249 lines
6.7 KiB
Plaintext
249 lines
6.7 KiB
Plaintext
|
// (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_8_HPP
|
||
|
|
#define BOOST_MATH_TOOLS_RAT_EVAL_8_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 mpl::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 mpl::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 mpl::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 mpl::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 mpl::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 mpl::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 mpl::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]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class T, class U, class V>
|
||
|
|
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) BOOST_MATH_NOEXCEPT(V)
|
||
|
|
{
|
||
|
|
if(x <= 1)
|
||
|
|
{
|
||
|
|
V x2 = x * x;
|
||
|
|
V t[4];
|
||
|
|
t[0] = a[6] * x2 + a[4];
|
||
|
|
t[1] = a[5] * x2 + a[3];
|
||
|
|
t[2] = b[6] * x2 + b[4];
|
||
|
|
t[3] = b[5] * x2 + b[3];
|
||
|
|
t[0] *= x2;
|
||
|
|
t[1] *= x2;
|
||
|
|
t[2] *= x2;
|
||
|
|
t[3] *= x2;
|
||
|
|
t[0] += static_cast<V>(a[2]);
|
||
|
|
t[1] += static_cast<V>(a[1]);
|
||
|
|
t[2] += static_cast<V>(b[2]);
|
||
|
|
t[3] += static_cast<V>(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[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] *= z2;
|
||
|
|
t[2] *= z2;
|
||
|
|
t[0] += static_cast<V>(a[6]);
|
||
|
|
t[2] += static_cast<V>(b[6]);
|
||
|
|
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 mpl::int_<8>*) BOOST_MATH_NOEXCEPT(V)
|
||
|
|
{
|
||
|
|
if(x <= 1)
|
||
|
|
{
|
||
|
|
V x2 = x * x;
|
||
|
|
V t[4];
|
||
|
|
t[0] = a[7] * x2 + a[5];
|
||
|
|
t[1] = a[6] * x2 + a[4];
|
||
|
|
t[2] = b[7] * x2 + b[5];
|
||
|
|
t[3] = b[6] * x2 + b[4];
|
||
|
|
t[0] *= x2;
|
||
|
|
t[1] *= x2;
|
||
|
|
t[2] *= x2;
|
||
|
|
t[3] *= x2;
|
||
|
|
t[0] += static_cast<V>(a[3]);
|
||
|
|
t[1] += static_cast<V>(a[2]);
|
||
|
|
t[2] += static_cast<V>(b[3]);
|
||
|
|
t[3] += static_cast<V>(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] *= z2;
|
||
|
|
t[1] *= z2;
|
||
|
|
t[2] *= z2;
|
||
|
|
t[3] *= z2;
|
||
|
|
t[0] += static_cast<V>(a[6]);
|
||
|
|
t[1] += static_cast<V>(a[7]);
|
||
|
|
t[2] += static_cast<V>(b[6]);
|
||
|
|
t[3] += static_cast<V>(b[7]);
|
||
|
|
t[0] *= z;
|
||
|
|
t[2] *= z;
|
||
|
|
return (t[0] + t[1]) / (t[2] + t[3]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
}}}} // namespaces
|
||
|
|
|
||
|
|
#endif // include guard
|
||
|
|
|