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1//===----------------------------------------------------------------------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#ifndef _LIBCPP___MATH_HYPOT_H10#define _LIBCPP___MATH_HYPOT_H11 12#include <__config>13#include <__math/abs.h>14#include <__math/exponential_functions.h>15#include <__math/min_max.h>16#include <__math/roots.h>17#include <__type_traits/enable_if.h>18#include <__type_traits/is_arithmetic.h>19#include <__type_traits/is_same.h>20#include <__type_traits/promote.h>21#include <limits>22 23#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)24# pragma GCC system_header25#endif26 27_LIBCPP_PUSH_MACROS28#include <__undef_macros>29 30_LIBCPP_BEGIN_NAMESPACE_STD31 32namespace __math {33 34inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); }35 36template <class = int>37_LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT {38 return __builtin_hypot(__x, __y);39}40 41inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT {42 return __builtin_hypotl(__x, __y);43}44 45template <class _A1, class _A2, __enable_if_t<is_arithmetic<_A1>::value && is_arithmetic<_A2>::value, int> = 0>46inline _LIBCPP_HIDE_FROM_ABI __promote_t<_A1, _A2> hypot(_A1 __x, _A2 __y) _NOEXCEPT {47 using __result_type = __promote_t<_A1, _A2>;48 static_assert(!(_IsSame<_A1, __result_type>::value && _IsSame<_A2, __result_type>::value), "");49 return __math::hypot((__result_type)__x, (__result_type)__y);50}51 52#if _LIBCPP_STD_VER >= 1753// Computes the three-dimensional hypotenuse: `std::hypot(x,y,z)`.54// The naive implementation might over-/underflow which is why this implementation is more involved:55// If the square of an argument might run into issues, we scale the arguments appropriately.56// See https://llvm.org/PR92782 for a detailed discussion and summary.57template <class _Real>58_LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) {59 // Factors needed to determine if over-/underflow might happen60 constexpr int __exp = std::numeric_limits<_Real>::max_exponent / 2;61 const _Real __overflow_threshold = __math::ldexp(_Real(1), __exp);62 const _Real __overflow_scale = __math::ldexp(_Real(1), -(__exp + 20));63 64 // Scale arguments depending on their size65 const _Real __max_abs = __math::fmax(__math::fabs(__x), __math::fmax(__math::fabs(__y), __math::fabs(__z)));66 _Real __scale;67 if (__max_abs > __overflow_threshold) { // x*x + y*y + z*z might overflow68 __scale = __overflow_scale;69 } else if (__max_abs < 1 / __overflow_threshold) { // x*x + y*y + z*z might underflow70 __scale = 1 / __overflow_scale;71 } else {72 __scale = 1;73 }74 __x *= __scale;75 __y *= __scale;76 __z *= __scale;77 78 // Compute hypot of scaled arguments and undo scaling79 return __math::sqrt(__x * __x + __y * __y + __z * __z) / __scale;80}81 82inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); }83 84inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); }85 86inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) {87 return __math::__hypot(__x, __y, __z);88}89 90template <class _A1,91 class _A2,92 class _A3,93 std::enable_if_t< is_arithmetic_v<_A1> && is_arithmetic_v<_A2> && is_arithmetic_v<_A3>, int> = 0 >94_LIBCPP_HIDE_FROM_ABI __promote_t<_A1, _A2, _A3> hypot(_A1 __x, _A2 __y, _A3 __z) _NOEXCEPT {95 using __result_type = __promote_t<_A1, _A2, _A3>;96 static_assert(!(97 std::is_same_v<_A1, __result_type> && std::is_same_v<_A2, __result_type> && std::is_same_v<_A3, __result_type>));98 return __math::__hypot(99 static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z));100}101#endif102 103} // namespace __math104 105_LIBCPP_END_NAMESPACE_STD106_LIBCPP_POP_MACROS107 108#endif // _LIBCPP___MATH_HYPOT_H109