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
33namespace __math {
34
35inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); }
36
37template <class = int>
38_LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT {
39 return __builtin_hypot(__x, __y);
40}
41
42inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT {
43 return __builtin_hypotl(__x, __y);
44}
45
46template <class _A1, class _A2, __enable_if_t<is_arithmetic<_A1>::value && is_arithmetic<_A2>::value, int> = 0>
47inline _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.
58template <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
83inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); }
84
85inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); }
86
87inline _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
91template <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