xref: /llvm-project/libcxx/include/__math/hypot.h (revision 23f6c3370b8bc0bf773e69a41bf90454c0a10120)
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