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

Unlike most of the library, the extended Euclidean algorithm requires C++11 features.

[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
http://www.boost.org/LICENSE_1_0.txt).
]