sn or on: |
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2835 if on == 1 and sn == 0: |
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2836 return self._fix(context) |
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2837 if sn == 1 and on == 0: |
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2838 return other._fix(context) |
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2839 return self._check_nans(other, context) |
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2840 |
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2841 c = self._cmp(other) |
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2842 if c == 0: |
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2843 # If both operands are finite and equal in numerical value |
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2844 # then an ordering is applied: |
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2845 # |
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2846 # If the signs differ then max returns the operand with the |
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2847 # positive sign and min returns the operand with the negative sign |
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2848 # |
|
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2849 # If the signs are the same then the exponent is used to select |
|
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2850 # the result. This is exactly the ordering used in compare_total. |
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2851 c = self.compare_total(other) |
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2852 |
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2853 if c == -1: |
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2854 ans = other |
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2855 else: |
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2856 ans = self |
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2857 |
|
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2858 return ans._fix(context) |
|
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2859 |
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2860 def min(self, other, context=None): |
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2861 """Returns the smaller value. |
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2862 |
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2863 Like min(self, other) except if one is not a number, returns |
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2864 NaN (and signals if one is sNaN). Also rounds. |
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2865 """ |
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2866 other = _convert_other(other, raiseit=True) |
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2867 |
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2868 if context is None: |
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2869 context = getcontext() |
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2870 |
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2871 if self._is_special or other._is_special: |
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2872 # If one operand is a quiet NaN and the other is number, then the |
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2873 # number is always returned |
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2874 sn = self._isnan() |
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2875 on = other._isnan() |
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2876 if sn or on: |
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2877 if on == 1 and sn == 0: |
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2878 return self._fix(context) |
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2879 if sn == 1 and on == 0: |
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2880 return other._fix(context) |
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2881 return self._check_nans(other, context) |
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2882 |
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2883 c = self._cmp(other) |
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2884 if c == 0: |
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2885 c = self.compare_total(other) |
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2886 |
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2887 if c == -1: |
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2888 ans = self |
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2889 else: |
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2890 ans = other |
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2891 |
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2892 return ans._fix(context) |
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2893 |
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2894 def _isinteger(self): |
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2895 """Returns whether self is an integer""" |
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2896 if self._is_special: |
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2897 return False |
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2898 if self._exp >= 0: |
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2899 return True |
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2900 rest = self._int[self._exp:] |
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2901 return rest == '0'*len(rest) |
|
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2902 |
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2903 def _iseven(self): |
|
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2904 """Returns True if self is even. Assumes self is an integer.""" |
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2905 if not self or self._exp > 0: |
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2906 return True |
|
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2907 return self._int[-1+self._exp] in '02468' |
|
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2908 |
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2909 def adjusted(self): |
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2910 """Return the adjusted exponent of self""" |
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2911 try: |
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2912 return self._exp + len(self._int) - 1 |
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2913 # If NaN or Infinity, self._exp is string |
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2914 except TypeError: |
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2915 return 0 |
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2916 |
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2917 def canonical(self, context=None): |
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2918 """Returns the same Decimal object. |
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2919 |
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2920 As we do not have different encodings for the same number, the |
|
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|
2921 received object already is in its canonical form. |
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2922 """ |
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2923 return self |
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2924 |
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|
2925 def compare_signal(self, other, context=None): |
|
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|
2926 """Compares self to the other operand numerically. |
|
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2927 |
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|
2928 It's pretty much like compare(), but all NaNs signal, with signaling |
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|
2929 NaNs taking precedence over quiet NaNs. |
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|
2930 """ |
|
45244
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2931 other = _convert_other(other, raiseit = True) |
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|
2932 ans = self._compare_check_nans(other, context) |
|
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2933 if ans: |
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2934 return ans |
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2935 return self.compare(other, context=context) |
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2936 |
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2937 def compare_total(self, other): |
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2938 """Compares self to other using the abstract representations. |
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2939 |
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|
2940 This is not like the standard compare, which use their numerical |
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2941 value. Note that a total ordering is defined for all possible abstract |
|
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|
2942 representations. |
|
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2943 """ |
|
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2944 other = _convert_other(other, raiseit=True) |
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2945 |
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2946 # if one is negative and the other is positive, it's easy |
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2947 if self._sign and not other._sign: |
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2948 return _NegativeOne |
|
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|
2949 if not self._sign and other._sign: |
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2950 return _One |
|
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|
2951 sign = self._sign |
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2952 |
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|
2953 # let's handle both NaN types |
|
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|
2954 self_nan = self._isnan() |
|
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|
2955 other_nan = other._isnan() |
|
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|
2956 if self_nan or other_nan: |
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|
2957 if self_nan == other_nan: |
|
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|
2958 # compare payloads as though they're integers |
|
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|
2959 self_key = len(self._int), self._int |
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2960 other_key = len(other._int), other._int |
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2961 if self_key < other_key: |
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2962 if sign: |
|
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|
2963 return _One |
|
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2964 else: |
|
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2965 return _NegativeOne |
|
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2966 if self_key > other_key: |
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|
2967 if sign: |
|
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|
2968 return _NegativeOne |
|
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2969 else: |
|
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|
2970 return _One |
|
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|
2971 return _Zero |
|
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|
2972 |
|
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|
2973 if sign: |
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|
2974 if self_nan == 1: |
|
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|
2975 return _NegativeOne |
|
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|
2976 if other_nan == 1: |
|
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|
2977 return _One |
|
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|
2978 if self_nan == 2: |
|
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|
2979 return _NegativeOne |
|
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|
2980 if other_nan == 2: |
|
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|
2981 return _One |
|
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2982 else: |
|
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2983 if self_nan == 1: |
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|
2984 return _One |
|
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2985 if other_nan == 1: |
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2986 return _NegativeOne |
|
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2987 if self_nan == 2: |
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2988 return _One |
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2989 if other_nan == 2: |
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|
2990 return _NegativeOne |
|
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2991 |
|
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2992 if self < other: |
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2993 return _NegativeOne |
|
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2994 if self > other: |
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2995 return _One |
|
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2996 |
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2997 if self._exp < other._exp: |
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2998 if sign: |
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2999 return _One |
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3000 else: |
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3001 return _NegativeOne |
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3002 if self._exp > other._exp: |
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3003 if sign: |
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3004 return _NegativeOne |
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3005 else: |
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3006 return _One |
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3007 return _Zero |
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3008 |
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3009 |
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3010 def compare_total_mag(self, other): |
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3011 """Compares self to other using abstract repr., ignoring sign. |
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3012 |
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3013 Like compare_total, but with operand's sign ignored and assumed to be 0. |
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3014 """ |
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3015 other = _convert_other(other, raiseit=True) |
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3016 |
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3017 s = self.copy_abs() |
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3018 o = other.copy_abs() |
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3019 return s.compare_total(o) |
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3020 |
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3021 def copy_abs(self): |
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3022 """Returns a copy with the sign set to 0. """ |
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3023 return _dec_from_triple(0, self._int, self._exp, self._is_special) |
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3024 |
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3025 def copy_negate(self): |
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3026 """Returns a copy with the sign inverted.""" |
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3027 if self._sign: |
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3028 return _dec_from_triple(0, self._int, self._exp, self._is_special) |
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3029 else: |
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3030 return _dec_from_triple(1, self._int, self._exp, self._is_special) |
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3031 |
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3032 def copy_sign(self, other): |
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3033 """Returns self with the sign of other.""" |
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3034 other = _convert_other(other, raiseit=True) |
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3035 return _dec_from_triple(other._sign, self._int, |
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3036 self._exp, self._is_special) |
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3037 |
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3038 def exp(self, context=None): |
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3039 """Returns e ** self.""" |
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3040 |
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3041 if context is None: |
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3042 context = getcontext() |
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3043 |
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3044 # exp(NaN) = NaN |
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3045 ans = self._check_nans(context=context) |
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3046 if ans: |
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3047 return ans |
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3048 |
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3049 # exp(-Infinity) = 0 |
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3050 if self._isinfinity() == -1: |
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3051 return _Zero |
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3052 |
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3053 # exp(0) = 1 |
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3054 if not self: |
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3055 return _One |
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3056 |
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3057 # exp(Infinity) = Infinity |
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3058 if self._isinfinity() == 1: |
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3059 return Decimal(self) |
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3060 |
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3061 # the result is now guaranteed to be inexact (the true |
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3062 # mathematical result is transcendental). There's no need to |
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3063 # raise Rounded and Inexact here---they'll always be raised as |
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3064 # a result of the call to _fix. |
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3065 p = context.prec |
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3066 adj = self.adjusted() |
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3067 |
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3068 # we only need to do any computation for quite a small range |
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3069 # of adjusted exponents---for example, -29 <= adj <= 10 for |
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3070 # the default context. For smaller exponent the result is |
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3071 # indistinguishable from 1 at the given precision, while for |
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3072 # larger exponent the result either overflows or underflows. |
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3073 if self._sign == 0 and adj > len(str((context.Emax+1)*3)): |
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3074 # overflow |
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3075 ans = _dec_from_triple(0, '1', context.Emax+1) |
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3076 elif self._sign == 1 and adj > len(str((-context.Etiny()+1)*3)): |
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3077 # underflow to 0 |
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3078 ans = _dec_from_triple(0, '1', context.Etiny()-1) |
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3079 elif self._sign == 0 and adj < -p: |
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3080 # p+1 digits; final round will raise correct flags |
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3081 ans = _dec_from_triple(0, '1' + '0'*(p-1) + '1', -p) |
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3082 elif self._sign == 1 and adj < -p-1: |
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3083 # p+1 digits; final round will raise correct flags |
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3084 ans = _dec_from_triple(0, '9'*(p+1), -p-1) |
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3085 # general case |
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3086 else: |
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3087 op = _WorkRep(self) |
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3088 c, e = op.int, op.exp |
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3089 if op.sign == 1: |
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3090 c = -c |
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3091 |
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3092 # compute correctly rounded result: increase precision by |
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3093 # 3 digits at a time until we get an unambiguously |
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3094 # roundable result |
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3095 extra = 3 |
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3096 while True: |
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3097 coeff, exp = _dexp(c, e, p+extra) |
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3098 if coeff % (5*10**(len(str(coeff))-p-1)): |
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3099 break |
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3100 extra += 3 |
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3101 |
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3102 ans = _dec_from_triple(0, str(coeff), exp) |
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3103 |
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3104 # at this stage, ans should round correctly with *any* |
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3105 # rounding mode, not just with ROUND_HALF_EVEN |
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3106 context = context._shallow_copy() |
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3107 rounding = context._set_rounding(ROUND_HALF_EVEN) |
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3108 ans = ans._fix(context) |
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3109 context.rounding = rounding |
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3110 |
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3111 return ans |
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3112 |
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3113 def is_canonical(self): |
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3114 """Return True if self is canonical; otherwise return False. |
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3115 |
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3116 Currently, the encoding of a Decimal instance is always |
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3117 canonical, so this method returns True for any Decimal. |
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3118 """ |
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3119 return True |
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3120 |
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3121 def is_finite(self): |
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3122 """Return True if self is finite; otherwise return False. |
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3123 |
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3124 A Decimal instance is considered finite if it is neither |
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3125 infinite nor a NaN. |
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3126 """ |
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3127 return not self._is_special |
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3128 |
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3129 def is_infinite(self): |
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3130 """Return True if self is infinite; otherwise return False.""" |
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3131 return self._exp == 'F' |
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3132 |
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3133 def is_nan(self): |
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3134 """Return True if self is a qNaN or sNaN; otherwise return False.""" |
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3135 return self._exp in ('n', 'N') |
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3136 |
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3137 def is_normal(self, context=None): |
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3138 """Return True if self is a normal number; otherwise return False.""" |
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3139 if self._is_special or not self: |
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3140 return False |
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3141 if context is None: |
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3142 context = getcontext() |
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3143 return context.Emin <= self.adjusted() |
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3144 |
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3145 def is_qnan(self): |
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3146 """Return True if self is a quiet NaN; otherwise return False.""" |
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3147 return self._exp == 'n' |
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3148 |
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3149 def is_signed(self): |
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3150 """Return True if self is negative; otherwise return False.""" |
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3151 return self._sign == 1 |
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3152 |
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3153 def is_snan(self): |
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3154 """Return True if self is a signaling NaN; otherwise return False.""" |
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3155 return self._exp == 'N' |
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3156 |
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3157 def is_subnormal(self, context=None): |
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3158 """Return True if self is subnormal; otherwise return False.""" |
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3159 if self._is_special or not self: |
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3160 return False |
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3161 if context is None: |
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3162 context = getcontext() |
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3163 return self.adjusted() < context.Emin |
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3164 |
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3165 def is_zero(self): |
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3166 """Return True if self is a zero; otherwise return False.""" |
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3167 return not self._is_special and self._int == '0' |
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3168 |
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3169 def _ln_exp_bound(self): |
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3170 """Compute a lower bound for the adjusted exponent of self.ln(). |
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3171 In other words, compute r such that self.ln() >= 10**r. Assumes |
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3172 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 0.1 <= x <= 10 we use the inequalities 1-1/x <= ln(x) <= x-1 |
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3176 adj = self._exp + len(self._int) - 1 |
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3177 if adj >= 1: |
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3178 # argument >= 10; we use 23/10 = 2.3 as a lower bound for ln(10) |
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3179 return len(str(adj*23//10)) - 1 |
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3180 if adj <= -2: |
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3181 # argument <= 0.1 |
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3182 return len(str((-1-adj)*23//10)) - 1 |
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3183 op = _WorkRep(self) |
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3184 c, e = op.int, op.exp |
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3185 if adj == 0: |
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3186 # 1 < self < 10 |
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3187 num = str(c-10**-e) |
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3188 den = str(c) |
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3189 return len(num) - len(den) - (num < den) |
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3190 # adj == -1, 0.1 <= self < 1 |
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3191 return e + len(str(10**-e - c)) - 1 |
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3192 |
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3193 |
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3194 def ln(self, context=None): |
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3195 """Returns the natural (base e) logarithm of self.""" |
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3196 |
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3197 if context is None: |
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3198 context = getcontext() |
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3199 |
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3200 # ln(NaN) = NaN |
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3201 ans = self._check_nans(context=context) |
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3202 if ans: |
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3203 return ans |
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3204 |
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3205 # ln(0.0) == -Infinity |
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3206 if not self: |
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3207 return _NegativeInfinity |
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43400
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3208 |
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3209 # ln(Infinity) = Infinity |
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3210 if self._isinfinity() == 1: |
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3211 return _Infinity |
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3212 |
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3213 # ln(1.0) == 0.0 |
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3214 if self == _One: |
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3215 return _Zero |
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3216 |
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3217 # ln(negative) raises InvalidOperation |
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3218 if self._sign == 1: |
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3219 return context._raise_error(InvalidOperation, |
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3220 'ln of a negative value') |
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3221 |
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3222 # result is irrational, so necessarily inexact |
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3223 op = _WorkRep(self) |
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3224 c, e = op.int, op.exp |
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3225 p = context.prec |
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3226 |
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3227 # correctly rounded result: repeatedly increase precision by 3 |
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3228 # until we get an unambiguously roundable result |
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3229 places = p - self._ln_exp_bound() + 2 # at least p+3 places |
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3230 while True: |
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3231 coeff = _dlog(c, e, places) |
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3232 # assert len(str(abs(coeff)))-p >= 1 |
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3233 if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
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3234 break |
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3235 places += 3 |
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44025
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3236 ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
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3237 |
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3238 context = context._shallow_copy() |
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3239 rounding = context._set_rounding(ROUND_HALF_EVEN) |
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3240 ans = ans._fix(context) |
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3241 context.rounding = rounding |
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3242 return ans |
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3243 |
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3244 def _log10_exp_bound(self): |
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3245 """Compute a lower bound for the adjusted exponent of self.log10(). |
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3246 In other words, find r such that self.log10() >= 10**r. |
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3247 Assumes that self is finite and positive and that self != 1. |
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3248 """ |
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3249 |
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3250 # For x >= 10 or x < 0.1 we only need a bound on the integer |
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3251 # part of log10(self), and this comes directly from the |
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3252 # exponent of x. For 0.1 <= x <= 10 we use the inequalities |
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3253 # 1-1/x <= log(x) <= x-1. If x > 1 we have |log10(x)| > |
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3254 # (1-1/x)/2.31 > 0. If x < 1 then |log10(x)| > (1-x)/2.31 > 0 |
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3255 |
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3256 adj = self._exp + len(self._int) - 1 |
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3257 if adj >= 1: |
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3258 # self >= 10 |
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3259 return len(str(adj))-1 |
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3260 if adj <= -2: |
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3261 # self < 0.1 |
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3262 return len(str(-1-adj))-1 |
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3263 op = _WorkRep(self) |
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3264 c, e = op.int, op.exp |
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3265 if adj == 0: |
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3266 # 1 < self < 10 |
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3267 num = str(c-10**-e) |
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3268 den = str(231*c) |
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3269 return len(num) - len(den) - (num < den) + 2 |
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3270 # adj == -1, 0.1 <= self < 1 |
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3271 num = str(10**-e-c) |
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3272 return len(num) + e - (num < "231") - 1 |
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3273 |
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3274 def log10(self, context=None): |
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3275 """Returns the base 10 logarithm of self.""" |
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3276 |
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3277 if context is None: |
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3278 context = getcontext() |
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3279 |
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3280 # log10(NaN) = NaN |
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3281 ans = self._check_nans(context=context) |
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3282 if ans: |
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3283 return ans |
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3284 |
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3285 # log10(0.0) == -Infinity |
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3286 if not self: |
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3287 return _NegativeInfinity |
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3288 |
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3289 # log10(Infinity) = Infinity |
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3290 if self._isinfinity() == 1: |
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3291 return _Infinity |
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3292 |
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3293 # log10(negative or -Infinity) raises InvalidOperation |
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3294 if self._sign == 1: |
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3295 return context._raise_error(InvalidOperation, |
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3296 'log10 of a negative value') |
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3297 |
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3298 # log10(10**n) = n |
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3299 if self._int[0] == '1' and self._int[1:] == '0'*(len(self._int) - 1): |
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3300 # answer may need rounding |
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3301 ans = Decimal(self._exp + len(self._int) - 1) |
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3302 else: |
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3303 # result is irrational, so necessarily inexact |
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3304 op = _WorkRep(self) |
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3305 c, e = op.int, op.exp |
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3306 p = context.prec |
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3307 |
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3308 # correctly rounded result: repeatedly increase precision |
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3309 # until result is unambiguously roundable |
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3310 places = p-self._log10_exp_bound()+2 |
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3311 while True: |
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3312 coeff = _dlog10(c, e, places) |
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3313 # assert len(str(abs(coeff)))-p >= 1 |
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3314 if coeff % (5*10**(len(str(abs(coeff)))-p-1)): |
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3315 break |
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3316 places += 3 |
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3317 ans = _dec_from_triple(int(coeff<0), str(abs(coeff)), -places) |
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3318 |
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3319 context = context._shallow_copy() |
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3320 rounding = context._set_rounding(ROUND_HALF_EVEN) |
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3321 ans = ans._fix(context) |
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3322 context.rounding = rounding |
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3323 return ans |
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3324 |
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3325 def logb(self, context=None): |
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3326 """ Returns the exponent of the magnitude of self's MSD. |
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3327 |
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3328 The result is the integer which is the exponent of the magnitude |
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3329 of the most significant digit of self (as though it were truncated |
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3330 to a single digit while maintaining the value of that digit and |
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3331 without limiting the resulting exponent). |
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3332 """ |
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3333 # logb(NaN) = NaN |
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3334 ans = self._check_nans(context=context) |
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3335 if ans: |
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3336 return ans |
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3337 |
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3338 if context is None: |
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3339 context = getcontext() |
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3340 |
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3341 # logb(+/-Inf) = +Inf |
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3342 if self._isinfinity(): |
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3343 return _Infinity |
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3344 |
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3345 # logb(0) = -Inf, DivisionByZero |
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3346 if not self: |
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3347 return context._raise_error(DivisionByZero, 'logb(0)', 1) |
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3348 |
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3349 # otherwise, simply return the adjusted exponent of self, as a |
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3350 # Decimal. Note that no attempt is made to fit the result |
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3351 # into the current context. |
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3352 ans = Decimal(self.adjusted()) |
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3353 return ans._fix(context) |
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3354 |
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3355 def _islogical(self): |
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3356 """Return True if self is a logical operand. |
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3357 |
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3358 For being logical, it must be a finite number with a sign of 0, |
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3359 an exponent of 0, and a coefficient whose digits must all be |
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3360 either 0 or 1. |
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3361 """ |
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3362 if self._sign != 0 or self._exp != 0: |
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3363 return False |
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3364 for dig in self._int: |
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3365 if dig not in '01': |
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3366 return False |
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3367 return True |
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3368 |
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3369 def _fill_logical(self, context, opa, opb): |
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3370 dif = context.prec - len(opa) |
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3371 if dif > 0: |
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3372 opa = '0'*dif + opa |
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3373 elif dif < 0: |
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3374 opa = opa[-context.prec:] |
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3375 dif = context.prec - len(opb) |
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3376 if dif > 0: |
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3377 opb = '0'*dif + opb |
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3378 elif dif < 0: |
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3379 opb = opb[-context.prec:] |
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3380 return opa, opb |
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3381 |
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3382 def logical_and(self, other, context=None): |
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3383 """Applies an 'and' operation between self and other's digits.""" |
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3384 if context is None: |
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3385 context = getcontext() |
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3386 |
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3387 other = _convert_other(other, raiseit=True) |
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3388 |
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3389 if not self._islogical() or not other._islogical(): |
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3390 return context._raise_error(InvalidOperation) |
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3391 |
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3392 # fill to context.prec |
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3393 (opa, opb) = self._fill_logical(context, self._int, other._int) |
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3394 |
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3395 # make the operation, and clean starting zeroes |
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3396 result = "".join([str(int(a)&int(b)) for a,b in zip(opa,opb)]) |
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3397 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
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3398 |
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3399 def logical_invert(self, context=None): |
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3400 """Invert all its digits.""" |
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3401 if context is None: |
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3402 context = getcontext() |
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3403 return self.logical_xor(_dec_from_triple(0,'1'*context.prec,0), |
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3404 context) |
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3405 |
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3406 def logical_or(self, other, context=None): |
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3407 """Applies an 'or' operation between self and other's digits.""" |
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3408 if context is None: |
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3409 context = getcontext() |
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3410 |
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3411 other = _convert_other(other, raiseit=True) |
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3412 |
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3413 if not self._islogical() or not other._islogical(): |
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3414 return context._raise_error(InvalidOperation) |
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3415 |
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3416 # fill to context.prec |
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3417 (opa, opb) = self._fill_logical(context, self._int, other._int) |
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3418 |
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3419 # make the operation, and clean starting zeroes |
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3420 result = "".join([str(int(a)|int(b)) for a,b in zip(opa,opb)]) |
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3421 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
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3422 |
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3423 def logical_xor(self, other, context=None): |
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3424 """Applies an 'xor' operation between self and other's digits.""" |
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3425 if context is None: |
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3426 context = getcontext() |
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3427 |
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3428 other = _convert_other(other, raiseit=True) |
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3429 |
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3430 if not self._islogical() or not other._islogical(): |
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3431 return context._raise_error(InvalidOperation) |
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3432 |
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3433 # fill to context.prec |
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3434 (opa, opb) = self._fill_logical(context, self._int, other._int) |
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3435 |
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3436 # make the operation, and clean starting zeroes |
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3437 result = "".join([str(int(a)^int(b)) for a,b in zip(opa,opb)]) |
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3438 return _dec_from_triple(0, result.lstrip('0') or '0', 0) |
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3439 |
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3440 def max_mag(self, other, context=None): |
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3441 """Compares the values numerically with their sign ignored.""" |
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3442 other = _convert_other(other, raiseit=True) |
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3443 |
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3444 if context is None: |
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3445 context = getcontext() |
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3446 |
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3447 if self._is_special or other._is_special: |
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3448 # If one operand is a quiet NaN and the other is number, then the |
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3449 # number is always returned |
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3450 sn = self._isnan() |
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3451 on = other._isnan() |
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3452 if sn or on: |
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3453 if on == 1 and sn == 0: |
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3454 return self._fix(context) |
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3455 if sn == 1 and on == 0: |
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3456 return other._fix(context) |
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3457 return self._check_nans(other, context) |
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3458 |
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3459 c = self.copy_abs()._cmp(other.copy_abs()) |
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3460 if c == 0: |
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3461 c = self.compare_total(other) |
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3462 |
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3463 if c == -1: |
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3464 ans = other |
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3465 else: |
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3466 ans = self |
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3467 |
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3468 return ans._fix(context) |
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3469 |
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3470 def min_mag(self, other, context=None): |
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3471 """Compares the values numerically with their sign ignored.""" |
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3472 other = _convert_other(other, raiseit=True) |
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3473 |
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3474 if context is None: |
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3475 context = getcontext() |
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3476 |
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3477 if self._is_special or other._is_special: |
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3478 # If one operand is a quiet NaN and the other is number, then the |
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3479 # number is always returned |
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3480 sn = self._isnan() |
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3481 on = other._isnan() |
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3482 if sn or on: |
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3483 if on == 1 and sn == 0: |
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3484 return self._fix(context) |
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3485 if sn == 1 and on == 0: |
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3486 return other._fix(context) |
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3487 return self._check_nans(other, context) |
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3488 |
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3489 c = self.copy_abs()._cmp(other.copy_abs()) |
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3490 if c == 0: |
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3491 c = self.compare_total(other) |
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3492 |
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3493 if c == -1: |
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3494 ans = self |
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3495 else: |
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3496 ans = other |
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3497 |
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44329
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3498 return ans._fix(context) |
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3499 |
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3500 def next_minus(self, context=None): |
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3501 """Returns the largest representable number smaller than itself.""" |
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3502 if context is None: |
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3503 context = getcontext() |
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3504 |
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3505 ans = self._check_nans(context=context) |
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3506 if ans: |
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3507 return ans |
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3508 |
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3509 if self._isinfinity() == -1: |
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3510 return _NegativeInfinity |
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3511 if self._isinfinity() == 1: |
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3512 return _dec_from_triple(0, '9'*context.prec, context.Etop()) |
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3513 |
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3514 context = context.copy() |
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3515 context._set_rounding(ROUND_FLOOR) |
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3516 context._ignore_all_flags() |
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3517 new_self = self._fix(context) |
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3518 if new_self != self: |
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3519 return new_self |
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3520 return self.__sub__(_dec_from_triple(0, '1', context.Etiny()-1), |
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|
3521 context) |
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3522 |
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3523 def next_plus(self, context=None): |
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3524 """Returns the smallest representable number larger than itself.""" |
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3525 if context is None: |
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3526 context = getcontext() |
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3527 |
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3528 ans = self._check_nans(context=context) |
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3529 if ans: |
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3530 return ans |
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3531 |
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3532 if self._isinfinity() == 1: |
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3533 return _Infinity |
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3534 if self._isinfinity() == -1: |
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3535 return _dec_from_triple(1, '9'*context.prec, context.Etop()) |
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3536 |
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3537 context = context.copy() |
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3538 context._set_rounding(ROUND_CEILING) |
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3539 context._ignore_all_flags() |
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3540 new_self = self._fix(context) |
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3541 if new_self != self: |
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3542 return new_self |
|
44025
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3543 return self.__add__(_dec_from_triple(0, '1', context.Etiny()-1), |
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|
3544 context) |
|
43400
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3545 |
|
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3546 def next_toward(self, other, context=None): |
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3547 """Returns the number closest to self, in the direction towards other. |
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3548 |
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|
3549 The result is the closest representable number to self |
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|
3550 (excluding self) that is in the direction towards other, |
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3551 unless both have the same value. If the two operands are |
|
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3552 numerically equal, then the result is a copy of self with the |
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3553 sign set to be the same as the sign of other. |
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3554 """ |
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3555 other = _convert_other(other, raiseit=True) |
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3556 |
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3557 if context is None: |
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3558 context = getcontext() |
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3559 |
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3560 ans = self._check_nans(other, context) |
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3561 if ans: |
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3562 return ans |
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3563 |
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3564 comparison = self._cmp(other) |
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3565 if comparison == 0: |
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3566 return self.copy_sign(other) |
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3567 |
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3568 if comparison == -1: |
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3569 ans = self.next_plus(context) |
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3570 else: # comparison == 1 |
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3571 ans = self.next_minus(context) |
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3572 |
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3573 # decide which flags to raise using value of ans |
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3574 if ans._isinfinity(): |
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3575 context._raise_error(Overflow, |
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3576 'Infinite result from next_toward', |
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3577 ans._sign) |
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61214
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3578 context._raise_error(Inexact) |
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3579 context._raise_error(Rounded) |
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3580 elif ans.adjusted() < context.Emin: |
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3581 context._raise_error(Underflow) |
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3582 context._raise_error(Subnormal) |
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3583 context._raise_error(Inexact) |
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3584 context._raise_error(Rounded) |
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3585 # if precision == 1 then we don't raise Clamped for a |
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3586 # result 0E-Etiny. |
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3587 if not ans: |
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3588 context._raise_error(Clamped) |
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3589 |
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3590 return ans |
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3591 |
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3592 def number_class(self, context=None): |
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3593 """Returns an indication of the class of self. |
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3594 |
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3595 The class is one of the following strings: |
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44373
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3596 sNaN |
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3597 NaN |
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43400
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3598 -Infinity |
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3599 -Normal |
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3600 -Subnormal |
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3601 -Zero |
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3602 +Zero |
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3603 +Subnormal |
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3604 +Normal |
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3605 +Infinity |
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3606 """ |
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3607 if self.is_snan(): |
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3608 return "sNaN" |
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3609 if self.is_qnan(): |
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3610 return "NaN" |
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3611 inf = self._isinfinity() |
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3612 if inf == 1: |
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3613 return "+Infinity" |
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3614 if inf == -1: |
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3615 return "-Infinity" |
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3616 if self.is_zero(): |
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3617 if self._sign: |
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3618 return "-Zero" |
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3619 else: |
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3620 return "+Zero" |
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3621 if context is None: |
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3622 context = getcontext() |
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3623 if self.is_subnormal(context=context): |
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3624 if self._sign: |
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3625 return "-Subnormal" |
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3626 else: |
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3627 return "+Subnormal" |
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3628 # just a normal, regular, boring number, :) |
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3629 if self._sign: |
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3630 return "-Normal" |
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3631 else: |
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3632 return "+Normal" |
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3633 |
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3634 def radix(self): |
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3635 """Just returns 10, as this is Decimal, :)""" |
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3636 return Decimal(10) |
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3637 |
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3638 def rotate(self, other, context=None): |
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3639 """Returns a rotated copy of self, value-of-other times.""" |
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3640 if context is None: |
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3641 context = getcontext() |
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3642 |
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3643 other = _convert_other(other, raiseit=True) |
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3644 |
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3645 ans = self._check_nans(other, context) |
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3646 if ans: |
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3647 return ans |
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3648 |
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3649 if other._exp != 0: |
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3650 return context._raise_error(InvalidOperation) |
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3651 if not (-context.prec <= int(other) <= context.prec): |
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3652 return context._raise_error(InvalidOperation) |
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3653 |
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3654 if self._isinfinity(): |
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3655 return Decimal(self) |
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3656 |
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3657 # get values, pad if necessary |
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3658 torot = int(other) |
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3659 rotdig = self._int |
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3660 topad = context.prec - len(rotdig) |
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3661 if topad > 0: |
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44025
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3662 rotdig = '0'*topad + rotdig |
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3663 elif topad < 0: |
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3664 rotdig = rotdig[-topad:] |
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3665 |
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3666 # let's rotate! |
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3667 rotated = rotdig[torot:] + rotdig[:torot] |
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3668 return _dec_from_triple(self._sign, |
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3669 rotated.lstrip('0') or '0', self._exp) |
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3670 |
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3671 def scaleb(self, other, context=None): |
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3672 """Returns self operand after adding the second value to its exp.""" |
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3673 if context is None: |
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3674 context = getcontext() |
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3675 |
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3676 other = _convert_other(other, raiseit=True) |
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3677 |
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3678 ans = self._check_nans(other, context) |
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3679 if ans: |
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3680 return ans |
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3681 |
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3682 if other._exp != 0: |
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3683 return context._raise_error(InvalidOperation) |
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3684 liminf = -2 * (context.Emax + context.prec) |
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3685 limsup = 2 * (context.Emax + context.prec) |
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3686 if not (liminf <= int(other) <= limsup): |
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3687 return context._raise_error(InvalidOperation) |
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3688 |
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3689 if self._isinfinity(): |
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3690 return Decimal(self) |
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3691 |
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3692 d = _dec_from_triple(self._sign, self._int, self._exp + int(other)) |
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3693 d = d._fix(context) |
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3694 return d |
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3695 |
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3696 def shift(self, other, context=None): |
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3697 """Returns a shifted copy of self, value-of-other times.""" |
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3698 if context is None: |
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3699 context = getcontext() |
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3700 |
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3701 other = _convert_other(other, raiseit=True) |
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3702 |
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3703 ans = self._check_nans(other, context) |
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3704 if ans: |
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3705 return ans |
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3706 |
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3707 if other._exp != 0: |
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3708 return context._raise_error(InvalidOperation) |
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3709 if not (-context.prec <= int(other) <= context.prec): |
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3710 return context._raise_error(InvalidOperation) |
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3711 |
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3712 if self._isinfinity(): |
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3713 return Decimal(self) |
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3714 |
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3715 # get values, pad if necessary |
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3716 torot = int(other) |
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3717 rotdig = self._int |
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3718 topad = context.prec - len(rotdig) |
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3719 if topad > 0: |
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3720 rotdig = '0'*topad + rotdig |
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3721 elif topad < 0: |
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3722 rotdig = rotdig[-topad:] |
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3723 |
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3724 # let's shift! |
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3725 if torot < 0: |
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3726 shifted = rotdig[:torot] |
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3727 else: |
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3728 shifted = rotdig + '0'*torot |
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3729 shifted = shifted[-context.prec:] |
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3730 |
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3731 return _dec_from_triple(self._sign, |
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3732 shifted.lstrip('0') or '0', self._exp) |
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3733 |
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3734 # Support for pickling, copy, and deepcopy |
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3735 def __reduce__(self): |
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3736 return (self.__class__, (str(self),)) |
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3737 |
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3738 def __copy__(self): |
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3739 if type(self) is Decimal: |
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3740 return self # I'm immutable; therefore I am my own clone |
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3741 return self.__class__(str(self)) |
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3742 |
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3743 def __deepcopy__(self, memo): |
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3744 if type(self) is Decimal: |
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3745 return self # My components are also immutable |
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3746 return self.__class__(str(self)) |
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3747 |
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3748 # PEP 3101 support. the _localeconv keyword argument should be |
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3749 # considered private: it's provided for ease of testing only. |
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3750 def __format__(self, specifier, context=None, _localeconv=None): |
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3751 """Format a Decimal instance according to the given specifier. |
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3752 |
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3753 The specifier should be a standard format specifier, with the |
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3754 form described in PEP 3101. Formatting types 'e', 'E', 'f', |
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3755 'F', 'g', 'G', 'n' and '%' are supported. If the formatting |
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3756 type is omitted it defaults to 'g' or 'G', depending on the |
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3757 value of context.capitals. |
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3758 """ |
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3759 |
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3760 # Note: PEP 3101 says that if the type is not present then |
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3761 # there should be at least one digit after the decimal point. |
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3762 # We take the liberty of ignoring this requirement for |
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3763 # Decimal---it's presumably there to make sure that |
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3764 # format(float, '') behaves similarly to str(float). |
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3765 if context is None: |
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3766 context = getcontext() |
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3767 |
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3768 spec = _parse_format_specifier(specifier, _localeconv=_localeconv) |
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3769 |
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3770 # special values don't care about the type or precision |
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3771 if self._is_special: |
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3772 sign = _format_sign(self._sign, spec) |
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3773 body = str(self.copy_abs()) |
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3774 return _format_align(sign, body, spec) |
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3775 |
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3776 # a type of None defaults to 'g' or 'G', depending on context |
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3777 if spec['type'] is None: |
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3778 spec['type'] = ['g', 'G'][context.capitals] |
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3779 |
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3780 # if type is '%', adjust exponent of self accordingly |
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3781 if spec['type'] == '%': |
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3782 self = _dec_from_triple(self._sign, self._int, self._exp+2) |
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3783 |
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3784 # round if necessary, taking rounding mode from the context |
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3785 rounding = context.rounding |
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3786 precision = spec['precision'] |
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3787 if precision is not None: |
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3788 if spec['type'] in 'eE': |
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3789 self = self._round(precision+1, rounding) |
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3790 elif spec['type'] in 'fF%': |
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3791 self = self._rescale(-precision, rounding) |
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3792 elif spec['type'] in 'gG' and len(self._int) > precision: |
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3793 self = self._round(precision, rounding) |
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3794 # special case: zeros with a positive exponent can't be |
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3795 # represented in fixed point; rescale them to 0e0. |
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3796 if not self and self._exp > 0 and spec['type'] in 'fF%': |
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3797 self = self._rescale(0, rounding) |
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3798 |
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3799 # figure out placement of the decimal point |
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3800 leftdigits = self._exp + len(self._int) |
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3801 if spec['type'] in 'eE': |
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3802 if not self and precision is not None: |
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3803 dotplace = 1 - precision |
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3804 else: |
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3805 dotplace = 1 |
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3806 elif spec['type'] in 'fF%': |
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3807 dotplace = leftdigits |
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3808 elif spec['type'] in 'gG': |
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3809 if self._exp <= 0 and leftdigits > -6: |
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3810 dotplace = leftdigits |
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3811 else: |
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3812 dotplace = 1 |
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3813 |
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3814 # find digits before and after decimal point, and get exponent |
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3815 if dotplace < 0: |
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3816 intpart = '0' |
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3817 fracpart = '0'*(-dotplace) + self._int |
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3818 elif dotplace > len(self._int): |
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3819 intpart = self._int + '0'*(dotplace-len(self._int)) |
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3820 fracpart = '' |
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3821 else: |
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3822 intpart = self._int[:dotplace] or '0' |
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3823 fracpart = self._int[dotplace:] |
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3824 exp = leftdigits-dotplace |
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3825 |
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3826 # done with the decimal-specific stuff; hand over the rest |
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3827 # of the formatting to the _format_number function |
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3828 return _format_number(self._sign, intpart, fracpart, exp, spec) |
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3829 |
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3830 def _dec_from_triple(sign, coefficient, exponent, special=False): |
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3831 """Create a decimal instance directly, without any validation, |
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3832 normalization (e.g. removal of leading zeros) or argument |
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3833 conversion. |
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3834 |
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3835 This function is for *internal use only*. |
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3836 """ |
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3837 |
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3838 self = object.__new__(Decimal) |
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3839 self._sign = sign |
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3840 self._int = coefficient |
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3841 self._exp = exponent |
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3842 self._is_special = special |
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|
3843 |
|
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|
3844 return self |
|
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changeset
|
3845 |
|
51297
5b713045ea90
Register decimals as numbers.Number
Raymond Hettinger <python@rcn.com>
parents:
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diff
changeset
|
3846 # Register Decimal as a kind of Number (an abstract base class). |
|
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Register decimals as numbers.Number
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parents:
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diff
changeset
|
3847 # However, do not register it as Real (because Decimals are not |
|
5b713045ea90
Register decimals as numbers.Number
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parents:
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diff
changeset
|
3848 # interoperable with floats). |
|
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Register decimals as numbers.Number
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parents:
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diff
changeset
|
3849 _numbers.Number.register(Decimal) |
|
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Register decimals as numbers.Number
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parents:
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diff
changeset
|
3850 |
|
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Register decimals as numbers.Number
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diff
changeset
|
3851 |
|
41554
06145fbc7ab9
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|
3852 ##### Context class ####################################################### |
|
32477
bc586db9945a
Work through several open todos:
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parents:
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diff
changeset
|
3853 |
|
40450
cc992d75d5b3
Four months of trunk changes (including a few releases...)
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parents:
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diff
changeset
|
3854 class _ContextManager(object): |
|
cc992d75d5b3
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parents:
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diff
changeset
|
3855 """Context manager class to support localcontext(). |
|
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parents:
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diff
changeset
|
3856 |
|
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parents:
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diff
changeset
|
3857 Sets a copy of the supplied context in __enter__() and restores |
|
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Four months of trunk changes (including a few releases...)
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parents:
40404
diff
changeset
|
3858 the previous decimal context in __exit__() |
|
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|
3859 """ |
|
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Updates to the with-statement:
Guido van Rossum <guido@python.org>
parents:
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diff
changeset
|
3860 def __init__(self, new_context): |
|
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|
3861 self.new_context = new_context.copy() |
|
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|
3862 def __enter__(self): |
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parents:
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diff
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|
3863 self.saved_context = getcontext() |
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diff
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|
3864 setcontext(self.new_context) |
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diff
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|
3865 return self.new_context |
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parents:
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diff
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|
3866 def __exit__(self, t, v, tb): |
|
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parents:
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diff
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|
3867 setcontext(self.saved_context) |
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Updates to the with-statement:
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parents:
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|
3868 |
|
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d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
3869 class Context(object): |
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
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|
3870 """Contains the context for a Decimal instance. |
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
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3871 |
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
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diff
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3872 Contains: |
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diff
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|
3873 prec - precision (for use in rounding, division, square roots..) |
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|
3874 rounding - rounding type (how you round) |
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32576
83cbc025bfc7
Improve Context construction and representation:
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3875 traps - If traps[exception] = 1, then the exception is |
|
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diff
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3876 raised when it is caused. Otherwise, a value is |
|
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3877 substituted in. |
|
45092
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Context flags get set, not incremented.
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|
3878 flags - When an exception is caused, flags[exception] is set. |
|
32451
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diff
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3879 (Whether or not the trap_enabler is set) |
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Move Decimal from the sandbox into production.
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parents:
diff
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|
3880 Should be reset by user of Decimal instance. |
|
32489
ab0a2b74ddfd
Changed the rounding constant values to match their variable names.
Raymond Hettinger <python@rcn.com>
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diff
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|
3881 Emin - Minimum exponent |
|
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Changed the rounding constant values to match their variable names.
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|
3882 Emax - Maximum exponent |
|
32451
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Move Decimal from the sandbox into production.
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parents:
diff
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|
3883 capitals - If 1, 1*10^1 is printed as 1E+1. |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
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|
3884 If 0, printed as 1e1 |
|
61864
6fee26c89f6e
#Issue 8540: Make Context._clamp attribute public in decimal module.
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
changeset
|
3885 clamp - If 1, change exponents if too high (Default 0) |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
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|
3886 """ |
| 32482 | 3887 |
|
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parents:
73091
diff
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|
3888 def __init__(self, prec=None, rounding=None, Emin=None, Emax=None, |
|
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parents:
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diff
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|
3889 capitals=None, clamp=None, flags=None, traps=None, |
|
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parents:
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|
3890 _ignored_flags=None): |
|
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|
3891 # Set defaults; for everything except flags and _ignored_flags, |
|
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|
3892 # inherit from DefaultContext. |
|
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|
3893 try: |
|
9752b85c0119
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|
3894 dc = DefaultContext |
|
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|
3895 except NameError: |
|
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|
3896 pass |
|
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|
3897 |
|
9752b85c0119
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|
3898 self.prec = prec if prec is not None else dc.prec |
|
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|
3899 self.rounding = rounding if rounding is not None else dc.rounding |
|
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|
3900 self.Emin = Emin if Emin is not None else dc.Emin |
|
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|
3901 self.Emax = Emax if Emax is not None else dc.Emax |
|
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|
3902 self.capitals = capitals if capitals is not None else dc.capitals |
|
62869
09f5fd013c0b
Issue #9136: Profiling Decimal gave 'dictionary changed size during iteration'.
Mark Dickinson <dickinsm@gmail.com>
parents:
62865
diff
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|
3903 self.clamp = clamp if clamp is not None else dc.clamp |
|
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|
3904 |
|
33722
74a57e6684f3
Don't use mutable values for method defaults.
Raymond Hettinger <python@rcn.com>
parents:
33695
diff
changeset
|
3905 if _ignored_flags is None: |
|
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|
3906 self._ignored_flags = [] |
|
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|
3907 else: |
|
9752b85c0119
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|
3908 self._ignored_flags = _ignored_flags |
|
9752b85c0119
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|
3909 |
|
9752b85c0119
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|
3910 if traps is None: |
|
9752b85c0119
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|
3911 self.traps = dc.traps.copy() |
|
9752b85c0119
Merged revisions 82654 via svnmerge from
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|
3912 elif not isinstance(traps, dict): |
|
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7355550d5357
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Stefan Krah <skrah@bytereef.org>
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73091
diff
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|
3913 self.traps = dict((s, int(s in traps)) for s in _signals + traps) |
|
62870
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|
3914 else: |
|
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|
3915 self.traps = traps |
|
9752b85c0119
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|
3916 |
|
9752b85c0119
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|
3917 if flags is None: |
|
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|
3918 self.flags = dict.fromkeys(_signals, 0) |
|
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|
3919 elif not isinstance(flags, dict): |
|
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Stefan Krah <skrah@bytereef.org>
parents:
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diff
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|
3920 self.flags = dict((s, int(s in flags)) for s in _signals + flags) |
|
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|
3921 else: |
|
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|
3922 self.flags = flags |
|
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Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
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|
3923 |
|
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parents:
73091
diff
changeset
|
3924 def _set_integer_check(self, name, value, vmin, vmax): |
|
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parents:
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|
3925 if not isinstance(value, int): |
|
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parents:
73091
diff
changeset
|
3926 raise TypeError("%s must be an integer" % name) |
|
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parents:
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diff
changeset
|
3927 if vmin == '-inf': |
|
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parents:
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diff
changeset
|
3928 if value > vmax: |
|
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parents:
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diff
changeset
|
3929 raise ValueError("%s must be in [%s, %d]. got: %s" % (name, vmin, vmax, value)) |
|
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diff
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|
3930 elif vmax == 'inf': |
|
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parents:
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diff
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|
3931 if value < vmin: |
|
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parents:
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diff
changeset
|
3932 raise ValueError("%s must be in [%d, %s]. got: %s" % (name, vmin, vmax, value)) |
|
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|
3933 else: |
|
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parents:
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diff
changeset
|
3934 if value < vmin or value > vmax: |
|
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parents:
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diff
changeset
|
3935 raise ValueError("%s must be in [%d, %d]. got %s" % (name, vmin, vmax, value)) |
|
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|
3936 return object.__setattr__(self, name, value) |
|
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|
3937 |
|
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diff
changeset
|
3938 def _set_signal_dict(self, name, d): |
|
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|
3939 if not isinstance(d, dict): |
|
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|
3940 raise TypeError("%s must be a signal dict" % d) |
|
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|
3941 for key in d: |
|
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diff
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|
3942 if not key in _signals: |
|
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diff
changeset
|
3943 raise KeyError("%s is not a valid signal dict" % d) |
|
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|
3944 for key in _signals: |
|
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changeset
|
3945 if not key in d: |
|
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diff
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|
3946 raise KeyError("%s is not a valid signal dict" % d) |
|
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|
3947 return object.__setattr__(self, name, d) |
|
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|
3948 |
|
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diff
changeset
|
3949 def __setattr__(self, name, value): |
|
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changeset
|
3950 if name == 'prec': |
|
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diff
changeset
|
3951 return self._set_integer_check(name, value, 1, 'inf') |
|
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changeset
|
3952 elif name == 'Emin': |
|
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changeset
|
3953 return self._set_integer_check(name, value, '-inf', 0) |
|
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|
3954 elif name == 'Emax': |
|
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|
3955 return self._set_integer_check(name, value, 0, 'inf') |
|
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|
3956 elif name == 'capitals': |
|
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|
3957 return self._set_integer_check(name, value, 0, 1) |
|
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|
3958 elif name == 'clamp': |
|
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|
3959 return self._set_integer_check(name, value, 0, 1) |
|
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|
3960 elif name == 'rounding': |
|
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|
3961 if not value in _rounding_modes: |
|
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|
3962 # raise TypeError even for strings to have consistency |
|
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|
3963 # among various implementations. |
|
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|
3964 raise TypeError("%s: invalid rounding mode" % value) |
|
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|
3965 return object.__setattr__(self, name, value) |
|
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|
3966 elif name == 'flags' or name == 'traps': |
|
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|
3967 return self._set_signal_dict(name, value) |
|
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|
3968 elif name == '_ignored_flags': |
|
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|
3969 return object.__setattr__(self, name, value) |
|
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|
3970 else: |
|
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|
3971 raise AttributeError( |
|
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|
3972 "'decimal.Context' object has no attribute '%s'" % name) |
|
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|
3973 |
|
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|
3974 def __delattr__(self, name): |
|
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|
3975 raise AttributeError("%s cannot be deleted" % name) |
|
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|
3976 |
|
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|
3977 # Support for pickling, copy, and deepcopy |
|
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|
3978 def __reduce__(self): |
|
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|
3979 flags = [sig for sig, v in self.flags.items() if v] |
|
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|
3980 traps = [sig for sig, v in self.traps.items() if v] |
|
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|
3981 return (self.__class__, |
|
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|
3982 (self.prec, self.rounding, self.Emin, self.Emax, |
|
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|
3983 self.capitals, self.clamp, flags, traps)) |
|
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|
3984 |
|
32487
fa23a9b18967
Fix clear_flags(). Make a readable (not evalable) Context repr.
Raymond Hettinger <python@rcn.com>
parents:
32482
diff
changeset
|
3985 def __repr__(self): |
|
32576
83cbc025bfc7
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|
3986 """Show the current context.""" |
|
32487
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Fix clear_flags(). Make a readable (not evalable) Context repr.
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|
3987 s = [] |
|
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|
3988 s.append('Context(prec=%(prec)d, rounding=%(rounding)s, ' |
|
61864
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#Issue 8540: Make Context._clamp attribute public in decimal module.
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parents:
61745
diff
changeset
|
3989 'Emin=%(Emin)d, Emax=%(Emax)d, capitals=%(capitals)d, ' |
|
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#Issue 8540: Make Context._clamp attribute public in decimal module.
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diff
changeset
|
3990 'clamp=%(clamp)d' |
|
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|
3991 % vars(self)) |
|
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|
3992 names = [f.__name__ for f, v in self.flags.items() if v] |
|
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|
3993 s.append('flags=[' + ', '.join(names) + ']') |
|
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|
3994 names = [t.__name__ for t, v in self.traps.items() if v] |
|
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|
3995 s.append('traps=[' + ', '.join(names) + ']') |
|
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|
3996 return ', '.join(s) + ')' |
|
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|
3997 |
|
32477
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|
3998 def clear_flags(self): |
|
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changeset
|
3999 """Reset all flags to zero""" |
|
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|
4000 for flag in self.flags: |
|
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|
4001 self.flags[flag] = 0 |
|
32477
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|
4002 |
|
75850
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|
4003 def clear_traps(self): |
|
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|
4004 """Reset all traps to zero""" |
|
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|
4005 for flag in self.traps: |
|
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|
4006 self.traps[flag] = 0 |
|
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|
4007 |
|
33044
2749334d71a4
* Context.copy() now makes a deepcopy.
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parents:
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diff
changeset
|
4008 def _shallow_copy(self): |
|
2749334d71a4
* Context.copy() now makes a deepcopy.
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diff
changeset
|
4009 """Returns a shallow copy from self.""" |
|
75850
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changeset
|
4010 nc = Context(self.prec, self.rounding, self.Emin, self.Emax, |
|
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|
4011 self.capitals, self.clamp, self.flags, self.traps, |
|
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|
4012 self._ignored_flags) |
|
33044
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|
4013 return nc |
|
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* Context.copy() now makes a deepcopy.
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|
4014 |
|
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parents:
diff
changeset
|
4015 def copy(self): |
|
33044
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* Context.copy() now makes a deepcopy.
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changeset
|
4016 """Returns a deep copy from self.""" |
|
75850
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changeset
|
4017 nc = Context(self.prec, self.rounding, self.Emin, self.Emax, |
|
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|
4018 self.capitals, self.clamp, |
|
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changeset
|
4019 self.flags.copy(), self.traps.copy(), |
|
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|
4020 self._ignored_flags) |
|
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parents:
diff
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|
4021 return nc |
| 32482 | 4022 __copy__ = copy |
|
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|
4023 |
| 32560 | 4024 def _raise_error(self, condition, explanation = None, *args): |
|
32451
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|
4025 """Handles an error |
|
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|
4026 |
|
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diff
changeset
|
4027 If the flag is in _ignored_flags, returns the default response. |
|
45092
faa88ff4cce4
Context flags get set, not incremented.
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parents:
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diff
changeset
|
4028 Otherwise, it sets the flag, then, if the corresponding |
|
61746
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parents:
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diff
changeset
|
4029 trap_enabler is set, it reraises the exception. Otherwise, it returns |
|
45092
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parents:
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diff
changeset
|
4030 the default value after setting the flag. |
|
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parents:
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|
4031 """ |
| 32560 | 4032 error = _condition_map.get(condition, condition) |
|
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|
4033 if error in self._ignored_flags: |
|
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changeset
|
4034 # Don't touch the flag |
|
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|
4035 return error().handle(self, *args) |
|
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|
4036 |
|
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changeset
|
4037 self.flags[error] = 1 |
|
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|
4038 if not self.traps[error]: |
|
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changeset
|
4039 # The errors define how to handle themselves. |
| 32560 | 4040 return condition().handle(self, *args) |
|
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|
4041 |
|
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changeset
|
4042 # Errors should only be risked on copies of the context |
|
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|
4043 # self._ignored_flags = [] |
|
43020
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Collin Winter <collinw@gmail.com>
parents:
42629
diff
changeset
|
4044 raise error(explanation) |
|
32451
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|
4045 |
|
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|
4046 def _ignore_all_flags(self): |
|
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parents:
diff
changeset
|
4047 """Ignore all flags, if they are raised""" |
|
32666
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* Rename "Signals" to "_signals" making it non-public.
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diff
changeset
|
4048 return self._ignore_flags(*_signals) |
|
32451
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|
4049 |
|
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changeset
|
4050 def _ignore_flags(self, *flags): |
|
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parents:
diff
changeset
|
4051 """Ignore the flags, if they are raised""" |
|
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changeset
|
4052 # Do not mutate-- This way, copies of a context leave the original |
|
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|
4053 # alone. |
|
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changeset
|
4054 self._ignored_flags = (self._ignored_flags + list(flags)) |
|
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changeset
|
4055 return list(flags) |
|
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changeset
|
4056 |
|
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diff
changeset
|
4057 def _regard_flags(self, *flags): |
|
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changeset
|
4058 """Stop ignoring the flags, if they are raised""" |
|
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changeset
|
4059 if flags and isinstance(flags[0], (tuple,list)): |
|
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|
4060 flags = flags[0] |
|
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diff
changeset
|
4061 for flag in flags: |
|
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|
4062 self._ignored_flags.remove(flag) |
|
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|
4063 |
|
48475
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|
4064 # We inherit object.__hash__, so we must deny this explicitly |
|
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|
4065 __hash__ = None |
| 32560 | 4066 |
|
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4067 def Etiny(self): |
|
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4068 """Returns Etiny (= Emin - prec + 1)""" |
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4069 return int(self.Emin - self.prec + 1) |
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4070 |
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4071 def Etop(self): |
| 32496 | 4072 """Returns maximum exponent (= Emax - prec + 1)""" |
|
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4073 return int(self.Emax - self.prec + 1) |
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4074 |
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4075 def _set_rounding(self, type): |
|
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4076 """Sets the rounding type. |
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4077 |
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4078 Sets the rounding type, and returns the current (previous) |
|
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4079 rounding type. Often used like: |
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4080 |
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4081 context = context.copy() |
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4082 # so you don't change the calling context |
|
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4083 # if an error occurs in the middle. |
|
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4084 rounding = context._set_rounding(ROUND_UP) |
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4085 val = self.__sub__(other, context=context) |
|
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4086 context._set_rounding(rounding) |
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4087 |
|
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4088 This will make it round up for that operation. |
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4089 """ |
|
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4090 rounding = self.rounding |
|
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4091 self.rounding= type |
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4092 return rounding |
|
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4093 |
|
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4094 def create_decimal(self, num='0'): |
|
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4095 """Creates a new Decimal instance but using self as context. |
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4096 |
|
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4097 This method implements the to-number operation of the |
|
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4098 IBM Decimal specification.""" |
|
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4099 |
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4100 if isinstance(num, str) and num != num.strip(): |
|
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4101 return self._raise_error(ConversionSyntax, |
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4102 "no trailing or leading whitespace is " |
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4103 "permitted.") |
|
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4104 |
|
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4105 d = Decimal(num, context=self) |
|
61864
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|
4106 if d._isnan() and len(d._int) > self.prec - self.clamp: |
|
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4107 return self._raise_error(ConversionSyntax, |
|
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|
4108 "diagnostic info too long in NaN") |
| 33695 | 4109 return d._fix(self) |
|
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4110 |
|
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4111 def create_decimal_from_float(self, f): |
|
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4112 """Creates a new Decimal instance from a float but rounding using self |
|
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4113 as the context. |
|
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4114 |
|
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|
4115 >>> context = Context(prec=5, rounding=ROUND_DOWN) |
|
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|
4116 >>> context.create_decimal_from_float(3.1415926535897932) |
|
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|
4117 Decimal('3.1415') |
|
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|
4118 >>> context = Context(prec=5, traps=[Inexact]) |
|
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|
4119 >>> context.create_decimal_from_float(3.1415926535897932) |
|
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|
4120 Traceback (most recent call last): |
|
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|
4121 ... |
|
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|
4122 decimal.Inexact: None |
|
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4123 |
|
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|
4124 """ |
|
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|
4125 d = Decimal.from_float(f) # An exact conversion |
|
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|
4126 return d._fix(self) # Apply the context rounding |
|
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|
4127 |
|
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|
4128 # Methods |
|
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4129 def abs(self, a): |
|
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|
4130 """Returns the absolute value of the operand. |
|
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|
4131 |
|
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|
4132 If the operand is negative, the result is the same as using the minus |
|
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|
4133 operation on the operand. Otherwise, the result is the same as using |
|
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|
4134 the plus operation on the operand. |
|
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4135 |
| 32482 | 4136 >>> ExtendedContext.abs(Decimal('2.1')) |
|
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|
4137 Decimal('2.1') |
| 32482 | 4138 >>> ExtendedContext.abs(Decimal('-100')) |
|
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|
4139 Decimal('100') |
| 32482 | 4140 >>> ExtendedContext.abs(Decimal('101.5')) |
|
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|
4141 Decimal('101.5') |
| 32482 | 4142 >>> ExtendedContext.abs(Decimal('-101.5')) |
|
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|
4143 Decimal('101.5') |
|
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4144 >>> ExtendedContext.abs(-1) |
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4145 Decimal('1') |
|
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4146 """ |
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4147 a = _convert_other(a, raiseit=True) |
|
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4148 return a.__abs__(context=self) |
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4149 |
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4150 def add(self, a, b): |
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4151 """Return the sum of the two operands. |
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4152 |
| 32482 | 4153 >>> ExtendedContext.add(Decimal('12'), Decimal('7.00')) |
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4154 Decimal('19.00') |
| 32482 | 4155 >>> ExtendedContext.add(Decimal('1E+2'), Decimal('1.01E+4')) |
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4156 Decimal('1.02E+4') |
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4157 >>> ExtendedContext.add(1, Decimal(2)) |
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4158 Decimal('3') |
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4159 >>> ExtendedContext.add(Decimal(8), 5) |
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4160 Decimal('13') |
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4161 >>> ExtendedContext.add(5, 5) |
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4162 Decimal('10') |
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4163 """ |
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4164 a = _convert_other(a, raiseit=True) |
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4165 r = a.__add__(b, context=self) |
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4166 if r is NotImplemented: |
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4167 raise TypeError("Unable to convert %s to Decimal" % b) |
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4168 else: |
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4169 return r |
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4170 |
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4171 def _apply(self, a): |
| 33695 | 4172 return str(a._fix(self)) |
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4173 |
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4174 def canonical(self, a): |
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4175 """Returns the same Decimal object. |
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4176 |
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4177 As we do not have different encodings for the same number, the |
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4178 received object already is in its canonical form. |
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4179 |
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4180 >>> ExtendedContext.canonical(Decimal('2.50')) |
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4181 Decimal('2.50') |
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4182 """ |
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4183 if not isinstance(a, Decimal): |
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4184 raise TypeError("canonical requires a Decimal as an argument.") |
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4185 return a.canonical(context=self) |
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4186 |
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4187 def compare(self, a, b): |
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4188 """Compares values numerically. |
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4189 |
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4190 If the signs of the operands differ, a value representing each operand |
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4191 ('-1' if the operand is less than zero, '0' if the operand is zero or |
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4192 negative zero, or '1' if the operand is greater than zero) is used in |
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4193 place of that operand for the comparison instead of the actual |
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4194 operand. |
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4195 |
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4196 The comparison is then effected by subtracting the second operand from |
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4197 the first and then returning a value according to the result of the |
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4198 subtraction: '-1' if the result is less than zero, '0' if the result is |
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4199 zero or negative zero, or '1' if the result is greater than zero. |
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4200 |
| 32482 | 4201 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('3')) |
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4202 Decimal('-1') |
| 32482 | 4203 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.1')) |
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4204 Decimal('0') |
| 32482 | 4205 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('2.10')) |
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4206 Decimal('0') |
| 32482 | 4207 >>> ExtendedContext.compare(Decimal('3'), Decimal('2.1')) |
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4208 Decimal('1') |
| 32482 | 4209 >>> ExtendedContext.compare(Decimal('2.1'), Decimal('-3')) |
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4210 Decimal('1') |
| 32482 | 4211 >>> ExtendedContext.compare(Decimal('-3'), Decimal('2.1')) |
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4212 Decimal('-1') |
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4213 >>> ExtendedContext.compare(1, 2) |
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4214 Decimal('-1') |
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4215 >>> ExtendedContext.compare(Decimal(1), 2) |
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4216 Decimal('-1') |
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4217 >>> ExtendedContext.compare(1, Decimal(2)) |
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4218 Decimal('-1') |
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4219 """ |
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4220 a = _convert_other(a, raiseit=True) |
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4221 return a.compare(b, context=self) |
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4222 |
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4223 def compare_signal(self, a, b): |
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4224 """Compares the values of the two operands numerically. |
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4225 |
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4226 It's pretty much like compare(), but all NaNs signal, with signaling |
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4227 NaNs taking precedence over quiet NaNs. |
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4228 |
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4229 >>> c = ExtendedContext |
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4230 >>> c.compare_signal(Decimal('2.1'), Decimal('3')) |
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4231 Decimal('-1') |
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4232 >>> c.compare_signal(Decimal('2.1'), Decimal('2.1')) |
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4233 Decimal('0') |
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4234 >>> c.flags[InvalidOperation] = 0 |
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4235 >>> print(c.flags[InvalidOperation]) |
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4236 0 |
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4237 >>> c.compare_signal(Decimal('NaN'), Decimal('2.1')) |
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4238 Decimal('NaN') |
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4239 >>> print(c.flags[InvalidOperation]) |
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4240 1 |
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4241 >>> c.flags[InvalidOperation] = 0 |
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4242 >>> print(c.flags[InvalidOperation]) |
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4243 0 |
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4244 >>> c.compare_signal(Decimal('sNaN'), Decimal('2.1')) |
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4245 Decimal('NaN') |
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4246 >>> print(c.flags[InvalidOperation]) |
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4247 1 |
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4248 >>> c.compare_signal(-1, 2) |
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4249 Decimal('-1') |
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4250 >>> c.compare_signal(Decimal(-1), 2) |
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4251 Decimal('-1') |
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4252 >>> c.compare_signal(-1, Decimal(2)) |
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4253 Decimal('-1') |
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4254 """ |
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4255 a = _convert_other(a, raiseit=True) |
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4256 return a.compare_signal(b, context=self) |
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4257 |
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4258 def compare_total(self, a, b): |
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4259 """Compares two operands using their abstract representation. |
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4260 |
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4261 This is not like the standard compare, which use their numerical |
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4262 value. Note that a total ordering is defined for all possible abstract |
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4263 representations. |
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4264 |
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4265 >>> ExtendedContext.compare_total(Decimal('12.73'), Decimal('127.9')) |
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4266 Decimal('-1') |
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4267 >>> ExtendedContext.compare_total(Decimal('-127'), Decimal('12')) |
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4268 Decimal('-1') |
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4269 >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.3')) |
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4270 Decimal('-1') |
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4271 >>> ExtendedContext.compare_total(Decimal('12.30'), Decimal('12.30')) |
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4272 Decimal('0') |
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4273 >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('12.300')) |
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4274 Decimal('1') |
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4275 >>> ExtendedContext.compare_total(Decimal('12.3'), Decimal('NaN')) |
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4276 Decimal('-1') |
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4277 >>> ExtendedContext.compare_total(1, 2) |
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4278 Decimal('-1') |
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4279 >>> ExtendedContext.compare_total(Decimal(1), 2) |
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4280 Decimal('-1') |
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4281 >>> ExtendedContext.compare_total(1, Decimal(2)) |
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4282 Decimal('-1') |
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4283 """ |
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4284 a = _convert_other(a, raiseit=True) |
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4285 return a.compare_total(b) |
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4286 |
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4287 def compare_total_mag(self, a, b): |
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4288 """Compares two operands using their abstract representation ignoring sign. |
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4289 |
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4290 Like compare_total, but with operand's sign ignored and assumed to be 0. |
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4291 """ |
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4292 a = _convert_other(a, raiseit=True) |
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4293 return a.compare_total_mag(b) |
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4294 |
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4295 def copy_abs(self, a): |
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4296 """Returns a copy of the operand with the sign set to 0. |
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4297 |
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4298 >>> ExtendedContext.copy_abs(Decimal('2.1')) |
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4299 Decimal('2.1') |
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4300 >>> ExtendedContext.copy_abs(Decimal('-100')) |
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4301 Decimal('100') |
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4302 >>> ExtendedContext.copy_abs(-1) |
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4303 Decimal('1') |
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4304 """ |
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4305 a = _convert_other(a, raiseit=True) |
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4306 return a.copy_abs() |
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4307 |
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4308 def copy_decimal(self, a): |
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4309 """Returns a copy of the decimal object. |
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4310 |
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4311 >>> ExtendedContext.copy_decimal(Decimal('2.1')) |
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4312 Decimal('2.1') |
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4313 >>> ExtendedContext.copy_decimal(Decimal('-1.00')) |
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4314 Decimal('-1.00') |
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4315 >>> ExtendedContext.copy_decimal(1) |
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4316 Decimal('1') |
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4317 """ |
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4318 a = _convert_other(a, raiseit=True) |
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4319 return Decimal(a) |
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4320 |
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4321 def copy_negate(self, a): |
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4322 """Returns a copy of the operand with the sign inverted. |
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4323 |
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4324 >>> ExtendedContext.copy_negate(Decimal('101.5')) |
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4325 Decimal('-101.5') |
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4326 >>> ExtendedContext.copy_negate(Decimal('-101.5')) |
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4327 Decimal('101.5') |
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4328 >>> ExtendedContext.copy_negate(1) |
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4329 Decimal('-1') |
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4330 """ |
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4331 a = _convert_other(a, raiseit=True) |
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4332 return a.copy_negate() |
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4333 |
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4334 def copy_sign(self, a, b): |
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4335 """Copies the second operand's sign to the first one. |
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4336 |
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4337 In detail, it returns a copy of the first operand with the sign |
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4338 equal to the sign of the second operand. |
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4339 |
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4340 >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('7.33')) |
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4341 Decimal('1.50') |
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4342 >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('7.33')) |
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4343 Decimal('1.50') |
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4344 >>> ExtendedContext.copy_sign(Decimal( '1.50'), Decimal('-7.33')) |
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4345 Decimal('-1.50') |
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4346 >>> ExtendedContext.copy_sign(Decimal('-1.50'), Decimal('-7.33')) |
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4347 Decimal('-1.50') |
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4348 >>> ExtendedContext.copy_sign(1, -2) |
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4349 Decimal('-1') |
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4350 >>> ExtendedContext.copy_sign(Decimal(1), -2) |
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4351 Decimal('-1') |
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4352 >>> ExtendedContext.copy_sign(1, Decimal(-2)) |
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4353 Decimal('-1') |
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4354 """ |
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4355 a = _convert_other(a, raiseit=True) |
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4356 return a.copy_sign(b) |
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4357 |
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4358 def divide(self, a, b): |
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4359 """Decimal division in a specified context. |
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4360 |
| 32482 | 4361 >>> ExtendedContext.divide(Decimal('1'), Decimal('3')) |
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4362 Decimal('0.333333333') |
| 32482 | 4363 >>> ExtendedContext.divide(Decimal('2'), Decimal('3')) |
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Christian Heimes <christian@cheimes.de>
parents:
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|
4364 Decimal('0.666666667') |
| 32482 | 4365 >>> ExtendedContext.divide(Decimal('5'), Decimal('2')) |
|
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|
4366 Decimal('2.5') |
| 32482 | 4367 >>> ExtendedContext.divide(Decimal('1'), Decimal('10')) |
|
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parents:
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|
4368 Decimal('0.1') |
| 32482 | 4369 >>> ExtendedContext.divide(Decimal('12'), Decimal('12')) |
|
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|
4370 Decimal('1') |
| 32482 | 4371 >>> ExtendedContext.divide(Decimal('8.00'), Decimal('2')) |
|
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|
4372 Decimal('4.00') |
| 32482 | 4373 >>> ExtendedContext.divide(Decimal('2.400'), Decimal('2.0')) |
|
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|
4374 Decimal('1.20') |
| 32482 | 4375 >>> ExtendedContext.divide(Decimal('1000'), Decimal('100')) |
|
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|
4376 Decimal('10') |
| 32482 | 4377 >>> ExtendedContext.divide(Decimal('1000'), Decimal('1')) |
|
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|
4378 Decimal('1000') |
| 32482 | 4379 >>> ExtendedContext.divide(Decimal('2.40E+6'), Decimal('2')) |
|
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|
4380 Decimal('1.20E+6') |
|
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4381 >>> ExtendedContext.divide(5, 5) |
|
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|
4382 Decimal('1') |
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|
4383 >>> ExtendedContext.divide(Decimal(5), 5) |
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4384 Decimal('1') |
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4385 >>> ExtendedContext.divide(5, Decimal(5)) |
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4386 Decimal('1') |
|
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4387 """ |
|
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4388 a = _convert_other(a, raiseit=True) |
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4389 r = a.__truediv__(b, context=self) |
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|
4390 if r is NotImplemented: |
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4391 raise TypeError("Unable to convert %s to Decimal" % b) |
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4392 else: |
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|
4393 return r |
|
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4394 |
|
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|
4395 def divide_int(self, a, b): |
|
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4396 """Divides two numbers and returns the integer part of the result. |
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4397 |
| 32482 | 4398 >>> ExtendedContext.divide_int(Decimal('2'), Decimal('3')) |
|
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|
4399 Decimal('0') |
| 32482 | 4400 >>> ExtendedContext.divide_int(Decimal('10'), Decimal('3')) |
|
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|
4401 Decimal('3') |
| 32482 | 4402 >>> ExtendedContext.divide_int(Decimal('1'), Decimal('0.3')) |
|
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|
4403 Decimal('3') |
|
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4404 >>> ExtendedContext.divide_int(10, 3) |
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4405 Decimal('3') |
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4406 >>> ExtendedContext.divide_int(Decimal(10), 3) |
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4407 Decimal('3') |
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4408 >>> ExtendedContext.divide_int(10, Decimal(3)) |
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4409 Decimal('3') |
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4410 """ |
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4411 a = _convert_other(a, raiseit=True) |
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4412 r = a.__floordiv__(b, context=self) |
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4413 if r is NotImplemented: |
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4414 raise TypeError("Unable to convert %s to Decimal" % b) |
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4415 else: |
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4416 return r |
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4417 |
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4418 def divmod(self, a, b): |
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4419 """Return (a // b, a % b). |
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4420 |
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4421 >>> ExtendedContext.divmod(Decimal(8), Decimal(3)) |
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4422 (Decimal('2'), Decimal('2')) |
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4423 >>> ExtendedContext.divmod(Decimal(8), Decimal(4)) |
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4424 (Decimal('2'), Decimal('0')) |
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4425 >>> ExtendedContext.divmod(8, 4) |
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4426 (Decimal('2'), Decimal('0')) |
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4427 >>> ExtendedContext.divmod(Decimal(8), 4) |
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4428 (Decimal('2'), Decimal('0')) |
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4429 >>> ExtendedContext.divmod(8, Decimal(4)) |
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4430 (Decimal('2'), Decimal('0')) |
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4431 """ |
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4432 a = _convert_other(a, raiseit=True) |
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4433 r = a.__divmod__(b, context=self) |
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4434 if r is NotImplemented: |
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4435 raise TypeError("Unable to convert %s to Decimal" % b) |
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4436 else: |
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4437 return r |
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4438 |
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4439 def exp(self, a): |
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4440 """Returns e ** a. |
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4441 |
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4442 >>> c = ExtendedContext.copy() |
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4443 >>> c.Emin = -999 |
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4444 >>> c.Emax = 999 |
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4445 >>> c.exp(Decimal('-Infinity')) |
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4446 Decimal('0') |
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4447 >>> c.exp(Decimal('-1')) |
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4448 Decimal('0.367879441') |
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4449 >>> c.exp(Decimal('0')) |
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4450 Decimal('1') |
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4451 >>> c.exp(Decimal('1')) |
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4452 Decimal('2.71828183') |
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4453 >>> c.exp(Decimal('0.693147181')) |
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4454 Decimal('2.00000000') |
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4455 >>> c.exp(Decimal('+Infinity')) |
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4456 Decimal('Infinity') |
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4457 >>> c.exp(10) |
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4458 Decimal('22026.4658') |
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4459 """ |
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4460 a =_convert_other(a, raiseit=True) |
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4461 return a.exp(context=self) |
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4462 |
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4463 def fma(self, a, b, c): |
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4464 """Returns a multiplied by b, plus c. |
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4465 |
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4466 The first two operands are multiplied together, using multiply, |
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4467 the third operand is then added to the result of that |
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4468 multiplication, using add, all with only one final rounding. |
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4469 |
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4470 >>> ExtendedContext.fma(Decimal('3'), Decimal('5'), Decimal('7')) |
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4471 Decimal('22') |
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4472 >>> ExtendedContext.fma(Decimal('3'), Decimal('-5'), Decimal('7')) |
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4473 Decimal('-8') |
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4474 >>> ExtendedContext.fma(Decimal('888565290'), Decimal('1557.96930'), Decimal('-86087.7578')) |
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4475 Decimal('1.38435736E+12') |
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4476 >>> ExtendedContext.fma(1, 3, 4) |
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4477 Decimal('7') |
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4478 >>> ExtendedContext.fma(1, Decimal(3), 4) |
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4479 Decimal('7') |
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4480 >>> ExtendedContext.fma(1, 3, Decimal(4)) |
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4481 Decimal('7') |
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4482 """ |
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4483 a = _convert_other(a, raiseit=True) |
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4484 return a.fma(b, c, context=self) |
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4485 |
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4486 def is_canonical(self, a): |
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4487 """Return True if the operand is canonical; otherwise return False. |
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4488 |
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4489 Currently, the encoding of a Decimal instance is always |
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4490 canonical, so this method returns True for any Decimal. |
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4491 |
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4492 >>> ExtendedContext.is_canonical(Decimal('2.50')) |
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4493 True |
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4494 """ |
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4495 if not isinstance(a, Decimal): |
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4496 raise TypeError("is_canonical requires a Decimal as an argument.") |
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4497 return a.is_canonical() |
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4498 |
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4499 def is_finite(self, a): |
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4500 """Return True if the operand is finite; otherwise return False. |
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4501 |
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4502 A Decimal instance is considered finite if it is neither |
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4503 infinite nor a NaN. |
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4504 |
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4505 >>> ExtendedContext.is_finite(Decimal('2.50')) |
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4506 True |
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4507 >>> ExtendedContext.is_finite(Decimal('-0.3')) |
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4508 True |
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4509 >>> ExtendedContext.is_finite(Decimal('0')) |
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4510 True |
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4511 >>> ExtendedContext.is_finite(Decimal('Inf')) |
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4512 False |
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4513 >>> ExtendedContext.is_finite(Decimal('NaN')) |
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4514 False |
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4515 >>> ExtendedContext.is_finite(1) |
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4516 True |
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4517 """ |
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4518 a = _convert_other(a, raiseit=True) |
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4519 return a.is_finite() |
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4520 |
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4521 def is_infinite(self, a): |
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4522 """Return True if the operand is infinite; otherwise return False. |
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4523 |
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4524 >>> ExtendedContext.is_infinite(Decimal('2.50')) |
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4525 False |
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4526 >>> ExtendedContext.is_infinite(Decimal('-Inf')) |
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4527 True |
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4528 >>> ExtendedContext.is_infinite(Decimal('NaN')) |
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4529 False |
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4530 >>> ExtendedContext.is_infinite(1) |
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4531 False |
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4532 """ |
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4533 a = _convert_other(a, raiseit=True) |
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4534 return a.is_infinite() |
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4535 |
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4536 def is_nan(self, a): |
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4537 """Return True if the operand is a qNaN or sNaN; |
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4538 otherwise return False. |
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4539 |
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4540 >>> ExtendedContext.is_nan(Decimal('2.50')) |
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4541 False |
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4542 >>> ExtendedContext.is_nan(Decimal('NaN')) |
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4543 True |
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4544 >>> ExtendedContext.is_nan(Decimal('-sNaN')) |
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4545 True |
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4546 >>> ExtendedContext.is_nan(1) |
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4547 False |
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4548 """ |
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4549 a = _convert_other(a, raiseit=True) |
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4550 return a.is_nan() |
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4551 |
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4552 def is_normal(self, a): |
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4553 """Return True if the operand is a normal number; |
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4554 otherwise return False. |
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4555 |
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4556 >>> c = ExtendedContext.copy() |
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4557 >>> c.Emin = -999 |
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4558 >>> c.Emax = 999 |
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4559 >>> c.is_normal(Decimal('2.50')) |
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4560 True |
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4561 >>> c.is_normal(Decimal('0.1E-999')) |
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4562 False |
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4563 >>> c.is_normal(Decimal('0.00')) |
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4564 False |
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4565 >>> c.is_normal(Decimal('-Inf')) |
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4566 False |
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4567 >>> c.is_normal(Decimal('NaN')) |
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4568 False |
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4569 >>> c.is_normal(1) |
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4570 True |
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4571 """ |
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4572 a = _convert_other(a, raiseit=True) |
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4573 return a.is_normal(context=self) |
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4574 |
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4575 def is_qnan(self, a): |
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4576 """Return True if the operand is a quiet NaN; otherwise return False. |
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4577 |
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4578 >>> ExtendedContext.is_qnan(Decimal('2.50')) |
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4579 False |
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4580 >>> ExtendedContext.is_qnan(Decimal('NaN')) |
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4581 True |
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4582 >>> ExtendedContext.is_qnan(Decimal('sNaN')) |
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4583 False |
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4584 >>> ExtendedContext.is_qnan(1) |
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4585 False |
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4586 """ |
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4587 a = _convert_other(a, raiseit=True) |
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4588 return a.is_qnan() |
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4589 |
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4590 def is_signed(self, a): |
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4591 """Return True if the operand is negative; otherwise return False. |
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4592 |
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4593 >>> ExtendedContext.is_signed(Decimal('2.50')) |
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4594 False |
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4595 >>> ExtendedContext.is_signed(Decimal('-12')) |
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4596 True |
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4597 >>> ExtendedContext.is_signed(Decimal('-0')) |
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4598 True |
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4599 >>> ExtendedContext.is_signed(8) |
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4600 False |
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4601 >>> ExtendedContext.is_signed(-8) |
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4602 True |
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4603 """ |
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4604 a = _convert_other(a, raiseit=True) |
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4605 return a.is_signed() |
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4606 |
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4607 def is_snan(self, a): |
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4608 """Return True if the operand is a signaling NaN; |
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4609 otherwise return False. |
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4610 |
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4611 >>> ExtendedContext.is_snan(Decimal('2.50')) |
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4612 False |
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4613 >>> ExtendedContext.is_snan(Decimal('NaN')) |
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4614 False |
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4615 >>> ExtendedContext.is_snan(Decimal('sNaN')) |
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4616 True |
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4617 >>> ExtendedContext.is_snan(1) |
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4618 False |
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4619 """ |
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4620 a = _convert_other(a, raiseit=True) |
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4621 return a.is_snan() |
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4622 |
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4623 def is_subnormal(self, a): |
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4624 """Return True if the operand is subnormal; otherwise return False. |
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4625 |
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4626 >>> c = ExtendedContext.copy() |
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4627 >>> c.Emin = -999 |
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4628 >>> c.Emax = 999 |
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4629 >>> c.is_subnormal(Decimal('2.50')) |
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4630 False |
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4631 >>> c.is_subnormal(Decimal('0.1E-999')) |
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4632 True |
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4633 >>> c.is_subnormal(Decimal('0.00')) |
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4634 False |
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4635 >>> c.is_subnormal(Decimal('-Inf')) |
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4636 False |
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4637 >>> c.is_subnormal(Decimal('NaN')) |
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4638 False |
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4639 >>> c.is_subnormal(1) |
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4640 False |
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4641 """ |
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4642 a = _convert_other(a, raiseit=True) |
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4643 return a.is_subnormal(context=self) |
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4644 |
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4645 def is_zero(self, a): |
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4646 """Return True if the operand is a zero; otherwise return False. |
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4647 |
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4648 >>> ExtendedContext.is_zero(Decimal('0')) |
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4649 True |
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4650 >>> ExtendedContext.is_zero(Decimal('2.50')) |
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4651 False |
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4652 >>> ExtendedContext.is_zero(Decimal('-0E+2')) |
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4653 True |
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4654 >>> ExtendedContext.is_zero(1) |
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4655 False |
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4656 >>> ExtendedContext.is_zero(0) |
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4657 True |
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4658 """ |
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4659 a = _convert_other(a, raiseit=True) |
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4660 return a.is_zero() |
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4661 |
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4662 def ln(self, a): |
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4663 """Returns the natural (base e) logarithm of the operand. |
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4664 |
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4665 >>> c = ExtendedContext.copy() |
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4666 >>> c.Emin = -999 |
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4667 >>> c.Emax = 999 |
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4668 >>> c.ln(Decimal('0')) |
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4669 Decimal('-Infinity') |
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4670 >>> c.ln(Decimal('1.000')) |
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4671 Decimal('0') |
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4672 >>> c.ln(Decimal('2.71828183')) |
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4673 Decimal('1.00000000') |
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4674 >>> c.ln(Decimal('10')) |
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4675 Decimal('2.30258509') |
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4676 >>> c.ln(Decimal('+Infinity')) |
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4677 Decimal('Infinity') |
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4678 >>> c.ln(1) |
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4679 Decimal('0') |
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4680 """ |
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4681 a = _convert_other(a, raiseit=True) |
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4682 return a.ln(context=self) |
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4683 |
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4684 def log10(self, a): |
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4685 """Returns the base 10 logarithm of the operand. |
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4686 |
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4687 >>> c = ExtendedContext.copy() |
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4688 >>> c.Emin = -999 |
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4689 >>> c.Emax = 999 |
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4690 >>> c.log10(Decimal('0')) |
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4691 Decimal('-Infinity') |
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4692 >>> c.log10(Decimal('0.001')) |
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4693 Decimal('-3') |
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4694 >>> c.log10(Decimal('1.000')) |
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4695 Decimal('0') |
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4696 >>> c.log10(Decimal('2')) |
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4697 Decimal('0.301029996') |
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4698 >>> c.log10(Decimal('10')) |
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4699 Decimal('1') |
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4700 >>> c.log10(Decimal('70')) |
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4701 Decimal('1.84509804') |
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4702 >>> c.log10(Decimal('+Infinity')) |
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4703 Decimal('Infinity') |
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4704 >>> c.log10(0) |
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4705 Decimal('-Infinity') |
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4706 >>> c.log10(1) |
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4707 Decimal('0') |
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4708 """ |
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4709 a = _convert_other(a, raiseit=True) |
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4710 return a.log10(context=self) |
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4711 |
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4712 def logb(self, a): |
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4713 """ Returns the exponent of the magnitude of the operand's MSD. |
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4714 |
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4715 The result is the integer which is the exponent of the magnitude |
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4716 of the most significant digit of the operand (as though the |
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4717 operand were truncated to a single digit while maintaining the |
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4718 value of that digit and without limiting the resulting exponent). |
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4719 |
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4720 >>> ExtendedContext.logb(Decimal('250')) |
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4721 Decimal('2') |
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4722 >>> ExtendedContext.logb(Decimal('2.50')) |
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4723 Decimal('0') |
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4724 >>> ExtendedContext.logb(Decimal('0.03')) |
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4725 Decimal('-2') |
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4726 >>> ExtendedContext.logb(Decimal('0')) |
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4727 Decimal('-Infinity') |
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4728 >>> ExtendedContext.logb(1) |
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4729 Decimal('0') |
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4730 >>> ExtendedContext.logb(10) |
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4731 Decimal('1') |
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4732 >>> ExtendedContext.logb(100) |
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4733 Decimal('2') |
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4734 """ |
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4735 a = _convert_other(a, raiseit=True) |
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4736 return a.logb(context=self) |
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4737 |
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4738 def logical_and(self, a, b): |
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4739 """Applies the logical operation 'and' between each operand's digits. |
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4740 |
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4741 The operands must be both logical numbers. |
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4742 |
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4743 >>> ExtendedContext.logical_and(Decimal('0'), Decimal('0')) |
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4744 Decimal('0') |
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4745 >>> ExtendedContext.logical_and(Decimal('0'), Decimal('1')) |
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4746 Decimal('0') |
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4747 >>> ExtendedContext.logical_and(Decimal('1'), Decimal('0')) |
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4748 Decimal('0') |
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4749 >>> ExtendedContext.logical_and(Decimal('1'), Decimal('1')) |
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4750 Decimal('1') |
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4751 >>> ExtendedContext.logical_and(Decimal('1100'), Decimal('1010')) |
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4752 Decimal('1000') |
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4753 >>> ExtendedContext.logical_and(Decimal('1111'), Decimal('10')) |
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4754 Decimal('10') |
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4755 >>> ExtendedContext.logical_and(110, 1101) |
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4756 Decimal('100') |
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4757 >>> ExtendedContext.logical_and(Decimal(110), 1101) |
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4758 Decimal('100') |
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4759 >>> ExtendedContext.logical_and(110, Decimal(1101)) |
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4760 Decimal('100') |
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4761 """ |
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4762 a = _convert_other(a, raiseit=True) |
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4763 return a.logical_and(b, context=self) |
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4764 |
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4765 def logical_invert(self, a): |
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4766 """Invert all the digits in the operand. |
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4767 |
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4768 The operand must be a logical number. |
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4769 |
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4770 >>> ExtendedContext.logical_invert(Decimal('0')) |
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4771 Decimal('111111111') |
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4772 >>> ExtendedContext.logical_invert(Decimal('1')) |
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4773 Decimal('111111110') |
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4774 >>> ExtendedContext.logical_invert(Decimal('111111111')) |
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4775 Decimal('0') |
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4776 >>> ExtendedContext.logical_invert(Decimal('101010101')) |
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4777 Decimal('10101010') |
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4778 >>> ExtendedContext.logical_invert(1101) |
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4779 Decimal('111110010') |
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4780 """ |
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4781 a = _convert_other(a, raiseit=True) |
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4782 return a.logical_invert(context=self) |
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4783 |
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4784 def logical_or(self, a, b): |
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4785 """Applies the logical operation 'or' between each operand's digits. |
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4786 |
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4787 The operands must be both logical numbers. |
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4788 |
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4789 >>> ExtendedContext.logical_or(Decimal('0'), Decimal('0')) |
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4790 Decimal('0') |
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4791 >>> ExtendedContext.logical_or(Decimal('0'), Decimal('1')) |
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4792 Decimal('1') |
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4793 >>> ExtendedContext.logical_or(Decimal('1'), Decimal('0')) |
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4794 Decimal('1') |
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4795 >>> ExtendedContext.logical_or(Decimal('1'), Decimal('1')) |
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4796 Decimal('1') |
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4797 >>> ExtendedContext.logical_or(Decimal('1100'), Decimal('1010')) |
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4798 Decimal('1110') |
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4799 >>> ExtendedContext.logical_or(Decimal('1110'), Decimal('10')) |
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4800 Decimal('1110') |
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4801 >>> ExtendedContext.logical_or(110, 1101) |
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4802 Decimal('1111') |
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4803 >>> ExtendedContext.logical_or(Decimal(110), 1101) |
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4804 Decimal('1111') |
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4805 >>> ExtendedContext.logical_or(110, Decimal(1101)) |
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4806 Decimal('1111') |
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4807 """ |
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4808 a = _convert_other(a, raiseit=True) |
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4809 return a.logical_or(b, context=self) |
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4810 |
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4811 def logical_xor(self, a, b): |
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4812 """Applies the logical operation 'xor' between each operand's digits. |
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4813 |
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4814 The operands must be both logical numbers. |
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4815 |
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4816 >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('0')) |
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4817 Decimal('0') |
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4818 >>> ExtendedContext.logical_xor(Decimal('0'), Decimal('1')) |
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4819 Decimal('1') |
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4820 >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('0')) |
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4821 Decimal('1') |
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4822 >>> ExtendedContext.logical_xor(Decimal('1'), Decimal('1')) |
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4823 Decimal('0') |
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4824 >>> ExtendedContext.logical_xor(Decimal('1100'), Decimal('1010')) |
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4825 Decimal('110') |
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4826 >>> ExtendedContext.logical_xor(Decimal('1111'), Decimal('10')) |
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4827 Decimal('1101') |
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4828 >>> ExtendedContext.logical_xor(110, 1101) |
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4829 Decimal('1011') |
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4830 >>> ExtendedContext.logical_xor(Decimal(110), 1101) |
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4831 Decimal('1011') |
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4832 >>> ExtendedContext.logical_xor(110, Decimal(1101)) |
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4833 Decimal('1011') |
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4834 """ |
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4835 a = _convert_other(a, raiseit=True) |
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4836 return a.logical_xor(b, context=self) |
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4837 |
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4838 def max(self, a, b): |
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4839 """max compares two values numerically and returns the maximum. |
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4840 |
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4841 If either operand is a NaN then the general rules apply. |
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4842 Otherwise, the operands are compared as though by the compare |
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4843 operation. If they are numerically equal then the left-hand operand |
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4844 is chosen as the result. Otherwise the maximum (closer to positive |
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4845 infinity) of the two operands is chosen as the result. |
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4846 |
| 32482 | 4847 >>> ExtendedContext.max(Decimal('3'), Decimal('2')) |
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4848 Decimal('3') |
| 32482 | 4849 >>> ExtendedContext.max(Decimal('-10'), Decimal('3')) |
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4850 Decimal('3') |
| 32482 | 4851 >>> ExtendedContext.max(Decimal('1.0'), Decimal('1')) |
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4852 Decimal('1') |
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4853 >>> ExtendedContext.max(Decimal('7'), Decimal('NaN')) |
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4854 Decimal('7') |
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4855 >>> ExtendedContext.max(1, 2) |
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4856 Decimal('2') |
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4857 >>> ExtendedContext.max(Decimal(1), 2) |
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4858 Decimal('2') |
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4859 >>> ExtendedContext.max(1, Decimal(2)) |
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4860 Decimal('2') |
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4861 """ |
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4862 a = _convert_other(a, raiseit=True) |
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4863 return a.max(b, context=self) |
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4864 |
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4865 def max_mag(self, a, b): |
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4866 """Compares the values numerically with their sign ignored. |
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4867 |
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4868 >>> ExtendedContext.max_mag(Decimal('7'), Decimal('NaN')) |
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4869 Decimal('7') |
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4870 >>> ExtendedContext.max_mag(Decimal('7'), Decimal('-10')) |
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4871 Decimal('-10') |
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4872 >>> ExtendedContext.max_mag(1, -2) |
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4873 Decimal('-2') |
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4874 >>> ExtendedContext.max_mag(Decimal(1), -2) |
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4875 Decimal('-2') |
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4876 >>> ExtendedContext.max_mag(1, Decimal(-2)) |
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4877 Decimal('-2') |
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4878 """ |
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4879 a = _convert_other(a, raiseit=True) |
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4880 return a.max_mag(b, context=self) |
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4881 |
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4882 def min(self, a, b): |
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4883 """min compares two values numerically and returns the minimum. |
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4884 |
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4885 If either operand is a NaN then the general rules apply. |
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4886 Otherwise, the operands are compared as though by the compare |
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4887 operation. If they are numerically equal then the left-hand operand |
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4888 is chosen as the result. Otherwise the minimum (closer to negative |
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4889 infinity) of the two operands is chosen as the result. |
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4890 |
| 32482 | 4891 >>> ExtendedContext.min(Decimal('3'), Decimal('2')) |
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4892 Decimal('2') |
| 32482 | 4893 >>> ExtendedContext.min(Decimal('-10'), Decimal('3')) |
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4894 Decimal('-10') |
| 32482 | 4895 >>> ExtendedContext.min(Decimal('1.0'), Decimal('1')) |
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4896 Decimal('1.0') |
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4897 >>> ExtendedContext.min(Decimal('7'), Decimal('NaN')) |
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4898 Decimal('7') |
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4899 >>> ExtendedContext.min(1, 2) |
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4900 Decimal('1') |
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4901 >>> ExtendedContext.min(Decimal(1), 2) |
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4902 Decimal('1') |
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4903 >>> ExtendedContext.min(1, Decimal(29)) |
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4904 Decimal('1') |
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4905 """ |
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4906 a = _convert_other(a, raiseit=True) |
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4907 return a.min(b, context=self) |
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4908 |
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4909 def min_mag(self, a, b): |
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4910 """Compares the values numerically with their sign ignored. |
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4911 |
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4912 >>> ExtendedContext.min_mag(Decimal('3'), Decimal('-2')) |
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4913 Decimal('-2') |
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4914 >>> ExtendedContext.min_mag(Decimal('-3'), Decimal('NaN')) |
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4915 Decimal('-3') |
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4916 >>> ExtendedContext.min_mag(1, -2) |
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4917 Decimal('1') |
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4918 >>> ExtendedContext.min_mag(Decimal(1), -2) |
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4919 Decimal('1') |
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4920 >>> ExtendedContext.min_mag(1, Decimal(-2)) |
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4921 Decimal('1') |
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4922 """ |
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4923 a = _convert_other(a, raiseit=True) |
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4924 return a.min_mag(b, context=self) |
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4925 |
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4926 def minus(self, a): |
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4927 """Minus corresponds to unary prefix minus in Python. |
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4928 |
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4929 The operation is evaluated using the same rules as subtract; the |
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4930 operation minus(a) is calculated as subtract('0', a) where the '0' |
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4931 has the same exponent as the operand. |
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4932 |
| 32482 | 4933 >>> ExtendedContext.minus(Decimal('1.3')) |
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4934 Decimal('-1.3') |
| 32482 | 4935 >>> ExtendedContext.minus(Decimal('-1.3')) |
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4936 Decimal('1.3') |
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4937 >>> ExtendedContext.minus(1) |
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4938 Decimal('-1') |
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4939 """ |
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4940 a = _convert_other(a, raiseit=True) |
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4941 return a.__neg__(context=self) |
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4942 |
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4943 def multiply(self, a, b): |
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4944 """multiply multiplies two operands. |
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4945 |
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4946 If either operand is a special value then the general rules apply. |
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4947 Otherwise, the operands are multiplied together |
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4948 ('long multiplication'), resulting in a number which may be as long as |
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4949 the sum of the lengths of the two operands. |
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4950 |
| 32482 | 4951 >>> ExtendedContext.multiply(Decimal('1.20'), Decimal('3')) |
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4952 Decimal('3.60') |
| 32482 | 4953 >>> ExtendedContext.multiply(Decimal('7'), Decimal('3')) |
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4954 Decimal('21') |
| 32482 | 4955 >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('0.8')) |
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4956 Decimal('0.72') |
| 32482 | 4957 >>> ExtendedContext.multiply(Decimal('0.9'), Decimal('-0')) |
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4958 Decimal('-0.0') |
| 32482 | 4959 >>> ExtendedContext.multiply(Decimal('654321'), Decimal('654321')) |
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4960 Decimal('4.28135971E+11') |
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4961 >>> ExtendedContext.multiply(7, 7) |
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4962 Decimal('49') |
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4963 >>> ExtendedContext.multiply(Decimal(7), 7) |
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4964 Decimal('49') |
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4965 >>> ExtendedContext.multiply(7, Decimal(7)) |
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4966 Decimal('49') |
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4967 """ |
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4968 a = _convert_other(a, raiseit=True) |
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4969 r = a.__mul__(b, context=self) |
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4970 if r is NotImplemented: |
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4971 raise TypeError("Unable to convert %s to Decimal" % b) |
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4972 else: |
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4973 return r |
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4974 |
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4975 def next_minus(self, a): |
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4976 """Returns the largest representable number smaller than a. |
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4977 |
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4978 >>> c = ExtendedContext.copy() |
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4979 >>> c.Emin = -999 |
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4980 >>> c.Emax = 999 |
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4981 >>> ExtendedContext.next_minus(Decimal('1')) |
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4982 Decimal('0.999999999') |
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4983 >>> c.next_minus(Decimal('1E-1007')) |
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4984 Decimal('0E-1007') |
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4985 >>> ExtendedContext.next_minus(Decimal('-1.00000003')) |
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4986 Decimal('-1.00000004') |
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4987 >>> c.next_minus(Decimal('Infinity')) |
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4988 Decimal('9.99999999E+999') |
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4989 >>> c.next_minus(1) |
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4990 Decimal('0.999999999') |
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4991 """ |
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4992 a = _convert_other(a, raiseit=True) |
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4993 return a.next_minus(context=self) |
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4994 |
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4995 def next_plus(self, a): |
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4996 """Returns the smallest representable number larger than a. |
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4997 |
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4998 >>> c = ExtendedContext.copy() |
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4999 >>> c.Emin = -999 |
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5000 >>> c.Emax = 999 |
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5001 >>> ExtendedContext.next_plus(Decimal('1')) |
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5002 Decimal('1.00000001') |
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5003 >>> c.next_plus(Decimal('-1E-1007')) |
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5004 Decimal('-0E-1007') |
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5005 >>> ExtendedContext.next_plus(Decimal('-1.00000003')) |
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5006 Decimal('-1.00000002') |
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5007 >>> c.next_plus(Decimal('-Infinity')) |
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5008 Decimal('-9.99999999E+999') |
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5009 >>> c.next_plus(1) |
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5010 Decimal('1.00000001') |
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5011 """ |
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5012 a = _convert_other(a, raiseit=True) |
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5013 return a.next_plus(context=self) |
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5014 |
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5015 def next_toward(self, a, b): |
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5016 """Returns the number closest to a, in direction towards b. |
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5017 |
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5018 The result is the closest representable number from the first |
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5019 operand (but not the first operand) that is in the direction |
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5020 towards the second operand, unless the operands have the same |
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5021 value. |
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5022 |
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5023 >>> c = ExtendedContext.copy() |
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5024 >>> c.Emin = -999 |
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5025 >>> c.Emax = 999 |
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5026 >>> c.next_toward(Decimal('1'), Decimal('2')) |
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5027 Decimal('1.00000001') |
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5028 >>> c.next_toward(Decimal('-1E-1007'), Decimal('1')) |
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5029 Decimal('-0E-1007') |
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5030 >>> c.next_toward(Decimal('-1.00000003'), Decimal('0')) |
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5031 Decimal('-1.00000002') |
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5032 >>> c.next_toward(Decimal('1'), Decimal('0')) |
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5033 Decimal('0.999999999') |
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5034 >>> c.next_toward(Decimal('1E-1007'), Decimal('-100')) |
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5035 Decimal('0E-1007') |
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5036 >>> c.next_toward(Decimal('-1.00000003'), Decimal('-10')) |
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5037 Decimal('-1.00000004') |
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5038 >>> c.next_toward(Decimal('0.00'), Decimal('-0.0000')) |
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5039 Decimal('-0.00') |
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5040 >>> c.next_toward(0, 1) |
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5041 Decimal('1E-1007') |
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5042 >>> c.next_toward(Decimal(0), 1) |
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5043 Decimal('1E-1007') |
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5044 >>> c.next_toward(0, Decimal(1)) |
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5045 Decimal('1E-1007') |
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5046 """ |
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5047 a = _convert_other(a, raiseit=True) |
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5048 return a.next_toward(b, context=self) |
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5049 |
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5050 def normalize(self, a): |
| 32496 | 5051 """normalize reduces an operand to its simplest form. |
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5052 |
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5053 Essentially a plus operation with all trailing zeros removed from the |
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5054 result. |
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5055 |
| 32482 | 5056 >>> ExtendedContext.normalize(Decimal('2.1')) |
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5057 Decimal('2.1') |
| 32482 | 5058 >>> ExtendedContext.normalize(Decimal('-2.0')) |
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5059 Decimal('-2') |
| 32482 | 5060 >>> ExtendedContext.normalize(Decimal('1.200')) |
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5061 Decimal('1.2') |
| 32482 | 5062 >>> ExtendedContext.normalize(Decimal('-120')) |
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5063 Decimal('-1.2E+2') |
| 32482 | 5064 >>> ExtendedContext.normalize(Decimal('120.00')) |
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5065 Decimal('1.2E+2') |
| 32482 | 5066 >>> ExtendedContext.normalize(Decimal('0.00')) |
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5067 Decimal('0') |
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5068 >>> ExtendedContext.normalize(6) |
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5069 Decimal('6') |
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5070 """ |
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5071 a = _convert_other(a, raiseit=True) |
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5072 return a.normalize(context=self) |
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5073 |
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5074 def number_class(self, a): |
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5075 """Returns an indication of the class of the operand. |
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5076 |
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5077 The class is one of the following strings: |
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5078 -sNaN |
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5079 -NaN |
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5080 -Infinity |
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5081 -Normal |
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5082 -Subnormal |
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5083 -Zero |
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5084 +Zero |
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5085 +Subnormal |
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5086 +Normal |
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5087 +Infinity |
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5088 |
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5089 >>> c = ExtendedContext.copy() |
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5090 >>> c.Emin = -999 |
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5091 >>> c.Emax = 999 |
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5092 >>> c.number_class(Decimal('Infinity')) |
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5093 '+Infinity' |
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5094 >>> c.number_class(Decimal('1E-10')) |
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5095 '+Normal' |
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5096 >>> c.number_class(Decimal('2.50')) |
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5097 '+Normal' |
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5098 >>> c.number_class(Decimal('0.1E-999')) |
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5099 '+Subnormal' |
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5100 >>> c.number_class(Decimal('0')) |
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5101 '+Zero' |
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5102 >>> c.number_class(Decimal('-0')) |
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5103 '-Zero' |
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5104 >>> c.number_class(Decimal('-0.1E-999')) |
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5105 '-Subnormal' |
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5106 >>> c.number_class(Decimal('-1E-10')) |
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5107 '-Normal' |
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5108 >>> c.number_class(Decimal('-2.50')) |
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5109 '-Normal' |
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5110 >>> c.number_class(Decimal('-Infinity')) |
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5111 '-Infinity' |
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5112 >>> c.number_class(Decimal('NaN')) |
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5113 'NaN' |
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5114 >>> c.number_class(Decimal('-NaN')) |
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5115 'NaN' |
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5116 >>> c.number_class(Decimal('sNaN')) |
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5117 'sNaN' |
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5118 >>> c.number_class(123) |
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5119 '+Normal' |
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5120 """ |
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5121 a = _convert_other(a, raiseit=True) |
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5122 return a.number_class(context=self) |
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5123 |
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5124 def plus(self, a): |
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5125 """Plus corresponds to unary prefix plus in Python. |
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5126 |
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5127 The operation is evaluated using the same rules as add; the |
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5128 operation plus(a) is calculated as add('0', a) where the '0' |
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5129 has the same exponent as the operand. |
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5130 |
| 32482 | 5131 >>> ExtendedContext.plus(Decimal('1.3')) |
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5132 Decimal('1.3') |
| 32482 | 5133 >>> ExtendedContext.plus(Decimal('-1.3')) |
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5134 Decimal('-1.3') |
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5135 >>> ExtendedContext.plus(-1) |
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5136 Decimal('-1') |
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5137 """ |
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5138 a = _convert_other(a, raiseit=True) |
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5139 return a.__pos__(context=self) |
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5140 |
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5141 def power(self, a, b, modulo=None): |
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5142 """Raises a to the power of b, to modulo if given. |
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5143 |
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5144 With two arguments, compute a**b. If a is negative then b |
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5145 must be integral. The result will be inexact unless b is |
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5146 integral and the result is finite and can be expressed exactly |
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5147 in 'precision' digits. |
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5148 |
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5149 With three arguments, compute (a**b) % modulo. For the |
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5150 three argument form, the following restrictions on the |
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5151 arguments hold: |
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5152 |
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5153 - all three arguments must be integral |
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5154 - b must be nonnegative |
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5155 - at least one of a or b must be nonzero |
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5156 - modulo must be nonzero and have at most 'precision' digits |
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5157 |
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5158 The result of pow(a, b, modulo) is identical to the result |
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5159 that would be obtained by computing (a**b) % modulo with |
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5160 unbounded precision, but is computed more efficiently. It is |
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5161 always exact. |
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5162 |
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5163 >>> c = ExtendedContext.copy() |
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5164 >>> c.Emin = -999 |
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5165 >>> c.Emax = 999 |
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5166 >>> c.power(Decimal('2'), Decimal('3')) |
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5167 Decimal('8') |
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5168 >>> c.power(Decimal('-2'), Decimal('3')) |
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5169 Decimal('-8') |
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5170 >>> c.power(Decimal('2'), Decimal('-3')) |
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5171 Decimal('0.125') |
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5172 >>> c.power(Decimal('1.7'), Decimal('8')) |
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5173 Decimal('69.7575744') |
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5174 >>> c.power(Decimal('10'), Decimal('0.301029996')) |
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5175 Decimal('2.00000000') |
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5176 >>> c.power(Decimal('Infinity'), Decimal('-1')) |
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Christian Heimes <christian@cheimes.de>
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5177 Decimal('0') |
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5178 >>> c.power(Decimal('Infinity'), Decimal('0')) |
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5179 Decimal('1') |
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5180 >>> c.power(Decimal('Infinity'), Decimal('1')) |
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5181 Decimal('Infinity') |
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5182 >>> c.power(Decimal('-Infinity'), Decimal('-1')) |
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5183 Decimal('-0') |
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5184 >>> c.power(Decimal('-Infinity'), Decimal('0')) |
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5185 Decimal('1') |
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5186 >>> c.power(Decimal('-Infinity'), Decimal('1')) |
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5187 Decimal('-Infinity') |
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5188 >>> c.power(Decimal('-Infinity'), Decimal('2')) |
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5189 Decimal('Infinity') |
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5190 >>> c.power(Decimal('0'), Decimal('0')) |
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5191 Decimal('NaN') |
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5192 |
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5193 >>> c.power(Decimal('3'), Decimal('7'), Decimal('16')) |
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5194 Decimal('11') |
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5195 >>> c.power(Decimal('-3'), Decimal('7'), Decimal('16')) |
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5196 Decimal('-11') |
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5197 >>> c.power(Decimal('-3'), Decimal('8'), Decimal('16')) |
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5198 Decimal('1') |
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5199 >>> c.power(Decimal('3'), Decimal('7'), Decimal('-16')) |
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5200 Decimal('11') |
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5201 >>> c.power(Decimal('23E12345'), Decimal('67E189'), Decimal('123456789')) |
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5202 Decimal('11729830') |
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5203 >>> c.power(Decimal('-0'), Decimal('17'), Decimal('1729')) |
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5204 Decimal('-0') |
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5205 >>> c.power(Decimal('-23'), Decimal('0'), Decimal('65537')) |
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5206 Decimal('1') |
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5207 >>> ExtendedContext.power(7, 7) |
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5208 Decimal('823543') |
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5209 >>> ExtendedContext.power(Decimal(7), 7) |
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5210 Decimal('823543') |
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5211 >>> ExtendedContext.power(7, Decimal(7), 2) |
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5212 Decimal('1') |
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5213 """ |
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5214 a = _convert_other(a, raiseit=True) |
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5215 r = a.__pow__(b, modulo, context=self) |
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5216 if r is NotImplemented: |
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5217 raise TypeError("Unable to convert %s to Decimal" % b) |
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5218 else: |
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5219 return r |
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5220 |
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5221 def quantize(self, a, b): |
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5222 """Returns a value equal to 'a' (rounded), having the exponent of 'b'. |
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5223 |
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5224 The coefficient of the result is derived from that of the left-hand |
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5225 operand. It may be rounded using the current rounding setting (if the |
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5226 exponent is being increased), multiplied by a positive power of ten (if |
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5227 the exponent is being decreased), or is unchanged (if the exponent is |
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5228 already equal to that of the right-hand operand). |
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5229 |
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5230 Unlike other operations, if the length of the coefficient after the |
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5231 quantize operation would be greater than precision then an Invalid |
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5232 operation condition is raised. This guarantees that, unless there is |
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5233 an error condition, the exponent of the result of a quantize is always |
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5234 equal to that of the right-hand operand. |
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5235 |
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5236 Also unlike other operations, quantize will never raise Underflow, even |
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5237 if the result is subnormal and inexact. |
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5238 |
| 32482 | 5239 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.001')) |
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5240 Decimal('2.170') |
| 32482 | 5241 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.01')) |
|
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5242 Decimal('2.17') |
| 32482 | 5243 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('0.1')) |
|
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5244 Decimal('2.2') |
| 32482 | 5245 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+0')) |
|
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|
5246 Decimal('2') |
| 32482 | 5247 >>> ExtendedContext.quantize(Decimal('2.17'), Decimal('1e+1')) |
|
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|
5248 Decimal('0E+1') |
| 32482 | 5249 >>> ExtendedContext.quantize(Decimal('-Inf'), Decimal('Infinity')) |
|
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|
5250 Decimal('-Infinity') |
| 32482 | 5251 >>> ExtendedContext.quantize(Decimal('2'), Decimal('Infinity')) |
|
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|
5252 Decimal('NaN') |
| 32482 | 5253 >>> ExtendedContext.quantize(Decimal('-0.1'), Decimal('1')) |
|
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5254 Decimal('-0') |
| 32482 | 5255 >>> ExtendedContext.quantize(Decimal('-0'), Decimal('1e+5')) |
|
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|
5256 Decimal('-0E+5') |
| 32482 | 5257 >>> ExtendedContext.quantize(Decimal('+35236450.6'), Decimal('1e-2')) |
|
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|
5258 Decimal('NaN') |
| 32482 | 5259 >>> ExtendedContext.quantize(Decimal('-35236450.6'), Decimal('1e-2')) |
|
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|
5260 Decimal('NaN') |
| 32482 | 5261 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-1')) |
|
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|
5262 Decimal('217.0') |
| 32482 | 5263 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e-0')) |
|
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Christian Heimes <christian@cheimes.de>
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|
5264 Decimal('217') |
| 32482 | 5265 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+1')) |
|
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Christian Heimes <christian@cheimes.de>
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|
5266 Decimal('2.2E+2') |
| 32482 | 5267 >>> ExtendedContext.quantize(Decimal('217'), Decimal('1e+2')) |
|
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Christian Heimes <christian@cheimes.de>
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|
5268 Decimal('2E+2') |
|
58936
f225d5e6e0e5
Merged revisions 78217-78218 via svnmerge from
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|
5269 >>> ExtendedContext.quantize(1, 2) |
|
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5270 Decimal('1') |
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|
5271 >>> ExtendedContext.quantize(Decimal(1), 2) |
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5272 Decimal('1') |
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|
5273 >>> ExtendedContext.quantize(1, Decimal(2)) |
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|
5274 Decimal('1') |
|
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5275 """ |
|
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|
5276 a = _convert_other(a, raiseit=True) |
|
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5277 return a.quantize(b, context=self) |
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5278 |
|
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|
5279 def radix(self): |
|
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|
5280 """Just returns 10, as this is Decimal, :) |
|
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5281 |
|
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|
5282 >>> ExtendedContext.radix() |
|
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|
5283 Decimal('10') |
|
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|
5284 """ |
|
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|
5285 return Decimal(10) |
|
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5286 |
|
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5287 def remainder(self, a, b): |
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|
5288 """Returns the remainder from integer division. |
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|
5289 |
|
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|
5290 The result is the residue of the dividend after the operation of |
|
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5291 calculating integer division as described for divide-integer, rounded |
|
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5292 to precision digits if necessary. The sign of the result, if |
|
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5293 non-zero, is the same as that of the original dividend. |
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5294 |
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5295 This operation will fail under the same conditions as integer division |
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|
5296 (that is, if integer division on the same two operands would fail, the |
|
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|
5297 remainder cannot be calculated). |
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5298 |
| 32482 | 5299 >>> ExtendedContext.remainder(Decimal('2.1'), Decimal('3')) |
|
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5300 Decimal('2.1') |
| 32482 | 5301 >>> ExtendedContext.remainder(Decimal('10'), Decimal('3')) |
|
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5302 Decimal('1') |
| 32482 | 5303 >>> ExtendedContext.remainder(Decimal('-10'), Decimal('3')) |
|
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5304 Decimal('-1') |
| 32482 | 5305 >>> ExtendedContext.remainder(Decimal('10.2'), Decimal('1')) |
|
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5306 Decimal('0.2') |
| 32482 | 5307 >>> ExtendedContext.remainder(Decimal('10'), Decimal('0.3')) |
|
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|
5308 Decimal('0.1') |
| 32482 | 5309 >>> ExtendedContext.remainder(Decimal('3.6'), Decimal('1.3')) |
|
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5310 Decimal('1.0') |
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5311 >>> ExtendedContext.remainder(22, 6) |
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5312 Decimal('4') |
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5313 >>> ExtendedContext.remainder(Decimal(22), 6) |
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5314 Decimal('4') |
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5315 >>> ExtendedContext.remainder(22, Decimal(6)) |
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5316 Decimal('4') |
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5317 """ |
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5318 a = _convert_other(a, raiseit=True) |
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5319 r = a.__mod__(b, context=self) |
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5320 if r is NotImplemented: |
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5321 raise TypeError("Unable to convert %s to Decimal" % b) |
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5322 else: |
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5323 return r |
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5324 |
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5325 def remainder_near(self, a, b): |
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5326 """Returns to be "a - b * n", where n is the integer nearest the exact |
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5327 value of "x / b" (if two integers are equally near then the even one |
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5328 is chosen). If the result is equal to 0 then its sign will be the |
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5329 sign of a. |
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5330 |
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5331 This operation will fail under the same conditions as integer division |
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5332 (that is, if integer division on the same two operands would fail, the |
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5333 remainder cannot be calculated). |
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5334 |
| 32482 | 5335 >>> ExtendedContext.remainder_near(Decimal('2.1'), Decimal('3')) |
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5336 Decimal('-0.9') |
| 32482 | 5337 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('6')) |
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5338 Decimal('-2') |
| 32482 | 5339 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('3')) |
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5340 Decimal('1') |
| 32482 | 5341 >>> ExtendedContext.remainder_near(Decimal('-10'), Decimal('3')) |
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5342 Decimal('-1') |
| 32482 | 5343 >>> ExtendedContext.remainder_near(Decimal('10.2'), Decimal('1')) |
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5344 Decimal('0.2') |
| 32482 | 5345 >>> ExtendedContext.remainder_near(Decimal('10'), Decimal('0.3')) |
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5346 Decimal('0.1') |
| 32482 | 5347 >>> ExtendedContext.remainder_near(Decimal('3.6'), Decimal('1.3')) |
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5348 Decimal('-0.3') |
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5349 >>> ExtendedContext.remainder_near(3, 11) |
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5350 Decimal('3') |
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5351 >>> ExtendedContext.remainder_near(Decimal(3), 11) |
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5352 Decimal('3') |
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5353 >>> ExtendedContext.remainder_near(3, Decimal(11)) |
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5354 Decimal('3') |
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5355 """ |
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5356 a = _convert_other(a, raiseit=True) |
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5357 return a.remainder_near(b, context=self) |
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5358 |
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5359 def rotate(self, a, b): |
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5360 """Returns a rotated copy of a, b times. |
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5361 |
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5362 The coefficient of the result is a rotated copy of the digits in |
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5363 the coefficient of the first operand. The number of places of |
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5364 rotation is taken from the absolute value of the second operand, |
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5365 with the rotation being to the left if the second operand is |
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5366 positive or to the right otherwise. |
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5367 |
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5368 >>> ExtendedContext.rotate(Decimal('34'), Decimal('8')) |
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5369 Decimal('400000003') |
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5370 >>> ExtendedContext.rotate(Decimal('12'), Decimal('9')) |
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5371 Decimal('12') |
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5372 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('-2')) |
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5373 Decimal('891234567') |
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5374 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('0')) |
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5375 Decimal('123456789') |
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5376 >>> ExtendedContext.rotate(Decimal('123456789'), Decimal('+2')) |
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5377 Decimal('345678912') |
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5378 >>> ExtendedContext.rotate(1333333, 1) |
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5379 Decimal('13333330') |
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5380 >>> ExtendedContext.rotate(Decimal(1333333), 1) |
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5381 Decimal('13333330') |
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5382 >>> ExtendedContext.rotate(1333333, Decimal(1)) |
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5383 Decimal('13333330') |
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5384 """ |
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5385 a = _convert_other(a, raiseit=True) |
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5386 return a.rotate(b, context=self) |
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5387 |
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5388 def same_quantum(self, a, b): |
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5389 """Returns True if the two operands have the same exponent. |
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5390 |
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5391 The result is never affected by either the sign or the coefficient of |
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5392 either operand. |
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5393 |
| 32482 | 5394 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.001')) |
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5395 False |
| 32482 | 5396 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('0.01')) |
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5397 True |
| 32482 | 5398 >>> ExtendedContext.same_quantum(Decimal('2.17'), Decimal('1')) |
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5399 False |
| 32482 | 5400 >>> ExtendedContext.same_quantum(Decimal('Inf'), Decimal('-Inf')) |
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5401 True |
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5402 >>> ExtendedContext.same_quantum(10000, -1) |
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5403 True |
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5404 >>> ExtendedContext.same_quantum(Decimal(10000), -1) |
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5405 True |
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5406 >>> ExtendedContext.same_quantum(10000, Decimal(-1)) |
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5407 True |
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5408 """ |
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5409 a = _convert_other(a, raiseit=True) |
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5410 return a.same_quantum(b) |
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5411 |
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5412 def scaleb (self, a, b): |
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5413 """Returns the first operand after adding the second value its exp. |
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5414 |
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5415 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('-2')) |
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5416 Decimal('0.0750') |
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5417 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('0')) |
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5418 Decimal('7.50') |
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5419 >>> ExtendedContext.scaleb(Decimal('7.50'), Decimal('3')) |
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5420 Decimal('7.50E+3') |
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5421 >>> ExtendedContext.scaleb(1, 4) |
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5422 Decimal('1E+4') |
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5423 >>> ExtendedContext.scaleb(Decimal(1), 4) |
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5424 Decimal('1E+4') |
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5425 >>> ExtendedContext.scaleb(1, Decimal(4)) |
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5426 Decimal('1E+4') |
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5427 """ |
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5428 a = _convert_other(a, raiseit=True) |
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5429 return a.scaleb(b, context=self) |
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5430 |
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5431 def shift(self, a, b): |
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5432 """Returns a shifted copy of a, b times. |
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5433 |
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5434 The coefficient of the result is a shifted copy of the digits |
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5435 in the coefficient of the first operand. The number of places |
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5436 to shift is taken from the absolute value of the second operand, |
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5437 with the shift being to the left if the second operand is |
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5438 positive or to the right otherwise. Digits shifted into the |
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5439 coefficient are zeros. |
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5440 |
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5441 >>> ExtendedContext.shift(Decimal('34'), Decimal('8')) |
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5442 Decimal('400000000') |
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5443 >>> ExtendedContext.shift(Decimal('12'), Decimal('9')) |
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5444 Decimal('0') |
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5445 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('-2')) |
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5446 Decimal('1234567') |
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5447 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('0')) |
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5448 Decimal('123456789') |
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5449 >>> ExtendedContext.shift(Decimal('123456789'), Decimal('+2')) |
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5450 Decimal('345678900') |
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5451 >>> ExtendedContext.shift(88888888, 2) |
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5452 Decimal('888888800') |
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5453 >>> ExtendedContext.shift(Decimal(88888888), 2) |
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5454 Decimal('888888800') |
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5455 >>> ExtendedContext.shift(88888888, Decimal(2)) |
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5456 Decimal('888888800') |
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5457 """ |
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5458 a = _convert_other(a, raiseit=True) |
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5459 return a.shift(b, context=self) |
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5460 |
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5461 def sqrt(self, a): |
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5462 """Square root of a non-negative number to context precision. |
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5463 |
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5464 If the result must be inexact, it is rounded using the round-half-even |
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5465 algorithm. |
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5466 |
| 32482 | 5467 >>> ExtendedContext.sqrt(Decimal('0')) |
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5468 Decimal('0') |
| 32482 | 5469 >>> ExtendedContext.sqrt(Decimal('-0')) |
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5470 Decimal('-0') |
| 32482 | 5471 >>> ExtendedContext.sqrt(Decimal('0.39')) |
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5472 Decimal('0.624499800') |
| 32482 | 5473 >>> ExtendedContext.sqrt(Decimal('100')) |
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5474 Decimal('10') |
| 32482 | 5475 >>> ExtendedContext.sqrt(Decimal('1')) |
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5476 Decimal('1') |
| 32482 | 5477 >>> ExtendedContext.sqrt(Decimal('1.0')) |
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5478 Decimal('1.0') |
| 32482 | 5479 >>> ExtendedContext.sqrt(Decimal('1.00')) |
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5480 Decimal('1.0') |
| 32482 | 5481 >>> ExtendedContext.sqrt(Decimal('7')) |
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5482 Decimal('2.64575131') |
| 32482 | 5483 >>> ExtendedContext.sqrt(Decimal('10')) |
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5484 Decimal('3.16227766') |
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5485 >>> ExtendedContext.sqrt(2) |
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5486 Decimal('1.41421356') |
| 32482 | 5487 >>> ExtendedContext.prec |
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5488 9 |
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5489 """ |
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5490 a = _convert_other(a, raiseit=True) |
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5491 return a.sqrt(context=self) |
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5492 |
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5493 def subtract(self, a, b): |
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5494 """Return the difference between the two operands. |
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5495 |
| 32482 | 5496 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.07')) |
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5497 Decimal('0.23') |
| 32482 | 5498 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('1.30')) |
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5499 Decimal('0.00') |
| 32482 | 5500 >>> ExtendedContext.subtract(Decimal('1.3'), Decimal('2.07')) |
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5501 Decimal('-0.77') |
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5502 >>> ExtendedContext.subtract(8, 5) |
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5503 Decimal('3') |
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5504 >>> ExtendedContext.subtract(Decimal(8), 5) |
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5505 Decimal('3') |
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5506 >>> ExtendedContext.subtract(8, Decimal(5)) |
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5507 Decimal('3') |
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5508 """ |
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5509 a = _convert_other(a, raiseit=True) |
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5510 r = a.__sub__(b, context=self) |
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5511 if r is NotImplemented: |
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5512 raise TypeError("Unable to convert %s to Decimal" % b) |
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5513 else: |
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5514 return r |
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5515 |
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5516 def to_eng_string(self, a): |
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5517 """Converts a number to a string, using scientific notation. |
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5518 |
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5519 The operation is not affected by the context. |
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5520 """ |
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5521 a = _convert_other(a, raiseit=True) |
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5522 return a.to_eng_string(context=self) |
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5523 |
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5524 def to_sci_string(self, a): |
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5525 """Converts a number to a string, using scientific notation. |
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5526 |
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5527 The operation is not affected by the context. |
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5528 """ |
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5529 a = _convert_other(a, raiseit=True) |
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5530 return a.__str__(context=self) |
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5531 |
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5532 def to_integral_exact(self, a): |
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5533 """Rounds to an integer. |
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5534 |
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5535 When the operand has a negative exponent, the result is the same |
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5536 as using the quantize() operation using the given operand as the |
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5537 left-hand-operand, 1E+0 as the right-hand-operand, and the precision |
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5538 of the operand as the precision setting; Inexact and Rounded flags |
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5539 are allowed in this operation. The rounding mode is taken from the |
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5540 context. |
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5541 |
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5542 >>> ExtendedContext.to_integral_exact(Decimal('2.1')) |
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5543 Decimal('2') |
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5544 >>> ExtendedContext.to_integral_exact(Decimal('100')) |
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5545 Decimal('100') |
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5546 >>> ExtendedContext.to_integral_exact(Decimal('100.0')) |
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5547 Decimal('100') |
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5548 >>> ExtendedContext.to_integral_exact(Decimal('101.5')) |
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5549 Decimal('102') |
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5550 >>> ExtendedContext.to_integral_exact(Decimal('-101.5')) |
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5551 Decimal('-102') |
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5552 >>> ExtendedContext.to_integral_exact(Decimal('10E+5')) |
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5553 Decimal('1.0E+6') |
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5554 >>> ExtendedContext.to_integral_exact(Decimal('7.89E+77')) |
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5555 Decimal('7.89E+77') |
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5556 >>> ExtendedContext.to_integral_exact(Decimal('-Inf')) |
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5557 Decimal('-Infinity') |
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5558 """ |
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5559 a = _convert_other(a, raiseit=True) |
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5560 return a.to_integral_exact(context=self) |
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5561 |
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5562 def to_integral_value(self, a): |
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5563 """Rounds to an integer. |
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5564 |
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5565 When the operand has a negative exponent, the result is the same |
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5566 as using the quantize() operation using the given operand as the |
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5567 left-hand-operand, 1E+0 as the right-hand-operand, and the precision |
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5568 of the operand as the precision setting, except that no flags will |
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5569 be set. The rounding mode is taken from the context. |
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5570 |
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5571 >>> ExtendedContext.to_integral_value(Decimal('2.1')) |
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5572 Decimal('2') |
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5573 >>> ExtendedContext.to_integral_value(Decimal('100')) |
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5574 Decimal('100') |
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5575 >>> ExtendedContext.to_integral_value(Decimal('100.0')) |
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5576 Decimal('100') |
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5577 >>> ExtendedContext.to_integral_value(Decimal('101.5')) |
|
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5578 Decimal('102') |
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5579 >>> ExtendedContext.to_integral_value(Decimal('-101.5')) |
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5580 Decimal('-102') |
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5581 >>> ExtendedContext.to_integral_value(Decimal('10E+5')) |
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5582 Decimal('1.0E+6') |
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5583 >>> ExtendedContext.to_integral_value(Decimal('7.89E+77')) |
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5584 Decimal('7.89E+77') |
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5585 >>> ExtendedContext.to_integral_value(Decimal('-Inf')) |
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5586 Decimal('-Infinity') |
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5587 """ |
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5588 a = _convert_other(a, raiseit=True) |
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5589 return a.to_integral_value(context=self) |
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5590 |
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5591 # the method name changed, but we provide also the old one, for compatibility |
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5592 to_integral = to_integral_value |
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5593 |
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5594 class _WorkRep(object): |
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5595 __slots__ = ('sign','int','exp') |
| 33851 | 5596 # sign: 0 or 1 |
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5597 # int: int |
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5598 # exp: None, int, or string |
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5599 |
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5600 def __init__(self, value=None): |
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5601 if value is None: |
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5602 self.sign = None |
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5603 self.int = 0 |
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5604 self.exp = None |
| 33851 | 5605 elif isinstance(value, Decimal): |
| 5606 self.sign = value._sign | |
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5607 self.int = int(value._int) |
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5608 self.exp = value._exp |
| 33851 | 5609 else: |
| 5610 # assert isinstance(value, tuple) | |
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5611 self.sign = value[0] |
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5612 self.int = value[1] |
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5613 self.exp = value[2] |
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5614 |
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5615 def __repr__(self): |
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5616 return "(%r, %r, %r)" % (self.sign, self.int, self.exp) |
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5617 |
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5618 __str__ = __repr__ |
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5619 |
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5620 |
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5621 |
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5622 def _normalize(op1, op2, prec = 0): |
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5623 """Normalizes op1, op2 to have the same exp and length of coefficient. |
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5624 |
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5625 Done during addition. |
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5626 """ |
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5627 if op1.exp < op2.exp: |
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5628 tmp = op2 |
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5629 other = op1 |
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5630 else: |
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5631 tmp = op1 |
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5632 other = op2 |
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5633 |
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5634 # Let exp = min(tmp.exp - 1, tmp.adjusted() - precision - 1). |
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5635 # Then adding 10**exp to tmp has the same effect (after rounding) |
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5636 # as adding any positive quantity smaller than 10**exp; similarly |
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5637 # for subtraction. So if other is smaller than 10**exp we replace |
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5638 # it with 10**exp. This avoids tmp.exp - other.exp getting too large. |
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5639 tmp_len = len(str(tmp.int)) |
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5640 other_len = len(str(other.int)) |
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5641 exp = tmp.exp + min(-1, tmp_len - prec - 2) |
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5642 if other_len + other.exp - 1 < exp: |
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5643 other.int = 1 |
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5644 other.exp = exp |
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5645 |
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5646 tmp.int *= 10 ** (tmp.exp - other.exp) |
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5647 tmp.exp = other.exp |
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5648 return op1, op2 |
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5649 |
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5650 ##### Integer arithmetic functions used by ln, log10, exp and __pow__ ##### |
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5651 |
|
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5652 _nbits = int.bit_length |
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5653 |
|
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5654 def _decimal_lshift_exact(n, e): |
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5655 """ Given integers n and e, return n * 10**e if it's an integer, else None. |
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5656 |
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|
5657 The computation is designed to avoid computing large powers of 10 |
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5658 unnecessarily. |
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5659 |
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5660 >>> _decimal_lshift_exact(3, 4) |
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5661 30000 |
|
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5662 >>> _decimal_lshift_exact(300, -999999999) # returns None |
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5663 |
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5664 """ |
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5665 if n == 0: |
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5666 return 0 |
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5667 elif e >= 0: |
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5668 return n * 10**e |
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5669 else: |
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5670 # val_n = largest power of 10 dividing n. |
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5671 str_n = str(abs(n)) |
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Mark Dickinson <mdickinson@enthought.com>
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5672 val_n = len(str_n) - len(str_n.rstrip('0')) |
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Mark Dickinson <mdickinson@enthought.com>
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5673 return None if val_n < -e else n // 10**-e |
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5674 |
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43400
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5675 def _sqrt_nearest(n, a): |
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5676 """Closest integer to the square root of the positive integer n. a is |
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5677 an initial approximation to the square root. Any positive integer |
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5678 will do for a, but the closer a is to the square root of n the |
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5679 faster convergence will be. |
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5680 |
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5681 """ |
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5682 if n <= 0 or a <= 0: |
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5683 raise ValueError("Both arguments to _sqrt_nearest should be positive.") |
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5684 |
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5685 b=0 |
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5686 while a != b: |
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5687 b, a = a, a--n//a>>1 |
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5688 return a |
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5689 |
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5690 def _rshift_nearest(x, shift): |
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5691 """Given an integer x and a nonnegative integer shift, return closest |
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5692 integer to x / 2**shift; use round-to-even in case of a tie. |
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5693 |
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5694 """ |
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5695 b, q = 1 << shift, x >> shift |
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5696 return q + (2*(x & (b-1)) + (q&1) > b) |
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5697 |
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5698 def _div_nearest(a, b): |
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5699 """Closest integer to a/b, a and b positive integers; rounds to even |
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5700 in the case of a tie. |
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5701 |
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32451
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5702 """ |
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5703 q, r = divmod(a, b) |
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5704 return q + (2*r + (q&1) > b) |
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5705 |
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5706 def _ilog(x, M, L = 8): |
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5707 """Integer approximation to M*log(x/M), with absolute error boundable |
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5708 in terms only of x/M. |
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5709 |
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5710 Given positive integers x and M, return an integer approximation to |
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5711 M * log(x/M). For L = 8 and 0.1 <= x/M <= 10 the difference |
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5712 between the approximation and the exact result is at most 22. For |
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5713 L = 8 and 1.0 <= x/M <= 10.0 the difference is at most 15. In |
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5714 both cases these are upper bounds on the error; it will usually be |
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5715 much smaller.""" |
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5716 |
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5717 # The basic algorithm is the following: let log1p be the function |
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5718 # log1p(x) = log(1+x). Then log(x/M) = log1p((x-M)/M). We use |
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5719 # the reduction |
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5720 # |
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5721 # log1p(y) = 2*log1p(y/(1+sqrt(1+y))) |
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5722 # |
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5723 # repeatedly until the argument to log1p is small (< 2**-L in |
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5724 # absolute value). For small y we can use the Taylor series |
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5725 # expansion |
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5726 # |
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5727 # log1p(y) ~ y - y**2/2 + y**3/3 - ... - (-y)**T/T |
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5728 # |
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5729 # truncating at T such that y**T is small enough. The whole |
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5730 # computation is carried out in a form of fixed-point arithmetic, |
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5731 # with a real number z being represented by an integer |
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5732 # approximation to z*M. To avoid loss of precision, the y below |
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5733 # is actually an integer approximation to 2**R*y*M, where R is the |
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5734 # number of reductions performed so far. |
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5735 |
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5736 y = x-M |
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5737 # argument reduction; R = number of reductions performed |
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5738 R = 0 |
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5739 while (R <= L and abs(y) << L-R >= M or |
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5740 R > L and abs(y) >> R-L >= M): |
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5741 y = _div_nearest((M*y) << 1, |
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5742 M + _sqrt_nearest(M*(M+_rshift_nearest(y, R)), M)) |
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5743 R += 1 |
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5744 |
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5745 # Taylor series with T terms |
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5746 T = -int(-10*len(str(M))//(3*L)) |
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5747 yshift = _rshift_nearest(y, R) |
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5748 w = _div_nearest(M, T) |
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5749 for k in range(T-1, 0, -1): |
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5750 w = _div_nearest(M, k) - _div_nearest(yshift*w, M) |
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5751 |
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5752 return _div_nearest(w*y, M) |
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5753 |
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5754 def _dlog10(c, e, p): |
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5755 """Given integers c, e and p with c > 0, p >= 0, compute an integer |
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5756 approximation to 10**p * log10(c*10**e), with an absolute error of |
|
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5757 at most 1. Assumes that c*10**e is not exactly 1.""" |
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5758 |
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5759 # increase precision by 2; compensate for this by dividing |
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5760 # final result by 100 |
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5761 p += 2 |
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5762 |
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5763 # write c*10**e as d*10**f with either: |
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5764 # f >= 0 and 1 <= d <= 10, or |
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5765 # f <= 0 and 0.1 <= d <= 1. |
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5766 # Thus for c*10**e close to 1, f = 0 |
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5767 l = len(str(c)) |
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5768 f = e+l - (e+l >= 1) |
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5769 |
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5770 if p > 0: |
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5771 M = 10**p |
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5772 k = e+p-f |
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5773 if k >= 0: |
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5774 c *= 10**k |
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5775 else: |
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5776 c = _div_nearest(c, 10**-k) |
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5777 |
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5778 log_d = _ilog(c, M) # error < 5 + 22 = 27 |
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5779 log_10 = _log10_digits(p) # error < 1 |
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5780 log_d = _div_nearest(log_d*M, log_10) |
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5781 log_tenpower = f*M # exact |
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5782 else: |
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5783 log_d = 0 # error < 2.31 |
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48848
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5784 log_tenpower = _div_nearest(f, 10**-p) # error < 0.5 |
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43400
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5785 |
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5786 return _div_nearest(log_tenpower+log_d, 100) |
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5787 |
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5788 def _dlog(c, e, p): |
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5789 """Given integers c, e and p with c > 0, compute an integer |
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5790 approximation to 10**p * log(c*10**e), with an absolute error of |
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5791 at most 1. Assumes that c*10**e is not exactly 1.""" |
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5792 |
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5793 # Increase precision by 2. The precision increase is compensated |
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5794 # for at the end with a division by 100. |
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5795 p += 2 |
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5796 |
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5797 # rewrite c*10**e as d*10**f with either f >= 0 and 1 <= d <= 10, |
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5798 # or f <= 0 and 0.1 <= d <= 1. Then we can compute 10**p * log(c*10**e) |
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5799 # as 10**p * log(d) + 10**p*f * log(10). |
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5800 l = len(str(c)) |
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5801 f = e+l - (e+l >= 1) |
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5802 |
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5803 # compute approximation to 10**p*log(d), with error < 27 |
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5804 if p > 0: |
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5805 k = e+p-f |
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5806 if k >= 0: |
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5807 c *= 10**k |
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5808 else: |
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5809 c = _div_nearest(c, 10**-k) # error of <= 0.5 in c |
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5810 |
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5811 # _ilog magnifies existing error in c by a factor of at most 10 |
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5812 log_d = _ilog(c, 10**p) # error < 5 + 22 = 27 |
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5813 else: |
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5814 # p <= 0: just approximate the whole thing by 0; error < 2.31 |
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5815 log_d = 0 |
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5816 |
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5817 # compute approximation to f*10**p*log(10), with error < 11. |
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5818 if f: |
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5819 extra = len(str(abs(f)))-1 |
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5820 if p + extra >= 0: |
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5821 # error in f * _log10_digits(p+extra) < |f| * 1 = |f| |
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5822 # after division, error < |f|/10**extra + 0.5 < 10 + 0.5 < 11 |
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5823 f_log_ten = _div_nearest(f*_log10_digits(p+extra), 10**extra) |
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5824 else: |
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5825 f_log_ten = 0 |
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5826 else: |
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5827 f_log_ten = 0 |
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5828 |
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5829 # error in sum < 11+27 = 38; error after division < 0.38 + 0.5 < 1 |
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5830 return _div_nearest(f_log_ten + log_d, 100) |
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5831 |
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5832 class _Log10Memoize(object): |
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5833 """Class to compute, store, and allow retrieval of, digits of the |
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5834 constant log(10) = 2.302585.... This constant is needed by |
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5835 Decimal.ln, Decimal.log10, Decimal.exp and Decimal.__pow__.""" |
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5836 def __init__(self): |
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5837 self.digits = "23025850929940456840179914546843642076011014886" |
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5838 |
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5839 def getdigits(self, p): |
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5840 """Given an integer p >= 0, return floor(10**p)*log(10). |
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5841 |
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5842 For example, self.getdigits(3) returns 2302. |
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5843 """ |
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5844 # digits are stored as a string, for quick conversion to |
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5845 # integer in the case that we've already computed enough |
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5846 # digits; the stored digits should always be correct |
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5847 # (truncated, not rounded to nearest). |
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5848 if p < 0: |
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5849 raise ValueError("p should be nonnegative") |
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5850 |
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5851 if p >= len(self.digits): |
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5852 # compute p+3, p+6, p+9, ... digits; continue until at |
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5853 # least one of the extra digits is nonzero |
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5854 extra = 3 |
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5855 while True: |
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5856 # compute p+extra digits, correct to within 1ulp |
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5857 M = 10**(p+extra+2) |
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5858 digits = str(_div_nearest(_ilog(10*M, M), 100)) |
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5859 if digits[-extra:] != '0'*extra: |
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5860 break |
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5861 extra += 3 |
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5862 # keep all reliable digits so far; remove trailing zeros |
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5863 # and next nonzero digit |
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5864 self.digits = digits.rstrip('0')[:-1] |
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5865 return int(self.digits[:p+1]) |
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5866 |
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5867 _log10_digits = _Log10Memoize().getdigits |
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5868 |
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43400
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5869 def _iexp(x, M, L=8): |
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5870 """Given integers x and M, M > 0, such that x/M is small in absolute |
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5871 value, compute an integer approximation to M*exp(x/M). For 0 <= |
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5872 x/M <= 2.4, the absolute error in the result is bounded by 60 (and |
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5873 is usually much smaller).""" |
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5874 |
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5875 # Algorithm: to compute exp(z) for a real number z, first divide z |
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5876 # by a suitable power R of 2 so that |z/2**R| < 2**-L. Then |
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5877 # compute expm1(z/2**R) = exp(z/2**R) - 1 using the usual Taylor |
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5878 # series |
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5879 # |
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5880 # expm1(x) = x + x**2/2! + x**3/3! + ... |
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5881 # |
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5882 # Now use the identity |
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5883 # |
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5884 # expm1(2x) = expm1(x)*(expm1(x)+2) |
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5885 # |
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5886 # R times to compute the sequence expm1(z/2**R), |
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5887 # expm1(z/2**(R-1)), ... , exp(z/2), exp(z). |
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5888 |
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5889 # Find R such that x/2**R/M <= 2**-L |
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5890 R = _nbits((x<<L)//M) |
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5891 |
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5892 # Taylor series. (2**L)**T > M |
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5893 T = -int(-10*len(str(M))//(3*L)) |
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5894 y = _div_nearest(x, T) |
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5895 Mshift = M<<R |
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5896 for i in range(T-1, 0, -1): |
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5897 y = _div_nearest(x*(Mshift + y), Mshift * i) |
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5898 |
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5899 # Expansion |
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5900 for k in range(R-1, -1, -1): |
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5901 Mshift = M<<(k+2) |
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5902 y = _div_nearest(y*(y+Mshift), Mshift) |
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5903 |
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5904 return M+y |
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5905 |
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5906 def _dexp(c, e, p): |
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5907 """Compute an approximation to exp(c*10**e), with p decimal places of |
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5908 precision. |
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5909 |
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43734
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5910 Returns integers d, f such that: |
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5911 |
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5912 10**(p-1) <= d <= 10**p, and |
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5913 (d-1)*10**f < exp(c*10**e) < (d+1)*10**f |
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5914 |
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5915 In other words, d*10**f is an approximation to exp(c*10**e) with p |
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5916 digits of precision, and with an error in d of at most 1. This is |
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5917 almost, but not quite, the same as the error being < 1ulp: when d |
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5918 = 10**(p-1) the error could be up to 10 ulp.""" |
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5919 |
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5920 # we'll call iexp with M = 10**(p+2), giving p+3 digits of precision |
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5921 p += 2 |
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5922 |
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5923 # compute log(10) with extra precision = adjusted exponent of c*10**e |
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43400
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5924 extra = max(0, e + len(str(c)) - 1) |
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5925 q = p + extra |
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5926 |
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5927 # compute quotient c*10**e/(log(10)) = c*10**(e+q)/(log(10)*10**q), |
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5928 # rounding down |
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5929 shift = e+q |
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5930 if shift >= 0: |
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5931 cshift = c*10**shift |
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5932 else: |
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5933 cshift = c//10**-shift |
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5934 quot, rem = divmod(cshift, _log10_digits(q)) |
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5935 |
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5936 # reduce remainder back to original precision |
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5937 rem = _div_nearest(rem, 10**extra) |
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5938 |
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5939 # error in result of _iexp < 120; error after division < 0.62 |
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5940 return _div_nearest(_iexp(rem, 10**p), 1000), quot - p + 3 |
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5941 |
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5942 def _dpower(xc, xe, yc, ye, p): |
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5943 """Given integers xc, xe, yc and ye representing Decimals x = xc*10**xe and |
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5944 y = yc*10**ye, compute x**y. Returns a pair of integers (c, e) such that: |
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5945 |
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5946 10**(p-1) <= c <= 10**p, and |
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5947 (c-1)*10**e < x**y < (c+1)*10**e |
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5948 |
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5949 in other words, c*10**e is an approximation to x**y with p digits |
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5950 of precision, and with an error in c of at most 1. (This is |
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5951 almost, but not quite, the same as the error being < 1ulp: when c |
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5952 == 10**(p-1) we can only guarantee error < 10ulp.) |
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5953 |
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5954 We assume that: x is positive and not equal to 1, and y is nonzero. |
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5955 """ |
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5956 |
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5957 # Find b such that 10**(b-1) <= |y| <= 10**b |
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5958 b = len(str(abs(yc))) + ye |
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5959 |
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5960 # log(x) = lxc*10**(-p-b-1), to p+b+1 places after the decimal point |
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5961 lxc = _dlog(xc, xe, p+b+1) |
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5962 |
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5963 # compute product y*log(x) = yc*lxc*10**(-p-b-1+ye) = pc*10**(-p-1) |
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5964 shift = ye-b |
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5965 if shift >= 0: |
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5966 pc = lxc*yc*10**shift |
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5967 else: |
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5968 pc = _div_nearest(lxc*yc, 10**-shift) |
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5969 |
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5970 if pc == 0: |
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5971 # we prefer a result that isn't exactly 1; this makes it |
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5972 # easier to compute a correctly rounded result in __pow__ |
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5973 if ((len(str(xc)) + xe >= 1) == (yc > 0)): # if x**y > 1: |
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5974 coeff, exp = 10**(p-1)+1, 1-p |
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5975 else: |
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5976 coeff, exp = 10**p-1, -p |
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5977 else: |
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5978 coeff, exp = _dexp(pc, -(p+1), p+1) |
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5979 coeff = _div_nearest(coeff, 10) |
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5980 exp += 1 |
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5981 |
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5982 return coeff, exp |
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5983 |
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5984 def _log10_lb(c, correction = { |
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5985 '1': 100, '2': 70, '3': 53, '4': 40, '5': 31, |
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5986 '6': 23, '7': 16, '8': 10, '9': 5}): |
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5987 """Compute a lower bound for 100*log10(c) for a positive integer c.""" |
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5988 if c <= 0: |
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5989 raise ValueError("The argument to _log10_lb should be nonnegative.") |
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5990 str_c = str(c) |
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5991 return 100*len(str_c) - correction[str_c[0]] |
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5992 |
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5993 ##### Helper Functions #################################################### |
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5994 |
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5995 def _convert_other(other, raiseit=False, allow_float=False): |
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5996 """Convert other to Decimal. |
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5997 |
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5998 Verifies that it's ok to use in an implicit construction. |
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5999 If allow_float is true, allow conversion from float; this |
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6000 is used in the comparison methods (__eq__ and friends). |
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6001 |
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6002 """ |
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6003 if isinstance(other, Decimal): |
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6004 return other |
|
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|
6005 if isinstance(other, int): |
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6006 return Decimal(other) |
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6007 if allow_float and isinstance(other, float): |
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6008 return Decimal.from_float(other) |
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6009 |
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43400
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6010 if raiseit: |
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6011 raise TypeError("Unable to convert %s to Decimal" % other) |
|
34812
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6012 return NotImplemented |
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6013 |
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62241
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6014 def _convert_for_comparison(self, other, equality_op=False): |
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6015 """Given a Decimal instance self and a Python object other, return |
|
62244
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6016 a pair (s, o) of Decimal instances such that "s op o" is |
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6017 equivalent to "self op other" for any of the 6 comparison |
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6018 operators "op". |
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6019 |
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6020 """ |
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6021 if isinstance(other, Decimal): |
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6022 return self, other |
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6023 |
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6024 # Comparison with a Rational instance (also includes integers): |
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6025 # self op n/d <=> self*d op n (for n and d integers, d positive). |
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6026 # A NaN or infinity can be left unchanged without affecting the |
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6027 # comparison result. |
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6028 if isinstance(other, _numbers.Rational): |
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6029 if not self._is_special: |
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6030 self = _dec_from_triple(self._sign, |
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6031 str(int(self._int) * other.denominator), |
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6032 self._exp) |
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6033 return self, Decimal(other.numerator) |
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6034 |
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6035 # Comparisons with float and complex types. == and != comparisons |
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6036 # with complex numbers should succeed, returning either True or False |
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6037 # as appropriate. Other comparisons return NotImplemented. |
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6038 if equality_op and isinstance(other, _numbers.Complex) and other.imag == 0: |
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6039 other = other.real |
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6040 if isinstance(other, float): |
|
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|
6041 context = getcontext() |
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6042 if equality_op: |
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|
6043 context.flags[FloatOperation] = 1 |
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6044 else: |
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|
6045 context._raise_error(FloatOperation, |
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6046 "strict semantics for mixing floats and Decimals are enabled") |
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6047 return self, Decimal.from_float(other) |
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6048 return NotImplemented, NotImplemented |
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6051 ##### Setup Specific Contexts ############################################ |
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6053 # The default context prototype used by Context() |
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6054 # Is mutable, so that new contexts can have different default values |
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6055 |
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6056 DefaultContext = Context( |
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6057 prec=28, rounding=ROUND_HALF_EVEN, |
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6058 traps=[DivisionByZero, Overflow, InvalidOperation], |
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6059 flags=[], |
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6060 Emax=999999, |
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6061 Emin=-999999, |
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6062 capitals=1, |
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6063 clamp=0 |
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6064 ) |
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6065 |
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6066 # Pre-made alternate contexts offered by the specification |
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6067 # Don't change these; the user should be able to select these |
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6068 # contexts and be able to reproduce results from other implementations |
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6069 # of the spec. |
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6070 |
| 32482 | 6071 BasicContext = Context( |
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6072 prec=9, rounding=ROUND_HALF_UP, |
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6073 traps=[DivisionByZero, Overflow, InvalidOperation, Clamped, Underflow], |
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6074 flags=[], |
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6075 ) |
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| 32482 | 6077 ExtendedContext = Context( |
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6078 prec=9, rounding=ROUND_HALF_EVEN, |
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6079 traps=[], |
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6080 flags=[], |
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6081 ) |
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6082 |
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6084 ##### crud for parsing strings ############################################# |
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6085 # |
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6086 # Regular expression used for parsing numeric strings. Additional |
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6087 # comments: |
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6088 # |
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6089 # 1. Uncomment the two '\s*' lines to allow leading and/or trailing |
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6090 # whitespace. But note that the specification disallows whitespace in |
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6091 # a numeric string. |
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6092 # |
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6093 # 2. For finite numbers (not infinities and NaNs) the body of the |
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6094 # number between the optional sign and the optional exponent must have |
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6095 # at least one decimal digit, possibly after the decimal point. The |
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6096 # lookahead expression '(?=\d|\.\d)' checks this. |
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6097 |
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6098 import re |
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6099 _parser = re.compile(r""" # A numeric string consists of: |
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6100 # \s* |
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6101 (?P<sign>[-+])? # an optional sign, followed by either... |
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6102 ( |
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6103 (?=\d|\.\d) # ...a number (with at least one digit) |
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6104 (?P<int>\d*) # having a (possibly empty) integer part |
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6105 (\.(?P<frac>\d*))? # followed by an optional fractional part |
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6106 (E(?P<exp>[-+]?\d+))? # followed by an optional exponent, or... |
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6107 | |
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6108 Inf(inity)? # ...an infinity, or... |
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6109 | |
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6110 (?P<signal>s)? # ...an (optionally signaling) |
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6111 NaN # NaN |
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6112 (?P<diag>\d*) # with (possibly empty) diagnostic info. |
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6113 ) |
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6114 # \s* |
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6115 \Z |
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6116 """, re.VERBOSE | re.IGNORECASE).match |
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6118 _all_zeros = re.compile('0*$').match |
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6119 _exact_half = re.compile('50*$').match |
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6120 |
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6121 ##### PEP3101 support functions ############################################## |
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6122 # The functions in this section have little to do with the Decimal |
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6123 # class, and could potentially be reused or adapted for other pure |
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6124 # Python numeric classes that want to implement __format__ |
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6125 # |
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6126 # A format specifier for Decimal looks like: |
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6127 # |
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6128 # [[fill]align][sign][#][0][minimumwidth][,][.precision][type] |
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6129 |
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6130 _parse_format_specifier_regex = re.compile(r"""\A |
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6131 (?: |
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6132 (?P<fill>.)? |
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6133 (?P<align>[<>=^]) |
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6134 )? |
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6135 (?P<sign>[-+ ])? |
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6136 (?P<alt>\#)? |
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6137 (?P<zeropad>0)? |
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6138 (?P<minimumwidth>(?!0)\d+)? |
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6139 (?P<thousands_sep>,)? |
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6140 (?:\.(?P<precision>0|(?!0)\d+))? |
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6141 (?P<type>[eEfFgGn%])? |
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6142 \Z |
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6143 """, re.VERBOSE) |
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6145 del re |
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6147 # The locale module is only needed for the 'n' format specifier. The |
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6148 # rest of the PEP 3101 code functions quite happily without it, so we |
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6149 # don't care too much if locale isn't present. |
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6150 try: |
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6151 import locale as _locale |
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6152 except ImportError: |
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6153 pass |
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6154 |
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6155 def _parse_format_specifier(format_spec, _localeconv=None): |
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6156 """Parse and validate a format specifier. |
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6157 |
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6158 Turns a standard numeric format specifier into a dict, with the |
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6159 following entries: |
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6160 |
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6161 fill: fill character to pad field to minimum width |
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6162 align: alignment type, either '<', '>', '=' or '^' |
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6163 sign: either '+', '-' or ' ' |
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6164 minimumwidth: nonnegative integer giving minimum width |
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6165 zeropad: boolean, indicating whether to pad with zeros |
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6166 thousands_sep: string to use as thousands separator, or '' |
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6167 grouping: grouping for thousands separators, in format |
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6168 used by localeconv |
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6169 decimal_point: string to use for decimal point |
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6170 precision: nonnegative integer giving precision, or None |
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6171 type: one of the characters 'eEfFgG%', or None |
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6172 |
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6173 """ |
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6174 m = _parse_format_specifier_regex.match(format_spec) |
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6175 if m is None: |
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6176 raise ValueError("Invalid format specifier: " + format_spec) |
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6177 |
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6178 # get the dictionary |
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6179 format_dict = m.groupdict() |
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6180 |
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6181 # zeropad; defaults for fill and alignment. If zero padding |
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6182 # is requested, the fill and align fields should be absent. |
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6183 fill = format_dict['fill'] |
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6184 align = format_dict['align'] |
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6185 format_dict['zeropad'] = (format_dict['zeropad'] is not None) |
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6186 if format_dict['zeropad']: |
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6187 if fill is not None: |
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6188 raise ValueError("Fill character conflicts with '0'" |
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6189 " in format specifier: " + format_spec) |
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6190 if align is not None: |
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6191 raise ValueError("Alignment conflicts with '0' in " |
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6192 "format specifier: " + format_spec) |
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6193 format_dict['fill'] = fill or ' ' |
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6194 # PEP 3101 originally specified that the default alignment should |
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6195 # be left; it was later agreed that right-aligned makes more sense |
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6196 # for numeric types. See http://bugs.python.org/issue6857. |
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6197 format_dict['align'] = align or '>' |
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6198 |
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6199 # default sign handling: '-' for negative, '' for positive |
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6200 if format_dict['sign'] is None: |
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6201 format_dict['sign'] = '-' |
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6202 |
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6203 # minimumwidth defaults to 0; precision remains None if not given |
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6204 format_dict['minimumwidth'] = int(format_dict['minimumwidth'] or '0') |
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6205 if format_dict['precision'] is not None: |
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6206 format_dict['precision'] = int(format_dict['precision']) |
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6207 |
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6208 # if format type is 'g' or 'G' then a precision of 0 makes little |
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6209 # sense; convert it to 1. Same if format type is unspecified. |
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6210 if format_dict['precision'] == 0: |
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6211 if format_dict['type'] is None or format_dict['type'] in 'gGn': |
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6212 format_dict['precision'] = 1 |
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6213 |
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6214 # determine thousands separator, grouping, and decimal separator, and |
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6215 # add appropriate entries to format_dict |
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6216 if format_dict['type'] == 'n': |
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6217 # apart from separators, 'n' behaves just like 'g' |
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6218 format_dict['type'] = 'g' |
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6219 if _localeconv is None: |
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6220 _localeconv = _locale.localeconv() |
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6221 if format_dict['thousands_sep'] is not None: |
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6222 raise ValueError("Explicit thousands separator conflicts with " |
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6223 "'n' type in format specifier: " + format_spec) |
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6224 format_dict['thousands_sep'] = _localeconv['thousands_sep'] |
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6225 format_dict['grouping'] = _localeconv['grouping'] |
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6226 format_dict['decimal_point'] = _localeconv['decimal_point'] |
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6227 else: |
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6228 if format_dict['thousands_sep'] is None: |
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6229 format_dict['thousands_sep'] = '' |
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6230 format_dict['grouping'] = [3, 0] |
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6231 format_dict['decimal_point'] = '.' |
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6232 |
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6233 return format_dict |
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6234 |
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6235 def _format_align(sign, body, spec): |
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6236 """Given an unpadded, non-aligned numeric string 'body' and sign |
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6237 string 'sign', add padding and alignment conforming to the given |
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6238 format specifier dictionary 'spec' (as produced by |
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6239 parse_format_specifier). |
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6240 |
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6241 """ |
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6242 # how much extra space do we have to play with? |
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6243 minimumwidth = spec['minimumwidth'] |
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6244 fill = spec['fill'] |
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6245 padding = fill*(minimumwidth - len(sign) - len(body)) |
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6246 |
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6247 align = spec['align'] |
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6248 if align == '<': |
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6249 result = sign + body + padding |
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6250 elif align == '>': |
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6251 result = padding + sign + body |
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6252 elif align == '=': |
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6253 result = sign + padding + body |
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6254 elif align == '^': |
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6255 half = len(padding)//2 |
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6256 result = padding[:half] + sign + body + padding[half:] |
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6257 else: |
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6258 raise ValueError('Unrecognised alignment field') |
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6259 |
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6260 return result |
|
44025
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6261 |
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6262 def _group_lengths(grouping): |
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6263 """Convert a localeconv-style grouping into a (possibly infinite) |
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6264 iterable of integers representing group lengths. |
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6265 |
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6266 """ |
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6267 # The result from localeconv()['grouping'], and the input to this |
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6268 # function, should be a list of integers in one of the |
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6269 # following three forms: |
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6270 # |
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6271 # (1) an empty list, or |
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6272 # (2) nonempty list of positive integers + [0] |
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6273 # (3) list of positive integers + [locale.CHAR_MAX], or |
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6274 |
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6275 from itertools import chain, repeat |
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6276 if not grouping: |
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6277 return [] |
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6278 elif grouping[-1] == 0 and len(grouping) >= 2: |
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6279 return chain(grouping[:-1], repeat(grouping[-2])) |
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6280 elif grouping[-1] == _locale.CHAR_MAX: |
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6281 return grouping[:-1] |
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6282 else: |
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6283 raise ValueError('unrecognised format for grouping') |
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6284 |
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6285 def _insert_thousands_sep(digits, spec, min_width=1): |
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6286 """Insert thousands separators into a digit string. |
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6287 |
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6288 spec is a dictionary whose keys should include 'thousands_sep' and |
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6289 'grouping'; typically it's the result of parsing the format |
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6290 specifier using _parse_format_specifier. |
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6291 |
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6292 The min_width keyword argument gives the minimum length of the |
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6293 result, which will be padded on the left with zeros if necessary. |
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6294 |
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6295 If necessary, the zero padding adds an extra '0' on the left to |
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6296 avoid a leading thousands separator. For example, inserting |
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6297 commas every three digits in '123456', with min_width=8, gives |
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6298 '0,123,456', even though that has length 9. |
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6299 |
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6300 """ |
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6301 |
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|
6302 sep = spec['thousands_sep'] |
|
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|
6303 grouping = spec['grouping'] |
|
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|
6304 |
|
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|
6305 groups = [] |
|
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|
6306 for l in _group_lengths(grouping): |
|
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|
6307 if l <= 0: |
|
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|
6308 raise ValueError("group length should be positive") |
|
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|
6309 # max(..., 1) forces at least 1 digit to the left of a separator |
|
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|
6310 l = min(max(len(digits), min_width, 1), l) |
|
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|
6311 groups.append('0'*(l - len(digits)) + digits[-l:]) |
|
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|
6312 digits = digits[:-l] |
|
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|
6313 min_width -= l |
|
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|
6314 if not digits and min_width <= 0: |
|
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|
6315 break |
|
52201
fcdffd85a8bd
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|
6316 min_width -= len(sep) |
|
52196
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|
6317 else: |
|
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|
6318 l = max(len(digits), min_width, 1) |
|
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|
6319 groups.append('0'*(l - len(digits)) + digits[-l:]) |
|
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|
6320 return sep.join(reversed(groups)) |
|
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|
6321 |
|
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|
6322 def _format_sign(is_negative, spec): |
|
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|
6323 """Determine sign character.""" |
|
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|
6324 |
|
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|
6325 if is_negative: |
|
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|
6326 return '-' |
|
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|
6327 elif spec['sign'] in ' +': |
|
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|
6328 return spec['sign'] |
|
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|
6329 else: |
|
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|
6330 return '' |
|
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|
6331 |
|
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|
6332 def _format_number(is_negative, intpart, fracpart, exp, spec): |
|
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|
6333 """Format a number, given the following data: |
|
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|
6334 |
|
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|
6335 is_negative: true if the number is negative, else false |
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|
6336 intpart: string of digits that must appear before the decimal point |
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|
6337 fracpart: string of digits that must come after the point |
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|
6338 exp: exponent, as an integer |
|
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|
6339 spec: dictionary resulting from parsing the format specifier |
|
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|
6340 |
|
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|
6341 This function uses the information in spec to: |
|
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|
6342 insert separators (decimal separator and thousands separators) |
|
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|
6343 format the sign |
|
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|
6344 format the exponent |
|
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|
6345 add trailing '%' for the '%' type |
|
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|
6346 zero-pad if necessary |
|
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|
6347 fill and align if necessary |
|
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|
6348 """ |
|
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|
6349 |
|
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|
6350 sign = _format_sign(is_negative, spec) |
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|
6351 |
|
66444
eded691497b7
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.
Eric Smith <eric@trueblade.com>
parents:
66346
diff
changeset
|
6352 if fracpart or spec['alt']: |
|
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6353 fracpart = spec['decimal_point'] + fracpart |
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|
6354 |
|
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|
6355 if exp != 0 or spec['type'] in 'eE': |
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|
6356 echar = {'E': 'E', 'e': 'e', 'G': 'E', 'g': 'e'}[spec['type']] |
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|
6357 fracpart += "{0}{1:+}".format(echar, exp) |
|
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|
6358 if spec['type'] == '%': |
|
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|
6359 fracpart += '%' |
|
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|
6360 |
|
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|
6361 if spec['zeropad']: |
|
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|
6362 min_width = spec['minimumwidth'] - len(fracpart) - len(sign) |
|
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|
6363 else: |
|
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|
6364 min_width = 0 |
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|
6365 intpart = _insert_thousands_sep(intpart, spec, min_width) |
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|
6366 |
|
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|
6367 return _format_align(sign, intpart+fracpart, spec) |
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|
6368 |
|
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|
6369 |
|
41554
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|
6370 ##### Useful Constants (internal use only) ################################ |
|
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|
6371 |
|
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|
6372 # Reusable defaults |
|
50482
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|
6373 _Infinity = Decimal('Inf') |
|
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|
6374 _NegativeInfinity = Decimal('-Inf') |
|
50473
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|
6375 _NaN = Decimal('NaN') |
|
50482
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|
6376 _Zero = Decimal(0) |
|
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|
6377 _One = Decimal(1) |
|
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|
6378 _NegativeOne = Decimal(-1) |
|
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|
6379 |
|
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|
6380 # _SignedInfinity[sign] is infinity w/ that sign |
|
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|
6381 _SignedInfinity = (_Infinity, _NegativeInfinity) |
|
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d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
6382 |
|
61873
0bc8ffe6ba9a
Issue #8188: Introduce a new scheme for computing hashes of numbers
Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
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|
6383 # Constants related to the hash implementation; hash(x) is based |
|
0bc8ffe6ba9a
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Mark Dickinson <dickinsm@gmail.com>
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|
6384 # on the reduction of x modulo _PyHASH_MODULUS |
|
0bc8ffe6ba9a
Issue #8188: Introduce a new scheme for computing hashes of numbers
Mark Dickinson <dickinsm@gmail.com>
parents:
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|
6385 _PyHASH_MODULUS = sys.hash_info.modulus |
|
0bc8ffe6ba9a
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Mark Dickinson <dickinsm@gmail.com>
parents:
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|
6386 # hash values to use for positive and negative infinities, and nans |
|
0bc8ffe6ba9a
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Mark Dickinson <dickinsm@gmail.com>
parents:
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diff
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|
6387 _PyHASH_INF = sys.hash_info.inf |
|
0bc8ffe6ba9a
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Mark Dickinson <dickinsm@gmail.com>
parents:
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|
6388 _PyHASH_NAN = sys.hash_info.nan |
|
0bc8ffe6ba9a
Issue #8188: Introduce a new scheme for computing hashes of numbers
Mark Dickinson <dickinsm@gmail.com>
parents:
61864
diff
changeset
|
6389 |
|
0bc8ffe6ba9a
Issue #8188: Introduce a new scheme for computing hashes of numbers
Mark Dickinson <dickinsm@gmail.com>
parents:
61864
diff
changeset
|
6390 # _PyHASH_10INV is the inverse of 10 modulo the prime _PyHASH_MODULUS |
|
0bc8ffe6ba9a
Issue #8188: Introduce a new scheme for computing hashes of numbers
Mark Dickinson <dickinsm@gmail.com>
parents:
61864
diff
changeset
|
6391 _PyHASH_10INV = pow(10, _PyHASH_MODULUS - 2, _PyHASH_MODULUS) |
|
75850
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
73091
diff
changeset
|
6392 del sys |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
73091
diff
changeset
|
6393 |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
73091
diff
changeset
|
6394 try: |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6395 import _decimal |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6396 except ImportError: |
|
7355550d5357
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Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6397 pass |
|
7355550d5357
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Stefan Krah <skrah@bytereef.org>
parents:
73091
diff
changeset
|
6398 else: |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
73091
diff
changeset
|
6399 s1 = set(dir()) |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6400 s2 = set(dir(_decimal)) |
|
7355550d5357
Issue #7652: Integrate the decimal floating point libmpdec library to speed
Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6401 for name in s1 - s2: |
|
7355550d5357
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Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6402 del globals()[name] |
|
7355550d5357
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Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6403 del s1, s2, name |
|
7355550d5357
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Stefan Krah <skrah@bytereef.org>
parents:
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diff
changeset
|
6404 from _decimal import * |
|
32451
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
6405 |
|
d2c1c7ae7cf4
Move Decimal from the sandbox into production.
Raymond Hettinger <python@rcn.com>
parents:
diff
changeset
|
6406 if __name__ == '__main__': |
|
67843
9e65951266a2
Get command-line doctest of Lib/decimal.py to work again.
Raymond Hettinger <python@rcn.com>
parents:
66575
diff
changeset
|
6407 import doctest, decimal |
|
9e65951266a2
Get command-line doctest of Lib/decimal.py to work again.
Raymond Hettinger <python@rcn.com>
parents:
66575
diff
changeset
|
6408 doctest.testmod(decimal) |