/* * (C) Copyright Nick Thompson 2018. * Use, modification and distribution are subject to 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) */ #ifndef BOOST_INTEGER_MOD_INVERSE_HPP #define BOOST_INTEGER_MOD_INVERSE_HPP #include #include #include namespace boost { namespace integer { // From "The Joy of Factoring", Algorithm 2.7. // Here's some others names I've found for this function: // PowerMod[a, -1, m] (Mathematica) // mpz_invert (gmplib) // modinv (some dude on stackoverflow) // Would mod_inverse be sometimes mistaken as the modular *additive* inverse? // In any case, I think this is the best name we can get for this function without agonizing. template Z mod_inverse(Z a, Z modulus) { if (modulus < Z(2)) { BOOST_THROW_EXCEPTION(std::domain_error("mod_inverse: modulus must be > 1")); } // make sure a < modulus: a = a % modulus; if (a == Z(0)) { // a doesn't have a modular multiplicative inverse: return Z(0); } boost::integer::euclidean_result_t u = boost::integer::extended_euclidean(a, modulus); if (u.gcd > Z(1)) { return Z(0); } // x might not be in the range 0 < x < m, let's fix that: while (u.x <= Z(0)) { u.x += modulus; } // While indeed this is an inexpensive and comforting check, // the multiplication overflows and hence makes the check itself buggy. //BOOST_ASSERT(u.x*a % modulus == 1); return u.x; } }} #endif