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https://github.com/PurpleI2P/Boost-for-Android-Prebuilt
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54 lines
1.6 KiB
C++
54 lines
1.6 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_MOD_INVERSE_HPP
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#define BOOST_INTEGER_MOD_INVERSE_HPP
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#include <stdexcept>
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#include <boost/throw_exception.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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// Here's some others names I've found for this function:
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// PowerMod[a, -1, m] (Mathematica)
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// mpz_invert (gmplib)
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// modinv (some dude on stackoverflow)
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// Would mod_inverse be sometimes mistaken as the modular *additive* inverse?
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// In any case, I think this is the best name we can get for this function without agonizing.
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template<class Z>
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Z mod_inverse(Z a, Z modulus)
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{
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if (modulus < Z(2))
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{
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BOOST_THROW_EXCEPTION(std::domain_error("mod_inverse: modulus must be > 1"));
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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 == Z(0))
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{
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// a doesn't have a modular multiplicative inverse:
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return Z(0);
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}
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boost::integer::euclidean_result_t<Z> u = boost::integer::extended_euclidean(a, modulus);
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if (u.gcd > Z(1))
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{
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return Z(0);
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}
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// x might not be in the range 0 < x < m, let's fix that:
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while (u.x <= Z(0))
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{
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u.x += modulus;
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}
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// While indeed this is an inexpensive and comforting check,
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// the multiplication overflows and hence makes the check itself buggy.
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//BOOST_ASSERT(u.x*a % modulus == 1);
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return u.x;
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}
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}}
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#endif
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