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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 | # Copyright 2007 Google, Inc. All Rights Reserved. # Licensed to PSF under a Contributor Agreement. """Abstract Base Classes (ABCs) for numbers, according to PEP 3141. TODO: Fill out more detailed documentation on the operators.""" from abc import ABCMeta, abstractmethod __all__ = ["Number", "Complex", "Real", "Rational", "Integral"] class Number(metaclass=ABCMeta): """All numbers inherit from this class. If you just want to check if an argument x is a number, without caring what kind, use isinstance(x, Number). """ __slots__ = () # Concrete numeric types must provide their own hash implementation __hash__ = None ## Notes on Decimal ## ---------------- ## Decimal has all of the methods specified by the Real abc, but it should ## not be registered as a Real because decimals do not interoperate with ## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But, ## abstract reals are expected to interoperate (i.e. R1 + R2 should be ## expected to work if R1 and R2 are both Reals). class Complex(Number): """Complex defines the operations that work on the builtin complex type. In short, those are: a conversion to complex, .real, .imag, +, -, *, /, abs(), .conjugate, ==, and !=. If it is given heterogenous arguments, and doesn't have special knowledge about them, it should fall back to the builtin complex type as described below. """ __slots__ = () @abstractmethod def __complex__(self): """Return a builtin complex instance. Called for complex(self).""" def __bool__(self): """True if self != 0. Called for bool(self).""" return self != 0 @property @abstractmethod def real(self): """Retrieve the real component of this number. This should subclass Real. """ raise NotImplementedError @property @abstractmethod def imag(self): """Retrieve the imaginary component of this number. This should subclass Real. """ raise NotImplementedError @abstractmethod def __add__(self, other): """self + other""" raise NotImplementedError @abstractmethod def __radd__(self, other): """other + self""" raise NotImplementedError @abstractmethod def __neg__(self): """-self""" raise NotImplementedError @abstractmethod def __pos__(self): """+self""" raise NotImplementedError def __sub__(self, other): """self - other""" return self + -other def __rsub__(self, other): """other - self""" return -self + other @abstractmethod def __mul__(self, other): """self * other""" raise NotImplementedError @abstractmethod def __rmul__(self, other): """other * self""" raise NotImplementedError @abstractmethod def __truediv__(self, other): """self / other: Should promote to float when necessary.""" raise NotImplementedError @abstractmethod def __rtruediv__(self, other): """other / self""" raise NotImplementedError @abstractmethod def __pow__(self, exponent): """self**exponent; should promote to float or complex when necessary.""" raise NotImplementedError @abstractmethod def __rpow__(self, base): """base ** self""" raise NotImplementedError @abstractmethod def __abs__(self): """Returns the Real distance from 0. Called for abs(self).""" raise NotImplementedError @abstractmethod def conjugate(self): """(x+y*i).conjugate() returns (x-y*i).""" raise NotImplementedError @abstractmethod def __eq__(self, other): """self == other""" raise NotImplementedError Complex.register(complex) class Real(Complex): """To Complex, Real adds the operations that work on real numbers. In short, those are: a conversion to float, trunc(), divmod, %, <, <=, >, and >=. Real also provides defaults for the derived operations. """ __slots__ = () @abstractmethod def __float__(self): """Any Real can be converted to a native float object. Called for float(self).""" raise NotImplementedError @abstractmethod def __trunc__(self): """trunc(self): Truncates self to an Integral. Returns an Integral i such that: * i>0 iff self>0; * abs(i) <= abs(self); * for any Integral j satisfying the first two conditions, abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. i.e. "truncate towards 0". """ raise NotImplementedError @abstractmethod def __floor__(self): """Finds the greatest Integral <= self.""" raise NotImplementedError @abstractmethod def __ceil__(self): """Finds the least Integral >= self.""" raise NotImplementedError @abstractmethod def __round__(self, ndigits=None): """Rounds self to ndigits decimal places, defaulting to 0. If ndigits is omitted or None, returns an Integral, otherwise returns a Real. Rounds half toward even. """ raise NotImplementedError def __divmod__(self, other): """divmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. """ return (self // other, self % other) def __rdivmod__(self, other): """divmod(other, self): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. """ return (other // self, other % self) @abstractmethod def __floordiv__(self, other): """self // other: The floor() of self/other.""" raise NotImplementedError @abstractmethod def __rfloordiv__(self, other): """other // self: The floor() of other/self.""" raise NotImplementedError @abstractmethod def __mod__(self, other): """self % other""" raise NotImplementedError @abstractmethod def __rmod__(self, other): """other % self""" raise NotImplementedError @abstractmethod def __lt__(self, other): """self < other < on Reals defines a total ordering, except perhaps for NaN.""" raise NotImplementedError @abstractmethod def __le__(self, other): """self <= other""" raise NotImplementedError # Concrete implementations of Complex abstract methods. def __complex__(self): """complex(self) == complex(float(self), 0)""" return complex(float(self)) @property def real(self): """Real numbers are their real component.""" return +self @property def imag(self): """Real numbers have no imaginary component.""" return 0 def conjugate(self): """Conjugate is a no-op for Reals.""" return +self Real.register(float) class Rational(Real): """.numerator and .denominator should be in lowest terms.""" __slots__ = () @property @abstractmethod def numerator(self): raise NotImplementedError @property @abstractmethod def denominator(self): raise NotImplementedError # Concrete implementation of Real's conversion to float. def __float__(self): """float(self) = self.numerator / self.denominator It's important that this conversion use the integer's "true" division rather than casting one side to float before dividing so that ratios of huge integers convert without overflowing. """ return self.numerator / self.denominator class Integral(Rational): """Integral adds a conversion to int and the bit-string operations.""" __slots__ = () @abstractmethod def __int__(self): """int(self)""" raise NotImplementedError def __index__(self): """Called whenever an index is needed, such as in slicing""" return int(self) @abstractmethod def __pow__(self, exponent, modulus=None): """self ** exponent % modulus, but maybe faster. Accept the modulus argument if you want to support the 3-argument version of pow(). Raise a TypeError if exponent < 0 or any argument isn't Integral. Otherwise, just implement the 2-argument version described in Complex. """ raise NotImplementedError @abstractmethod def __lshift__(self, other): """self << other""" raise NotImplementedError @abstractmethod def __rlshift__(self, other): """other << self""" raise NotImplementedError @abstractmethod def __rshift__(self, other): """self >> other""" raise NotImplementedError @abstractmethod def __rrshift__(self, other): """other >> self""" raise NotImplementedError @abstractmethod def __and__(self, other): """self & other""" raise NotImplementedError @abstractmethod def __rand__(self, other): """other & self""" raise NotImplementedError @abstractmethod def __xor__(self, other): """self ^ other""" raise NotImplementedError @abstractmethod def __rxor__(self, other): """other ^ self""" raise NotImplementedError @abstractmethod def __or__(self, other): """self | other""" raise NotImplementedError @abstractmethod def __ror__(self, other): """other | self""" raise NotImplementedError @abstractmethod def __invert__(self): """~self""" raise NotImplementedError # Concrete implementations of Rational and Real abstract methods. def __float__(self): """float(self) == float(int(self))""" return float(int(self)) @property def numerator(self): """Integers are their own numerators.""" return +self @property def denominator(self): """Integers have a denominator of 1.""" return 1 Integral.register(int)