Boost C++ Libraries

boost/math/tools/detail/rational_horner3_20.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_20_HPP
#define BOOST_MATH_TOOLS_RAT_EVAL_20_HPP

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

template <class T, class U, class V>
inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<0>*)
{
   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>*)
{
   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>*)
{
   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>*)
{
   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>*)
{
   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>*)
{
   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>*)
{
   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>*)
{
   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>*)
{
   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]);
   }
}

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_<9>*)
{
   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<V>(a[4]);
      t[1] += static_cast<V>(a[3]);
      t[2] += static_cast<V>(b[4]);
      t[3] += static_cast<V>(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[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] *= z2;
      t[2] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[2] += static_cast<V>(b[8]);
      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_<10>*)
{
   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<V>(a[5]);
      t[1] += static_cast<V>(a[4]);
      t[2] += static_cast<V>(b[5]);
      t[3] += static_cast<V>(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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      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_<11>*)
{
   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<V>(a[6]);
      t[1] += static_cast<V>(a[5]);
      t[2] += static_cast<V>(b[6]);
      t[3] += static_cast<V>(b[5]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[4]);
      t[1] += static_cast<V>(a[3]);
      t[2] += static_cast<V>(b[4]);
      t[3] += static_cast<V>(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[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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[2] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[2] += static_cast<V>(b[10]);
      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_<12>*)
{
   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<V>(a[7]);
      t[1] += static_cast<V>(a[6]);
      t[2] += static_cast<V>(b[7]);
      t[3] += static_cast<V>(b[6]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[5]);
      t[1] += static_cast<V>(a[4]);
      t[2] += static_cast<V>(b[5]);
      t[3] += static_cast<V>(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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      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_<13>*)
{
   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<V>(a[8]);
      t[1] += static_cast<V>(a[7]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[7]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[6]);
      t[1] += static_cast<V>(a[5]);
      t[2] += static_cast<V>(b[6]);
      t[3] += static_cast<V>(b[5]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[4]);
      t[1] += static_cast<V>(a[3]);
      t[2] += static_cast<V>(b[4]);
      t[3] += static_cast<V>(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[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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[2] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[2] += static_cast<V>(b[12]);
      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_<14>*)
{
   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<V>(a[9]);
      t[1] += static_cast<V>(a[8]);
      t[2] += static_cast<V>(b[9]);
      t[3] += static_cast<V>(b[8]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[7]);
      t[1] += static_cast<V>(a[6]);
      t[2] += static_cast<V>(b[7]);
      t[3] += static_cast<V>(b[6]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[5]);
      t[1] += static_cast<V>(a[4]);
      t[2] += static_cast<V>(b[5]);
      t[3] += static_cast<V>(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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      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_<15>*)
{
   if(x <= 1)
   {
      V x2 = x * x;
      V t[4];
      t[0] = a[14] * x2 + a[12];
      t[1] = a[13] * x2 + a[11];
      t[2] = b[14] * x2 + b[12];
      t[3] = b[13] * x2 + b[11];
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[7]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[7]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[6]);
      t[1] += static_cast<V>(a[5]);
      t[2] += static_cast<V>(b[6]);
      t[3] += static_cast<V>(b[5]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[4]);
      t[1] += static_cast<V>(a[3]);
      t[2] += static_cast<V>(b[4]);
      t[3] += static_cast<V>(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[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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= z2;
      t[2] *= z2;
      t[0] += static_cast<V>(a[14]);
      t[2] += static_cast<V>(b[14]);
      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_<16>*)
{
   if(x <= 1)
   {
      V x2 = x * x;
      V t[4];
      t[0] = a[15] * x2 + a[13];
      t[1] = a[14] * x2 + a[12];
      t[2] = b[15] * x2 + b[13];
      t[3] = b[14] * x2 + b[12];
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[11]);
      t[1] += static_cast<V>(a[10]);
      t[2] += static_cast<V>(b[11]);
      t[3] += static_cast<V>(b[10]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[9]);
      t[1] += static_cast<V>(a[8]);
      t[2] += static_cast<V>(b[9]);
      t[3] += static_cast<V>(b[8]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[7]);
      t[1] += static_cast<V>(a[6]);
      t[2] += static_cast<V>(b[7]);
      t[3] += static_cast<V>(b[6]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[5]);
      t[1] += static_cast<V>(a[4]);
      t[2] += static_cast<V>(b[5]);
      t[3] += static_cast<V>(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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[14]);
      t[1] += static_cast<V>(a[15]);
      t[2] += static_cast<V>(b[14]);
      t[3] += static_cast<V>(b[15]);
      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_<17>*)
{
   if(x <= 1)
   {
      V x2 = x * x;
      V t[4];
      t[0] = a[16] * x2 + a[14];
      t[1] = a[15] * x2 + a[13];
      t[2] = b[16] * x2 + b[14];
      t[3] = b[15] * x2 + b[13];
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[7]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[7]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[6]);
      t[1] += static_cast<V>(a[5]);
      t[2] += static_cast<V>(b[6]);
      t[3] += static_cast<V>(b[5]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[4]);
      t[1] += static_cast<V>(a[3]);
      t[2] += static_cast<V>(b[4]);
      t[3] += static_cast<V>(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[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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[14]);
      t[1] += static_cast<V>(a[15]);
      t[2] += static_cast<V>(b[14]);
      t[3] += static_cast<V>(b[15]);
      t[0] *= z2;
      t[2] *= z2;
      t[0] += static_cast<V>(a[16]);
      t[2] += static_cast<V>(b[16]);
      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_<18>*)
{
   if(x <= 1)
   {
      V x2 = x * x;
      V t[4];
      t[0] = a[17] * x2 + a[15];
      t[1] = a[16] * x2 + a[14];
      t[2] = b[17] * x2 + b[15];
      t[3] = b[16] * x2 + b[14];
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[13]);
      t[1] += static_cast<V>(a[12]);
      t[2] += static_cast<V>(b[13]);
      t[3] += static_cast<V>(b[12]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[11]);
      t[1] += static_cast<V>(a[10]);
      t[2] += static_cast<V>(b[11]);
      t[3] += static_cast<V>(b[10]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[9]);
      t[1] += static_cast<V>(a[8]);
      t[2] += static_cast<V>(b[9]);
      t[3] += static_cast<V>(b[8]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[7]);
      t[1] += static_cast<V>(a[6]);
      t[2] += static_cast<V>(b[7]);
      t[3] += static_cast<V>(b[6]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[5]);
      t[1] += static_cast<V>(a[4]);
      t[2] += static_cast<V>(b[5]);
      t[3] += static_cast<V>(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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[14]);
      t[1] += static_cast<V>(a[15]);
      t[2] += static_cast<V>(b[14]);
      t[3] += static_cast<V>(b[15]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[16]);
      t[1] += static_cast<V>(a[17]);
      t[2] += static_cast<V>(b[16]);
      t[3] += static_cast<V>(b[17]);
      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_<19>*)
{
   if(x <= 1)
   {
      V x2 = x * x;
      V t[4];
      t[0] = a[18] * x2 + a[16];
      t[1] = a[17] * x2 + a[15];
      t[2] = b[18] * x2 + b[16];
      t[3] = b[17] * x2 + b[15];
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[14]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[14]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[7]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[7]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[6]);
      t[1] += static_cast<V>(a[5]);
      t[2] += static_cast<V>(b[6]);
      t[3] += static_cast<V>(b[5]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[4]);
      t[1] += static_cast<V>(a[3]);
      t[2] += static_cast<V>(b[4]);
      t[3] += static_cast<V>(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[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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[14]);
      t[1] += static_cast<V>(a[15]);
      t[2] += static_cast<V>(b[14]);
      t[3] += static_cast<V>(b[15]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[16]);
      t[1] += static_cast<V>(a[17]);
      t[2] += static_cast<V>(b[16]);
      t[3] += static_cast<V>(b[17]);
      t[0] *= z2;
      t[2] *= z2;
      t[0] += static_cast<V>(a[18]);
      t[2] += static_cast<V>(b[18]);
      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_<20>*)
{
   if(x <= 1)
   {
      V x2 = x * x;
      V t[4];
      t[0] = a[19] * x2 + a[17];
      t[1] = a[18] * x2 + a[16];
      t[2] = b[19] * x2 + b[17];
      t[3] = b[18] * x2 + b[16];
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[15]);
      t[1] += static_cast<V>(a[14]);
      t[2] += static_cast<V>(b[15]);
      t[3] += static_cast<V>(b[14]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[13]);
      t[1] += static_cast<V>(a[12]);
      t[2] += static_cast<V>(b[13]);
      t[3] += static_cast<V>(b[12]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[11]);
      t[1] += static_cast<V>(a[10]);
      t[2] += static_cast<V>(b[11]);
      t[3] += static_cast<V>(b[10]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[9]);
      t[1] += static_cast<V>(a[8]);
      t[2] += static_cast<V>(b[9]);
      t[3] += static_cast<V>(b[8]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[7]);
      t[1] += static_cast<V>(a[6]);
      t[2] += static_cast<V>(b[7]);
      t[3] += static_cast<V>(b[6]);
      t[0] *= x2;
      t[1] *= x2;
      t[2] *= x2;
      t[3] *= x2;
      t[0] += static_cast<V>(a[5]);
      t[1] += static_cast<V>(a[4]);
      t[2] += static_cast<V>(b[5]);
      t[3] += static_cast<V>(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] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[8]);
      t[1] += static_cast<V>(a[9]);
      t[2] += static_cast<V>(b[8]);
      t[3] += static_cast<V>(b[9]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[10]);
      t[1] += static_cast<V>(a[11]);
      t[2] += static_cast<V>(b[10]);
      t[3] += static_cast<V>(b[11]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[12]);
      t[1] += static_cast<V>(a[13]);
      t[2] += static_cast<V>(b[12]);
      t[3] += static_cast<V>(b[13]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[14]);
      t[1] += static_cast<V>(a[15]);
      t[2] += static_cast<V>(b[14]);
      t[3] += static_cast<V>(b[15]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[16]);
      t[1] += static_cast<V>(a[17]);
      t[2] += static_cast<V>(b[16]);
      t[3] += static_cast<V>(b[17]);
      t[0] *= z2;
      t[1] *= z2;
      t[2] *= z2;
      t[3] *= z2;
      t[0] += static_cast<V>(a[18]);
      t[1] += static_cast<V>(a[19]);
      t[2] += static_cast<V>(b[18]);
      t[3] += static_cast<V>(b[19]);
      t[0] *= z;
      t[2] *= z;
      return (t[0] + t[1]) / (t[2] + t[3]);
   }
}


}}}} // namespaces

#endif // include guard