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boost/math/tools/detail/rational_horner3_6.hpp

```//  (C) Copyright John Maddock 2007.
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
//
//  This file is machine generated, do not edit by hand

// Polynomial evaluation using second order Horners rule
#ifndef BOOST_MATH_TOOLS_RAT_EVAL_6_HPP
#define BOOST_MATH_TOOLS_RAT_EVAL_6_HPP

namespace boost{ namespace math{ namespace tools{ namespace detail{

template <class T, class U, class V>
inline V evaluate_rational_c_imp(const T*, const U*, const V&, const std::integral_constant<int, 0>*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast<V>(0);
}

template <class T, class U, class V>
inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const std::integral_constant<int, 1>*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast<V>(a[0]) / static_cast<V>(b[0]);
}

template <class T, class U, class V>
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)
{
return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));
}

template <class T, class U, class V>
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)
{
return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
}

template <class T, class U, class V>
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)
{
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]));
}

template <class T, class U, class V>
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)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[4] * x2 + a[2];
t[1] = a[3] * x2 + a[1];
t[2] = b[4] * x2 + b[2];
t[3] = b[3] * x2 + b[1];
t[0] *= x2;
t[2] *= x2;
t[0] += static_cast<V>(a[0]);
t[2] += static_cast<V>(b[0]);
t[1] *= x;
t[3] *= x;
return (t[0] + t[1]) / (t[2] + t[3]);
}
else
{
V z = 1 / x;
V z2 = 1 / (x * x);
V t[4];
t[0] = a[0] * z2 + a[2];
t[1] = a[1] * z2 + a[3];
t[2] = b[0] * z2 + b[2];
t[3] = b[1] * z2 + b[3];
t[0] *= z2;
t[2] *= z2;
t[0] += static_cast<V>(a[4]);
t[2] += static_cast<V>(b[4]);
t[1] *= z;
t[3] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}

template <class T, class U, class V>
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)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[5] * x2 + a[3];
t[1] = a[4] * x2 + a[2];
t[2] = b[5] * x2 + b[3];
t[3] = b[4] * x2 + b[2];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast<V>(a[1]);
t[1] += static_cast<V>(a[0]);
t[2] += static_cast<V>(b[1]);
t[3] += static_cast<V>(b[0]);
t[0] *= x;
t[2] *= x;
return (t[0] + t[1]) / (t[2] + t[3]);
}
else
{
V z = 1 / x;
V z2 = 1 / (x * x);
V t[4];
t[0] = a[0] * z2 + a[2];
t[1] = a[1] * z2 + a[3];
t[2] = b[0] * z2 + b[2];
t[3] = b[1] * z2 + b[3];
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast<V>(a[4]);
t[1] += static_cast<V>(a[5]);
t[2] += static_cast<V>(b[4]);
t[3] += static_cast<V>(b[5]);
t[0] *= z;
t[2] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}

}}}} // namespaces

#endif // include guard

```