Return integer with zero signaling common factor rather than boost::optional<Z>.

doc/modular_arithmetic/mod_inverse.qbk

@@ -14,7 +14,7 @@ A fast algorithm for computing modular multiplicative inverses based on the exte
     namespace boost { namespace integer {
 
     template<class Z>
-    boost::optional<Z> mod_inverse(Z a, Z m);
+    Z mod_inverse(Z a, Z m);
 
     }}
 
@@ -22,20 +22,19 @@ A fast algorithm for computing modular multiplicative inverses based on the exte
 
 [section Usage]
 
-Multiplicative modular inverses exist if and only if /a/ and /m/ are coprime.
-So for example
+    int x = mod_inverse(2, 5);
+    // prints x = 3:
+    std::cout << "x = " << x << "\n";
 
-    auto x = mod_inverse(2, 5);
-    if (x)
-    {
-        int should_be_three = x.value();
-    }
-    auto y = mod_inverse(2, 4);
-    if (!y)
+    int y = mod_inverse(2, 4);
+    if (y == 0)
     {
         std::cout << "There is no inverse of 2 mod 4\n";
     }
 
+Multiplicative modular inverses exist if and only if /a/ and /m/ are coprime.
+If /a/ and /m/ share a common factor, then `mod_inverse(a, m)` returns zero.
+
 [endsect]
 
 [section References]

include/boost/integer/mod_inverse.hpp

@@ -8,7 +8,6 @@
 #define BOOST_INTEGER_MOD_INVERSE_HPP
 #include <stdexcept>
 #include <boost/throw_exception.hpp>
-#include <boost/optional.hpp>
 #include <boost/integer/extended_euclidean.hpp>
 
 namespace boost { namespace integer {
@@ -21,7 +20,7 @@ namespace boost { namespace integer {
 // 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>
-boost::optional<Z> mod_inverse(Z a, Z modulus)
+Z mod_inverse(Z a, Z modulus)
 {
     if (modulus < 2)
     {
@@ -32,12 +31,12 @@ boost::optional<Z> mod_inverse(Z a, Z modulus)
     if (a == 0)
     {
         // a doesn't have a modular multiplicative inverse:
-        return boost::none;
+        return 0;
     }
     euclidean_result_t<Z> u = extended_euclidean(a, modulus);
     if (u.gcd > 1)
     {
-        return boost::none;
+        return 0;
     }
     // x might not be in the range 0 < x < m, let's fix that:
     while (u.x <= 0)

test/mod_inverse_test.cpp

@@ -36,17 +36,17 @@ void test_mod_inverse()
         for (Z a = 1; a < modulus; ++a)
         {
             Z gcdam = gcd(a, modulus);
-            boost::optional<Z> inv_a = mod_inverse(a, modulus);
+            Z inv_a = mod_inverse(a, modulus);
             // Should fail if gcd(a, mod) != 1:
             if (gcdam > 1)
             {
-                BOOST_TEST(!inv_a);
+                BOOST_TEST(inv_a == 0);
             }
             else
             {
-                BOOST_TEST(inv_a.value() > 0);
+                BOOST_TEST(inv_a > 0);
                 // Cast to a bigger type so the multiplication won't overflow.
-                int256_t a_inv = inv_a.value();
+                int256_t a_inv = inv_a;
                 int256_t big_a = a;
                 int256_t m = modulus;
                 int256_t outta_be_one = (a_inv*big_a) % m;