tools/detail/rational_horner2_10.hpp

0001 //  (C) Copyright John Maddock 2007.
0002 //  Use, modification and distribution are subject to the
0003 //  Boost Software License, Version 1.0. (See accompanying file
0004 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0005 //
0006 //  This file is machine generated, do not edit by hand
0007
0008 // Polynomial evaluation using second order Horners rule
0009 #ifndef BOOST_MATH_TOOLS_RAT_EVAL_10_HPP
0010 #define BOOST_MATH_TOOLS_RAT_EVAL_10_HPP
0011
0012 namespace boost{ namespace math{ namespace tools{ namespace detail{
0013
0014 template <class T, class U, class V>
0015 inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
0016 {
0017    return static_cast<V>(0);
0018 }
0019
0020 template <class T, class U, class V>
0021 inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
0022 {
0023    return static_cast<V>(a[0]) / static_cast<V>(b[0]);
0024 }
0025
0026 template <class T, class U, class V>
0027 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 2>*) BOOST_MATH_NOEXCEPT(V)
0028 {
0029    return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
0030 }
0031
0032 template <class T, class U, class V>
0033 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 3>*) BOOST_MATH_NOEXCEPT(V)
0034 {
0035    return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
0036 }
0037
0038 template <class T, class U, class V>
0039 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 4>*) BOOST_MATH_NOEXCEPT(V)
0040 {
0041    return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
0042 }
0043
0044 template <class T, class U, class V>
0045 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 5>*) BOOST_MATH_NOEXCEPT(V)
0046 {
0047    if(x <= 1)
0048    {
0049       V x2 = x * x;
0050       return static_cast<V>(((a[4] * x2 + a[2]) * x2 + a[0] + (a[3] * x2 + a[1]) * x) / ((b[4] * x2 + b[2]) * x2 + b[0] + (b[3] * x2 + b[1]) * x));
0051    }
0052    else
0053    {
0054       V z = 1 / x;
0055       V z2 = 1 / (x * x);
0056       return static_cast<V>(((a[0] * z2 + a[2]) * z2 + a[4] + (a[1] * z2 + a[3]) * z) / ((b[0] * z2 + b[2]) * z2 + b[4] + (b[1] * z2 + b[3]) * z));
0057    }
0058 }
0059
0060 template <class T, class U, class V>
0061 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 6>*) BOOST_MATH_NOEXCEPT(V)
0062 {
0063    if(x <= 1)
0064    {
0065       V x2 = x * x;
0066       return static_cast<V>((((a[5] * x2 + a[3]) * x2 + a[1]) * x + (a[4] * x2 + a[2]) * x2 + a[0]) / (((b[5] * x2 + b[3]) * x2 + b[1]) * x + (b[4] * x2 + b[2]) * x2 + b[0]));
0067    }
0068    else
0069    {
0070       V z = 1 / x;
0071       V z2 = 1 / (x * x);
0072       return static_cast<V>((((a[0] * z2 + a[2]) * z2 + a[4]) * z + (a[1] * z2 + a[3]) * z2 + a[5]) / (((b[0] * z2 + b[2]) * z2 + b[4]) * z + (b[1] * z2 + b[3]) * z2 + b[5]));
0073    }
0074 }
0075
0076 template <class T, class U, class V>
0077 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 7>*) BOOST_MATH_NOEXCEPT(V)
0078 {
0079    if(x <= 1)
0080    {
0081       V x2 = x * x;
0082       return static_cast<V>((((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + ((a[5] * x2 + a[3]) * x2 + a[1]) * x) / (((b[6] * x2 + b[4]) * x2 + b[2]) * x2 + b[0] + ((b[5] * x2 + b[3]) * x2 + b[1]) * x));
0083    }
0084    else
0085    {
0086       V z = 1 / x;
0087       V z2 = 1 / (x * x);
0088       return static_cast<V>((((a[0] * z2 + a[2]) * z2 + a[4]) * z2 + a[6] + ((a[1] * z2 + a[3]) * z2 + a[5]) * z) / (((b[0] * z2 + b[2]) * z2 + b[4]) * z2 + b[6] + ((b[1] * z2 + b[3]) * z2 + b[5]) * z));
0089    }
0090 }
0091
0092 template <class T, class U, class V>
0093 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 8>*) BOOST_MATH_NOEXCEPT(V)
0094 {
0095    if(x <= 1)
0096    {
0097       V x2 = x * x;
0098       return static_cast<V>(((((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + ((a[6] * x2 + a[4]) * x2 + a[2]) * x2 + a[0]) / ((((b[7] * x2 + b[5]) * x2 + b[3]) * x2 + b[1]) * x + ((b[6] * x2 + b[4]) * x2 + b[2]) * x2 + b[0]));
0099    }
0100    else
0101    {
0102       V z = 1 / x;
0103       V z2 = 1 / (x * x);
0104       return static_cast<V>(((((a[0] * z2 + a[2]) * z2 + a[4]) * z2 + a[6]) * z + ((a[1] * z2 + a[3]) * z2 + a[5]) * z2 + a[7]) / ((((b[0] * z2 + b[2]) * z2 + b[4]) * z2 + b[6]) * z + ((b[1] * z2 + b[3]) * z2 + b[5]) * z2 + b[7]));
0105    }
0106 }
0107
0108 template <class T, class U, class V>
0109 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 9>*) BOOST_MATH_NOEXCEPT(V)
0110 {
0111    if(x <= 1)
0112    {
0113       V x2 = x * x;
0114       return static_cast<V>(((((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0] + (((a[7] * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x) / ((((b[8] * x2 + b[6]) * x2 + b[4]) * x2 + b[2]) * x2 + b[0] + (((b[7] * x2 + b[5]) * x2 + b[3]) * x2 + b[1]) * x));
0115    }
0116    else
0117    {
0118       V z = 1 / x;
0119       V z2 = 1 / (x * x);
0120       return static_cast<V>(((((a[0] * z2 + a[2]) * z2 + a[4]) * z2 + a[6]) * z2 + a[8] + (((a[1] * z2 + a[3]) * z2 + a[5]) * z2 + a[7]) * z) / ((((b[0] * z2 + b[2]) * z2 + b[4]) * z2 + b[6]) * z2 + b[8] + (((b[1] * z2 + b[3]) * z2 + b[5]) * z2 + b[7]) * z));
0121    }
0122 }
0123
0124 template <class T, class U, class V>
0125 inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const std::integral_constant<int, 10>*) BOOST_MATH_NOEXCEPT(V)
0126 {
0127    if(x <= 1)
0128    {
0129       V x2 = x * x;
0130       return static_cast<V>((((((a[9] * x2 + a[7]) * x2 + a[5]) * x2 + a[3]) * x2 + a[1]) * x + (((a[8] * x2 + a[6]) * x2 + a[4]) * x2 + a[2]) * x2 + a[0]) / (((((b[9] * x2 + b[7]) * x2 + b[5]) * x2 + b[3]) * x2 + b[1]) * x + (((b[8] * x2 + b[6]) * x2 + b[4]) * x2 + b[2]) * x2 + b[0]));
0131    }
0132    else
0133    {
0134       V z = 1 / x;
0135       V z2 = 1 / (x * x);
0136       return static_cast<V>((((((a[0] * z2 + a[2]) * z2 + a[4]) * z2 + a[6]) * z2 + a[8]) * z + (((a[1] * z2 + a[3]) * z2 + a[5]) * z2 + a[7]) * z2 + a[9]) / (((((b[0] * z2 + b[2]) * z2 + b[4]) * z2 + b[6]) * z2 + b[8]) * z + (((b[1] * z2 + b[3]) * z2 + b[5]) * z2 + b[7]) * z2 + b[9]));
0137    }
0138 }
0139
0140
0141 }}}} // namespaces
0142
0143 #endif // include guard
0144