forked from boostorg/integer
51 lines
1.3 KiB
C++
51 lines
1.3 KiB
C++
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/*
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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_MODULAR_MULTIPLICATIVE_INVERSE_HPP
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#define BOOST_INTEGER_MODULAR_MULTIPLICATIVE_INVERSE_HPP
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#include <limits>
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#include <boost/optional.hpp>
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#include <boost/integer/extended_euclidean.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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template<class Z>
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boost::optional<Z> modular_multiplicative_inverse(Z a, Z modulus)
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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 modular multiplicative inverse works on integral types.\n");
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if (modulus < 2)
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{
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throw std::domain_error("Modulus must be > 1.\n");
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}
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// make sure a < modulus:
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a = a % modulus;
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if (a == 0)
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{
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// a doesn't have a modular multiplicative inverse:
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return {};
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}
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auto u = extended_euclidean(a, modulus);
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Z gcd = std::get<0>(u);
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if (gcd > 1)
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{
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return {};
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}
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Z x = std::get<1>(u);
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// x might not be in the range 0 < x < m, let's fix that:
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x = x % modulus;
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while (x <= 0)
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{
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x += modulus;
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}
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return x;
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}
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}}
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#endif
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