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 <__algorithm/max.h> 13 #include <__config> 14 #include <__math/abs.h> 15 #include <__math/exponential_functions.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 <__utility/pair.h> 22 #include <limits> 23 24 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 25 # pragma GCC system_header 26 #endif 27 28 _LIBCPP_PUSH_MACROS 29 #include <__undef_macros> 30 31 _LIBCPP_BEGIN_NAMESPACE_STD 32 33 namespace __math { 34 35 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); } 36 37 template <class = int> 38 _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT { 39 return __builtin_hypot(__x, __y); 40 } 41 42 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT { 43 return __builtin_hypotl(__x, __y); 44 } 45 46 template <class _A1, class _A2, __enable_if_t<is_arithmetic<_A1>::value && is_arithmetic<_A2>::value, int> = 0> 47 inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type hypot(_A1 __x, _A2 __y) _NOEXCEPT { 48 using __result_type = typename __promote<_A1, _A2>::type; 49 static_assert(!(_IsSame<_A1, __result_type>::value && _IsSame<_A2, __result_type>::value), ""); 50 return __math::hypot((__result_type)__x, (__result_type)__y); 51 } 52 53 #if _LIBCPP_STD_VER >= 17 54 // Computes the three-dimensional hypotenuse: `std::hypot(x,y,z)`. 55 // The naive implementation might over-/underflow which is why this implementation is more involved: 56 // If the square of an argument might run into issues, we scale the arguments appropriately. 57 // See https://github.com/llvm/llvm-project/issues/92782 for a detailed discussion and summary. 58 template <class _Real> 59 _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) { 60 // Factors needed to determine if over-/underflow might happen 61 constexpr int __exp = std::numeric_limits<_Real>::max_exponent / 2; 62 const _Real __overflow_threshold = __math::ldexp(_Real(1), __exp); 63 const _Real __overflow_scale = __math::ldexp(_Real(1), -(__exp + 20)); 64 65 // Scale arguments depending on their size 66 const _Real __max_abs = std::max(__math::fabs(__x), std::max(__math::fabs(__y), __math::fabs(__z))); 67 _Real __scale; 68 if (__max_abs > __overflow_threshold) { // x*x + y*y + z*z might overflow 69 __scale = __overflow_scale; 70 } else if (__max_abs < 1 / __overflow_threshold) { // x*x + y*y + z*z might underflow 71 __scale = 1 / __overflow_scale; 72 } else { 73 __scale = 1; 74 } 75 __x *= __scale; 76 __y *= __scale; 77 __z *= __scale; 78 79 // Compute hypot of scaled arguments and undo scaling 80 return __math::sqrt(__x * __x + __y * __y + __z * __z) / __scale; 81 } 82 83 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); } 84 85 inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); } 86 87 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) { 88 return __math::__hypot(__x, __y, __z); 89 } 90 91 template <class _A1, 92 class _A2, 93 class _A3, 94 std::enable_if_t< is_arithmetic_v<_A1> && is_arithmetic_v<_A2> && is_arithmetic_v<_A3>, int> = 0 > 95 _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2 __y, _A3 __z) _NOEXCEPT { 96 using __result_type = typename __promote<_A1, _A2, _A3>::type; 97 static_assert(!( 98 std::is_same_v<_A1, __result_type> && std::is_same_v<_A2, __result_type> && std::is_same_v<_A3, __result_type>)); 99 return __math::__hypot( 100 static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z)); 101 } 102 #endif 103 104 } // namespace __math 105 106 _LIBCPP_END_NAMESPACE_STD 107 _LIBCPP_POP_MACROS 108 109 #endif // _LIBCPP___MATH_HYPOT_H 110