diff --git a/include/boost/integer/extended_euclidean.hpp b/include/boost/integer/extended_euclidean.hpp
index 64d10d9..93c8c54 100644
--- a/include/boost/integer/extended_euclidean.hpp
+++ b/include/boost/integer/extended_euclidean.hpp
@@ -13,9 +13,8 @@
 
 namespace boost { namespace integer {
 
-// From "The Joy of Factoring", Algorithm 2.7.
+// From "The Joy of Factoring", Algorithm 2.7, with a small optimization to remove tmps from Wikipedia.
 // Solves mx + ny = gcd(m,n). Returns tuple with (gcd(m,n), x, y).
-// Is this the natural ordering?, or must people simply have to read the docs?
 
 template<class Z>
 struct euclidean_result_t {
@@ -38,45 +37,27 @@ euclidean_result_t<Z> extended_euclidean(Z m, Z n)
     {
         BOOST_THROW_EXCEPTION(std::domain_error("Arguments must be strictly positive.\n"));
     }
-    bool swapped = false;
-    if (m < n)
-    {
-        swapped = true;
-        std::swap(m, n);
-    }
-    Z u0 = m;
-    Z u1 = 1;
-    Z u2 = 0;
-    Z v0 = n;
-    Z v1 = 0;
-    Z v2 = 1;
-    Z w0;
-    Z w1;
-    Z w2;
-    while(v0 > 0)
-    {
-        Z q = u0/v0;
-        w0 = u0 - q*v0;
-        w1 = u1 - q*v1;
-        w2 = u2 - q*v2;
-        u0 = v0;
-        u1 = v1;
-        u2 = v2;
-        v0 = w0;
-        v1 = w1;
-        v2 = w2;
-    }
-    if (swapped)
-    {
-        std::swap(u1, u2);
-        BOOST_ASSERT(u2*m+u1*n==u0);
-    }
-    else
-    {
-        BOOST_ASSERT(u1*m+u2*n==u0);
+
+    Z s = 0;
+    Z old_s = 1;
+    Z r = n;
+    Z old_r = m;
+
+    while (r != 0) {
+      Z q = old_r/r;
+      Z tmp = r;
+      r = old_r - q*tmp;
+      old_r = tmp;
+
+      tmp = s;
+      s = old_s - q*tmp;
+      old_s = tmp;
     }
 
-    return {u0, u1, u2};
+    Z y = (old_r - old_s*m)/n;
+
+    BOOST_ASSERT(old_s*m+y*n==old_r);
+    return {old_r, old_s, y};
 }
 
 }}