[libcxx-commits] [libcxx] [libc++][math] Fix undue overflowing of `std::hypot(x, y, z)` (PR #93350)

via libcxx-commits libcxx-commits at lists.llvm.org
Sat Jul 20 11:31:10 PDT 2024


https://github.com/PaulXiCao updated https://github.com/llvm/llvm-project/pull/93350

>From ced7b5248a3ddec668dea66f29a4cfa647d7ff13 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:12 +0200
Subject: [PATCH 01/17] make use of C++17 is_same_v

---
 .../test/std/numerics/c.math/cmath.pass.cpp   | 30 +++++++++----------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/libcxx/test/std/numerics/c.math/cmath.pass.cpp b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
index 9379084499792..ad4b46b3713fc 100644
--- a/libcxx/test/std/numerics/c.math/cmath.pass.cpp
+++ b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
@@ -1136,21 +1136,21 @@ void test_hypot()
     assert(std::hypot(3,4) == 5);
 
 #if TEST_STD_VER > 14
-    static_assert((std::is_same<decltype(std::hypot((float)0, (float)0, (float)0)), float>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (bool)0, (float)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (unsigned short)0, (double)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (int)0, (long double)0)), long double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (double)0, (long)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (long double)0, (unsigned long)0)), long double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (int)0, (long long)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (int)0, (unsigned long long)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (double)0, (double)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (long double)0, (long double)0)), long double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (float)0, (double)0)), double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (float)0, (long double)0)), long double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((float)0, (double)0, (long double)0)), long double>::value), "");
-    static_assert((std::is_same<decltype(std::hypot((int)0, (int)0, (int)0)), double>::value), "");
-    static_assert((std::is_same<decltype(hypot(Ambiguous(), Ambiguous(), Ambiguous())), Ambiguous>::value), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0, (float)0)), float>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (bool)0, (float)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (unsigned short)0, (double)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0, (long double)0)), long double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0, (long)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (long double)0, (unsigned long)0)), long double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0, (long long)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0, (unsigned long long)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0, (double)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (long double)0, (long double)0)), long double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0, (double)0)), double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0, (long double)0)), long double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0, (long double)0)), long double>), "");
+    static_assert((std::is_same_v<decltype(std::hypot((int)0, (int)0, (int)0)), double>), "");
+    static_assert((std::is_same_v<decltype(hypot(Ambiguous(), Ambiguous(), Ambiguous())), Ambiguous>), "");
 
     assert(std::hypot(2,3,6) == 7);
     assert(std::hypot(1,4,8) == 9);

>From f38b1dc4d9d476ef620f004f8669f11caaa3b2b8 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:13 +0200
Subject: [PATCH 02/17] style change: align argument types

---
 .../test/std/numerics/c.math/cmath.pass.cpp   | 32 ++++++++++---------
 1 file changed, 17 insertions(+), 15 deletions(-)

diff --git a/libcxx/test/std/numerics/c.math/cmath.pass.cpp b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
index ad4b46b3713fc..a16aa0724dffc 100644
--- a/libcxx/test/std/numerics/c.math/cmath.pass.cpp
+++ b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
@@ -1136,21 +1136,23 @@ void test_hypot()
     assert(std::hypot(3,4) == 5);
 
 #if TEST_STD_VER > 14
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0, (float)0)), float>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (bool)0, (float)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (unsigned short)0, (double)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0, (long double)0)), long double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0, (long)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (long double)0, (unsigned long)0)), long double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0, (long long)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0, (unsigned long long)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0, (double)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (long double)0, (long double)0)), long double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0, (double)0)), double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0, (long double)0)), long double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0, (long double)0)), long double>), "");
-    static_assert((std::is_same_v<decltype(std::hypot((int)0, (int)0, (int)0)), double>), "");
-    static_assert((std::is_same_v<decltype(hypot(Ambiguous(), Ambiguous(), Ambiguous())), Ambiguous>), "");
+    // clang-format off
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0,          (float)0)),              float>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (bool)0,           (float)0)),              double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (unsigned short)0, (double)0)),             double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0,            (long double)0)),        long double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0,         (long)0)),               double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (long double)0,    (unsigned long)0)),      long double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0,            (long long)0)),          double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (int)0,            (unsigned long long)0)), double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0,         (double)0)),             double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (long double)0,    (long double)0)),        long double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0,          (double)0)),             double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (float)0,          (long double)0)),        long double>));
+    static_assert((std::is_same_v<decltype(std::hypot((float)0, (double)0,         (long double)0)),        long double>));
+    static_assert((std::is_same_v<decltype(std::hypot((int)0,   (int)0,            (int)0)),                double>));
+    static_assert((std::is_same_v<decltype(hypot(Ambiguous(), Ambiguous(), Ambiguous())), Ambiguous>));
+    // clang-format on
 
     assert(std::hypot(2,3,6) == 7);
     assert(std::hypot(1,4,8) == 9);

>From 08c57fb775e9e8203c8ef46064c1c5594a168225 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:13 +0200
Subject: [PATCH 03/17] implementation+testing

---
 libcxx/include/__math/hypot.h                 | 78 +++++++++++++++++++
 libcxx/include/cmath                          | 25 +-----
 .../test/std/numerics/c.math/cmath.pass.cpp   | 45 +++++++++++
 3 files changed, 124 insertions(+), 24 deletions(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 1bf193a9ab7ee..430640f5e167d 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -9,11 +9,16 @@
 #ifndef _LIBCPP___MATH_HYPOT_H
 #define _LIBCPP___MATH_HYPOT_H
 
+#include <__algorithm/max.h>
 #include <__config>
+#include <__math/abs.h>
+#include <__math/roots.h>
 #include <__type_traits/enable_if.h>
 #include <__type_traits/is_arithmetic.h>
 #include <__type_traits/is_same.h>
 #include <__type_traits/promote.h>
+#include <array>
+#include <limits>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
@@ -41,6 +46,79 @@ inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type hypot(_A1 __x, _
   return __math::hypot((__result_type)__x, (__result_type)__y);
 }
 
+#if _LIBCPP_STD_VER >= 17
+template <class _Real>
+struct __hypot_factors {
+  _Real __threshold;
+  _Real __scale_xyz;
+  _Real __scale_M;
+};
+
+// returns [underflow_factors, overflow_factors]
+template <class _Real>
+std::array<__hypot_factors<_Real>, 2> __create_factors() {
+  static_assert(std::numeric_limits<_Real>::is_iec559);
+
+  __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 = __hypot_factors<_Real>{0x1.0p-62f, 0x1.0p70f, 0x1.0p-70f};
+    __overflow  = __hypot_factors<_Real>{0x1.0p62f, 0x1.0p-70f, 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 = __hypot_factors<_Real>{0x1.0p-510, 0x1.0p600, 0x1.0p-600};
+    __overflow  = __hypot_factors<_Real>{0x1.0p510, 0x1.0p-600, 0x1.0p+600};
+  } else { // long double
+    static_assert(std::is_same_v<_Real, long double>);
+    static_assert(-16'381 == std::numeric_limits<_Real>::min_exponent);
+    static_assert(+16'384 == std::numeric_limits<_Real>::max_exponent);
+    __underflow = __hypot_factors<_Real>{0x1.0p-8'190l, 0x1.0p9'000l, 0x1.0p-9'000l};
+    __overflow  = __hypot_factors<_Real>{0x1.0p8'190l, 0x1.0p-9'000l, 0x1.0p+9'000l};
+  }
+  return {__underflow, __overflow};
+}
+
+template <class _Real>
+_Real __hypot(_Real __x, _Real __y, _Real __z) {
+  const auto [__underflow, __overflow] = __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;
+  } else
+    __M = 1;
+  return __M * __math::sqrt(__x * __x + __y * __y + __z * __z);
+}
+
+inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __hypot(__x, __y, __z); }
+
+inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __hypot(__x, __y, __z); }
+
+inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) {
+  return __hypot(__x, __y, __z);
+}
+
+template <class _A1,
+          class _A2,
+          class _A3,
+          std::enable_if_t< is_arithmetic_v<_A1> && is_arithmetic_v<_A2> && is_arithmetic_v<_A3>, int> = 0 >
+_LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2 __y, _A3 __z) _NOEXCEPT {
+  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 __hypot(static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z));
+}
+#endif
+
 } // namespace __math
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/cmath b/libcxx/include/cmath
index 7a87e35c84603..e74b50ac86f67 100644
--- a/libcxx/include/cmath
+++ b/libcxx/include/cmath
@@ -305,6 +305,7 @@ constexpr long double lerp(long double a, long double b, long double t) noexcept
 */
 
 #include <__config>
+#include <__math/hypot.h>
 #include <__type_traits/enable_if.h>
 #include <__type_traits/is_arithmetic.h>
 #include <__type_traits/is_constant_evaluated.h>
@@ -544,30 +545,6 @@ using ::scalbnl _LIBCPP_USING_IF_EXISTS;
 using ::tgammal _LIBCPP_USING_IF_EXISTS;
 using ::truncl _LIBCPP_USING_IF_EXISTS;
 
-#if _LIBCPP_STD_VER >= 17
-inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) {
-  return sqrt(__x * __x + __y * __y + __z * __z);
-}
-inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) {
-  return sqrt(__x * __x + __y * __y + __z * __z);
-}
-inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) {
-  return sqrt(__x * __x + __y * __y + __z * __z);
-}
-
-template <class _A1, class _A2, class _A3>
-inline _LIBCPP_HIDE_FROM_ABI
-typename enable_if_t< is_arithmetic<_A1>::value && is_arithmetic<_A2>::value && is_arithmetic<_A3>::value,
-                      __promote<_A1, _A2, _A3> >::type
-hypot(_A1 __lcpp_x, _A2 __lcpp_y, _A3 __lcpp_z) _NOEXCEPT {
-  typedef typename __promote<_A1, _A2, _A3>::type __result_type;
-  static_assert(
-      !(is_same<_A1, __result_type>::value && is_same<_A2, __result_type>::value && is_same<_A3, __result_type>::value),
-      "");
-  return std::hypot((__result_type)__lcpp_x, (__result_type)__lcpp_y, (__result_type)__lcpp_z);
-}
-#endif
-
 template <class _A1, __enable_if_t<is_floating_point<_A1>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR bool __constexpr_isnan(_A1 __lcpp_x) _NOEXCEPT {
 #if __has_builtin(__builtin_isnan)
diff --git a/libcxx/test/std/numerics/c.math/cmath.pass.cpp b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
index a16aa0724dffc..544c197ceb1af 100644
--- a/libcxx/test/std/numerics/c.math/cmath.pass.cpp
+++ b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
@@ -12,14 +12,17 @@
 
 // <cmath>
 
+#include <array>
 #include <cmath>
 #include <limits>
 #include <type_traits>
 #include <cassert>
 
+#include "fp_compare.h"
 #include "test_macros.h"
 #include "hexfloat.h"
 #include "truncate_fp.h"
+#include "type_algorithms.h"
 
 // convertible to int/float/double/etc
 template <class T, int N=0>
@@ -1113,6 +1116,44 @@ void test_fmin()
     assert(std::fmin(1,0) == 0);
 }
 
+struct TestHypot3 {
+    template <class Real>
+    static void operator()() {
+        const auto check = [](Real elem, Real abs_tol) {
+            assert(std::isfinite(std::hypot(elem, Real(0), Real(0))));
+            assert(fptest_close(std::hypot(elem, Real(0), Real(0)), elem, abs_tol));
+            assert(std::isfinite(std::hypot(elem, elem, Real(0))));
+            assert(fptest_close(std::hypot(elem, elem, Real(0)), std::sqrt(Real(2)) * elem, abs_tol));
+            assert(std::isfinite(std::hypot(elem, elem, elem)));
+            assert(fptest_close(std::hypot(elem, elem, elem), std::sqrt(Real(3)) * elem, abs_tol));
+        };
+
+        { // check for overflow
+            const auto [elem, abs_tol] = []() -> std::array<Real, 2> {
+                if constexpr (std::is_same_v<Real, float>)
+                    return {1e20f, 1e16f};
+                else if constexpr (std::is_same_v<Real, double>)
+                    return {1e300, 1e287};
+                else // long double
+                    return {1e4000l, 1e3985l};
+            }();
+            check(elem, abs_tol);
+        }
+
+        { // check for underflow
+            const auto [elem, abs_tol] = []() -> std::array<Real, 2> {
+                if constexpr (std::is_same_v<Real, float>)
+                    return {1e-20f, 1e-24f};
+                else if constexpr (std::is_same_v<Real, double>)
+                    return {1e-287, 1e-300};
+                else // long double
+                    return {1e-3985l, 1e-4000l};
+            }();
+            check(elem, abs_tol);
+        }
+    }
+};
+
 void test_hypot()
 {
     static_assert((std::is_same<decltype(std::hypot((float)0, (float)0)), float>::value), "");
@@ -1156,6 +1197,10 @@ void test_hypot()
 
     assert(std::hypot(2,3,6) == 7);
     assert(std::hypot(1,4,8) == 9);
+
+    // Check for undue over-/underflows of intermediate results.
+    // See discussion at https://github.com/llvm/llvm-project/issues/92782.
+    types::for_each(types::floating_point_types(), TestHypot3());
 #endif
 }
 

>From 5d7bc79986e5e0216710e31d5cb2a7438481b275 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:14 +0200
Subject: [PATCH 04/17] handle case: sizeof(double) == sizeof(long double)

---
 libcxx/include/__math/hypot.h | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 430640f5e167d..15414cfb7cd1b 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -72,10 +72,14 @@ std::array<__hypot_factors<_Real>, 2> __create_factors() {
     __overflow  = __hypot_factors<_Real>{0x1.0p510, 0x1.0p-600, 0x1.0p+600};
   } else { // long double
     static_assert(std::is_same_v<_Real, long double>);
-    static_assert(-16'381 == std::numeric_limits<_Real>::min_exponent);
-    static_assert(+16'384 == std::numeric_limits<_Real>::max_exponent);
-    __underflow = __hypot_factors<_Real>{0x1.0p-8'190l, 0x1.0p9'000l, 0x1.0p-9'000l};
-    __overflow  = __hypot_factors<_Real>{0x1.0p8'190l, 0x1.0p-9'000l, 0x1.0p+9'000l};
+    if constexpr (sizeof(_Real) == sizeof(double))
+      return static_cast<std::array<__hypot_factors<_Real>, 2>>(__create_factors<double>());
+    else {
+      static_assert(-16'381 == std::numeric_limits<_Real>::min_exponent);
+      static_assert(+16'384 == std::numeric_limits<_Real>::max_exponent);
+      __underflow = __hypot_factors<_Real>{0x1.0p-8'190l, 0x1.0p9'000l, 0x1.0p-9'000l};
+      __overflow  = __hypot_factors<_Real>{0x1.0p8'190l, 0x1.0p-9'000l, 0x1.0p+9'000l};
+    }
   }
   return {__underflow, __overflow};
 }

>From 5c32b7729946174c77e31c5459379494c75b35fb Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:14 +0200
Subject: [PATCH 05/17] add hide_from_abi macro to internal functions

---
 libcxx/include/__math/hypot.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 15414cfb7cd1b..b5a803f3f8ee9 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -56,7 +56,7 @@ struct __hypot_factors {
 
 // returns [underflow_factors, overflow_factors]
 template <class _Real>
-std::array<__hypot_factors<_Real>, 2> __create_factors() {
+_LIBCPP_HIDE_FROM_ABI std::array<__hypot_factors<_Real>, 2> __create_factors() {
   static_assert(std::numeric_limits<_Real>::is_iec559);
 
   __hypot_factors<_Real> __underflow, __overflow;
@@ -85,7 +85,7 @@ std::array<__hypot_factors<_Real>, 2> __create_factors() {
 }
 
 template <class _Real>
-_Real __hypot(_Real __x, _Real __y, _Real __z) {
+_LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) {
   const auto [__underflow, __overflow] = __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

>From dfbf54cd5c1c19513375cb99dd072d7576fc6cc4 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:14 +0200
Subject: [PATCH 06/17] fully qualify local function calls

---
 libcxx/include/__math/hypot.h | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index b5a803f3f8ee9..a0d207c6ca60d 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -56,29 +56,29 @@ struct __hypot_factors {
 
 // returns [underflow_factors, overflow_factors]
 template <class _Real>
-_LIBCPP_HIDE_FROM_ABI std::array<__hypot_factors<_Real>, 2> __create_factors() {
+_LIBCPP_HIDE_FROM_ABI std::array<__math::__hypot_factors<_Real>, 2> __create_factors() {
   static_assert(std::numeric_limits<_Real>::is_iec559);
 
-  __hypot_factors<_Real> __underflow, __overflow;
+  __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 = __hypot_factors<_Real>{0x1.0p-62f, 0x1.0p70f, 0x1.0p-70f};
-    __overflow  = __hypot_factors<_Real>{0x1.0p62f, 0x1.0p-70f, 0x1.0p+70f};
+    __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};
   } 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 = __hypot_factors<_Real>{0x1.0p-510, 0x1.0p600, 0x1.0p-600};
-    __overflow  = __hypot_factors<_Real>{0x1.0p510, 0x1.0p-600, 0x1.0p+600};
+    __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};
   } else { // long double
     static_assert(std::is_same_v<_Real, long double>);
     if constexpr (sizeof(_Real) == sizeof(double))
-      return static_cast<std::array<__hypot_factors<_Real>, 2>>(__create_factors<double>());
+      return static_cast<std::array<__math::__hypot_factors<_Real>, 2>>(__math::__create_factors<double>());
     else {
       static_assert(-16'381 == std::numeric_limits<_Real>::min_exponent);
       static_assert(+16'384 == std::numeric_limits<_Real>::max_exponent);
-      __underflow = __hypot_factors<_Real>{0x1.0p-8'190l, 0x1.0p9'000l, 0x1.0p-9'000l};
-      __overflow  = __hypot_factors<_Real>{0x1.0p8'190l, 0x1.0p-9'000l, 0x1.0p+9'000l};
+      __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 {__underflow, __overflow};
@@ -86,7 +86,7 @@ _LIBCPP_HIDE_FROM_ABI std::array<__hypot_factors<_Real>, 2> __create_factors() {
 
 template <class _Real>
 _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) {
-  const auto [__underflow, __overflow] = __create_factors<_Real>();
+  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;
@@ -103,12 +103,12 @@ _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) {
   return __M * __math::sqrt(__x * __x + __y * __y + __z * __z);
 }
 
-inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __hypot(__x, __y, __z); }
+inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); }
 
-inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __hypot(__x, __y, __z); }
+inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); }
 
 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) {
-  return __hypot(__x, __y, __z);
+  return __math::__hypot(__x, __y, __z);
 }
 
 template <class _A1,
@@ -119,7 +119,7 @@ _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 __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
 

>From 912833ea2db23e2fe0cde3c7d87ae0c2f73f1c6b Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:15 +0200
Subject: [PATCH 07/17] remove for operator(): friendlier for older compilers

---
 libcxx/test/std/numerics/c.math/cmath.pass.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libcxx/test/std/numerics/c.math/cmath.pass.cpp b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
index 544c197ceb1af..6ed37c272192e 100644
--- a/libcxx/test/std/numerics/c.math/cmath.pass.cpp
+++ b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
@@ -1118,7 +1118,7 @@ void test_fmin()
 
 struct TestHypot3 {
     template <class Real>
-    static void operator()() {
+    void operator()() const {
         const auto check = [](Real elem, Real abs_tol) {
             assert(std::isfinite(std::hypot(elem, Real(0), Real(0))));
             assert(fptest_close(std::hypot(elem, Real(0), Real(0)), elem, abs_tol));

>From 458b0d3e3d75a2cfefea686ee2d238c3e795dcf2 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:15 +0200
Subject: [PATCH 08/17] document non-naive implementation

---
 libcxx/include/__math/hypot.h | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index a0d207c6ca60d..6636644c77834 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -47,6 +47,7 @@ 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)`.
 template <class _Real>
 struct __hypot_factors {
   _Real __threshold;
@@ -54,7 +55,8 @@ struct __hypot_factors {
   _Real __scale_M;
 };
 
-// returns [underflow_factors, overflow_factors]
+// 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 std::array<__math::__hypot_factors<_Real>, 2> __create_factors() {
   static_assert(std::numeric_limits<_Real>::is_iec559);
@@ -84,6 +86,10 @@ _LIBCPP_HIDE_FROM_ABI std::array<__math::__hypot_factors<_Real>, 2> __create_fac
   return {__underflow, __overflow};
 }
 
+// Computes the three-dimensional hypotenuse: `std::hypot(x,y,z)`.
+// The naive implementation might over-/underflow which is why this implementation is more involved:
+//    If the square of an argument might run into issues, we scale the arguments appropriately.
+// 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>();

>From 9ef79dc60a49e92b10250ebdceec8004020222dd Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:15 +0200
Subject: [PATCH 09/17] remove unnecessary qualifying of std::array in function
 return type

---
 libcxx/include/__math/hypot.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 6636644c77834..5694e10197617 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -58,7 +58,7 @@ struct __hypot_factors {
 // 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 std::array<__math::__hypot_factors<_Real>, 2> __create_factors() {
+_LIBCPP_HIDE_FROM_ABI array<__math::__hypot_factors<_Real>, 2> __create_factors() {
   static_assert(std::numeric_limits<_Real>::is_iec559);
 
   __math::__hypot_factors<_Real> __underflow, __overflow;

>From 36a162ba653a3cbcad7a4fbdb63901f558070ba1 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sun, 7 Jul 2024 19:40:16 +0200
Subject: [PATCH 10/17] refactor __hypot_factors, e.g. replace std::array usage
 by std::pair

---
 libcxx/include/__math/hypot.h | 59 ++++++++++++++---------------------
 1 file changed, 24 insertions(+), 35 deletions(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 5694e10197617..45608f36eb580 100644
--- a/libcxx/include/__math/hypot.h
+++ b/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
 

>From c276104420491039c46a09a09797a0097176d11f Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Tue, 16 Jul 2024 19:22:20 +0200
Subject: [PATCH 11/17] fix std::max not available: undef macros

---
 libcxx/include/__math/hypot.h | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 45608f36eb580..60934516e245c 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -24,6 +24,9 @@
 #  pragma GCC system_header
 #endif
 
+_LIBCPP_PUSH_MACROS
+#include <__undef_macros>
+
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 namespace __math {
@@ -121,5 +124,6 @@ _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2
 } // namespace __math
 
 _LIBCPP_END_NAMESPACE_STD
+_LIBCPP_POP_MACROS
 
 #endif // _LIBCPP___MATH_HYPOT_H

>From cd4ac8a1695049564e0e932a12c24e4841c2ce8c Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Fri, 19 Jul 2024 20:37:39 +0200
Subject: [PATCH 12/17] large literal number throwing error: replace if
 constexpr by macro guards

---
 libcxx/include/__math/hypot.h | 19 ++++++++++++-------
 1 file changed, 12 insertions(+), 7 deletions(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 60934516e245c..195c8621ed448 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -66,13 +66,18 @@ _LIBCPP_HIDE_FROM_ABI std::pair<_Real, _Real> __hypot_factors() {
     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::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);
-      return {0x1.0p+8'190l, 0x1.0p-9'000l};
-    }
+
+    // preprocessor guard necessary, otherwise literals (e.g. `0x1.0p+8'190l`) throw warnings even when shielded by `if
+    // constexpr`
+#  if __DBL_MAX_EXP__ == __LDBL_MAX_EXP__
+    static_assert(sizeof(_Real) == sizeof(double));
+    return static_cast<std::pair<_Real, _Real>>(__math::__hypot_factors<double>());
+#  else
+    static_assert(sizeof(_Real) > sizeof(double));
+    static_assert(-16'381 == std::numeric_limits<_Real>::min_exponent);
+    static_assert(+16'384 == std::numeric_limits<_Real>::max_exponent);
+    return {0x1.0p+8'190l, 0x1.0p-9'000l};
+#  endif
   }
 }
 

>From 9b0603725bf1adff2ba3c8436e73fd8e766bd449 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Fri, 19 Jul 2024 20:39:46 +0200
Subject: [PATCH 13/17] run clang format

---
 .../test/std/numerics/c.math/cmath.pass.cpp   | 68 +++++++++----------
 1 file changed, 34 insertions(+), 34 deletions(-)

diff --git a/libcxx/test/std/numerics/c.math/cmath.pass.cpp b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
index 6ed37c272192e..2fa94d388b87a 100644
--- a/libcxx/test/std/numerics/c.math/cmath.pass.cpp
+++ b/libcxx/test/std/numerics/c.math/cmath.pass.cpp
@@ -1117,41 +1117,41 @@ void test_fmin()
 }
 
 struct TestHypot3 {
-    template <class Real>
-    void operator()() const {
-        const auto check = [](Real elem, Real abs_tol) {
-            assert(std::isfinite(std::hypot(elem, Real(0), Real(0))));
-            assert(fptest_close(std::hypot(elem, Real(0), Real(0)), elem, abs_tol));
-            assert(std::isfinite(std::hypot(elem, elem, Real(0))));
-            assert(fptest_close(std::hypot(elem, elem, Real(0)), std::sqrt(Real(2)) * elem, abs_tol));
-            assert(std::isfinite(std::hypot(elem, elem, elem)));
-            assert(fptest_close(std::hypot(elem, elem, elem), std::sqrt(Real(3)) * elem, abs_tol));
-        };
-
-        { // check for overflow
-            const auto [elem, abs_tol] = []() -> std::array<Real, 2> {
-                if constexpr (std::is_same_v<Real, float>)
-                    return {1e20f, 1e16f};
-                else if constexpr (std::is_same_v<Real, double>)
-                    return {1e300, 1e287};
-                else // long double
-                    return {1e4000l, 1e3985l};
-            }();
-            check(elem, abs_tol);
-        }
-
-        { // check for underflow
-            const auto [elem, abs_tol] = []() -> std::array<Real, 2> {
-                if constexpr (std::is_same_v<Real, float>)
-                    return {1e-20f, 1e-24f};
-                else if constexpr (std::is_same_v<Real, double>)
-                    return {1e-287, 1e-300};
-                else // long double
-                    return {1e-3985l, 1e-4000l};
-            }();
-            check(elem, abs_tol);
-        }
+  template <class Real>
+  void operator()() const {
+    const auto check = [](Real elem, Real abs_tol) {
+      assert(std::isfinite(std::hypot(elem, Real(0), Real(0))));
+      assert(fptest_close(std::hypot(elem, Real(0), Real(0)), elem, abs_tol));
+      assert(std::isfinite(std::hypot(elem, elem, Real(0))));
+      assert(fptest_close(std::hypot(elem, elem, Real(0)), std::sqrt(Real(2)) * elem, abs_tol));
+      assert(std::isfinite(std::hypot(elem, elem, elem)));
+      assert(fptest_close(std::hypot(elem, elem, elem), std::sqrt(Real(3)) * elem, abs_tol));
+    };
+
+    { // check for overflow
+      const auto [elem, abs_tol] = []() -> std::array<Real, 2> {
+        if constexpr (std::is_same_v<Real, float>)
+          return {1e20f, 1e16f};
+        else if constexpr (std::is_same_v<Real, double>)
+          return {1e300, 1e287};
+        else // long double
+          return {1e4000l, 1e3985l};
+      }();
+      check(elem, abs_tol);
     }
+
+    { // check for underflow
+      const auto [elem, abs_tol] = []() -> std::array<Real, 2> {
+        if constexpr (std::is_same_v<Real, float>)
+          return {1e-20f, 1e-24f};
+        else if constexpr (std::is_same_v<Real, double>)
+          return {1e-287, 1e-300};
+        else // long double
+          return {1e-3985l, 1e-4000l};
+      }();
+      check(elem, abs_tol);
+    }
+  }
 };
 
 void test_hypot()

>From 296c520eced0b20ac1cfa56c9b49fca428c0910c Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sat, 20 Jul 2024 20:11:03 +0200
Subject: [PATCH 14/17] workaround for std::max(std::initializer_list) not
 found

---
 libcxx/include/__math/hypot.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/libcxx/include/__math/hypot.h b/libcxx/include/__math/hypot.h
index 195c8621ed448..bd19f57b5e810 100644
--- a/libcxx/include/__math/hypot.h
+++ b/libcxx/include/__math/hypot.h
@@ -87,7 +87,7 @@ _LIBCPP_HIDE_FROM_ABI std::pair<_Real, _Real> __hypot_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 _Real __max_abs = std::max({__math::fabs(__x), __math::fabs(__y), __math::fabs(__z)});
+  const _Real __max_abs = std::max(__math::fabs(__x), std::max(__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

>From a4dd9911ef5858c3f53b9860756a72ee2f3d8f87 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sat, 20 Jul 2024 20:26:17 +0200
Subject: [PATCH 15/17] make fp_compare.h ready for pre C++11 tests

---
 libcxx/test/support/fp_compare.h | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/libcxx/test/support/fp_compare.h b/libcxx/test/support/fp_compare.h
index 1d1933b0bcd81..9bbf64458601a 100644
--- a/libcxx/test/support/fp_compare.h
+++ b/libcxx/test/support/fp_compare.h
@@ -12,13 +12,14 @@
 #include <cmath>      // for std::abs
 #include <algorithm>  // for std::max
 #include <cassert>
+#include <__config>
 
 // See https://www.boost.org/doc/libs/1_70_0/libs/test/doc/html/boost_test/testing_tools/extended_comparison/floating_point/floating_points_comparison_theory.html
 
 template<typename T>
 bool fptest_close(T val, T expected, T eps)
 {
-    constexpr T zero = T(0);
+    _LIBCPP_CONSTEXPR T zero = T(0);
     assert(eps >= zero);
 
     // Handle the zero cases
@@ -33,7 +34,7 @@ bool fptest_close(T val, T expected, T eps)
 template<typename T>
 bool fptest_close_pct(T val, T expected, T percent)
 {
-    constexpr T zero = T(0);
+    _LIBCPP_CONSTEXPR T zero = T(0);
     assert(percent >= zero);
 
     // Handle the zero cases

>From 7aa67285a84d189ffb28d4d5ae85a1f480df6083 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sat, 20 Jul 2024 20:27:38 +0200
Subject: [PATCH 16/17] fp_compare: DRY remove duplicate test

---
 libcxx/test/support/fp_compare.h | 2 --
 1 file changed, 2 deletions(-)

diff --git a/libcxx/test/support/fp_compare.h b/libcxx/test/support/fp_compare.h
index 9bbf64458601a..b6f5d7257d4b3 100644
--- a/libcxx/test/support/fp_compare.h
+++ b/libcxx/test/support/fp_compare.h
@@ -37,8 +37,6 @@ bool fptest_close_pct(T val, T expected, T percent)
     _LIBCPP_CONSTEXPR T zero = T(0);
     assert(percent >= zero);
 
-    // Handle the zero cases
-    if (percent == zero) return val == expected;
     T eps = (percent / T(100)) * std::max(std::abs(val), std::abs(expected));
 
     return fptest_close(val, expected, eps);

>From 4294e879aee321999845077412dcbe8580152147 Mon Sep 17 00:00:00 2001
From: Paul <paulxicao7 at gmail.com>
Date: Sat, 20 Jul 2024 20:30:51 +0200
Subject: [PATCH 17/17] fp_compare: remove unused variable

---
 libcxx/test/support/fp_compare.h | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/libcxx/test/support/fp_compare.h b/libcxx/test/support/fp_compare.h
index b6f5d7257d4b3..4e344added4b9 100644
--- a/libcxx/test/support/fp_compare.h
+++ b/libcxx/test/support/fp_compare.h
@@ -34,11 +34,8 @@ bool fptest_close(T val, T expected, T eps)
 template<typename T>
 bool fptest_close_pct(T val, T expected, T percent)
 {
-    _LIBCPP_CONSTEXPR T zero = T(0);
-    assert(percent >= zero);
-
+    assert(percent >= T(0));
     T eps = (percent / T(100)) * std::max(std::abs(val), std::abs(expected));
-
     return fptest_close(val, expected, eps);
 }
 



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