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
hypot(float __x,float __y)35 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); }
36
37 template <class = int>
hypot(double __x,double __y)38 _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT {
39 return __builtin_hypot(__x, __y);
40 }
41
hypot(long double __x,long double __y)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>
hypot(_A1 __x,_A2 __y)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>
__hypot(_Real __x,_Real __y,_Real __z)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
hypot(float __x,float __y,float __z)83 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); }
84
hypot(double __x,double __y,double __z)85 inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); }
86
hypot(long double __x,long double __y,long double __z)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 >
hypot(_A1 __x,_A2 __y,_A3 __z)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