"""
The routines here were removed from numbers.py, power.py,
digits.py and factor_.py so they could be imported into core
without raising circular import errors.

Although the name 'intfunc' was chosen to represent functions that
work with integers, it can also be thought of as containing
internal/core functions that are needed by the classes of the core.
"""

from ..external.gmpy import (gcdext)

def igcdex(a, b):
    """Returns x, y, g such that g = x*a + y*b = gcd(a, b).

    Examples
    ========

    >>> from sympy.core.intfunc import igcdex
    >>> igcdex(2, 3)
    (-1, 1, 1)
    >>> igcdex(10, 12)
    (-1, 1, 2)

    >>> x, y, g = igcdex(100, 2004)
    >>> x, y, g
    (-20, 1, 4)
    >>> x*100 + y*2004
    4

    """
    if (not a) and (not b):
        return (0, 1, 0)
    g, x, y = gcdext(int(a), int(b))
    return x, y, g