diff --git a/include/boost/integer/extended_euclidean.hpp b/include/boost/integer/extended_euclidean.hpp
index edca600..f89a540 100644
--- a/include/boost/integer/extended_euclidean.hpp
+++ b/include/boost/integer/extended_euclidean.hpp
@@ -6,12 +6,9 @@
  */
 #ifndef BOOST_INTEGER_EXTENDED_EUCLIDEAN_HPP
 #define BOOST_INTEGER_EXTENDED_EUCLIDEAN_HPP
-#include <tuple>
 #include <limits>
 #include <stdexcept>
 #include <boost/throw_exception.hpp>
-#include <boost/assert.hpp>
-#include <iostream>
 
 namespace boost { namespace integer {
 
@@ -71,14 +68,8 @@ euclidean_result_t<Z> extended_euclidean(Z m, Z n)
 
     if (swapped)
     {
-        std::swap(u1, u2);
-        BOOST_ASSERT(u2*m+u1*n==u0);
+        return {u0, u2, u2};
     }
-    else
-    {
-        BOOST_ASSERT(u1*m+u2*n==u0);
-    }
-
     return {u0, u1, u2};
 }
 
diff --git a/include/boost/integer/mod_inverse.hpp b/include/boost/integer/mod_inverse.hpp
index 9a93585..7053efc 100644
--- a/include/boost/integer/mod_inverse.hpp
+++ b/include/boost/integer/mod_inverse.hpp
@@ -35,20 +35,19 @@ boost::optional<Z> mod_inverse(Z a, Z modulus)
         return {};
     }
     euclidean_result_t<Z> u = extended_euclidean(a, modulus);
-    Z gcd = u.gcd;
-    if (gcd > 1)
+    if (u.gcd > 1)
     {
         return {};
     }
-    Z x = u.x;
-    x = x % modulus;
     // x might not be in the range 0 < x < m, let's fix that:
-    while (x <= 0)
+    while (u.x <= 0)
     {
-        x += modulus;
+        u.x += modulus;
     }
-    BOOST_ASSERT(x*a % modulus == 1);
-    return x;
+    // 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;
 }
 
 }}
diff --git a/test/extended_euclidean_test.cpp b/test/extended_euclidean_test.cpp
index 2179016..16fc0ff 100644
--- a/test/extended_euclidean_test.cpp
+++ b/test/extended_euclidean_test.cpp
@@ -11,6 +11,7 @@
 #include <boost/integer/extended_euclidean.hpp>
 
 using boost::multiprecision::int128_t;
+using boost::multiprecision::int256_t;
 using boost::integer::extended_euclidean;
 using boost::integer::gcd;
 
@@ -18,26 +19,29 @@ template<class Z>
 void test_extended_euclidean()
 {
     std::cout << "Testing the extended Euclidean algorithm on type " << boost::typeindex::type_id<Z>().pretty_name() << "\n";
+    // Stress test:
+    //Z max_arg = std::numeric_limits<Z>::max();
     Z max_arg = 500;
-    for (Z m = 1; m < max_arg; ++m)
+    for (Z m = max_arg; m > 0; --m)
     {
-        for (Z n = 1; n < max_arg; ++n)
+        for (Z n = m; n > 0; --n)
         {
             boost::integer::euclidean_result_t u = extended_euclidean(m, n);
-            Z gcdmn = gcd(m, n);
-            Z x = u.x;
-            Z y = u.y;
+            int256_t gcdmn = gcd(m, n);
+            int256_t x = u.x;
+            int256_t y = u.y;
             BOOST_CHECK_EQUAL(u.gcd, gcdmn);
             BOOST_CHECK_EQUAL(m*x + n*y, gcdmn);
         }
     }
 }
 
+
+
 BOOST_AUTO_TEST_CASE(extended_euclidean_test)
 {
-    test_extended_euclidean<short int>();
-    test_extended_euclidean<int>();
-    test_extended_euclidean<long>();
-    test_extended_euclidean<long long>();
+    test_extended_euclidean<int16_t>();
+    test_extended_euclidean<int32_t>();
+    test_extended_euclidean<int64_t>();
     test_extended_euclidean<int128_t>();
 }
diff --git a/test/mod_inverse_test.cpp b/test/mod_inverse_test.cpp
index ac7862f..4ab02f8 100644
--- a/test/mod_inverse_test.cpp
+++ b/test/mod_inverse_test.cpp
@@ -19,10 +19,15 @@ template<class Z>
 void test_mod_inverse()
 {
     std::cout << "Testing the modular multiplicative inverse on type " << boost::typeindex::type_id<Z>().pretty_name() << "\n";
+    //Z max_arg = std::numeric_limits<Z>::max();
     Z max_arg = 500;
     for (Z modulus = 2; modulus < max_arg; ++modulus)
     {
-        for (Z a = 1; a < max_arg; ++a)
+        if (modulus % 1000 == 0)
+        {
+            std::cout << "Testing all inverses modulo " << modulus << std::endl;
+        }
+        for (Z a = 1; a < modulus; ++a)
         {
             Z gcdam = gcd(a, modulus);
             boost::optional<Z> inv_a = mod_inverse(a, modulus);
@@ -34,7 +39,11 @@ void test_mod_inverse()
             else
             {
                 BOOST_CHECK(inv_a.value() > 0);
-                Z outta_be_one = (inv_a.value()*a) % modulus;
+                // Cast to a bigger type so the multiplication won't overflow.
+                int256_t a_inv = inv_a.value();
+                int256_t big_a = a;
+                int256_t m = modulus;
+                int256_t outta_be_one = (a_inv*big_a) % m;
                 BOOST_CHECK_EQUAL(outta_be_one, 1);
             }
         }
@@ -43,10 +52,8 @@ void test_mod_inverse()
 
 BOOST_AUTO_TEST_CASE(mod_inverse_test)
 {
-    test_mod_inverse<short int>();
-    test_mod_inverse<int>();
-    test_mod_inverse<long>();
-    test_mod_inverse<long long>();
+    test_mod_inverse<int16_t>();
+    test_mod_inverse<int32_t>();
+    test_mod_inverse<int64_t>();
     test_mod_inverse<int128_t>();
-    test_mod_inverse<int256_t>();
 }