Mercurial > cpython-lru_cache-weakref

annotate Lib/numbers.py @ 58925:eecf1bef052d 2.6

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Merged revisions 78207 via svnmerge from svn+ssh://pythondev@svn.python.org/python/trunk ........ r78207 | ezio.melotti | 2010-02-17 01:26:09 +0200 (Wed, 17 Feb 2010) | 1 line #7930: fix stripid ........
author Ezio Melotti <ezio.melotti@gmail.com>
date Tue, 16 Feb 2010 23:29:44 +0000
parents 31645ead4c35
children 5c082f197ddf
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1 # Copyright 2007 Google, Inc. All Rights Reserved.
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2 # Licensed to PSF under a Contributor Agreement.
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3
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4 """Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
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5
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6 TODO: Fill out more detailed documentation on the operators."""
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8 from __future__ import division
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9 from abc import ABCMeta, abstractmethod, abstractproperty
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10
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11 __all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
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12
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13 class Number(object):
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14 """All numbers inherit from this class.
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15
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16 If you just want to check if an argument x is a number, without
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17 caring what kind, use isinstance(x, Number).
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18 """
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19 __metaclass__ = ABCMeta
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20 __slots__ = ()
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21
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22 # Concrete numeric types must provide their own hash implementation
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23 __hash__ = None
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25
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26 ## Notes on Decimal
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27 ## ----------------
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28 ## Decimal has all of the methods specified by the Real abc, but it should
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29 ## not be registered as a Real because decimals do not interoperate with
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30 ## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But,
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31 ## abstract reals are expected to interoperate (i.e. R1 + R2 should be
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32 ## expected to work if R1 and R2 are both Reals).
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34 class Complex(Number):
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35 """Complex defines the operations that work on the builtin complex type.
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36
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37 In short, those are: a conversion to complex, .real, .imag, +, -,
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38 *, /, abs(), .conjugate, ==, and !=.
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39
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40 If it is given heterogenous arguments, and doesn't have special
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41 knowledge about them, it should fall back to the builtin complex
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42 type as described below.
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43 """
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44
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45 __slots__ = ()
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47 @abstractmethod
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48 def __complex__(self):
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49 """Return a builtin complex instance. Called for complex(self)."""
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51 # Will be __bool__ in 3.0.
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52 def __nonzero__(self):
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53 """True if self != 0. Called for bool(self)."""
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54 return self != 0
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55
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56 @abstractproperty
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57 def real(self):
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58 """Retrieve the real component of this number.
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59
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60 This should subclass Real.
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61 """
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62 raise NotImplementedError
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63
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64 @abstractproperty
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65 def imag(self):
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66 """Retrieve the real component of this number.
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67
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68 This should subclass Real.
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69 """
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70 raise NotImplementedError
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71
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72 @abstractmethod
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73 def __add__(self, other):
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74 """self + other"""
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75 raise NotImplementedError
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76
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77 @abstractmethod
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78 def __radd__(self, other):
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79 """other + self"""
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80 raise NotImplementedError
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81
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82 @abstractmethod
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83 def __neg__(self):
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84 """-self"""
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85 raise NotImplementedError
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86
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87 @abstractmethod
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88 def __pos__(self):
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89 """+self"""
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90 raise NotImplementedError
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91
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92 def __sub__(self, other):
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93 """self - other"""
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94 return self + -other
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95
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96 def __rsub__(self, other):
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97 """other - self"""
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98 return -self + other
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99
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100 @abstractmethod
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101 def __mul__(self, other):
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102 """self * other"""
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103 raise NotImplementedError
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104
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105 @abstractmethod
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106 def __rmul__(self, other):
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107 """other * self"""
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108 raise NotImplementedError
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109
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110 @abstractmethod
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111 def __div__(self, other):
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112 """self / other without __future__ division
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113
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114 May promote to float.
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115 """
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116 raise NotImplementedError
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117
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118 @abstractmethod
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119 def __rdiv__(self, other):
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120 """other / self without __future__ division"""
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121 raise NotImplementedError
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122
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123 @abstractmethod
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124 def __truediv__(self, other):
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125 """self / other with __future__ division.
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126
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127 Should promote to float when necessary.
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128 """
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129 raise NotImplementedError
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130
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131 @abstractmethod
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132 def __rtruediv__(self, other):
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133 """other / self with __future__ division"""
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134 raise NotImplementedError
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135
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136 @abstractmethod
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137 def __pow__(self, exponent):
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138 """self**exponent; should promote to float or complex when necessary."""
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139 raise NotImplementedError
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140
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141 @abstractmethod
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142 def __rpow__(self, base):
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143 """base ** self"""
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144 raise NotImplementedError
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145
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146 @abstractmethod
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147 def __abs__(self):
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148 """Returns the Real distance from 0. Called for abs(self)."""
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149 raise NotImplementedError
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150
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151 @abstractmethod
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152 def conjugate(self):
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153 """(x+y*i).conjugate() returns (x-y*i)."""
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154 raise NotImplementedError
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155
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156 @abstractmethod
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157 def __eq__(self, other):
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158 """self == other"""
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159 raise NotImplementedError
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160
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161 def __ne__(self, other):
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162 """self != other"""
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163 # The default __ne__ doesn't negate __eq__ until 3.0.
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164 return not (self == other)
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165
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166 Complex.register(complex)
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167
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168
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169 class Real(Complex):
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170 """To Complex, Real adds the operations that work on real numbers.
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171
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172 In short, those are: a conversion to float, trunc(), divmod,
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173 %, <, <=, >, and >=.
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174
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175 Real also provides defaults for the derived operations.
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176 """
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177
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178 __slots__ = ()
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179
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180 @abstractmethod
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181 def __float__(self):
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182 """Any Real can be converted to a native float object.
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183
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184 Called for float(self)."""
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185 raise NotImplementedError
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186
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187 @abstractmethod
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188 def __trunc__(self):
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189 """trunc(self): Truncates self to an Integral.
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190
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191 Returns an Integral i such that:
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192 * i>0 iff self>0;
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193 * abs(i) <= abs(self);
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194 * for any Integral j satisfying the first two conditions,
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195 abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
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196 i.e. "truncate towards 0".
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197 """
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198 raise NotImplementedError
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199
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200 def __divmod__(self, other):
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201 """divmod(self, other): The pair (self // other, self % other).
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202
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203 Sometimes this can be computed faster than the pair of
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204 operations.
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205 """
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206 return (self // other, self % other)
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207
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208 def __rdivmod__(self, other):
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209 """divmod(other, self): The pair (self // other, self % other).
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210
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211 Sometimes this can be computed faster than the pair of
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212 operations.
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213 """
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214 return (other // self, other % self)
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215
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216 @abstractmethod
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217 def __floordiv__(self, other):
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218 """self // other: The floor() of self/other."""
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219 raise NotImplementedError
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220
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221 @abstractmethod
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222 def __rfloordiv__(self, other):
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223 """other // self: The floor() of other/self."""
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224 raise NotImplementedError
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225
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226 @abstractmethod
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227 def __mod__(self, other):
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228 """self % other"""
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229 raise NotImplementedError
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230
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231 @abstractmethod
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232 def __rmod__(self, other):
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233 """other % self"""
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234 raise NotImplementedError
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235
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236 @abstractmethod
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237 def __lt__(self, other):
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238 """self < other
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239
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240 < on Reals defines a total ordering, except perhaps for NaN."""
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241 raise NotImplementedError
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242
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243 @abstractmethod
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244 def __le__(self, other):
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245 """self <= other"""
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246 raise NotImplementedError
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247
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248 # Concrete implementations of Complex abstract methods.
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249 def __complex__(self):
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250 """complex(self) == complex(float(self), 0)"""
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251 return complex(float(self))
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252
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253 @property
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254 def real(self):
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255 """Real numbers are their real component."""
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256 return +self
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257
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258 @property
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259 def imag(self):
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260 """Real numbers have no imaginary component."""
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261 return 0
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262
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263 def conjugate(self):
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264 """Conjugate is a no-op for Reals."""
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265 return +self
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266
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267 Real.register(float)
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268
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269
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270 class Rational(Real):
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271 """.numerator and .denominator should be in lowest terms."""
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272
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273 __slots__ = ()
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274
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275 @abstractproperty
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276 def numerator(self):
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277 raise NotImplementedError
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278
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279 @abstractproperty
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280 def denominator(self):
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281 raise NotImplementedError
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282
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283 # Concrete implementation of Real's conversion to float.
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284 def __float__(self):
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285 """float(self) = self.numerator / self.denominator
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286
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287 It's important that this conversion use the integer's "true"
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288 division rather than casting one side to float before dividing
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289 so that ratios of huge integers convert without overflowing.
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290
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291 """
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292 return self.numerator / self.denominator
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293
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294
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295 class Integral(Rational):
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296 """Integral adds a conversion to long and the bit-string operations."""
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297
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298 __slots__ = ()
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299
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300 @abstractmethod
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301 def __long__(self):
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302 """long(self)"""
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303 raise NotImplementedError
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304
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305 def __index__(self):
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306 """index(self)"""
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307 return long(self)
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308
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309 @abstractmethod
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310 def __pow__(self, exponent, modulus=None):
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311 """self ** exponent % modulus, but maybe faster.
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312
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313 Accept the modulus argument if you want to support the
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314 3-argument version of pow(). Raise a TypeError if exponent < 0
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315 or any argument isn't Integral. Otherwise, just implement the
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316 2-argument version described in Complex.
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317 """
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318 raise NotImplementedError
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319
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320 @abstractmethod
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321 def __lshift__(self, other):
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322 """self << other"""
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323 raise NotImplementedError
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324
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325 @abstractmethod
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326 def __rlshift__(self, other):
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327 """other << self"""
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328 raise NotImplementedError
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329
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330 @abstractmethod
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331 def __rshift__(self, other):
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332 """self >> other"""
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333 raise NotImplementedError
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334
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335 @abstractmethod
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336 def __rrshift__(self, other):
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337 """other >> self"""
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338 raise NotImplementedError
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339
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340 @abstractmethod
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341 def __and__(self, other):
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342 """self & other"""
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343 raise NotImplementedError
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344
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345 @abstractmethod
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346 def __rand__(self, other):
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347 """other & self"""
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348 raise NotImplementedError
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349
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350 @abstractmethod
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351 def __xor__(self, other):
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352 """self ^ other"""
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353 raise NotImplementedError
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354
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355 @abstractmethod
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356 def __rxor__(self, other):
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357 """other ^ self"""
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358 raise NotImplementedError
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359
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360 @abstractmethod
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361 def __or__(self, other):
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362 """self | other"""
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363 raise NotImplementedError
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364
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365 @abstractmethod
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366 def __ror__(self, other):
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367 """other | self"""
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368 raise NotImplementedError
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369
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370 @abstractmethod
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371 def __invert__(self):
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372 """~self"""
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373 raise NotImplementedError
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374
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375 # Concrete implementations of Rational and Real abstract methods.
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376 def __float__(self):
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377 """float(self) == float(long(self))"""
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378 return float(long(self))
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379
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380 @property
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381 def numerator(self):
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382 """Integers are their own numerators."""
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383 return +self
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384
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385 @property
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386 def denominator(self):
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387 """Integers have a denominator of 1."""
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388 return 1
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389
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390 Integral.register(int)
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391 Integral.register(long)