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WSJT-X/boost/libs/math/tools/generate_rational_code.cpp

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// (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)
#include <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <sstream>
int max_order = 20;
const char* path_prefix = "..\\..\\..\\boost\\math\\tools\\detail\\polynomial_";
const char* path_prefix2 = "..\\..\\..\\boost\\math\\tools\\detail\\rational_";
const char* copyright_string =
"// (C) Copyright John Maddock 2007.\n"
"// Use, modification and distribution are subject to the\n"
"// Boost Software License, Version 1.0. (See accompanying file\n"
"// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)\n"
"//\n"
"// This file is machine generated, do not edit by hand\n\n";
void print_polynomials(int max_order)
{
for(int i = 2; i <= max_order; ++i)
{
std::stringstream filename;
filename << path_prefix << "horner1_" << i << ".hpp";
std::ofstream ofs(filename.str().c_str());
if(ofs.bad())
break;
//
// Output the boilerplate at the top of the header:
//
ofs << copyright_string <<
"// Polynomial evaluation using Horners rule\n"
"#ifndef BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n"
"#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
"namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)\n"
"{\n"
" return static_cast<V>(0);\n"
"}\n"
"\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)\n"
"{\n"
" return static_cast<V>(a[0]);\n"
"}\n\n";
for(int order = 2; order <= i; ++order)
{
ofs <<
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<" << order << ">*)\n"
"{\n"
" return static_cast<V>(";
for(int bracket = 2; bracket < order; ++bracket)
ofs << "(";
ofs << "a[" << order - 1 << "] * x + a[" << order - 2 << "]" ;
for(int item = order - 3; item >= 0; --item)
{
ofs << ") * x + a[" << item << "]";
}
ofs << ");\n"
"}\n\n";
}
//
// And finally the boilerplate at the end of the header:
//
ofs << "\n}}}} // namespaces\n\n#endif // include guard\n\n";
filename.str("");
filename << path_prefix << "horner2_" << i << ".hpp";
ofs.close();
ofs.open(filename.str().c_str());
if(ofs.bad())
break;
//
// Output the boilerplate at the top of the header:
//
ofs << copyright_string <<
"// Polynomial evaluation using second order Horners rule\n"
"#ifndef BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n"
"#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
"namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)\n"
"{\n"
" return static_cast<V>(0);\n"
"}\n"
"\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)\n"
"{\n"
" return static_cast<V>(a[0]);\n"
"}\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)\n"
"{\n"
" return static_cast<V>(a[1] * x + a[0]);\n"
"}\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)\n"
"{\n"
" return static_cast<V>((a[2] * x + a[1]) * x + a[0]);\n"
"}\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)\n"
"{\n"
" return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);\n"
"}\n\n";
for(int order = 5; order <= i; ++order)
{
ofs <<
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<" << order << ">*)\n"
"{\n"
" V x2 = x * x;\n"
" return static_cast<V>(";
if(order & 1)
{
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << order - 1 << "] * x2 + a[" << order - 3 << "]" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
ofs << " + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << order - 2 << "] * x2 + a[" << order - 4 << "]" ;
for(int item = order - 6; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
ofs << ") * x";
}
else
{
for(int bracket = 0; bracket < (order - 1) / 2; ++bracket)
ofs << "(";
ofs << "a[" << order - 1 << "] * x2 + a[" << order - 3 << "]" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
ofs << ") * x + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << order - 2 << "] * x2 + a[" << order - 4 << "]" ;
for(int item = order - 6; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
}
ofs << ");\n"
"}\n\n";
}
//
// And finally the boilerplate at the end of the header:
//
ofs << "\n}}}} // namespaces\n\n#endif // include guard\n\n";
filename.str("");
filename << path_prefix << "horner3_" << i << ".hpp";
ofs.close();
ofs.open(filename.str().c_str());
if(ofs.bad())
break;
//
// Output the boilerplate at the top of the header:
//
ofs << copyright_string <<
"// Unrolled polynomial evaluation using second order Horners rule\n"
"#ifndef BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n"
"#define BOOST_MATH_TOOLS_POLY_EVAL_" << i << "_HPP\n\n"
"namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T*, const V&, const mpl::int_<0>*)\n"
"{\n"
" return static_cast<V>(0);\n"
"}\n"
"\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V&, const mpl::int_<1>*)\n"
"{\n"
" return static_cast<V>(a[0]);\n"
"}\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<2>*)\n"
"{\n"
" return static_cast<V>(a[1] * x + a[0]);\n"
"}\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<3>*)\n"
"{\n"
" return static_cast<V>((a[2] * x + a[1]) * x + a[0]);\n"
"}\n\n"
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<4>*)\n"
"{\n"
" return static_cast<V>(((a[3] * x + a[2]) * x + a[1]) * x + a[0]);\n"
"}\n\n";
for(int order = 5; order <= i; ++order)
{
ofs <<
"template <class T, class V>\n"
"inline V evaluate_polynomial_c_imp(const T* a, const V& x, const mpl::int_<" << order << ">*)\n"
"{\n"
" V x2 = x * x;\n"
" V t[2];\n";
if(order & 1)
{
ofs << " t[0] = static_cast<V>(a[" << order - 1 << "] * x2 + a[" << order - 3 << "]);\n" ;
ofs << " t[1] = static_cast<V>(a[" << order - 2 << "] * x2 + a[" << order - 4 << "]);\n" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << " t[0] *= x2;\n";
if(item - 1 >= 0)
ofs << " t[1] *= x2;\n";
ofs << " t[0] += static_cast<V>(a[" << item << "]);\n";
if(item - 1 >= 0)
ofs << " t[1] += static_cast<V>(a[" << item - 1 << "]);\n";
}
ofs <<
" t[1] *= x;\n"
" return t[0] + t[1];\n";
}
else
{
ofs << " t[0] = a[" << order - 1 << "] * x2 + a[" << order - 3 << "];\n" ;
ofs << " t[1] = a[" << order - 2 << "] * x2 + a[" << order - 4 << "];\n" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << " t[0] *= x2;\n";
if(item - 1 >= 0)
ofs << " t[1] *= x2;\n";
ofs << " t[0] += static_cast<V>(a[" << item << "]);\n";
if(item - 1 >= 0)
ofs << " t[1] += static_cast<V>(a[" << item - 1 << "]);\n";
}
ofs << " t[0] *= x;\n";
ofs << " return t[0] + t[1];\n";
}
ofs << "}\n\n";
}
//
// And finally the boilerplate at the end of the header:
//
ofs << "\n}}}} // namespaces\n\n#endif // include guard\n\n";
}
}
void print_rationals(int max_order)
{
for(int i = 2; i <= max_order; ++i)
{
std::stringstream filename;
filename << path_prefix2 << "horner1_" << i << ".hpp";
std::ofstream ofs(filename.str().c_str());
if(ofs.bad())
break;
//
// Output the boilerplate at the top of the header:
//
ofs << copyright_string <<
"// Polynomial evaluation using Horners rule\n"
"#ifndef BOOST_MATH_TOOLS_POLY_RAT_" << i << "_HPP\n"
"#define BOOST_MATH_TOOLS_POLY_RAT_" << i << "_HPP\n\n"
"namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)\n"
"{\n"
" return static_cast<V>(0);\n"
"}\n"
"\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)\n"
"{\n"
" return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
"}\n\n";
for(int order = 2; order <= i; ++order)
{
ofs <<
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<" << order << ">*)\n"
"{\n"
" if(x <= 1)\n"
" return static_cast<V>((";
for(int bracket = 2; bracket < order; ++bracket)
ofs << "(";
ofs << "a[" << order - 1 << "] * x + a[" << order - 2 << "]" ;
for(int item = order - 3; item >= 0; --item)
{
ofs << ") * x + a[" << item << "]";
}
ofs << ") / (";
for(int bracket = 2; bracket < order; ++bracket)
ofs << "(";
ofs << "b[" << order - 1 << "] * x + b[" << order - 2 << "]" ;
for(int item = order - 3; item >= 0; --item)
{
ofs << ") * x + b[" << item << "]";
}
ofs << "));\n else\n {\n V z = 1 / x;\n return static_cast<V>((";
for(int bracket = order - 1; bracket > 1; --bracket)
ofs << "(";
ofs << "a[" << 0 << "] * z + a[" << 1 << "]" ;
for(int item = 2; item <= order - 1; ++item)
{
ofs << ") * z + a[" << item << "]";
}
ofs << ") / (";
for(int bracket = 2; bracket < order; ++bracket)
ofs << "(";
ofs << "b[" << 0 << "] * z + b[" << 1 << "]" ;
for(int item = 2; item <= order - 1; ++item)
{
ofs << ") * z + b[" << item << "]";
}
ofs << "));\n }\n";
ofs << "}\n\n";
}
//
// And finally the boilerplate at the end of the header:
//
ofs << "\n}}}} // namespaces\n\n#endif // include guard\n\n";
filename.str("");
filename << path_prefix2 << "horner2_" << i << ".hpp";
ofs.close();
ofs.open(filename.str().c_str());
if(ofs.bad())
break;
//
// Output the boilerplate at the top of the header:
//
ofs << copyright_string <<
"// Polynomial evaluation using second order Horners rule\n"
"#ifndef BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n"
"#define BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n\n"
"namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)\n"
"{\n"
" return static_cast<V>(0);\n"
"}\n"
"\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)\n"
"{\n"
" return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
"}\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)\n"
"{\n"
" return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));\n"
"}\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)\n"
"{\n"
" return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));\n"
"}\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)\n"
"{\n"
" 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]));\n"
"}\n\n";
for(int order = 5; order <= i; ++order)
{
ofs <<
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<" << order << ">*)\n"
"{\n"
" if(x <= 1)\n {\n"
" V x2 = x * x;\n"
" return static_cast<V>((";
if(order & 1)
{
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << order - 1 << "] * x2 + a[" << order - 3 << "]" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
ofs << " + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << order - 2 << "] * x2 + a[" << order - 4 << "]" ;
for(int item = order - 6; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
ofs << ") * x";
}
else
{
for(int bracket = 0; bracket < (order - 1) / 2; ++bracket)
ofs << "(";
ofs << "a[" << order - 1 << "] * x2 + a[" << order - 3 << "]" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
ofs << ") * x + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << order - 2 << "] * x2 + a[" << order - 4 << "]" ;
for(int item = order - 6; item >= 0; item -= 2)
{
ofs << ") * x2 + a[" << item << "]";
}
}
ofs << ") / (";
if(order & 1)
{
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "b[" << order - 1 << "] * x2 + b[" << order - 3 << "]" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << ") * x2 + b[" << item << "]";
}
ofs << " + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "b[" << order - 2 << "] * x2 + b[" << order - 4 << "]" ;
for(int item = order - 6; item >= 0; item -= 2)
{
ofs << ") * x2 + b[" << item << "]";
}
ofs << ") * x";
}
else
{
for(int bracket = 0; bracket < (order - 1) / 2; ++bracket)
ofs << "(";
ofs << "b[" << order - 1 << "] * x2 + b[" << order - 3 << "]" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << ") * x2 + b[" << item << "]";
}
ofs << ") * x + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "b[" << order - 2 << "] * x2 + b[" << order - 4 << "]" ;
for(int item = order - 6; item >= 0; item -= 2)
{
ofs << ") * x2 + b[" << item << "]";
}
}
ofs << "));\n }\n else\n {\n V z = 1 / x;\n V z2 = 1 / (x * x);\n return static_cast<V>((";
if(order & 1)
{
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << 0 << "] * z2 + a[" << 2 << "]" ;
for(int item = 4; item < order; item += 2)
{
ofs << ") * z2 + a[" << item << "]";
}
ofs << " + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << 1 << "] * z2 + a[" << 3 << "]" ;
for(int item = 5; item < order; item += 2)
{
ofs << ") * z2 + a[" << item << "]";
}
ofs << ") * z";
}
else
{
for(int bracket = 0; bracket < (order - 1) / 2; ++bracket)
ofs << "(";
ofs << "a[" << 0 << "] * z2 + a[" << 2 << "]" ;
for(int item = 4; item < order; item += 2)
{
ofs << ") * z2 + a[" << item << "]";
}
ofs << ") * z + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "a[" << 1 << "] * z2 + a[" << 3 << "]" ;
for(int item = 5; item < order; item += 2)
{
ofs << ") * z2 + a[" << item << "]";
}
}
ofs << ") / (";
if(order & 1)
{
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "b[" << 0 << "] * z2 + b[" << 2 << "]" ;
for(int item = 4; item < order; item += 2)
{
ofs << ") * z2 + b[" << item << "]";
}
ofs << " + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "b[" << 1 << "] * z2 + b[" << 3 << "]" ;
for(int item = 5; item < order; item += 2)
{
ofs << ") * z2 + b[" << item << "]";
}
ofs << ") * z";
}
else
{
for(int bracket = 0; bracket < (order - 1) / 2; ++bracket)
ofs << "(";
ofs << "b[" << 0 << "] * z2 + b[" << 2 << "]" ;
for(int item = 4; item < order; item += 2)
{
ofs << ") * z2 + b[" << item << "]";
}
ofs << ") * z + ";
for(int bracket = 0; bracket < (order - 1) / 2 - 1; ++bracket)
ofs << "(";
ofs << "b[" << 1 << "] * z2 + b[" << 3 << "]" ;
for(int item = 5; item < order; item += 2)
{
ofs << ") * z2 + b[" << item << "]";
}
}
ofs << "));\n }\n";
ofs << "}\n\n";
}
//
// And finally the boilerplate at the end of the header:
//
ofs << "\n}}}} // namespaces\n\n#endif // include guard\n\n";
filename.str("");
filename << path_prefix2 << "horner3_" << i << ".hpp";
ofs.close();
ofs.open(filename.str().c_str());
if(ofs.bad())
break;
//
// Output the boilerplate at the top of the header:
//
ofs << copyright_string <<
"// Polynomial evaluation using second order Horners rule\n"
"#ifndef BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n"
"#define BOOST_MATH_TOOLS_RAT_EVAL_" << i << "_HPP\n\n"
"namespace boost{ namespace math{ namespace tools{ namespace detail{\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T*, const U*, const V&, const mpl::int_<0>*)\n"
"{\n"
" return static_cast<V>(0);\n"
"}\n"
"\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*)\n"
"{\n"
" return static_cast<V>(a[0]) / static_cast<V>(b[0]);\n"
"}\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*)\n"
"{\n"
" return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0]));\n"
"}\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*)\n"
"{\n"
" return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0]));\n"
"}\n\n"
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*)\n"
"{\n"
" 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]));\n"
"}\n\n";
for(int order = 5; order <= i; ++order)
{
ofs <<
"template <class T, class U, class V>\n"
"inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<" << order << ">*)\n"
"{\n"
" if(x <= 1)\n {\n"
" V x2 = x * x;\n"
" V t[4];\n";
if(order & 1)
{
ofs << " t[0] = a[" << order - 1 << "] * x2 + a[" << order - 3 << "];\n" ;
ofs << " t[1] = a[" << order - 2 << "] * x2 + a[" << order - 4 << "];\n" ;
ofs << " t[2] = b[" << order - 1 << "] * x2 + b[" << order - 3 << "];\n" ;
ofs << " t[3] = b[" << order - 2 << "] * x2 + b[" << order - 4 << "];\n" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << " t[0] *= x2;\n";
if(item - 1 >= 0)
ofs << " t[1] *= x2;\n";
ofs << " t[2] *= x2;\n";
if(item - 1 >= 0)
ofs << " t[3] *= x2;\n";
ofs << " t[0] += static_cast<V>(a[" << item << "]);\n";
if(item - 1 >= 0)
ofs << " t[1] += static_cast<V>(a[" << item - 1 << "]);\n";
ofs << " t[2] += static_cast<V>(b[" << item << "]);\n";
if(item - 1 >= 0)
ofs << " t[3] += static_cast<V>(b[" << item - 1 << "]);\n";
}
ofs << " t[1] *= x;\n";
ofs << " t[3] *= x;\n";
}
else
{
ofs << " t[0] = a[" << order - 1 << "] * x2 + a[" << order - 3 << "];\n" ;
ofs << " t[1] = a[" << order - 2 << "] * x2 + a[" << order - 4 << "];\n" ;
ofs << " t[2] = b[" << order - 1 << "] * x2 + b[" << order - 3 << "];\n" ;
ofs << " t[3] = b[" << order - 2 << "] * x2 + b[" << order - 4 << "];\n" ;
for(int item = order - 5; item >= 0; item -= 2)
{
ofs << " t[0] *= x2;\n";
if(item - 1 >= 0)
ofs << " t[1] *= x2;\n";
ofs << " t[2] *= x2;\n";
if(item - 1 >= 0)
ofs << " t[3] *= x2;\n";
ofs << " t[0] += static_cast<V>(a[" << item << "]);\n";
if(item - 1 >= 0)
ofs << " t[1] += static_cast<V>(a[" << item - 1 << "]);\n";
ofs << " t[2] += static_cast<V>(b[" << item << "]);\n";
if(item - 1 >= 0)
ofs << " t[3] += static_cast<V>(b[" << item - 1 << "]);\n";
}
ofs << " t[0] *= x;\n";
ofs << " t[2] *= x;\n";
}
ofs << " return (t[0] + t[1]) / (t[2] + t[3]);\n";
ofs << " }\n else\n {\n V z = 1 / x;\n V z2 = 1 / (x * x);\n V t[4];\n";
if(order & 1)
{
ofs << " t[0] = a[" << 0 << "] * z2 + a[" << 2 << "];\n" ;
ofs << " t[1] = a[" << 1 << "] * z2 + a[" << 3 << "];\n" ;
ofs << " t[2] = b[" << 0 << "] * z2 + b[" << 2 << "];\n" ;
ofs << " t[3] = b[" << 1 << "] * z2 + b[" << 3 << "];\n" ;
for(int item = 4; item < order; item += 2)
{
ofs << " t[0] *= z2;\n";
if(item + 1 < order)
ofs << " t[1] *= z2;\n";
ofs << " t[2] *= z2;\n";
if(item + 1 < order)
ofs << " t[3] *= z2;\n";
ofs << " t[0] += static_cast<V>(a[" << item << "]);\n";
if(item + 1 < order)
ofs << " t[1] += static_cast<V>(a[" << item + 1 << "]);\n";
ofs << " t[2] += static_cast<V>(b[" << item << "]);\n";
if(item + 1 < order)
ofs << " t[3] += static_cast<V>(b[" << item + 1 << "]);\n";
}
ofs << " t[1] *= z;\n";
ofs << " t[3] *= z;\n";
}
else
{
ofs << " t[0] = a[" << 0 << "] * z2 + a[" << 2 << "];\n" ;
ofs << " t[1] = a[" << 1 << "] * z2 + a[" << 3 << "];\n" ;
ofs << " t[2] = b[" << 0 << "] * z2 + b[" << 2 << "];\n" ;
ofs << " t[3] = b[" << 1 << "] * z2 + b[" << 3 << "];\n" ;
for(int item = 4; item < order; item += 2)
{
ofs << " t[0] *= z2;\n";
if(item + 1 < order)
ofs << " t[1] *= z2;\n";
ofs << " t[2] *= z2;\n";
if(item + 1 < order)
ofs << " t[3] *= z2;\n";
ofs << " t[0] += static_cast<V>(a[" << item << "]);\n";
if(item + 1 < order)
ofs << " t[1] += static_cast<V>(a[" << item + 1 << "]);\n";
ofs << " t[2] += static_cast<V>(b[" << item << "]);\n";
if(item + 1 < order)
ofs << " t[3] += static_cast<V>(b[" << item + 1 << "]);\n";
}
ofs << " t[0] *= z;\n";
ofs << " t[2] *= z;\n";
}
ofs << " return (t[0] + t[1]) / (t[2] + t[3]);\n }\n";
ofs << "}\n\n";
}
//
// And finally the boilerplate at the end of the header:
//
ofs << "\n}}}} // namespaces\n\n#endif // include guard\n\n";
}
}
int main()
{
for(int i = 2; i <= max_order; ++i)
{
print_polynomials(i);
print_rationals(i);
}
return 0;
}
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