libcxx/include/__math/special_functions.h

   1 // -*- C++ -*-
   2 //===----------------------------------------------------------------------===//
   3 //
   4 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   5 // See https://llvm.org/LICENSE.txt for license information.
   6 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   7 //
   8 //===----------------------------------------------------------------------===//
   9
  10 #ifndef _LIBCPP___MATH_SPECIAL_FUNCTIONS_H
  11 #define _LIBCPP___MATH_SPECIAL_FUNCTIONS_H
  12
  13 #include <__config>
  14 #include <__math/copysign.h>
  15 #include <__math/traits.h>
  16 #include <__type_traits/enable_if.h>
  17 #include <__type_traits/is_integral.h>
  18 #include <limits>
  19
  20 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
  21 #  pragma GCC system_header
  22 #endif
  23
  24 _LIBCPP_BEGIN_NAMESPACE_STD
  25
  26 #if _LIBCPP_STD_VER >= 17
  27
  28 template <class _Real>
  29 _LIBCPP_HIDE_FROM_ABI _Real __hermite(unsigned __n, _Real __x) {
  30   // The Hermite polynomial H_n(x).
  31   // The implementation is based on the recurrence formula: H_{n+1}(x) = 2x H_n(x) - 2n H_{n-1}.
  32   // Press, William H., et al. Numerical recipes 3rd edition: The art of scientific computing.
  33   // Cambridge university press, 2007, p. 183.
  34
  35   // NOLINTBEGIN(readability-identifier-naming)
  36   if (__math::isnan(__x))
  37     return __x;
  38
  39   _Real __H_0{1};
  40   if (__n == 0)
  41     return __H_0;
  42
  43   _Real __H_n_prev = __H_0;
  44   _Real __H_n      = 2 * __x;
  45   for (unsigned __i = 1; __i < __n; ++__i) {
  46     _Real __H_n_next = 2 * (__x * __H_n - __i * __H_n_prev);
  47     __H_n_prev       = __H_n;
  48     __H_n            = __H_n_next;
  49   }
  50
  51   if (!__math::isfinite(__H_n)) {
  52     // Overflow occured. Two possible cases:
  53     //    n is odd:  return infinity of the same sign as x.
  54     //    n is even: return +Inf
  55     _Real __inf = std::numeric_limits<_Real>::infinity();
  56     return (__n & 1) ? __math::copysign(__inf, __x) : __inf;
  57   }
  58   return __H_n;
  59   // NOLINTEND(readability-identifier-naming)
  60 }
  61
  62 inline _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, double __x) { return std::__hermite(__n, __x); }
  63
  64 inline _LIBCPP_HIDE_FROM_ABI float hermite(unsigned __n, float __x) {
  65   // use double internally -- float is too prone to overflow!
  66   return static_cast<float>(std::hermite(__n, static_cast<double>(__x)));
  67 }
  68
  69 inline _LIBCPP_HIDE_FROM_ABI long double hermite(unsigned __n, long double __x) { return std::__hermite(__n, __x); }
  70
  71 inline _LIBCPP_HIDE_FROM_ABI float hermitef(unsigned __n, float __x) { return std::hermite(__n, __x); }
  72
  73 inline _LIBCPP_HIDE_FROM_ABI long double hermitel(unsigned __n, long double __x) { return std::hermite(__n, __x); }
  74
  75 template <class _Integer, std::enable_if_t<std::is_integral_v<_Integer>, int> = 0>
  76 _LIBCPP_HIDE_FROM_ABI double hermite(unsigned __n, _Integer __x) {
  77   return std::hermite(__n, static_cast<double>(__x));
  78 }
  79
  80 #endif // _LIBCPP_STD_VER >= 17
  81
  82 _LIBCPP_END_NAMESPACE_STD
  83
  84 #endif // _LIBCPP___MATH_SPECIAL_FUNCTIONS_H