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 <__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_header 25 #endif 26 27 _LIBCPP_PUSH_MACROS 28 #include <__undef_macros> 29 30 _LIBCPP_BEGIN_NAMESPACE_STD 31 32 namespace __math { 33 34 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); } 35 36 template <class = int> 37 _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT { 38 return __builtin_hypot(__x, __y); 39 } 40 41 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT { 42 return __builtin_hypotl(__x, __y); 43 } 44 45 template <class _A1, class _A2, __enable_if_t<is_arithmetic<_A1>::value && is_arithmetic<_A2>::value, int> = 0> 46 inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type hypot(_A1 __x, _A2 __y) _NOEXCEPT { 47 using __result_type = typename __promote<_A1, _A2>::type; 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 >= 17 53 // 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://github.com/llvm/llvm-project/issues/92782 for a detailed discussion and summary. 57 template <class _Real> 58 _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) { 59 // Factors needed to determine if over-/underflow might happen 60 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 size 65 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 overflow 68 __scale = __overflow_scale; 69 } else if (__max_abs < 1 / __overflow_threshold) { // x*x + y*y + z*z might underflow 70 __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 scaling 79 return __math::sqrt(__x * __x + __y * __y + __z * __z) / __scale; 80 } 81 82 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); } 83 84 inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); } 85 86 inline _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 90 template <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 typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2 __y, _A3 __z) _NOEXCEPT { 95 using __result_type = typename __promote<_A1, _A2, _A3>::type; 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 #endif 102 103 } // namespace __math 104 105 _LIBCPP_END_NAMESPACE_STD 106 _LIBCPP_POP_MACROS 107 108 #endif // _LIBCPP___MATH_HYPOT_H 109