Mercurial > cpython-lru_cache-weakref

annotate Lib/numbers.py @ 78069:a8aa77458e12 3.2

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Add c_size_t and c_ssize_t to the ctypes summary table.
author Antoine Pitrou <solipsis@pitrou.net>
date Thu, 12 Jul 2012 20:31:50 +0200
parents 65e5b68b24b1
children e979b26a9172
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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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7
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8 from abc import ABCMeta, abstractmethod, abstractproperty
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10 __all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
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11
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12 class Number(metaclass=ABCMeta):
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13 """All numbers inherit from this class.
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14
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15 If you just want to check if an argument x is a number, without
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16 caring what kind, use isinstance(x, Number).
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17 """
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18 __slots__ = ()
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20 # Concrete numeric types must provide their own hash implementation
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21 __hash__ = None
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24 ## Notes on Decimal
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25 ## ----------------
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26 ## Decimal has all of the methods specified by the Real abc, but it should
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27 ## not be registered as a Real because decimals do not interoperate with
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28 ## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But,
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29 ## abstract reals are expected to interoperate (i.e. R1 + R2 should be
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30 ## expected to work if R1 and R2 are both Reals).
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32 class Complex(Number):
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33 """Complex defines the operations that work on the builtin complex type.
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34
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35 In short, those are: a conversion to complex, .real, .imag, +, -,
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36 *, /, abs(), .conjugate, ==, and !=.
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37
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38 If it is given heterogenous arguments, and doesn't have special
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39 knowledge about them, it should fall back to the builtin complex
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40 type as described below.
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41 """
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42
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43 __slots__ = ()
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44
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45 @abstractmethod
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46 def __complex__(self):
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47 """Return a builtin complex instance. Called for complex(self)."""
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48
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49 def __bool__(self):
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50 """True if self != 0. Called for bool(self)."""
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51 return self != 0
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52
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53 @abstractproperty
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54 def real(self):
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55 """Retrieve the real component of this number.
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56
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57 This should subclass Real.
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58 """
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59 raise NotImplementedError
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60
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61 @abstractproperty
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62 def imag(self):
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63 """Retrieve the imaginary component of this number.
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64
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65 This should subclass Real.
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66 """
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67 raise NotImplementedError
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68
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69 @abstractmethod
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70 def __add__(self, other):
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71 """self + other"""
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72 raise NotImplementedError
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73
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74 @abstractmethod
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75 def __radd__(self, other):
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76 """other + self"""
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77 raise NotImplementedError
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78
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79 @abstractmethod
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80 def __neg__(self):
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81 """-self"""
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82 raise NotImplementedError
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83
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84 @abstractmethod
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85 def __pos__(self):
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86 """+self"""
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87 raise NotImplementedError
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88
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89 def __sub__(self, other):
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90 """self - other"""
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91 return self + -other
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92
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93 def __rsub__(self, other):
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94 """other - self"""
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95 return -self + other
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96
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97 @abstractmethod
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98 def __mul__(self, other):
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99 """self * other"""
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100 raise NotImplementedError
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101
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102 @abstractmethod
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103 def __rmul__(self, other):
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104 """other * self"""
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105 raise NotImplementedError
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106
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107 @abstractmethod
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108 def __truediv__(self, other):
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109 """self / other: Should promote to float when necessary."""
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110 raise NotImplementedError
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111
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112 @abstractmethod
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113 def __rtruediv__(self, other):
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114 """other / self"""
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115 raise NotImplementedError
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116
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117 @abstractmethod
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118 def __pow__(self, exponent):
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119 """self**exponent; should promote to float or complex when necessary."""
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120 raise NotImplementedError
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121
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122 @abstractmethod
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123 def __rpow__(self, base):
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124 """base ** self"""
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125 raise NotImplementedError
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126
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127 @abstractmethod
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128 def __abs__(self):
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129 """Returns the Real distance from 0. Called for abs(self)."""
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130 raise NotImplementedError
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131
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132 @abstractmethod
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133 def conjugate(self):
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134 """(x+y*i).conjugate() returns (x-y*i)."""
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135 raise NotImplementedError
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136
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137 @abstractmethod
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138 def __eq__(self, other):
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139 """self == other"""
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140 raise NotImplementedError
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141
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142 def __ne__(self, other):
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143 """self != other"""
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144 # The default __ne__ doesn't negate __eq__ until 3.0.
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145 return not (self == other)
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146
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147 Complex.register(complex)
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148
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149
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150 class Real(Complex):
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151 """To Complex, Real adds the operations that work on real numbers.
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152
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153 In short, those are: a conversion to float, trunc(), divmod,
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154 %, <, <=, >, and >=.
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155
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156 Real also provides defaults for the derived operations.
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157 """
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158
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159 __slots__ = ()
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160
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161 @abstractmethod
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162 def __float__(self):
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163 """Any Real can be converted to a native float object.
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164
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165 Called for float(self)."""
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166 raise NotImplementedError
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167
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168 @abstractmethod
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169 def __trunc__(self):
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170 """trunc(self): Truncates self to an Integral.
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171
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172 Returns an Integral i such that:
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173 * i>0 iff self>0;
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174 * abs(i) <= abs(self);
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175 * for any Integral j satisfying the first two conditions,
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176 abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
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177 i.e. "truncate towards 0".
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178 """
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179 raise NotImplementedError
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180
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181 @abstractmethod
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182 def __floor__(self):
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183 """Finds the greatest Integral <= self."""
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184 raise NotImplementedError
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185
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186 @abstractmethod
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187 def __ceil__(self):
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188 """Finds the least Integral >= self."""
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189 raise NotImplementedError
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190
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191 @abstractmethod
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192 def __round__(self, ndigits=None):
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193 """Rounds self to ndigits decimal places, defaulting to 0.
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194
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195 If ndigits is omitted or None, returns an Integral, otherwise
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196 returns a Real. Rounds half toward even.
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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 int 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 __int__(self):
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302 """int(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 """Called whenever an index is needed, such as in slicing"""
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307 return int(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(int(self))"""
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378 return float(int(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)