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651 lines
21 KiB
C++
651 lines
21 KiB
C++
// (C) Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#define BOOST_TEST_MODULE foobar
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#define BOOST_UBLAS_TYPE_CHECK_EPSILON (type_traits<real_type>::type_sqrt (boost::math::tools::epsilon <real_type>()))
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#define BOOST_UBLAS_TYPE_CHECK_MIN (type_traits<real_type>::type_sqrt ( boost::math::tools::min_value<real_type>()))
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#define BOOST_UBLAS_NDEBUG
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#include "multiprecision.hpp"
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#include <boost/math/tools/remez.hpp>
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#include <boost/math/tools/test.hpp>
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#include <boost/math/special_functions/binomial.hpp>
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#include <boost/spirit/include/classic_core.hpp>
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#include <boost/spirit/include/classic_actor.hpp>
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#include <boost/lexical_cast.hpp>
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#include <iostream>
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#include <iomanip>
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#include <string>
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#include <boost/test/included/unit_test.hpp> // for test_main
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#include <boost/multiprecision/cpp_bin_float.hpp>
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extern mp_type f(const mp_type& x, int variant);
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extern void show_extra(
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const boost::math::tools::polynomial<mp_type>& n,
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const boost::math::tools::polynomial<mp_type>& d,
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const mp_type& x_offset,
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const mp_type& y_offset,
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int variant);
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using namespace boost::spirit::classic;
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mp_type a(0), b(1); // range to optimise over
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bool rel_error(true);
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bool pin(false);
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int orderN(3);
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int orderD(1);
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int target_precision = boost::math::tools::digits<long double>();
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int working_precision = target_precision * 2;
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bool started(false);
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int variant(0);
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int skew(0);
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int brake(50);
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mp_type x_offset(0), y_offset(0), x_scale(1);
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bool auto_offset_y;
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boost::shared_ptr<boost::math::tools::remez_minimax<mp_type> > p_remez;
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mp_type the_function(const mp_type& val)
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{
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return f(x_scale * (val + x_offset), variant) + y_offset;
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}
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void step_some(unsigned count)
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{
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try{
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set_working_precision(working_precision);
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if(!started)
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{
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//
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// If we have an automatic y-offset calculate it now:
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//
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if(auto_offset_y)
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{
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mp_type fa, fb, fm;
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fa = f(x_scale * (a + x_offset), variant);
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fb = f(x_scale * (b + x_offset), variant);
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fm = f(x_scale * ((a+b)/2 + x_offset), variant);
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y_offset = -(fa + fb + fm) / 3;
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set_output_precision(5);
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std::cout << "Setting auto-y-offset to " << y_offset << std::endl;
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}
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//
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// Truncate offsets to float precision:
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//
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x_offset = round_to_precision(x_offset, 20);
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y_offset = round_to_precision(y_offset, 20);
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//
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// Construct new Remez state machine:
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//
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p_remez.reset(new boost::math::tools::remez_minimax<mp_type>(
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&the_function,
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orderN, orderD,
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a, b,
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pin,
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rel_error,
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skew,
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working_precision));
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std::cout << "Max error in interpolated form: " << std::setprecision(3) << std::scientific << boost::math::tools::real_cast<double>(p_remez->max_error()) << std::endl;
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//
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// Signal that we've started:
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//
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started = true;
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}
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unsigned i;
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for(i = 0; i < count; ++i)
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{
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std::cout << "Stepping..." << std::endl;
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p_remez->set_brake(brake);
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mp_type r = p_remez->iterate();
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set_output_precision(3);
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std::cout
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<< "Maximum Deviation Found: " << std::setprecision(3) << std::scientific << boost::math::tools::real_cast<double>(p_remez->max_error()) << std::endl
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<< "Expected Error Term: " << std::setprecision(3) << std::scientific << boost::math::tools::real_cast<double>(p_remez->error_term()) << std::endl
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<< "Maximum Relative Change in Control Points: " << std::setprecision(3) << std::scientific << boost::math::tools::real_cast<double>(r) << std::endl;
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}
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}
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catch(const std::exception& e)
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{
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std::cout << "Step failed with exception: " << e.what() << std::endl;
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}
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}
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void step(const char*, const char*)
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{
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step_some(1);
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}
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void show(const char*, const char*)
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{
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set_working_precision(working_precision);
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if(started)
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{
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boost::math::tools::polynomial<mp_type> n = p_remez->numerator();
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boost::math::tools::polynomial<mp_type> d = p_remez->denominator();
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std::vector<mp_type> cn = n.chebyshev();
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std::vector<mp_type> cd = d.chebyshev();
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int prec = 2 + (target_precision * 3010LL)/10000;
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std::cout << std::scientific << std::setprecision(prec);
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set_output_precision(prec);
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boost::numeric::ublas::vector<mp_type> v = p_remez->zero_points();
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std::cout << " Zeros = {\n";
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unsigned i;
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for(i = 0; i < v.size(); ++i)
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{
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std::cout << " " << v[i] << std::endl;
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}
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std::cout << " }\n";
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v = p_remez->chebyshev_points();
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std::cout << " Chebeshev Control Points = {\n";
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for(i = 0; i < v.size(); ++i)
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{
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std::cout << " " << v[i] << std::endl;
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}
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std::cout << " }\n";
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std::cout << "X offset: " << x_offset << std::endl;
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std::cout << "X scale: " << x_scale << std::endl;
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std::cout << "Y offset: " << y_offset << std::endl;
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std::cout << "P = {";
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for(i = 0; i < n.size(); ++i)
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{
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std::cout << " " << n[i] << "L," << std::endl;
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}
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std::cout << " }\n";
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std::cout << "Q = {";
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for(i = 0; i < d.size(); ++i)
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{
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std::cout << " " << d[i] << "L," << std::endl;
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}
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std::cout << " }\n";
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std::cout << "CP = {";
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for(i = 0; i < cn.size(); ++i)
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{
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std::cout << " " << cn[i] << "L," << std::endl;
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}
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std::cout << " }\n";
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std::cout << "CQ = {";
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for(i = 0; i < cd.size(); ++i)
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{
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std::cout << " " << cd[i] << "L," << std::endl;
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}
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std::cout << " }\n";
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show_extra(n, d, x_offset, y_offset, variant);
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}
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else
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{
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std::cerr << "Nothing to display" << std::endl;
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}
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}
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void do_graph(unsigned points)
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{
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set_working_precision(working_precision);
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mp_type step = (b - a) / (points - 1);
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mp_type x = a;
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while(points > 1)
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{
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set_output_precision(10);
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std::cout << std::setprecision(10) << std::setw(30) << std::left
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<< boost::lexical_cast<std::string>(x) << the_function(x) << std::endl;
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--points;
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x += step;
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}
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std::cout << std::setprecision(10) << std::setw(30) << std::left
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<< boost::lexical_cast<std::string>(b) << the_function(b) << std::endl;
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}
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void graph(const char*, const char*)
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{
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do_graph(3);
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}
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template <class T>
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mp_type convert_to_rr(const T& val)
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{
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return val;
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}
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template <class Backend, boost::multiprecision::expression_template_option ET>
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mp_type convert_to_rr(const boost::multiprecision::number<Backend, ET>& val)
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{
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return boost::lexical_cast<mp_type>(val.str());
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}
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template <class T>
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void do_test(T, const char* name)
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{
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set_working_precision(working_precision);
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if(started)
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{
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//
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// We want to test the approximation at fixed precision:
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// either float, double or long double. Begin by getting the
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// polynomials:
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//
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boost::math::tools::polynomial<T> n, d;
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boost::math::tools::polynomial<mp_type> nr, dr;
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nr = p_remez->numerator();
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dr = p_remez->denominator();
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n = nr;
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d = dr;
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std::vector<mp_type> cn1, cd1;
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cn1 = nr.chebyshev();
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cd1 = dr.chebyshev();
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std::vector<T> cn, cd;
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for(unsigned i = 0; i < cn1.size(); ++i)
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{
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cn.push_back(boost::math::tools::real_cast<T>(cn1[i]));
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}
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for(unsigned i = 0; i < cd1.size(); ++i)
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{
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cd.push_back(boost::math::tools::real_cast<T>(cd1[i]));
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}
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//
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// We'll test at the Chebeshev control points which is where
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// (in theory) the largest deviation should occur. For good
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// measure we'll test at the zeros as well:
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//
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boost::numeric::ublas::vector<mp_type>
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zeros(p_remez->zero_points()),
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cheb(p_remez->chebyshev_points());
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mp_type max_error(0), cheb_max_error(0);
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//
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// Do the tests at the zeros:
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//
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std::cout << "Starting tests at " << name << " precision...\n";
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std::cout << "Absissa Error (Poly) Error (Cheb)\n";
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for(unsigned i = 0; i < zeros.size(); ++i)
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{
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mp_type true_result = the_function(zeros[i]);
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T absissa = boost::math::tools::real_cast<T>(zeros[i]);
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mp_type test_result = convert_to_rr(n.evaluate(absissa) / d.evaluate(absissa));
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mp_type cheb_result = convert_to_rr(boost::math::tools::evaluate_chebyshev(cn, absissa) / boost::math::tools::evaluate_chebyshev(cd, absissa));
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mp_type err, cheb_err;
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if(rel_error)
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{
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err = boost::math::tools::relative_error(test_result, true_result);
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cheb_err = boost::math::tools::relative_error(cheb_result, true_result);
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}
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else
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{
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err = fabs(test_result - true_result);
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cheb_err = fabs(cheb_result - true_result);
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}
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if(err > max_error)
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max_error = err;
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if(cheb_err > cheb_max_error)
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cheb_max_error = cheb_err;
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std::cout << std::setprecision(6) << std::setw(15) << std::left << absissa
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<< std::setw(15) << std::left << boost::math::tools::real_cast<T>(err) << boost::math::tools::real_cast<T>(cheb_err) << std::endl;
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}
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//
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// Do the tests at the Chebeshev control points:
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//
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for(unsigned i = 0; i < cheb.size(); ++i)
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{
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mp_type true_result = the_function(cheb[i]);
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T absissa = boost::math::tools::real_cast<T>(cheb[i]);
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mp_type test_result = convert_to_rr(n.evaluate(absissa) / d.evaluate(absissa));
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mp_type cheb_result = convert_to_rr(boost::math::tools::evaluate_chebyshev(cn, absissa) / boost::math::tools::evaluate_chebyshev(cd, absissa));
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mp_type err, cheb_err;
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if(rel_error)
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{
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err = boost::math::tools::relative_error(test_result, true_result);
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cheb_err = boost::math::tools::relative_error(cheb_result, true_result);
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}
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else
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{
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err = fabs(test_result - true_result);
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cheb_err = fabs(cheb_result - true_result);
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}
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if(err > max_error)
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max_error = err;
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std::cout << std::setprecision(6) << std::setw(15) << std::left << absissa
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<< std::setw(15) << std::left << boost::math::tools::real_cast<T>(err) <<
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boost::math::tools::real_cast<T>(cheb_err) << std::endl;
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}
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std::string msg = "Max Error found at ";
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msg += name;
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msg += " precision = ";
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msg.append(62 - 17 - msg.size(), ' ');
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std::cout << msg << std::setprecision(6) << "Poly: " << std::setw(20) << std::left
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<< boost::math::tools::real_cast<T>(max_error) << "Cheb: " << boost::math::tools::real_cast<T>(cheb_max_error) << std::endl;
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}
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else
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{
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std::cout << "Nothing to test: try converging an approximation first!!!" << std::endl;
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}
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}
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void test_float(const char*, const char*)
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{
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do_test(float(0), "float");
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}
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void test_double(const char*, const char*)
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{
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do_test(double(0), "double");
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}
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void test_long(const char*, const char*)
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{
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do_test((long double)(0), "long double");
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}
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void test_float80(const char*, const char*)
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{
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do_test((boost::multiprecision::cpp_bin_float_double_extended)(0), "float80");
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}
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void test_float128(const char*, const char*)
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{
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do_test((boost::multiprecision::cpp_bin_float_quad)(0), "float128");
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}
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void test_all(const char*, const char*)
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{
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do_test(float(0), "float");
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do_test(double(0), "double");
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do_test((long double)(0), "long double");
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}
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template <class T>
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void do_test_n(T, const char* name, unsigned count)
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{
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set_working_precision(working_precision);
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if(started)
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{
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//
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// We want to test the approximation at fixed precision:
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// either float, double or long double. Begin by getting the
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// polynomials:
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//
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boost::math::tools::polynomial<T> n, d;
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boost::math::tools::polynomial<mp_type> nr, dr;
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nr = p_remez->numerator();
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dr = p_remez->denominator();
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n = nr;
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d = dr;
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std::vector<mp_type> cn1, cd1;
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cn1 = nr.chebyshev();
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cd1 = dr.chebyshev();
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std::vector<T> cn, cd;
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for(unsigned i = 0; i < cn1.size(); ++i)
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{
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cn.push_back(boost::math::tools::real_cast<T>(cn1[i]));
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}
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for(unsigned i = 0; i < cd1.size(); ++i)
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{
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cd.push_back(boost::math::tools::real_cast<T>(cd1[i]));
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}
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mp_type max_error(0), max_cheb_error(0);
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mp_type step = (b - a) / count;
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//
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// Do the tests at the zeros:
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//
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std::cout << "Starting tests at " << name << " precision...\n";
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std::cout << "Absissa Error (poly) Error (Cheb)\n";
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for(mp_type x = a; x <= b; x += step)
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{
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mp_type true_result = the_function(x);
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//std::cout << true_result << std::endl;
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T absissa = boost::math::tools::real_cast<T>(x);
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mp_type test_result = convert_to_rr(n.evaluate(absissa) / d.evaluate(absissa));
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//std::cout << test_result << std::endl;
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mp_type cheb_result = convert_to_rr(boost::math::tools::evaluate_chebyshev(cn, absissa) / boost::math::tools::evaluate_chebyshev(cd, absissa));
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//std::cout << cheb_result << std::endl;
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mp_type err, cheb_err;
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if(rel_error)
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{
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err = boost::math::tools::relative_error(test_result, true_result);
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cheb_err = boost::math::tools::relative_error(cheb_result, true_result);
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}
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else
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{
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err = fabs(test_result - true_result);
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cheb_err = fabs(cheb_result - true_result);
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}
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if(err > max_error)
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max_error = err;
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if(cheb_err > max_cheb_error)
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max_cheb_error = cheb_err;
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std::cout << std::setprecision(6) << std::setw(15) << std::left << boost::math::tools::real_cast<double>(absissa)
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<< (test_result < true_result ? "-" : "") << std::setw(20) << std::left
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<< boost::math::tools::real_cast<double>(err)
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<< boost::math::tools::real_cast<double>(cheb_err) << std::endl;
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}
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std::string msg = "Max Error found at ";
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msg += name;
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msg += " precision = ";
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//msg.append(62 - 17 - msg.size(), ' ');
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std::cout << msg << "Poly: " << std::setprecision(6)
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//<< std::setw(15) << std::left
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<< boost::math::tools::real_cast<T>(max_error)
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<< " Cheb: " << boost::math::tools::real_cast<T>(max_cheb_error) << std::endl;
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}
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else
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{
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std::cout << "Nothing to test: try converging an approximation first!!!" << std::endl;
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}
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}
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void test_n(unsigned n)
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{
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do_test_n(mp_type(), "mp_type", n);
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}
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void test_float_n(unsigned n)
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{
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do_test_n(float(0), "float", n);
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}
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void test_double_n(unsigned n)
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{
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do_test_n(double(0), "double", n);
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}
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void test_long_n(unsigned n)
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{
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do_test_n((long double)(0), "long double", n);
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}
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void test_float80_n(unsigned n)
|
|
{
|
|
do_test_n((boost::multiprecision::cpp_bin_float_double_extended)(0), "float80", n);
|
|
}
|
|
|
|
void test_float128_n(unsigned n)
|
|
{
|
|
do_test_n((boost::multiprecision::cpp_bin_float_quad)(0), "float128", n);
|
|
}
|
|
|
|
void rotate(const char*, const char*)
|
|
{
|
|
if(p_remez)
|
|
{
|
|
p_remez->rotate();
|
|
}
|
|
else
|
|
{
|
|
std::cerr << "Nothing to rotate" << std::endl;
|
|
}
|
|
}
|
|
|
|
void rescale(const char*, const char*)
|
|
{
|
|
if(p_remez)
|
|
{
|
|
p_remez->rescale(a, b);
|
|
}
|
|
else
|
|
{
|
|
std::cerr << "Nothing to rescale" << std::endl;
|
|
}
|
|
}
|
|
|
|
void graph_poly(const char*, const char*)
|
|
{
|
|
int i = 50;
|
|
set_working_precision(working_precision);
|
|
if(started)
|
|
{
|
|
//
|
|
// We want to test the approximation at fixed precision:
|
|
// either float, double or long double. Begin by getting the
|
|
// polynomials:
|
|
//
|
|
boost::math::tools::polynomial<mp_type> n, d;
|
|
n = p_remez->numerator();
|
|
d = p_remez->denominator();
|
|
|
|
mp_type max_error(0);
|
|
mp_type step = (b - a) / i;
|
|
|
|
std::cout << "Evaluating Numerator...\n";
|
|
mp_type val;
|
|
for(val = a; val <= b; val += step)
|
|
std::cout << n.evaluate(val) << std::endl;
|
|
std::cout << "Evaluating Denominator...\n";
|
|
for(val = a; val <= b; val += step)
|
|
std::cout << d.evaluate(val) << std::endl;
|
|
}
|
|
else
|
|
{
|
|
std::cout << "Nothing to test: try converging an approximation first!!!" << std::endl;
|
|
}
|
|
}
|
|
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
|
{
|
|
std::string line;
|
|
real_parser<long double/*mp_type*/ > const rr_p;
|
|
while(std::getline(std::cin, line))
|
|
{
|
|
if(parse(line.c_str(), str_p("quit"), space_p).full)
|
|
return;
|
|
if(false == parse(line.c_str(),
|
|
(
|
|
|
|
str_p("range")[assign_a(started, false)] && real_p[assign_a(a)] && real_p[assign_a(b)]
|
|
||
|
|
str_p("relative")[assign_a(started, false)][assign_a(rel_error, true)]
|
|
||
|
|
str_p("absolute")[assign_a(started, false)][assign_a(rel_error, false)]
|
|
||
|
|
str_p("pin")[assign_a(started, false)] && str_p("true")[assign_a(pin, true)]
|
|
||
|
|
str_p("pin")[assign_a(started, false)] && str_p("false")[assign_a(pin, false)]
|
|
||
|
|
str_p("pin")[assign_a(started, false)] && str_p("1")[assign_a(pin, true)]
|
|
||
|
|
str_p("pin")[assign_a(started, false)] && str_p("0")[assign_a(pin, false)]
|
|
||
|
|
str_p("pin")[assign_a(started, false)][assign_a(pin, true)]
|
|
||
|
|
str_p("order")[assign_a(started, false)] && uint_p[assign_a(orderN)] && uint_p[assign_a(orderD)]
|
|
||
|
|
str_p("order")[assign_a(started, false)] && uint_p[assign_a(orderN)]
|
|
||
|
|
str_p("target-precision") && uint_p[assign_a(target_precision)]
|
|
||
|
|
str_p("working-precision")[assign_a(started, false)] && uint_p[assign_a(working_precision)]
|
|
||
|
|
str_p("variant")[assign_a(started, false)] && int_p[assign_a(variant)]
|
|
||
|
|
str_p("skew")[assign_a(started, false)] && int_p[assign_a(skew)]
|
|
||
|
|
str_p("brake") && int_p[assign_a(brake)]
|
|
||
|
|
str_p("step") && int_p[&step_some]
|
|
||
|
|
str_p("step")[&step]
|
|
||
|
|
str_p("poly")[&graph_poly]
|
|
||
|
|
str_p("info")[&show]
|
|
||
|
|
str_p("graph") && uint_p[&do_graph]
|
|
||
|
|
str_p("graph")[&graph]
|
|
||
|
|
str_p("x-offset") && real_p[assign_a(x_offset)]
|
|
||
|
|
str_p("x-scale") && real_p[assign_a(x_scale)]
|
|
||
|
|
str_p("y-offset") && str_p("auto")[assign_a(auto_offset_y, true)]
|
|
||
|
|
str_p("y-offset") && real_p[assign_a(y_offset)][assign_a(auto_offset_y, false)]
|
|
||
|
|
str_p("test") && str_p("float") && uint_p[&test_float_n]
|
|
||
|
|
str_p("test") && str_p("float")[&test_float]
|
|
||
|
|
str_p("test") && str_p("double") && uint_p[&test_double_n]
|
|
||
|
|
str_p("test") && str_p("double")[&test_double]
|
|
||
|
|
str_p("test") && str_p("long") && uint_p[&test_long_n]
|
|
||
|
|
str_p("test") && str_p("long")[&test_long]
|
|
||
|
|
str_p("test") && str_p("float80") && uint_p[&test_float80_n]
|
|
||
|
|
str_p("test") && str_p("float80")[&test_float80]
|
|
||
|
|
str_p("test") && str_p("float128") && uint_p[&test_float128_n]
|
|
||
|
|
str_p("test") && str_p("float128")[&test_float128]
|
|
||
|
|
str_p("test") && str_p("all")[&test_all]
|
|
||
|
|
str_p("test") && uint_p[&test_n]
|
|
||
|
|
str_p("rotate")[&rotate]
|
|
||
|
|
str_p("rescale") && real_p[assign_a(a)] && real_p[assign_a(b)] && epsilon_p[&rescale]
|
|
|
|
), space_p).full)
|
|
{
|
|
std::cout << "Unable to parse directive: \"" << line << "\"" << std::endl;
|
|
}
|
|
else
|
|
{
|
|
std::cout << "Variant = " << variant << std::endl;
|
|
std::cout << "range = [" << a << "," << b << "]" << std::endl;
|
|
std::cout << "Relative Error = " << rel_error << std::endl;
|
|
std::cout << "Pin to Origin = " << pin << std::endl;
|
|
std::cout << "Order (Num/Denom) = " << orderN << "/" << orderD << std::endl;
|
|
std::cout << "Target Precision = " << target_precision << std::endl;
|
|
std::cout << "Working Precision = " << working_precision << std::endl;
|
|
std::cout << "Skew = " << skew << std::endl;
|
|
std::cout << "Brake = " << brake << std::endl;
|
|
std::cout << "X Offset = " << x_offset << std::endl;
|
|
std::cout << "X scale = " << x_scale << std::endl;
|
|
std::cout << "Y Offset = ";
|
|
if(auto_offset_y)
|
|
std::cout << "Auto (";
|
|
std::cout << y_offset;
|
|
if(auto_offset_y)
|
|
std::cout << ")";
|
|
std::cout << std::endl;
|
|
}
|
|
}
|
|
}
|