// (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) #define BOOST_MATH_POLY_METHOD 0 #define BOOST_MATH_RATIONAL_METHOD 0 #include #include #include #include #include int main() { using namespace boost::math; using namespace boost::math::tools; static const unsigned max_order = 20; boost::math::ntl::RR::SetPrecision(500); boost::math::ntl::RR::SetOutputPrecision(40); std::tr1::mt19937 rnd; std::tr1::variate_generator< std::tr1::mt19937, std::tr1::uniform_int<> > gen(rnd, std::tr1::uniform_int<>(1, 12)); for(unsigned i = 1; i < max_order; ++i) { std::vector coef; for(unsigned j = 0; j < i; ++j) { coef.push_back(gen()); } std::cout << std::scientific; std::cout << " //\n" " // Polynomials of order " << i-1 << "\n" " //\n" " static const U n" << i << "c[" << i << "] = { "; for(unsigned j = 0; j < i; ++j) { if(j) std::cout << ", "; std::cout << coef[j]; } std::cout << " };\n"; std::cout << " static const boost::array n" << i << "a = { "; for(unsigned j = 0; j < i; ++j) { if(j) std::cout << ", "; std::cout << coef[j]; } std::cout << " };\n"; boost::math::ntl::RR r1 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.125), i); boost::math::ntl::RR r2 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.25), i); boost::math::ntl::RR r3 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.75), i); boost::math::ntl::RR r4 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(1) - boost::math::ntl::RR(1) / 64, i); boost::math::ntl::RR r5 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(6.5), i); boost::math::ntl::RR r6 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(10247.25), i); std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(0.125), " << i << "),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(0.25), " << i << "),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(0.75), " << i << "),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(1.0f - 1.0f/64.0f), " << i << "),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(6.5), " << i << "),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(10247.25), " << i << "),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(0.125)),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(0.25)),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(0.75)),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(6.5)),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "c, static_cast(10247.25)),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast(0.125)),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast(0.25)),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast(0.75)),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast(6.5)),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_polynomial(n" << i << "a, static_cast(10247.25)),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; r1 = boost::math::tools::evaluate_even_polynomial(&coef[0], boost::math::ntl::RR(0.125), i); r2 = boost::math::tools::evaluate_even_polynomial(&coef[0], boost::math::ntl::RR(0.25), i); r3 = boost::math::tools::evaluate_even_polynomial(&coef[0], boost::math::ntl::RR(0.75), i); r4 = boost::math::tools::evaluate_even_polynomial(&coef[0], boost::math::ntl::RR(1) - boost::math::ntl::RR(1) / 64, i); r5 = boost::math::tools::evaluate_even_polynomial(&coef[0], boost::math::ntl::RR(6.5), i); r6 = boost::math::tools::evaluate_even_polynomial(&coef[0], boost::math::ntl::RR(10247.25), i); std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(0.125), " << i << "),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(0.25), " << i << "),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(0.75), " << i << "),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(1.0f - 1.0f/64.0f), " << i << "),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(6.5f), " << i << "),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(10247.25f), " << i << "),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(0.125)),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(0.25)),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(0.75)),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(6.5f)),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "c, static_cast(10247.25f)),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast(0.125)),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast(0.25)),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast(0.75)),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast(6.5f)),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_even_polynomial(n" << i << "a, static_cast(10247.25f)),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; if(i > 1) { r1 = boost::math::tools::evaluate_odd_polynomial(&coef[0], boost::math::ntl::RR(0.125), i); r2 = boost::math::tools::evaluate_odd_polynomial(&coef[0], boost::math::ntl::RR(0.25), i); r3 = boost::math::tools::evaluate_odd_polynomial(&coef[0], boost::math::ntl::RR(0.75), i); r4 = boost::math::tools::evaluate_odd_polynomial(&coef[0], boost::math::ntl::RR(1) - boost::math::ntl::RR(1) / 64, i); r5 = boost::math::tools::evaluate_odd_polynomial(&coef[0], boost::math::ntl::RR(6.5), i); r6 = boost::math::tools::evaluate_odd_polynomial(&coef[0], boost::math::ntl::RR(10247.25), i); std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(0.125), " << i << "),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(0.25), " << i << "),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(0.75), " << i << "),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(1.0f - 1.0f/64.0f), " << i << "),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(6.5f), " << i << "),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(10247.25f), " << i << "),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(0.125)),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(0.25)),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(0.75)),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(6.5f)),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "c, static_cast(10247.25f)),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast(0.125)),\n" " static_cast(" << r1 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast(0.25)),\n" " static_cast(" << r2 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast(0.75)),\n" " static_cast(" << r3 << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4 << "L),\n" " tolerance);\n"; if(fabs(r5) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast(6.5f)),\n" " static_cast(" << r5 << "L),\n" " tolerance);\n"; if(fabs(r6) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_odd_polynomial(n" << i << "a, static_cast(10247.25f)),\n" " static_cast(" << r6 << "L),\n" " tolerance);\n\n"; } r1 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.125), i); r2 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.25), i); r3 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.75), i); r4 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(1) - boost::math::ntl::RR(1) / 64, i); r5 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(6.5), i); r6 = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(10247.25), i); coef.clear(); for(unsigned j = 0; j < i; ++j) { coef.push_back(gen()); } std::cout << " //\n" " // Rational functions of order " << i-1 << "\n" " //\n" " static const U d" << i << "c[" << i << "] = { "; for(unsigned j = 0; j < i; ++j) { if(j) std::cout << ", "; std::cout << coef[j]; } std::cout << " };\n"; std::cout << " static const boost::array d" << i << "a = { "; for(unsigned j = 0; j < i; ++j) { if(j) std::cout << ", "; std::cout << coef[j]; } std::cout << " };\n"; boost::math::ntl::RR r1d = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.125), i); boost::math::ntl::RR r2d = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.25), i); boost::math::ntl::RR r3d = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(0.75), i); boost::math::ntl::RR r4d = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(1) - boost::math::ntl::RR(1) / 64, i); boost::math::ntl::RR r5d = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(6.5), i); boost::math::ntl::RR r6d = boost::math::tools::evaluate_polynomial(&coef[0], boost::math::ntl::RR(10247.25), i); std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(0.125), " << i << "),\n" " static_cast(" << r1/r1d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(0.25), " << i << "),\n" " static_cast(" << r2/r2d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(0.75), " << i << "),\n" " static_cast(" << r3/r3d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(1.0f - 1.0f/64.0f), " << i << "),\n" " static_cast(" << r4/r4d << "L),\n" " tolerance);\n"; if(fabs(r5/r5d) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(6.5f), " << i << "),\n" " static_cast(" << r5/r5d << "L),\n" " tolerance);\n"; if(fabs(r6/r6d) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(10247.25f), " << i << "),\n" " static_cast(" << r6/r6d << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(0.125)),\n" " static_cast(" << r1/r1d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(0.25)),\n" " static_cast(" << r2/r2d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(0.75)),\n" " static_cast(" << r3/r3d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4/r4d << "L),\n" " tolerance);\n"; if(fabs(r5/r5d) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(6.5f)),\n" " static_cast(" << r5/r5d << "L),\n" " tolerance);\n"; if(fabs(r6/r6d) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "c, d" << i << "c, static_cast(10247.25f)),\n" " static_cast(" << r6/r6d << "L),\n" " tolerance);\n\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast(0.125)),\n" " static_cast(" << r1/r1d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast(0.25)),\n" " static_cast(" << r2/r2d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast(0.75)),\n" " static_cast(" << r3/r3d << "L),\n" " tolerance);\n"; std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast(1.0f - 1.0f/64.0f)),\n" " static_cast(" << r4/r4d << "L),\n" " tolerance);\n"; if(fabs(r5/r5d) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast(6.5f)),\n" " static_cast(" << r5/r5d << "L),\n" " tolerance);\n"; if(fabs(r6/r6d) < tools::max_value()) std::cout << " BOOST_CHECK_CLOSE(\n" " boost::math::tools::evaluate_rational(n" << i << "a, d" << i << "a, static_cast(10247.25f)),\n" " static_cast(" << r6/r6d << "L),\n" " tolerance);\n\n"; } return 0; }