/usr/include/boost/math/tools/detail
Edit: /usr/include/boost/math/tools/detail/rational_horner3_19.hpp (38587B)
// (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_19_HPP
#define BOOST_MATH_TOOLS_RAT_EVAL_19_HPP
namespace boost{ namespace math{ namespace tools{ namespace detail{
template
inline V evaluate_rational_c_imp(const T*, const U*, const V&, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast(0);
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast(a[0]) / static_cast(b[0]);
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast((a[1] * x + a[0]) / (b[1] * x + b[0]));
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
return static_cast((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0]));
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) 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(a[0]);
t[2] += static_cast(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(a[4]);
t[2] += static_cast(b[4]);
t[1] *= z;
t[3] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) 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(a[1]);
t[1] += static_cast(a[0]);
t[2] += static_cast(b[1]);
t[3] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z;
t[2] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) 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(a[2]);
t[1] += static_cast(a[1]);
t[2] += static_cast(b[2]);
t[3] += static_cast(b[1]);
t[0] *= x2;
t[2] *= x2;
t[0] += static_cast(a[0]);
t[2] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[2] *= z2;
t[0] += static_cast(a[6]);
t[2] += static_cast(b[6]);
t[1] *= z;
t[3] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) 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(a[3]);
t[1] += static_cast(a[2]);
t[2] += static_cast(b[3]);
t[3] += static_cast(b[2]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[1]);
t[1] += static_cast(a[0]);
t[2] += static_cast(b[1]);
t[3] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z;
t[2] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[8] * x2 + a[6];
t[1] = a[7] * x2 + a[5];
t[2] = b[8] * x2 + b[6];
t[3] = b[7] * x2 + b[5];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[4]);
t[1] += static_cast(a[3]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[3]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[2]);
t[1] += static_cast(a[1]);
t[2] += static_cast(b[2]);
t[3] += static_cast(b[1]);
t[0] *= x2;
t[2] *= x2;
t[0] += static_cast(a[0]);
t[2] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z2;
t[2] *= z2;
t[0] += static_cast(a[8]);
t[2] += static_cast(b[8]);
t[1] *= z;
t[3] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[9] * x2 + a[7];
t[1] = a[8] * x2 + a[6];
t[2] = b[9] * x2 + b[7];
t[3] = b[8] * x2 + b[6];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[5]);
t[1] += static_cast(a[4]);
t[2] += static_cast(b[5]);
t[3] += static_cast(b[4]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[3]);
t[1] += static_cast(a[2]);
t[2] += static_cast(b[3]);
t[3] += static_cast(b[2]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[1]);
t[1] += static_cast(a[0]);
t[2] += static_cast(b[1]);
t[3] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[8]);
t[1] += static_cast(a[9]);
t[2] += static_cast(b[8]);
t[3] += static_cast(b[9]);
t[0] *= z;
t[2] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[10] * x2 + a[8];
t[1] = a[9] * x2 + a[7];
t[2] = b[10] * x2 + b[8];
t[3] = b[9] * x2 + b[7];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[5]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[4]);
t[1] += static_cast(a[3]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[3]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[2]);
t[1] += static_cast(a[1]);
t[2] += static_cast(b[2]);
t[3] += static_cast(b[1]);
t[0] *= x2;
t[2] *= x2;
t[0] += static_cast(a[0]);
t[2] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[8]);
t[1] += static_cast(a[9]);
t[2] += static_cast(b[8]);
t[3] += static_cast(b[9]);
t[0] *= z2;
t[2] *= z2;
t[0] += static_cast(a[10]);
t[2] += static_cast(b[10]);
t[1] *= z;
t[3] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[11] * x2 + a[9];
t[1] = a[10] * x2 + a[8];
t[2] = b[11] * x2 + b[9];
t[3] = b[10] * x2 + b[8];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[7]);
t[1] += static_cast(a[6]);
t[2] += static_cast(b[7]);
t[3] += static_cast(b[6]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[5]);
t[1] += static_cast(a[4]);
t[2] += static_cast(b[5]);
t[3] += static_cast(b[4]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[3]);
t[1] += static_cast(a[2]);
t[2] += static_cast(b[3]);
t[3] += static_cast(b[2]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[1]);
t[1] += static_cast(a[0]);
t[2] += static_cast(b[1]);
t[3] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[8]);
t[1] += static_cast(a[9]);
t[2] += static_cast(b[8]);
t[3] += static_cast(b[9]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[10]);
t[1] += static_cast(a[11]);
t[2] += static_cast(b[10]);
t[3] += static_cast(b[11]);
t[0] *= z;
t[2] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[12] * x2 + a[10];
t[1] = a[11] * x2 + a[9];
t[2] = b[12] * x2 + b[10];
t[3] = b[11] * x2 + b[9];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[8]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[8]);
t[3] += static_cast(b[7]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[5]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[4]);
t[1] += static_cast(a[3]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[3]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[2]);
t[1] += static_cast(a[1]);
t[2] += static_cast(b[2]);
t[3] += static_cast(b[1]);
t[0] *= x2;
t[2] *= x2;
t[0] += static_cast(a[0]);
t[2] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[8]);
t[1] += static_cast(a[9]);
t[2] += static_cast(b[8]);
t[3] += static_cast(b[9]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[10]);
t[1] += static_cast(a[11]);
t[2] += static_cast(b[10]);
t[3] += static_cast(b[11]);
t[0] *= z2;
t[2] *= z2;
t[0] += static_cast(a[12]);
t[2] += static_cast(b[12]);
t[1] *= z;
t[3] *= z;
return (t[0] + t[1]) / (t[2] + t[3]);
}
}
template
inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const boost::integral_constant*) BOOST_MATH_NOEXCEPT(V)
{
if(x <= 1)
{
V x2 = x * x;
V t[4];
t[0] = a[13] * x2 + a[11];
t[1] = a[12] * x2 + a[10];
t[2] = b[13] * x2 + b[11];
t[3] = b[12] * x2 + b[10];
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[9]);
t[1] += static_cast(a[8]);
t[2] += static_cast(b[9]);
t[3] += static_cast(b[8]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[7]);
t[1] += static_cast(a[6]);
t[2] += static_cast(b[7]);
t[3] += static_cast(b[6]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[5]);
t[1] += static_cast(a[4]);
t[2] += static_cast(b[5]);
t[3] += static_cast(b[4]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[3]);
t[1] += static_cast(a[2]);
t[2] += static_cast(b[3]);
t[3] += static_cast(b[2]);
t[0] *= x2;
t[1] *= x2;
t[2] *= x2;
t[3] *= x2;
t[0] += static_cast(a[1]);
t[1] += static_cast(a[0]);
t[2] += static_cast(b[1]);
t[3] += static_cast(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(a[4]);
t[1] += static_cast(a[5]);
t[2] += static_cast(b[4]);
t[3] += static_cast(b[5]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[6]);
t[1] += static_cast(a[7]);
t[2] += static_cast(b[6]);
t[3] += static_cast(b[7]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[8]);
t[1] += static_cast(a[9]);
t[2] += static_cast(b[8]);
t[3] += static_cast(b[9]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast(a[10]);
t[1] += static_cast(a[11]);
t[2] += static_cast(b[10]);
t[3] += static_cast(b[11]);
t[0] *= z2;
t[1] *= z2;
t[2] *= z2;
t[3] *= z2;
t[0] += static_cast