libcxx/include/__math/hypot.h

   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