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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-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
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 >= 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.
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 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
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#endif
102
103} // namespace __math
104
105_LIBCPP_END_NAMESPACE_STD
106_LIBCPP_POP_MACROS
107
108#endif // _LIBCPP___MATH_HYPOT_H