libs/integer/doc/modular_arithmetic/extended_euclidean.qbk
[section:extended_euclidean Extended Euclidean Algorithm]
[section Introduction]
The extended Euclidean algorithm solves the integer relation /mx + ny/ = gcd(/m/, /n/) for /x/ and /y/.
[endsect]
[section Synopsis]
#include <boost/integer/extended_euclidean.hpp>
namespace boost { namespace integer {
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);
}}
[endsect]
[section Usage]
int m = 12;
int n = 15;
auto res = extended_euclidean(m, n);
int gcd = res.gcd;
int x = res.x;
int y = res.y;
// mx + ny = gcd(m,n) should now hold
[endsect]
[section References]
Wagstaff, Samuel S., ['The Joy of Factoring], Vol. 68. American Mathematical Soc., 2013.
[endsect]
[endsect]
[/
Copyright 2018 Nick Thompson.
Distributed under 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).
]
