boost_integer/include/boost/integer/extended_euclidean.hpp

/*
 *  (C) Copyright Nick Thompson 2018.
 *  Use, modification and distribution are subject to the
 *  Boost Software License, Version 1.0. (See accompanying file
 *  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 */
#ifndef BOOST_INTEGER_EXTENDED_EUCLIDEAN_HPP
#define BOOST_INTEGER_EXTENDED_EUCLIDEAN_HPP
#include <limits>
#include <stdexcept>
#include <boost/throw_exception.hpp>

namespace boost { namespace integer {

// From "The Joy of Factoring", Algorithm 2.7, with a small optimization to remove tmps from Wikipedia.
// Solves mx + ny = gcd(m,n). Returns tuple with (gcd(m,n), x, y).

template<class Z>
struct euclidean_result_t {
  Z gcd;
  Z x;
  Z y;
};

template<class Z>
euclidean_result_t<Z> extended_euclidean(Z m, Z n)
{
    using std::numeric_limits;
    static_assert(numeric_limits<Z>::is_integer,
                  "The extended Euclidean algorithm works on integral types.\n");

    static_assert(numeric_limits<Z>::is_signed,
                  "The extended Euclidean algorithm only works on signed integer types.\n");

    if (m < 1 || n < 1)
    {
        BOOST_THROW_EXCEPTION(std::domain_error("Arguments must be strictly positive.\n"));
    }

    bool swapped = false;
    if (m < n)
    {
      swapped = true;
      std::swap(m, n);
    }
    Z u0 = m;
    Z u1 = 1;
    Z u2 = 0;
    Z v0 = n;
    Z v1 = 0;
    Z v2 = 1;
    Z w0;
    Z w1;
    Z w2;
    while(v0 > 0)
    {
      Z q = u0/v0;
      w0 = u0 - q*v0;
      w1 = u1 - q*v1;
      w2 = u2 - q*v2;
      u0 = v0;
      u1 = v1;
      u2 = v2;
      v0 = w0;
      v1 = w1;
      v2 = w2;
    }

    if (swapped)
    {
        return {u0, u2, u1};
    }
    return {u0, u1, u2};
}

}}
#endif