[libc++] Fix sub-overflow in std::gcd implementation (#117984)

Fix #117249

Author: serge-sans-paille

libcxx/include/__numeric/gcd_lcm.h

@@ -55,7 +55,8 @@ template <class _Tp>
 constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) {
   static_assert(!is_signed<_Tp>::value, "");
 
-  // From: https://lemire.me/blog/2013/12/26/fastest-way-to-compute-the-greatest-common-divisor
+  // Using Binary GCD algorithm https://en.wikipedia.org/wiki/Binary_GCD_algorithm, based on an implementation
+  // from https://lemire.me/blog/2024/04/13/greatest-common-divisor-the-extended-euclidean-algorithm-and-speed/
   //
   // If power of two divides both numbers, we can push it out.
   // - gcd( 2^x * a, 2^x * b) = 2^x * gcd(a, b)
@@ -76,21 +77,17 @@ constexpr _LIBCPP_HIDDEN _Tp __gcd(_Tp __a, _Tp __b) {
   if (__a == 0)
     return __b;
 
-  int __az    = std::__countr_zero(__a);
-  int __bz    = std::__countr_zero(__b);
-  int __shift = std::min(__az, __bz);
-  __a >>= __az;
-  __b >>= __bz;
+  _Tp __c     = __a | __b;
+  int __shift = std::__countr_zero(__c);
+  __a >>= std::__countr_zero(__a);
   do {
-    _Tp __diff = __a - __b;
-    if (__a > __b) {
-      __a = __b;
-      __b = __diff;
+    _Tp __t = __b >> std::__countr_zero(__b);
+    if (__a > __t) {
+      __b = __a - __t;
+      __a = __t;
     } else {
-      __b = __b - __a;
+      __b = __t - __a;
     }
-    if (__diff != 0)
-      __b >>= std::__countr_zero(__diff);
   } while (__b != 0);
   return __a << __shift;
 }

libcxx/test/std/numerics/numeric.ops/numeric.ops.gcd/gcd.pass.cpp

@@ -27,17 +27,7 @@ constexpr struct {
   int x;
   int y;
   int expect;
-} Cases[] = {
-    {0, 0, 0},
-    {1, 0, 1},
-    {0, 1, 1},
-    {1, 1, 1},
-    {2, 3, 1},
-    {2, 4, 2},
-    {36, 17, 1},
-    {36, 18, 18}
-};
-
+} Cases[] = {{0, 0, 0}, {1, 0, 1}, {0, 1, 1}, {1, 1, 1}, {2, 3, 1}, {2, 4, 2}, {11, 9, 1}, {36, 17, 1}, {36, 18, 18}};
 
 template <typename Input1, typename Input2, typename Output>
 constexpr bool test0(int in1, int in2, int out)