add boost on mac

macx64/include/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