# 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 __future__ import division

from abc import ABCMeta, abstractmethod, abstractproperty

__all__ = ["Number", "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

    # 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.

    """

    @abstractmethod

    def __complex__(self):

        """Return a builtin complex instance. Called for complex(self)."""

    # Will be __bool__ in 3.0.

    def __nonzero__(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

    @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 __div__(self, other):

        """self / other without __future__ division

        May promote to float.

        """

        raise NotImplementedError

    @abstractmethod

    def __rdiv__(self, other):

        """other / self without __future__ division"""

        raise NotImplementedError

    @abstractmethod

    def __truediv__(self, other):

        """self / other with __future__ division.

        Should promote to float when necessary.

        """

        raise NotImplementedError

    @abstractmethod

    def __rtruediv__(self, other):

        """other / self with __future__ division"""

        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

    def __ne__(self, other):

        """self != other"""

        # The default __ne__ doesn't negate __eq__ until 3.0.

        return not (self == other)

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

    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."""

    @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

        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 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)