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369 lines
9.2 KiB
Python
369 lines
9.2 KiB
Python
# Copyright 2007 Google, Inc. All Rights Reserved.
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# Licensed to PSF under a Contributor Agreement.
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"""Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
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TODO: Fill out more detailed documentation on the operators."""
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from abc import ABCMeta, abstractmethod, abstractproperty
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__all__ = ["Number", "Exact", "Inexact",
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"Complex", "Real", "Rational", "Integral",
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]
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class Number(metaclass=ABCMeta):
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"""All numbers inherit from this class.
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If you just want to check if an argument x is a number, without
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caring what kind, use isinstance(x, Number).
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"""
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class Exact(Number):
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"""Operations on instances of this type are exact.
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As long as the result of a homogenous operation is of the same
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type, you can assume that it was computed exactly, and there are
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no round-off errors. Laws like commutativity and associativity
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hold.
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"""
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Exact.register(int)
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class Inexact(Number):
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"""Operations on instances of this type are inexact.
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Given X, an instance of Inexact, it is possible that (X + -X) + 3
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== 3, but X + (-X + 3) == 0. The exact form this error takes will
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vary by type, but it's generally unsafe to compare this type for
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equality.
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"""
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Inexact.register(complex)
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Inexact.register(float)
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class Complex(Number):
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"""Complex defines the operations that work on the builtin complex type.
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In short, those are: a conversion to complex, .real, .imag, +, -,
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*, /, abs(), .conjugate, ==, and !=.
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If it is given heterogenous arguments, and doesn't have special
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knowledge about them, it should fall back to the builtin complex
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type as described below.
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"""
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@abstractmethod
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def __complex__(self):
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"""Return a builtin complex instance. Called for complex(self)."""
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def __bool__(self):
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"""True if self != 0. Called for bool(self)."""
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return self != 0
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@abstractproperty
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def real(self):
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"""Retrieve the real component of this number.
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This should subclass Real.
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"""
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raise NotImplementedError
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@abstractproperty
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def imag(self):
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"""Retrieve the real component of this number.
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This should subclass Real.
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"""
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raise NotImplementedError
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@abstractmethod
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def __add__(self, other):
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"""self + other"""
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raise NotImplementedError
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@abstractmethod
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def __radd__(self, other):
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"""other + self"""
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raise NotImplementedError
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@abstractmethod
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def __neg__(self):
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"""-self"""
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raise NotImplementedError
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def __pos__(self):
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"""+self"""
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return self
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def __sub__(self, other):
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"""self - other"""
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return self + -other
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def __rsub__(self, other):
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"""other - self"""
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return -self + other
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@abstractmethod
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def __mul__(self, other):
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"""self * other"""
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raise NotImplementedError
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@abstractmethod
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def __rmul__(self, other):
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"""other * self"""
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raise NotImplementedError
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@abstractmethod
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def __div__(self, other):
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"""self / other"""
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raise NotImplementedError
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@abstractmethod
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def __rdiv__(self, other):
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"""other / self"""
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raise NotImplementedError
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@abstractmethod
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def __pow__(self, exponent):
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"""Like division, self**exponent should promote to complex when necessary."""
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raise NotImplementedError
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@abstractmethod
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def __rpow__(self, base):
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"""base ** self"""
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raise NotImplementedError
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@abstractmethod
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def __abs__(self):
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"""Returns the Real distance from 0. Called for abs(self)."""
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raise NotImplementedError
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@abstractmethod
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def conjugate(self):
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"""(x+y*i).conjugate() returns (x-y*i)."""
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raise NotImplementedError
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@abstractmethod
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def __eq__(self, other):
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"""self == other"""
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raise NotImplementedError
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def __ne__(self, other):
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"""self != other"""
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return not (self == other)
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Complex.register(complex)
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class Real(Complex):
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"""To Complex, Real adds the operations that work on real numbers.
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In short, those are: a conversion to float, trunc(), divmod,
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%, <, <=, >, and >=.
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Real also provides defaults for the derived operations.
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"""
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@abstractmethod
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def __float__(self):
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"""Any Real can be converted to a native float object.
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Called for float(self)."""
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raise NotImplementedError
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@abstractmethod
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def __trunc__(self):
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"""trunc(self): Truncates self to an Integral.
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Returns an Integral i such that:
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* i>0 iff self>0
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* abs(i) <= abs(self).
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"""
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raise NotImplementedError
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def __divmod__(self, other):
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"""divmod(self, other): The pair (self // other, self % other).
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Sometimes this can be computed faster than the pair of
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operations.
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"""
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return (self // other, self % other)
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def __rdivmod__(self, other):
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"""divmod(other, self): The pair (self // other, self % other).
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Sometimes this can be computed faster than the pair of
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operations.
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"""
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return (other // self, other % self)
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@abstractmethod
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def __floordiv__(self, other):
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"""self // other: The floor() of self/other."""
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raise NotImplementedError
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@abstractmethod
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def __rfloordiv__(self, other):
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"""other // self: The floor() of other/self."""
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raise NotImplementedError
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@abstractmethod
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def __mod__(self, other):
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"""self % other"""
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raise NotImplementedError
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@abstractmethod
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def __rmod__(self, other):
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"""other % self"""
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raise NotImplementedError
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@abstractmethod
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def __lt__(self, other):
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"""self < other
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< on Reals defines a total ordering, except perhaps for NaN."""
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raise NotImplementedError
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@abstractmethod
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def __le__(self, other):
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"""self <= other"""
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raise NotImplementedError
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# Concrete implementations of Complex abstract methods.
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def __complex__(self):
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"""complex(self) == complex(float(self), 0)"""
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return complex(float(self))
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@property
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def real(self):
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"""Real numbers are their real component."""
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return self
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@property
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def imag(self):
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"""Real numbers have no imaginary component."""
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return 0
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def conjugate(self):
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"""Conjugate is a no-op for Reals."""
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return self
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Real.register(float)
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class Rational(Real, Exact):
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""".numerator and .denominator should be in lowest terms."""
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@abstractproperty
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def numerator(self):
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raise NotImplementedError
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@abstractproperty
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def denominator(self):
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raise NotImplementedError
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# Concrete implementation of Real's conversion to float.
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def __float__(self):
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"""float(self) = self.numerator / self.denominator"""
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return self.numerator / self.denominator
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class Integral(Rational):
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"""Integral adds a conversion to int and the bit-string operations."""
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@abstractmethod
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def __int__(self):
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"""int(self)"""
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raise NotImplementedError
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def __index__(self):
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"""index(self)"""
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return int(self)
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@abstractmethod
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def __pow__(self, exponent, modulus=None):
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"""self ** exponent % modulus, but maybe faster.
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Accept the modulus argument if you want to support the
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3-argument version of pow(). Raise a TypeError if exponent < 0
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or any argument isn't Integral. Otherwise, just implement the
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2-argument version described in Complex.
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"""
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raise NotImplementedError
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@abstractmethod
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def __lshift__(self, other):
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"""self << other"""
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raise NotImplementedError
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@abstractmethod
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def __rlshift__(self, other):
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"""other << self"""
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raise NotImplementedError
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@abstractmethod
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def __rshift__(self, other):
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"""self >> other"""
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raise NotImplementedError
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@abstractmethod
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def __rrshift__(self, other):
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"""other >> self"""
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raise NotImplementedError
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@abstractmethod
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def __and__(self, other):
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"""self & other"""
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raise NotImplementedError
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@abstractmethod
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def __rand__(self, other):
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"""other & self"""
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raise NotImplementedError
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@abstractmethod
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def __xor__(self, other):
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"""self ^ other"""
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raise NotImplementedError
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@abstractmethod
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def __rxor__(self, other):
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"""other ^ self"""
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raise NotImplementedError
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@abstractmethod
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def __or__(self, other):
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"""self | other"""
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raise NotImplementedError
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@abstractmethod
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def __ror__(self, other):
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"""other | self"""
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raise NotImplementedError
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@abstractmethod
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def __invert__(self):
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"""~self"""
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raise NotImplementedError
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# Concrete implementations of Rational and Real abstract methods.
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def __float__(self):
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"""float(self) == float(int(self))"""
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return float(int(self))
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@property
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def numerator(self):
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"""Integers are their own numerators."""
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return self
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@property
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def denominator(self):
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"""Integers have a denominator of 1."""
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return 1
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Integral.register(int)
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