| /* |
| * (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 https://www.boost.org/LICENSE_1_0.txt) |
| */ |
| #ifndef BOOST_INTEGER_MOD_INVERSE_HPP |
| #define BOOST_INTEGER_MOD_INVERSE_HPP |
| #include <stdexcept> |
| #include <boost/throw_exception.hpp> |
| #include <boost/integer/extended_euclidean.hpp> |
| |
| 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<class Z> |
| 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<Z> 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 |