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Diffstat (limited to 'boost/integer/mod_inverse.hpp')
-rw-r--r-- | boost/integer/mod_inverse.hpp | 53 |
1 files changed, 53 insertions, 0 deletions
diff --git a/boost/integer/mod_inverse.hpp b/boost/integer/mod_inverse.hpp new file mode 100644 index 0000000000..04b6e81932 --- /dev/null +++ b/boost/integer/mod_inverse.hpp @@ -0,0 +1,53 @@ +/* + * (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 <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 |