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-exception 6 // 7 //===----------------------------------------------------------------------===// 8 9 #ifndef _LIBCPP___MATH_HYPOT_H 10 #define _LIBCPP___MATH_HYPOT_H 11 12 #include <__config> 13 #include <__type_traits/enable_if.h> 14 #include <__type_traits/is_arithmetic.h> 15 #include <__type_traits/is_same.h> 16 #include <__type_traits/promote.h> 17 18 #if _LIBCPP_STD_VER >= 17 19 # include <__algorithm/max.h> 20 # include <__math/abs.h> 21 # include <__math/roots.h> 22 # include <__utility/pair.h> 23 # include <limits> 24 #endif 25 26 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 27 # pragma GCC system_header 28 #endif 29 30 _LIBCPP_PUSH_MACROS 31 #include <__undef_macros> 32 33 _LIBCPP_BEGIN_NAMESPACE_STD 34 35 namespace __math { 36 37 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); } 38 39 template <class = int> 40 _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT { 41 return __builtin_hypot(__x, __y); 42 } 43 44 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT { 45 return __builtin_hypotl(__x, __y); 46 } 47 48 template <class _A1, class _A2, __enable_if_t<is_arithmetic<_A1>::value && is_arithmetic<_A2>::value, int> = 0> 49 inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type hypot(_A1 __x, _A2 __y) _NOEXCEPT { 50 using __result_type = typename __promote<_A1, _A2>::type; 51 static_assert(!(_IsSame<_A1, __result_type>::value && _IsSame<_A2, __result_type>::value), ""); 52 return __math::hypot((__result_type)__x, (__result_type)__y); 53 } 54 55 #if _LIBCPP_STD_VER >= 17 56 // Factors needed to determine if over-/underflow might happen for `std::hypot(x,y,z)`. 57 // returns [overflow_threshold, overflow_scale] 58 template <class _Real> 59 _LIBCPP_HIDE_FROM_ABI std::pair<_Real, _Real> __hypot_factors() { 60 static_assert(std::numeric_limits<_Real>::is_iec559); 61 62 if constexpr (std::is_same_v<_Real, float>) { 63 static_assert(-125 == std::numeric_limits<_Real>::min_exponent); 64 static_assert(+128 == std::numeric_limits<_Real>::max_exponent); 65 return {0x1.0p+62f, 0x1.0p-70f}; 66 } else if constexpr (std::is_same_v<_Real, double>) { 67 static_assert(-1021 == std::numeric_limits<_Real>::min_exponent); 68 static_assert(+1024 == std::numeric_limits<_Real>::max_exponent); 69 return {0x1.0p+510, 0x1.0p-600}; 70 } else { // long double 71 static_assert(std::is_same_v<_Real, long double>); 72 73 // preprocessor guard necessary, otherwise literals (e.g. `0x1.0p+8'190l`) throw warnings even when shielded by `if 74 // constexpr` 75 # if __DBL_MAX_EXP__ == __LDBL_MAX_EXP__ 76 static_assert(sizeof(_Real) == sizeof(double)); 77 return static_cast<std::pair<_Real, _Real>>(__math::__hypot_factors<double>()); 78 # else 79 static_assert(sizeof(_Real) > sizeof(double)); 80 static_assert(-16381 == std::numeric_limits<_Real>::min_exponent); 81 static_assert(+16384 == std::numeric_limits<_Real>::max_exponent); 82 return {0x1.0p+8190l, 0x1.0p-9000l}; 83 # endif 84 } 85 } 86 87 // Computes the three-dimensional hypotenuse: `std::hypot(x,y,z)`. 88 // The naive implementation might over-/underflow which is why this implementation is more involved: 89 // If the square of an argument might run into issues, we scale the arguments appropriately. 90 // See https://github.com/llvm/llvm-project/issues/92782 for a detailed discussion and summary. 91 template <class _Real> 92 _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) { 93 const _Real __max_abs = std::max(__math::fabs(__x), std::max(__math::fabs(__y), __math::fabs(__z))); 94 const auto [__overflow_threshold, __overflow_scale] = __math::__hypot_factors<_Real>(); 95 _Real __scale; 96 if (__max_abs > __overflow_threshold) { // x*x + y*y + z*z might overflow 97 __scale = __overflow_scale; 98 __x *= __scale; 99 __y *= __scale; 100 __z *= __scale; 101 } else if (__max_abs < 1 / __overflow_threshold) { // x*x + y*y + z*z might underflow 102 __scale = 1 / __overflow_scale; 103 __x *= __scale; 104 __y *= __scale; 105 __z *= __scale; 106 } else 107 __scale = 1; 108 return __math::sqrt(__x * __x + __y * __y + __z * __z) / __scale; 109 } 110 111 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); } 112 113 inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); } 114 115 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) { 116 return __math::__hypot(__x, __y, __z); 117 } 118 119 template <class _A1, 120 class _A2, 121 class _A3, 122 std::enable_if_t< is_arithmetic_v<_A1> && is_arithmetic_v<_A2> && is_arithmetic_v<_A3>, int> = 0 > 123 _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2 __y, _A3 __z) _NOEXCEPT { 124 using __result_type = typename __promote<_A1, _A2, _A3>::type; 125 static_assert(!( 126 std::is_same_v<_A1, __result_type> && std::is_same_v<_A2, __result_type> && std::is_same_v<_A3, __result_type>)); 127 return __math::__hypot( 128 static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z)); 129 } 130 #endif 131 132 } // namespace __math 133 134 _LIBCPP_END_NAMESPACE_STD 135 _LIBCPP_POP_MACROS 136 137 #endif // _LIBCPP___MATH_HYPOT_H 138