63e88f80
 Hu Chunming
提交三方库
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/*
* (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 https://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>
#include <boost/core/swap.hpp>
#include <boost/core/enable_if.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>
typename boost::enable_if_c< std::numeric_limits< Z >::is_signed, euclidean_result_t< Z > >::type
extended_euclidean(Z m, Z n)
{
if (m < 1 || n < 1)
{
BOOST_THROW_EXCEPTION(std::domain_error("extended_euclidean: arguments must be strictly positive"));
}
bool swapped = false;
if (m < n)
{
swapped = true;
boost::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;
}
euclidean_result_t< Z > result;
result.gcd = u0;
if (!swapped)
{
result.x = u1;
result.y = u2;
}
else
{
result.x = u2;
result.y = u1;
}
return result;
}
}}
#endif
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