v1/__math/hypot.h

0001 //===----------------------------------------------------------------------===//
0002 //
0003 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
0004 // See https://llvm.org/LICENSE.txt for license information.
0005 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
0006 //
0007 //===----------------------------------------------------------------------===//
0008
0009 #ifndef _LIBCPP___MATH_HYPOT_H
0010 #define _LIBCPP___MATH_HYPOT_H
0011
0012 #include <__config>
0013 #include <__math/abs.h>
0014 #include <__math/exponential_functions.h>
0015 #include <__math/min_max.h>
0016 #include <__math/roots.h>
0017 #include <__type_traits/enable_if.h>
0018 #include <__type_traits/is_arithmetic.h>
0019 #include <__type_traits/is_same.h>
0020 #include <__type_traits/promote.h>
0021 #include <limits>
0022
0023 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
0024 #  pragma GCC system_header
0025 #endif
0026
0027 _LIBCPP_PUSH_MACROS
0028 #include <__undef_macros>
0029
0030 _LIBCPP_BEGIN_NAMESPACE_STD
0031
0032 namespace __math {
0033
0034 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y) _NOEXCEPT { return __builtin_hypotf(__x, __y); }
0035
0036 template <class = int>
0037 _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y) _NOEXCEPT {
0038   return __builtin_hypot(__x, __y);
0039 }
0040
0041 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y) _NOEXCEPT {
0042   return __builtin_hypotl(__x, __y);
0043 }
0044
0045 template <class _A1, class _A2, __enable_if_t<is_arithmetic<_A1>::value && is_arithmetic<_A2>::value, int> = 0>
0046 inline _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2>::type hypot(_A1 __x, _A2 __y) _NOEXCEPT {
0047   using __result_type = typename __promote<_A1, _A2>::type;
0048   static_assert(!(_IsSame<_A1, __result_type>::value && _IsSame<_A2, __result_type>::value), "");
0049   return __math::hypot((__result_type)__x, (__result_type)__y);
0050 }
0051
0052 #if _LIBCPP_STD_VER >= 17
0053 // Computes the three-dimensional hypotenuse: `std::hypot(x,y,z)`.
0054 // The naive implementation might over-/underflow which is why this implementation is more involved:
0055 //    If the square of an argument might run into issues, we scale the arguments appropriately.
0056 // See https://github.com/llvm/llvm-project/issues/92782 for a detailed discussion and summary.
0057 template <class _Real>
0058 _LIBCPP_HIDE_FROM_ABI _Real __hypot(_Real __x, _Real __y, _Real __z) {
0059   // Factors needed to determine if over-/underflow might happen
0060   constexpr int __exp              = std::numeric_limits<_Real>::max_exponent / 2;
0061   const _Real __overflow_threshold = __math::ldexp(_Real(1), __exp);
0062   const _Real __overflow_scale     = __math::ldexp(_Real(1), -(__exp + 20));
0063
0064   // Scale arguments depending on their size
0065   const _Real __max_abs = __math::fmax(__math::fabs(__x), __math::fmax(__math::fabs(__y), __math::fabs(__z)));
0066   _Real __scale;
0067   if (__max_abs > __overflow_threshold) { // x*x + y*y + z*z might overflow
0068     __scale = __overflow_scale;
0069   } else if (__max_abs < 1 / __overflow_threshold) { // x*x + y*y + z*z might underflow
0070     __scale = 1 / __overflow_scale;
0071   } else {
0072     __scale = 1;
0073   }
0074   __x *= __scale;
0075   __y *= __scale;
0076   __z *= __scale;
0077
0078   // Compute hypot of scaled arguments and undo scaling
0079   return __math::sqrt(__x * __x + __y * __y + __z * __z) / __scale;
0080 }
0081
0082 inline _LIBCPP_HIDE_FROM_ABI float hypot(float __x, float __y, float __z) { return __math::__hypot(__x, __y, __z); }
0083
0084 inline _LIBCPP_HIDE_FROM_ABI double hypot(double __x, double __y, double __z) { return __math::__hypot(__x, __y, __z); }
0085
0086 inline _LIBCPP_HIDE_FROM_ABI long double hypot(long double __x, long double __y, long double __z) {
0087   return __math::__hypot(__x, __y, __z);
0088 }
0089
0090 template <class _A1,
0091           class _A2,
0092           class _A3,
0093           std::enable_if_t< is_arithmetic_v<_A1> && is_arithmetic_v<_A2> && is_arithmetic_v<_A3>, int> = 0 >
0094 _LIBCPP_HIDE_FROM_ABI typename __promote<_A1, _A2, _A3>::type hypot(_A1 __x, _A2 __y, _A3 __z) _NOEXCEPT {
0095   using __result_type = typename __promote<_A1, _A2, _A3>::type;
0096   static_assert(!(
0097       std::is_same_v<_A1, __result_type> && std::is_same_v<_A2, __result_type> && std::is_same_v<_A3, __result_type>));
0098   return __math::__hypot(
0099       static_cast<__result_type>(__x), static_cast<__result_type>(__y), static_cast<__result_type>(__z));
0100 }
0101 #endif
0102
0103 } // namespace __math
0104
0105 _LIBCPP_END_NAMESPACE_STD
0106 _LIBCPP_POP_MACROS
0107
0108 #endif // _LIBCPP___MATH_HYPOT_H