refactor __hypot_factors, e.g. replace std::array usage by std::pair

Author: PaulXiCao

libcxx/include/__math/hypot.h

@@ -17,7 +17,7 @@
 #include <__type_traits/is_arithmetic.h>
 #include <__type_traits/is_same.h>
 #include <__type_traits/promote.h>
-#include <array>
+#include <__utility/pair.h>
 #include <limits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
@@ -48,42 +48,29 @@ inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type hypot(_A1 __x, _
 
 #if _LIBCPP_STD_VER >= 17
 // Factors needed to determine if over-/underflow might happen for `std::hypot(x,y,z)`.
+// returns [overflow_threshold, overflow_scale]
 template <class _Real>
-struct __hypot_factors {
-  _Real __threshold;
-  _Real __scale_xyz;
-  _Real __scale_M;
-};
-
-// Computes `__hypot_factors` needed to determine if over-/underflow might happen for `std::hypot(x,y,z)`.
-// Returns: [underflow_factors, overflow_factors]
-template <class _Real>
-_LIBCPP_HIDE_FROM_ABI array<__math::__hypot_factors<_Real>, 2> __create_factors() {
+_LIBCPP_HIDE_FROM_ABI std::pair<_Real, _Real> __hypot_factors() {
   static_assert(std::numeric_limits<_Real>::is_iec559);
 
-  __math::__hypot_factors<_Real> __underflow, __overflow;
   if constexpr (std::is_same_v<_Real, float>) {
     static_assert(-125 == std::numeric_limits<_Real>::min_exponent);
     static_assert(+128 == std::numeric_limits<_Real>::max_exponent);
-    __underflow = __math::__hypot_factors<_Real>{0x1.0p-62f, 0x1.0p70f, 0x1.0p-70f};
-    __overflow  = __math::__hypot_factors<_Real>{0x1.0p62f, 0x1.0p-70f, 0x1.0p+70f};
+    return {0x1.0p+62f, 0x1.0p-70f};
   } else if constexpr (std::is_same_v<_Real, double>) {
     static_assert(-1021 == std::numeric_limits<_Real>::min_exponent);
     static_assert(+1024 == std::numeric_limits<_Real>::max_exponent);
-    __underflow = __math::__hypot_factors<_Real>{0x1.0p-510, 0x1.0p600, 0x1.0p-600};
-    __overflow  = __math::__hypot_factors<_Real>{0x1.0p510, 0x1.0p-600, 0x1.0p+600};
+    return {0x1.0p+510, 0x1.0p-600};
   } else { // long double
     static_assert(std::is_same_v<_Real, long double>);
     if constexpr (sizeof(_Real) == sizeof(double))
-      return static_cast<std::array<__math::__hypot_factors<_Real>, 2>>(__math::__create_factors<double>());
+      return static_cast<std::pair<_Real, _Real>>(__math::__hypot_factors<double>());
     else {
       static_assert(-16'381 == std::numeric_limits<_Real>::min_exponent);
       static_assert(+16'384 == std::numeric_limits<_Real>::max_exponent);
-      __underflow = __math::__hypot_factors<_Real>{0x1.0p-8'190l, 0x1.0p9'000l, 0x1.0p-9'000l};
-      __overflow  = __math::__hypot_factors<_Real>{0x1.0p8'190l, 0x1.0p-9'000l, 0x1.0p+9'000l};
+      return {0x1.0p+8'190l, 0x1.0p-9'000l};
     }
   }
-  return {__underflow, __overflow};
 }
 
 // Computes the three-dimensional hypotenuse: `std::hypot(x,y,z)`.
@@ -92,21 +79,22 @@ _LIBCPP_HIDE_FROM_ABI array<__math::__hypot_factors<_Real>, 2> __create_factors(
 // See https://github.com/llvm/llvm-project/issues/92782 for a detailed discussion and summary.
 template <class _Real>
 _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) {
-  const auto [__underflow, __overflow] = __math::__create_factors<_Real>();
-  _Real __M                            = std::max({__math::fabs(__x), __math::fabs(__y), __math::fabs(__z)});
-  if (__M > __overflow.__threshold) { // x*x + y*y + z*z might overflow
-    __x *= __overflow.__scale_xyz;
-    __y *= __overflow.__scale_xyz;
-    __z *= __overflow.__scale_xyz;
-    __M = __overflow.__scale_M;
-  } else if (__M < __underflow.__threshold) { // x*x + y*y + z*z might underflow
-    __x *= __underflow.__scale_xyz;
-    __y *= __underflow.__scale_xyz;
-    __z *= __underflow.__scale_xyz;
-    __M = __underflow.__scale_M;
+  const _Real __max_abs = std::max({__math::fabs(__x), __math::fabs(__y), __math::fabs(__z)});
+  const auto [__overflow_threshold, __overflow_scale] = __math::__hypot_factors<_Real>();
+  _Real __scale;
+  if (__max_abs > __overflow_threshold) { // x*x + y*y + z*z might overflow
+    __scale = __overflow_scale;
+    __x *= __scale;
+    __y *= __scale;
+    __z *= __scale;
+  } else if (__max_abs < 1 / __overflow_threshold) { // x*x + y*y + z*z might underflow
+    __scale = 1 / __overflow_scale;
+    __x *= __scale;
+    __y *= __scale;
+    __z *= __scale;
   } else
-    __M = 1;
-  return __M * __math::sqrt(__x * __x + __y * __y + __z * __z);
+    __scale = 1;
+  return __math::sqrt(__x * __x + __y * __y + __z * __z) / __scale;
 }
 
 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); }
@@ -125,7 +113,8 @@ _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2
   using __result_type = typename __promote<_A1, _A2, _A3>::type;
   static_assert(!(
       std::is_same_v<_A1, __result_type> && std::is_same_v<_A2, __result_type> && std::is_same_v<_A3, __result_type>));
-  return __math::__hypot(static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z));
+  return __math::__hypot(
+      static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z));
 }
 #endif