Backport PEP 3141 from the py3k branch to the trunk. This includes r50877 (just

the complex_pow part), r56649, r56652, r56715, r57296, r57302, r57359, r57361,
r57372, r57738, r57739, r58017, r58039, r58040, and r59390, and new
documentation. The only significant difference is that round(x) returns a float
to preserve backward-compatibility. See http://bugs.python.org/issue1689.

1 files changed, 393 insertions, 0 deletions

diff --git a/Lib/numbers.py b/Lib/numbers.py
new file mode 100644
index 0000000..d23fa34
--- /dev/null
+++ b/Lib/numbers.py
@@ -0,0 +1,393 @@
+# 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, abstractproperty
+
+__all__ = ["Number", "Exact", "Inexact",
+           "Complex", "Real", "Rational", "Integral",
+           ]
+
+
+class Number(object):
+    """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).
+    """
+    __metaclass__ = ABCMeta
+
+
+class Exact(Number):
+    """Operations on instances of this type are exact.
+
+    As long as the result of a homogenous operation is of the same
+    type, you can assume that it was computed exactly, and there are
+    no round-off errors. Laws like commutativity and associativity
+    hold.
+    """
+
+Exact.register(int)
+Exact.register(long)
+
+
+class Inexact(Number):
+    """Operations on instances of this type are inexact.
+
+    Given X, an instance of Inexact, it is possible that (X + -X) + 3
+    == 3, but X + (-X + 3) == 0. The exact form this error takes will
+    vary by type, but it's generally unsafe to compare this type for
+    equality.
+    """
+
+Inexact.register(complex)
+Inexact.register(float)
+# Inexact.register(decimal.Decimal)
+
+
+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.
+    """
+
+    @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
+
+    @abstractproperty
+    def real(self):
+        """Retrieve the real component of this number.
+
+        This should subclass Real.
+        """
+        raise NotImplementedError
+
+    @abstractproperty
+    def imag(self):
+        """Retrieve the real 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
+
+    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 __div__(self, other):
+        """self / other; should promote to float or complex when necessary."""
+        raise NotImplementedError
+
+    @abstractmethod
+    def __rdiv__(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
+
+    # __ne__ is inherited from object and negates whatever __eq__ does.
+
+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.
+    """
+
+    @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)
+# Real.register(decimal.Decimal)
+
+
+class Rational(Real, Exact):
+    """.numerator and .denominator should be in lowest terms."""
+
+    @abstractproperty
+    def numerator(self):
+        raise NotImplementedError
+
+    @abstractproperty
+    def denominator(self):
+        raise NotImplementedError
+
+    # Concrete implementation of Real's conversion to float.
+    def __float__(self):
+        """float(self) = self.numerator / self.denominator"""
+        return self.numerator / self.denominator
+
+
+class Integral(Rational):
+    """Integral adds a conversion to long and the bit-string operations."""
+
+    @abstractmethod
+    def __long__(self):
+        """long(self)"""
+        raise NotImplementedError
+
+    def __index__(self):
+        """index(self)"""
+        return long(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(long(self))"""
+        return float(long(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)
+Integral.register(long)