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84 lines
1.8 KiB
C++
84 lines
1.8 KiB
C++
/*
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* (C) Copyright Nick Thompson 2018.
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* Use, modification and distribution are subject to the
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* Boost Software License, Version 1.0. (See accompanying file
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* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_INTEGER_EXTENDED_EUCLIDEAN_HPP
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#define BOOST_INTEGER_EXTENDED_EUCLIDEAN_HPP
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#include <tuple>
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#include <limits>
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#include <stdexcept>
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#include <boost/throw_exception.hpp>
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namespace boost { namespace integer {
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// From "The Joy of Factoring", Algorithm 2.7.
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// Solves mx + ny = gcd(m,n). Returns tuple with (gcd(m,n), x, y).
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// Is this the natural ordering?, or must people simply have to read the docs?
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template<class Z>
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struct euclidean_result_t {
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Z gcd;
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Z x;
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Z y;
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};
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template<class Z>
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euclidean_result_t<Z> extended_euclidean(Z m, Z n)
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{
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using std::numeric_limits;
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static_assert(numeric_limits<Z>::is_integer,
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"The extended Euclidean algorithm works on integral types.\n");
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static_assert(numeric_limits<Z>::is_signed,
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"The extended Euclidean algorithm only works on signed integer types.\n");
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if (m < 1 || n < 1)
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{
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BOOST_THROW_EXCEPTION(std::domain_error("Arguments must be strictly positive.\n"));
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}
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bool swapped = false;
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if (m < n)
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{
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swapped = true;
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std::swap(m, n);
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}
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Z u0 = m;
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Z u1 = 1;
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Z u2 = 0;
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Z v0 = n;
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Z v1 = 0;
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Z v2 = 1;
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Z w0;
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Z w1;
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Z w2;
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while(v0 > 0)
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{
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Z q = u0/v0;
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w0 = u0 - q*v0;
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w1 = u1 - q*v1;
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w2 = u2 - q*v2;
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u0 = v0;
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u1 = v1;
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u2 = v2;
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v0 = w0;
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v1 = w1;
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v2 = w2;
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}
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if (swapped)
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{
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std::swap(u1, u2);
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BOOST_ASSERT(u2*m+u1*n==u0);
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}
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else
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{
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BOOST_ASSERT(u1*m+u2*n==u0);
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}
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return {u0, u1, u2};
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}
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}}
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#endif
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