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916 lines
34 KiB
C++
916 lines
34 KiB
C++
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// Copyright Paul A. Bristow 2015
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// Comparison of finding roots using TOMS748, Newton-Raphson, Schroder & Halley algorithms.
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// Note that this file contains Quickbook mark-up as well as code
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// and comments, don't change any of the special comment mark-ups!
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// root_finding_algorithms.cpp
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#include <boost/cstdlib.hpp>
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#include <boost/config.hpp>
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#include <boost/array.hpp>
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#include <boost/type_traits/is_floating_point.hpp>
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#include "table_type.hpp"
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// Copy of i:\modular-boost\libs\math\test\table_type.hpp
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// #include "handle_test_result.hpp"
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// Copy of i:\modular - boost\libs\math\test\handle_test_result.hpp
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#include <boost/math/tools/roots.hpp>
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//using boost::math::policies::policy;
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//using boost::math::tools::newton_raphson_iterate;
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//using boost::math::tools::halley_iterate; //
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//using boost::math::tools::eps_tolerance; // Binary functor for specified number of bits.
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//using boost::math::tools::bracket_and_solve_root;
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//using boost::math::tools::toms748_solve;
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//using boost::math::tools::schroder_iterate;
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#include <boost/math/special_functions/next.hpp> // For float_distance.
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#include <tuple> // for tuple and make_tuple.
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#include <boost/math/special_functions/cbrt.hpp> // For boost::math::cbrt.
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#include <boost/multiprecision/cpp_bin_float.hpp> // is binary.
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//#include <boost/multiprecision/cpp_dec_float.hpp> // is decimal.
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using boost::multiprecision::cpp_bin_float_100;
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using boost::multiprecision::cpp_bin_float_50;
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#include <boost/timer/timer.hpp>
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#include <boost/system/error_code.hpp>
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#include <boost/multiprecision/cpp_bin_float/io.hpp>
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#include <boost/preprocessor/stringize.hpp>
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// STL
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#include <iostream>
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#include <iomanip>
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#include <string>
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#include <vector>
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#include <limits>
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#include <fstream> // std::ofstream
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#include <cmath>
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#include <typeinfo> // for type name using typid(thingy).name();
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#ifndef BOOST_ROOT
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# define BOOST_ROOT i:/modular-boost/
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#endif
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// Need to find this
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#ifdef __FILE__
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std::string sourcefilename = __FILE__;
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#endif
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std::string chop_last(std::string s)
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{
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std::string::size_type pos = s.find_last_of("\\/");
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if(pos != std::string::npos)
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s.erase(pos);
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else if(s.empty())
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abort();
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else
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s.erase();
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return s;
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}
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std::string make_root()
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{
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std::string result;
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if(sourcefilename.find_first_of(":") != std::string::npos)
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{
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result = chop_last(sourcefilename); // lose filename part
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result = chop_last(result); // lose /example/
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result = chop_last(result); // lose /math/
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result = chop_last(result); // lose /libs/
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}
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else
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{
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result = chop_last(sourcefilename); // lose filename part
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if(result.empty())
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result = ".";
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result += "/../../..";
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}
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return result;
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}
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std::string short_file_name(std::string s)
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{
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std::string::size_type pos = s.find_last_of("\\/");
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if(pos != std::string::npos)
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s.erase(0, pos + 1);
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return s;
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}
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std::string boost_root = make_root();
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#ifdef _MSC_VER
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std::string filename = boost_root.append("/libs/math/doc/roots/root_comparison_tables_msvc.qbk");
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#else // assume GCC
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std::string filename = boost_root.append("/libs/math/doc/roots/root_comparison_tables_gcc.qbk");
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#endif
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std::ofstream fout (filename.c_str(), std::ios_base::out);
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//std::array<std::string, 6> float_type_names =
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//{
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// "float", "double", "long double", "cpp_bin_128", "cpp_dec_50", "cpp_dec_100"
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//};
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std::vector<std::string> algo_names =
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{
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"cbrt", "TOMS748", "Newton", "Halley", "Schr'''ö'''der"
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};
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std::vector<int> max_digits10s;
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std::vector<std::string> typenames; // Full computer generated type name.
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std::vector<std::string> names; // short name.
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uintmax_t iters; // Global as iterations is not returned by rooting function.
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const int convert = 1000; // convert nanoseconds to microseconds (assuming this is resolution).
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const int count = 1000000; // Number of iterations to average.
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struct root_info
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{ // for a floating-point type, float, double ...
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std::size_t max_digits10; // for type.
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std::string full_typename; // for type from type_id.name().
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std::string short_typename; // for type "float", "double", "cpp_bin_float_50" ....
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std::size_t bin_digits; // binary in floating-point type numeric_limits<T>::digits;
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int get_digits; // fraction of maximum possible accuracy required.
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// = digits * digits_accuracy
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// Vector of values for each algorithm, std::cbrt, boost::math::cbrt, TOMS748, Newton, Halley.
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//std::vector< boost::int_least64_t> times; converted to int.
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std::vector<int> times;
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//boost::int_least64_t min_time = std::numeric_limits<boost::int_least64_t>::max(); // Used to normalize times (as int).
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std::vector<double> normed_times;
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boost::int_least64_t min_time = (std::numeric_limits<boost::int_least64_t>::max)(); // Used to normalize times.
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std::vector<uintmax_t> iterations;
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std::vector<long int> distances;
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std::vector<cpp_bin_float_100> full_results;
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}; // struct root_info
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std::vector<root_info> root_infos; // One element for each type used.
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int type_no = -1; // float = 0, double = 1, ... indexing root_infos.
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inline std::string build_test_name(const char* type_name, const char* test_name)
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{
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std::string result(BOOST_COMPILER);
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result += "|";
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result += BOOST_STDLIB;
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result += "|";
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result += BOOST_PLATFORM;
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result += "|";
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result += type_name;
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result += "|";
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result += test_name;
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#if defined(_DEBUG ) || !defined(NDEBUG)
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result += "|";
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result += " debug";
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#else
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result += "|";
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result += " release";
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#endif
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result += "|";
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return result;
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}
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// No derivatives - using TOMS748 internally.
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template <class T>
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struct cbrt_functor_noderiv
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{ // cube root of x using only function - no derivatives.
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cbrt_functor_noderiv(T const& to_find_root_of) : a(to_find_root_of)
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{ // Constructor just stores value a to find root of.
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}
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T operator()(T const& x)
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{
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T fx = x*x*x - a; // Difference (estimate x^3 - a).
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return fx;
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}
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private:
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T a; // to be 'cube_rooted'.
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}; // template <class T> struct cbrt_functor_noderiv
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template <class T>
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T cbrt_noderiv(T x)
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{ // return cube root of x using bracket_and_solve (using NO derivatives).
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using namespace std; // Help ADL of std functions.
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using namespace boost::math::tools; // For bracket_and_solve_root.
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// Maybe guess should be double, or use enable_if to avoid warning about conversion double to float here?
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T guess;
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if (boost::is_fundamental<T>::value)
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{
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int exponent;
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frexp(x, &exponent); // Get exponent of z (ignore mantissa).
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guess = ldexp((T)1., exponent / 3); // Rough guess is to divide the exponent by three.
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}
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else
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{ // (boost::is_class<T>)
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double dx = static_cast<double>(x);
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guess = boost::math::cbrt<T>(dx); // Get guess using double.
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}
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T factor = 2; // How big steps to take when searching.
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const boost::uintmax_t maxit = 50; // Limit to maximum iterations.
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boost::uintmax_t it = maxit; // Initally our chosen max iterations, but updated with actual.
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bool is_rising = true; // So if result if guess^3 is too low, then try increasing guess.
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int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T.
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// Some fraction of digits is used to control how accurate to try to make the result.
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int get_digits = static_cast<int>(std::numeric_limits<T>::digits - 2);
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eps_tolerance<T> tol(get_digits); // Set the tolerance.
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std::pair<T, T> r =
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bracket_and_solve_root(cbrt_functor_noderiv<T>(x), guess, factor, is_rising, tol, it);
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iters = it;
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T result = r.first + (r.second - r.first) / 2; // Midway between brackets.
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return result;
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} // template <class T> T cbrt_noderiv(T x)
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// Using 1st derivative only Newton-Raphson
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template <class T>
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struct cbrt_functor_deriv
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{ // Functor also returning 1st derviative.
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cbrt_functor_deriv(T const& to_find_root_of) : a(to_find_root_of)
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{ // Constructor stores value a to find root of,
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// for example: calling cbrt_functor_deriv<T>(x) to use to get cube root of x.
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}
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std::pair<T, T> operator()(T const& x)
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{ // Return both f(x) and f'(x).
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T fx = x*x*x - a; // Difference (estimate x^3 - value).
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T dx = 3 * x*x; // 1st derivative = 3x^2.
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return std::make_pair(fx, dx); // 'return' both fx and dx.
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}
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private:
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T a; // to be 'cube_rooted'.
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};
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template <class T>
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T cbrt_deriv(T x)
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{ // return cube root of x using 1st derivative and Newton_Raphson.
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using namespace boost::math::tools;
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int exponent;
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T guess;
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if(boost::is_fundamental<T>::value)
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{
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frexp(x, &exponent); // Get exponent of z (ignore mantissa).
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guess = ldexp(static_cast<T>(1), exponent / 3); // Rough guess is to divide the exponent by three.
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}
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else
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guess = boost::math::cbrt(static_cast<double>(x));
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T min = guess / 2; // Minimum possible value is half our guess.
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T max = 2 * guess; // Maximum possible value is twice our guess.
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const int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T.
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int get_digits = static_cast<int>(std::numeric_limits<T>::digits * 0.6);
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const boost::uintmax_t maxit = 20;
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boost::uintmax_t it = maxit;
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T result = newton_raphson_iterate(cbrt_functor_deriv<T>(x), guess, min, max, get_digits, it);
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iters = it;
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return result;
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}
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// Using 1st and 2nd derivatives with Halley algorithm.
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template <class T>
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struct cbrt_functor_2deriv
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{ // Functor returning both 1st and 2nd derivatives.
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cbrt_functor_2deriv(T const& to_find_root_of) : a(to_find_root_of)
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{ // Constructor stores value a to find root of, for example:
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// calling cbrt_functor_2deriv<T>(x) to get cube root of x,
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}
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std::tuple<T, T, T> operator()(T const& x)
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{ // Return both f(x) and f'(x) and f''(x).
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T fx = x*x*x - a; // Difference (estimate x^3 - value).
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T dx = 3 * x*x; // 1st derivative = 3x^2.
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T d2x = 6 * x; // 2nd derivative = 6x.
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return std::make_tuple(fx, dx, d2x); // 'return' fx, dx and d2x.
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}
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private:
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T a; // to be 'cube_rooted'.
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};
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template <class T>
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T cbrt_2deriv(T x)
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{ // return cube root of x using 1st and 2nd derivatives and Halley.
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//using namespace std; // Help ADL of std functions.
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using namespace boost::math::tools;
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int exponent;
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T guess;
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if(boost::is_fundamental<T>::value)
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{
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frexp(x, &exponent); // Get exponent of z (ignore mantissa).
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guess = ldexp(static_cast<T>(1), exponent / 3); // Rough guess is to divide the exponent by three.
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}
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else
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guess = boost::math::cbrt(static_cast<double>(x));
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T min = guess / 2; // Minimum possible value is half our guess.
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T max = 2 * guess; // Maximum possible value is twice our guess.
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const int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T.
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// digits used to control how accurate to try to make the result.
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int get_digits = static_cast<int>(std::numeric_limits<T>::digits * 0.4);
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boost::uintmax_t maxit = 20;
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boost::uintmax_t it = maxit;
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T result = halley_iterate(cbrt_functor_2deriv<T>(x), guess, min, max, get_digits, it);
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iters = it;
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return result;
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}
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// Using 1st and 2nd derivatives using Schroder algorithm.
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template <class T>
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T cbrt_2deriv_s(T x)
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{ // return cube root of x using 1st and 2nd derivatives and Schroder algorithm.
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//using namespace std; // Help ADL of std functions.
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using namespace boost::math::tools;
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int exponent;
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T guess;
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if(boost::is_fundamental<T>::value)
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{
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|
|
frexp(x, &exponent); // Get exponent of z (ignore mantissa).
|
||
|
|
guess = ldexp(static_cast<T>(1), exponent / 3); // Rough guess is to divide the exponent by three.
|
||
|
|
}
|
||
|
|
else
|
||
|
|
guess = boost::math::cbrt(static_cast<double>(x));
|
||
|
|
T min = guess / 2; // Minimum possible value is half our guess.
|
||
|
|
T max = 2 * guess; // Maximum possible value is twice our guess.
|
||
|
|
const int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T.
|
||
|
|
// digits used to control how accurate to try to make the result.
|
||
|
|
int get_digits = static_cast<int>(std::numeric_limits<T>::digits * 0.4);
|
||
|
|
const boost::uintmax_t maxit = 20;
|
||
|
|
boost::uintmax_t it = maxit;
|
||
|
|
T result = schroder_iterate(cbrt_functor_2deriv<T>(x), guess, min, max, get_digits, it);
|
||
|
|
iters = it;
|
||
|
|
return result;
|
||
|
|
} // template <class T> T cbrt_2deriv_s(T x)
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
int test_root(cpp_bin_float_100 big_value, cpp_bin_float_100 answer, const char* type_name)
|
||
|
|
{
|
||
|
|
//T value = 28.; // integer (exactly representable as floating-point)
|
||
|
|
// whose cube root is *not* exactly representable.
|
||
|
|
// Wolfram Alpha command N[28 ^ (1 / 3), 100] computes cube root to 100 decimal digits.
|
||
|
|
// 3.036588971875662519420809578505669635581453977248111123242141654169177268411884961770250390838097895
|
||
|
|
|
||
|
|
std::size_t max_digits = 2 + std::numeric_limits<T>::digits * 3010 / 10000;
|
||
|
|
// For new versions use max_digits10
|
||
|
|
// std::cout.precision(std::numeric_limits<T>::max_digits10);
|
||
|
|
std::cout.precision(max_digits);
|
||
|
|
std::cout << std::showpoint << std::endl; // Trailing zeros too.
|
||
|
|
|
||
|
|
root_infos.push_back(root_info());
|
||
|
|
type_no++; // Another type.
|
||
|
|
|
||
|
|
root_infos[type_no].max_digits10 = max_digits;
|
||
|
|
root_infos[type_no].full_typename = typeid(T).name(); // Full typename.
|
||
|
|
root_infos[type_no].short_typename = type_name; // Short typename.
|
||
|
|
|
||
|
|
root_infos[type_no].bin_digits = std::numeric_limits<T>::digits;
|
||
|
|
|
||
|
|
root_infos[type_no].get_digits = std::numeric_limits<T>::digits;
|
||
|
|
|
||
|
|
T to_root = static_cast<T>(big_value);
|
||
|
|
T result; // root
|
||
|
|
T ans = static_cast<T>(answer);
|
||
|
|
int algo = 0; // Count of algorithms used.
|
||
|
|
|
||
|
|
using boost::timer::nanosecond_type;
|
||
|
|
using boost::timer::cpu_times;
|
||
|
|
using boost::timer::cpu_timer;
|
||
|
|
|
||
|
|
cpu_times now; // Holds wall, user and system times.
|
||
|
|
T sum = 0;
|
||
|
|
|
||
|
|
// std::cbrt is much the fastest, but not useful for this comparison because it only handles fundamental types.
|
||
|
|
// Using enable_if allows us to avoid a compile fail with multiprecision types, but still distorts the results too much.
|
||
|
|
|
||
|
|
//{
|
||
|
|
// algorithm_names.push_back("std::cbrt");
|
||
|
|
// cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
// ti.start();
|
||
|
|
// for (long i = 0; i < count; ++i)
|
||
|
|
// {
|
||
|
|
// stdcbrt(big_value);
|
||
|
|
// }
|
||
|
|
// now = ti.elapsed();
|
||
|
|
// int time = static_cast<int>(now.user / count);
|
||
|
|
// root_infos[type_no].times.push_back(time); // CPU time taken per root.
|
||
|
|
// if (time < root_infos[type_no].min_time)
|
||
|
|
// {
|
||
|
|
// root_infos[type_no].min_time = time;
|
||
|
|
// }
|
||
|
|
// ti.stop();
|
||
|
|
// long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
// root_infos[type_no].distances.push_back(distance);
|
||
|
|
// root_infos[type_no].iterations.push_back(0); // Not known.
|
||
|
|
// root_infos[type_no].full_results.push_back(result);
|
||
|
|
// algo++;
|
||
|
|
//}
|
||
|
|
//{
|
||
|
|
// //algorithm_names.push_back("boost::math::cbrt"); // .
|
||
|
|
// cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
// ti.start();
|
||
|
|
// for (long i = 0; i < count; ++i)
|
||
|
|
// {
|
||
|
|
// result = boost::math::cbrt(to_root); //
|
||
|
|
// }
|
||
|
|
// now = ti.elapsed();
|
||
|
|
// int time = static_cast<int>(now.user / count);
|
||
|
|
// root_infos[type_no].times.push_back(time); // CPU time taken.
|
||
|
|
// ti.stop();
|
||
|
|
// if (time < root_infos[type_no].min_time)
|
||
|
|
// {
|
||
|
|
// root_infos[type_no].min_time = time;
|
||
|
|
// }
|
||
|
|
// long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
// root_infos[type_no].distances.push_back(distance);
|
||
|
|
// root_infos[type_no].iterations.push_back(0); // Iterations not knowable.
|
||
|
|
// root_infos[type_no].full_results.push_back(result);
|
||
|
|
//}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
{
|
||
|
|
//algorithm_names.push_back("boost::math::cbrt"); // .
|
||
|
|
result = 0;
|
||
|
|
cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
ti.start();
|
||
|
|
for (long i = 0; i < count; ++i)
|
||
|
|
{
|
||
|
|
result = boost::math::cbrt(to_root); //
|
||
|
|
sum += result;
|
||
|
|
}
|
||
|
|
now = ti.elapsed();
|
||
|
|
boost:int_least64_t n = now.user;
|
||
|
|
|
||
|
|
long time = static_cast<long>(now.user/1000); // convert nanoseconds to microseconds (assuming this is resolution).
|
||
|
|
root_infos[type_no].times.push_back(time); // CPU time taken.
|
||
|
|
ti.stop();
|
||
|
|
if (time < root_infos[type_no].min_time)
|
||
|
|
{
|
||
|
|
root_infos[type_no].min_time = time;
|
||
|
|
}
|
||
|
|
long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
root_infos[type_no].distances.push_back(distance);
|
||
|
|
root_infos[type_no].iterations.push_back(0); // Iterations not knowable.
|
||
|
|
root_infos[type_no].full_results.push_back(result);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
//algorithm_names.push_back("TOMS748"); //
|
||
|
|
cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
ti.start();
|
||
|
|
for (long i = 0; i < count; ++i)
|
||
|
|
{
|
||
|
|
result = cbrt_noderiv<T>(to_root); //
|
||
|
|
sum += result;
|
||
|
|
}
|
||
|
|
now = ti.elapsed();
|
||
|
|
// int time = static_cast<int>(now.user / count);
|
||
|
|
long time = static_cast<long>(now.user/1000);
|
||
|
|
root_infos[type_no].times.push_back(time); // CPU time taken.
|
||
|
|
if (time < root_infos[type_no].min_time)
|
||
|
|
{
|
||
|
|
root_infos[type_no].min_time = time;
|
||
|
|
}
|
||
|
|
ti.stop();
|
||
|
|
long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
root_infos[type_no].distances.push_back(distance);
|
||
|
|
root_infos[type_no].iterations.push_back(iters); //
|
||
|
|
root_infos[type_no].full_results.push_back(result);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
// algorithm_names.push_back("Newton"); // algorithm
|
||
|
|
cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
ti.start();
|
||
|
|
for (long i = 0; i < count; ++i)
|
||
|
|
{
|
||
|
|
result = cbrt_deriv(to_root); //
|
||
|
|
sum += result;
|
||
|
|
}
|
||
|
|
now = ti.elapsed();
|
||
|
|
// int time = static_cast<int>(now.user / count);
|
||
|
|
long time = static_cast<long>(now.user/1000);
|
||
|
|
root_infos[type_no].times.push_back(time); // CPU time taken.
|
||
|
|
if (time < root_infos[type_no].min_time)
|
||
|
|
{
|
||
|
|
root_infos[type_no].min_time = time;
|
||
|
|
}
|
||
|
|
|
||
|
|
ti.stop();
|
||
|
|
long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
root_infos[type_no].distances.push_back(distance);
|
||
|
|
root_infos[type_no].iterations.push_back(iters); //
|
||
|
|
root_infos[type_no].full_results.push_back(result);
|
||
|
|
}
|
||
|
|
{
|
||
|
|
//algorithm_names.push_back("Halley"); // algorithm
|
||
|
|
cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
ti.start();
|
||
|
|
for (long i = 0; i < count; ++i)
|
||
|
|
{
|
||
|
|
result = cbrt_2deriv(to_root); //
|
||
|
|
sum += result;
|
||
|
|
}
|
||
|
|
now = ti.elapsed();
|
||
|
|
// int time = static_cast<int>(now.user / count);
|
||
|
|
long time = static_cast<long>(now.user/1000);
|
||
|
|
root_infos[type_no].times.push_back(time); // CPU time taken.
|
||
|
|
ti.stop();
|
||
|
|
if (time < root_infos[type_no].min_time)
|
||
|
|
{
|
||
|
|
root_infos[type_no].min_time = time;
|
||
|
|
}
|
||
|
|
long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
root_infos[type_no].distances.push_back(distance);
|
||
|
|
root_infos[type_no].iterations.push_back(iters); //
|
||
|
|
root_infos[type_no].full_results.push_back(result);
|
||
|
|
}
|
||
|
|
|
||
|
|
{
|
||
|
|
// algorithm_names.push_back("Shroeder"); // algorithm
|
||
|
|
cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
|
||
|
|
ti.start();
|
||
|
|
for (long i = 0; i < count; ++i)
|
||
|
|
{
|
||
|
|
result = cbrt_2deriv_s(to_root); //
|
||
|
|
sum += result;
|
||
|
|
}
|
||
|
|
now = ti.elapsed();
|
||
|
|
// int time = static_cast<int>(now.user / count);
|
||
|
|
long time = static_cast<long>(now.user/1000);
|
||
|
|
root_infos[type_no].times.push_back(time); // CPU time taken.
|
||
|
|
if (time < root_infos[type_no].min_time)
|
||
|
|
{
|
||
|
|
root_infos[type_no].min_time = time;
|
||
|
|
}
|
||
|
|
ti.stop();
|
||
|
|
long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans));
|
||
|
|
root_infos[type_no].distances.push_back(distance);
|
||
|
|
root_infos[type_no].iterations.push_back(iters); //
|
||
|
|
root_infos[type_no].full_results.push_back(result);
|
||
|
|
}
|
||
|
|
for (size_t i = 0; i != root_infos[type_no].times.size(); i++)
|
||
|
|
{ // Normalize times.
|
||
|
|
double normed_time = static_cast<double>(root_infos[type_no].times[i]);
|
||
|
|
normed_time /= root_infos[type_no].min_time;
|
||
|
|
root_infos[type_no].normed_times.push_back(normed_time);
|
||
|
|
}
|
||
|
|
algo++;
|
||
|
|
std::cout << "Accumulated sum was " << sum << std::endl;
|
||
|
|
return algo; // Count of how many algorithms used.
|
||
|
|
} // test_root
|
||
|
|
|
||
|
|
void table_root_info(cpp_bin_float_100 full_value, cpp_bin_float_100 full_answer)
|
||
|
|
{
|
||
|
|
// Fill the elements.
|
||
|
|
int type_count = 0;
|
||
|
|
type_count = test_root<float>(full_value, full_answer, "float");
|
||
|
|
type_count = test_root<double>(full_value, full_answer, "double");
|
||
|
|
type_count = test_root<long double>(full_value, full_answer, "long double");
|
||
|
|
type_count = test_root<cpp_bin_float_50>(full_value, full_answer, "cpp_bin_float_50");
|
||
|
|
//type_count = test_root<cpp_bin_float_100>(full_value, full_answer, "cpp_bin_float_100");
|
||
|
|
|
||
|
|
std::cout << root_infos.size() << " floating-point types tested:" << std::endl;
|
||
|
|
#ifndef NDEBUG
|
||
|
|
std::cout << "Compiled in debug mode." << std::endl;
|
||
|
|
#else
|
||
|
|
std::cout << "Compiled in optimise mode." << std::endl;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|
||
|
|
for (size_t tp = 0; tp != root_infos.size(); tp++)
|
||
|
|
{ // For all types:
|
||
|
|
|
||
|
|
std::cout << std::endl;
|
||
|
|
|
||
|
|
std::cout << "Floating-point type = " << root_infos[tp].short_typename << std::endl;
|
||
|
|
std::cout << "Floating-point type = " << root_infos[tp].full_typename << std::endl;
|
||
|
|
std::cout << "Max_digits10 = " << root_infos[tp].max_digits10 << std::endl;
|
||
|
|
std::cout << "Binary digits = " << root_infos[tp].bin_digits << std::endl;
|
||
|
|
std::cout << "Accuracy digits = " << root_infos[tp].get_digits - 2 << ", " << static_cast<int>(root_infos[tp].get_digits * 0.6) << ", " << static_cast<int>(root_infos[tp].get_digits * 0.4) << std::endl;
|
||
|
|
std::cout << "min_time = " << root_infos[tp].min_time << std::endl;
|
||
|
|
|
||
|
|
std::cout << std::setprecision(root_infos[tp].max_digits10 ) << "Roots = ";
|
||
|
|
std::copy(root_infos[tp].full_results.begin(), root_infos[tp].full_results.end(), std::ostream_iterator<cpp_bin_float_100>(std::cout, " "));
|
||
|
|
std::cout << std::endl;
|
||
|
|
|
||
|
|
// Header row.
|
||
|
|
std::cout << "Algorithm " << "Iterations " << "Times " << "Norm_times " << "Distance" << std::endl;
|
||
|
|
std::vector<std::string>::iterator al_iter = algo_names.begin();
|
||
|
|
|
||
|
|
// Row for all algorithms.
|
||
|
|
for (int algo = 0; algo != algo_names.size(); algo++)
|
||
|
|
{
|
||
|
|
std::cout
|
||
|
|
<< std::left << std::setw(20) << algo_names[algo] << " "
|
||
|
|
<< std::setw(8) << std::setprecision(2) << root_infos[tp].iterations[algo] << " "
|
||
|
|
<< std::setw(8) << std::setprecision(5) << root_infos[tp].times[algo] << " "
|
||
|
|
<< std::setw(8) << std::setprecision(3) << root_infos[tp].normed_times[algo] << " "
|
||
|
|
<< std::setw(8) << std::setprecision(2) << root_infos[tp].distances[algo]
|
||
|
|
<< std::endl;
|
||
|
|
} // for algo
|
||
|
|
} // for tp
|
||
|
|
|
||
|
|
// Print info as Quickbook table.
|
||
|
|
#if 0
|
||
|
|
fout << "[table:cbrt_5 Info for float, double, long double and cpp_bin_float_50\n"
|
||
|
|
<< "[[type name] [max_digits10] [binary digits] [required digits]]\n";// header.
|
||
|
|
|
||
|
|
for (size_t tp = 0; tp != root_infos.size(); tp++)
|
||
|
|
{ // For all types:
|
||
|
|
fout << "["
|
||
|
|
<< "[" << root_infos[tp].short_typename << "]"
|
||
|
|
<< "[" << root_infos[tp].max_digits10 << "]" // max_digits10
|
||
|
|
<< "[" << root_infos[tp].bin_digits << "]"// < "Binary digits
|
||
|
|
<< "[" << root_infos[tp].get_digits << "]]\n"; // Accuracy digits.
|
||
|
|
} // tp
|
||
|
|
fout << "] [/table cbrt_5] \n" << std::endl;
|
||
|
|
#endif
|
||
|
|
// Prepare Quickbook table of floating-point types.
|
||
|
|
fout << "[table:cbrt_4 Cube root(28) for float, double, long double and cpp_bin_float_50\n"
|
||
|
|
<< "[[][float][][][] [][double][][][] [][long d][][][] [][cpp50][][]]\n"
|
||
|
|
<< "[[Algorithm]";
|
||
|
|
for (size_t tp = 0; tp != root_infos.size(); tp++)
|
||
|
|
{ // For all types:
|
||
|
|
fout << "[Its]" << "[Times]" << "[Norm]" << "[Dis]" << "[ ]";
|
||
|
|
}
|
||
|
|
fout << "]" << std::endl;
|
||
|
|
|
||
|
|
// Row for all algorithms.
|
||
|
|
for (int algo = 0; algo != algo_names.size(); algo++)
|
||
|
|
{
|
||
|
|
fout << "[[" << std::left << std::setw(9) << algo_names[algo] << "]";
|
||
|
|
for (size_t tp = 0; tp != root_infos.size(); tp++)
|
||
|
|
{ // For all types:
|
||
|
|
|
||
|
|
fout
|
||
|
|
<< "[" << std::right << std::showpoint
|
||
|
|
<< std::setw(3) << std::setprecision(2) << root_infos[tp].iterations[algo] << "]["
|
||
|
|
<< std::setw(5) << std::setprecision(5) << root_infos[tp].times[algo] << "][";
|
||
|
|
if(fabs(root_infos[tp].normed_times[algo]) <= 1.05)
|
||
|
|
fout << "[role blue " << std::setw(3) << std::setprecision(2) << root_infos[tp].normed_times[algo] << "]";
|
||
|
|
else if(fabs(root_infos[tp].normed_times[algo]) > 4)
|
||
|
|
fout << "[role red " << std::setw(3) << std::setprecision(2) << root_infos[tp].normed_times[algo] << "]";
|
||
|
|
else
|
||
|
|
fout << std::setw(3) << std::setprecision(2) << root_infos[tp].normed_times[algo];
|
||
|
|
fout
|
||
|
|
<< "]["
|
||
|
|
<< std::setw(3) << std::setprecision(2) << root_infos[tp].distances[algo] << "][ ]";
|
||
|
|
} // tp
|
||
|
|
fout <<"]" << std::endl;
|
||
|
|
} // for algo
|
||
|
|
fout << "] [/end of table cbrt_4]\n";
|
||
|
|
} // void table_root_info
|
||
|
|
|
||
|
|
int main()
|
||
|
|
{
|
||
|
|
using namespace boost::multiprecision;
|
||
|
|
using namespace boost::math;
|
||
|
|
|
||
|
|
try
|
||
|
|
{
|
||
|
|
std::cout << "Tests run with " << BOOST_COMPILER << ", "
|
||
|
|
<< BOOST_STDLIB << ", " << BOOST_PLATFORM << ", ";
|
||
|
|
|
||
|
|
if (fout.is_open())
|
||
|
|
{
|
||
|
|
std::cout << "\nOutput to " << filename << std::endl;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{ // Failed to open.
|
||
|
|
std::cout << " Open file " << filename << " for output failed!" << std::endl;
|
||
|
|
std::cout << "error" << errno << std::endl;
|
||
|
|
return boost::exit_failure;
|
||
|
|
}
|
||
|
|
|
||
|
|
fout <<
|
||
|
|
"[/""\n"
|
||
|
|
"Copyright 2015 Paul A. Bristow.""\n"
|
||
|
|
"Copyright 2015 John Maddock.""\n"
|
||
|
|
"Distributed under the Boost Software License, Version 1.0.""\n"
|
||
|
|
"(See accompanying file LICENSE_1_0.txt or copy at""\n"
|
||
|
|
"http://www.boost.org/LICENSE_1_0.txt).""\n"
|
||
|
|
"]""\n"
|
||
|
|
<< std::endl;
|
||
|
|
std::string debug_or_optimize;
|
||
|
|
#ifdef _DEBUG
|
||
|
|
#if (_DEBUG == 0)
|
||
|
|
debug_or_optimize = "Compiled in debug mode.";
|
||
|
|
#else
|
||
|
|
debug_or_optimize = "Compiled in optimise mode.";
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// Print out the program/compiler/stdlib/platform names as a Quickbook comment:
|
||
|
|
fout << "\n[h5 Program " << short_file_name(sourcefilename) << ", "
|
||
|
|
<< BOOST_COMPILER << ", "
|
||
|
|
<< BOOST_STDLIB << ", "
|
||
|
|
<< BOOST_PLATFORM << (sizeof(void*) == 8 ? ", x64" : ", x86")
|
||
|
|
<< debug_or_optimize << "[br]"
|
||
|
|
<< count << " evaluations of each of " << algo_names.size() << " root_finding algorithms."
|
||
|
|
<< "]"
|
||
|
|
<< std::endl;
|
||
|
|
|
||
|
|
std::cout << count << " evaluations of root_finding." << std::endl;
|
||
|
|
|
||
|
|
BOOST_MATH_CONTROL_FP;
|
||
|
|
|
||
|
|
cpp_bin_float_100 full_value("28");
|
||
|
|
|
||
|
|
cpp_bin_float_100 full_answer ("3.036588971875662519420809578505669635581453977248111123242141654169177268411884961770250390838097895");
|
||
|
|
|
||
|
|
std::copy(max_digits10s.begin(), max_digits10s.end(), std::ostream_iterator<int>(std::cout, " "));
|
||
|
|
std::cout << std::endl;
|
||
|
|
|
||
|
|
table_root_info(full_value, full_answer);
|
||
|
|
|
||
|
|
|
||
|
|
return boost::exit_success;
|
||
|
|
}
|
||
|
|
catch (std::exception ex)
|
||
|
|
{
|
||
|
|
std::cout << "exception thrown: " << ex.what() << std::endl;
|
||
|
|
return boost::exit_failure;
|
||
|
|
}
|
||
|
|
} // int main()
|
||
|
|
|
||
|
|
/*
|
||
|
|
debug
|
||
|
|
|
||
|
|
1> float, maxdigits10 = 9
|
||
|
|
1> 6 algorithms used.
|
||
|
|
1> Digits required = 24.0000000
|
||
|
|
1> find root of 28.0000000, expected answer = 3.03658897
|
||
|
|
1> Times 156 312 18750 4375 3437 3906
|
||
|
|
1> Iterations: 0 0 8 6 4 5
|
||
|
|
1> Distance: 0 0 -1 0 0 0
|
||
|
|
1> Roots: 3.03658891 3.03658891 3.03658915 3.03658891 3.03658891 3.03658891
|
||
|
|
|
||
|
|
release
|
||
|
|
|
||
|
|
1> float, maxdigits10 = 9
|
||
|
|
1> 6 algorithms used.
|
||
|
|
1> Digits required = 24.0000000
|
||
|
|
1> find root of 28.0000000, expected answer = 3.03658897
|
||
|
|
1> Times 0 312 6875 937 937 937
|
||
|
|
1> Iterations: 0 0 8 6 4 5
|
||
|
|
1> Distance: 0 0 -1 0 0 0
|
||
|
|
1> Roots: 3.03658891 3.03658891 3.03658915 3.03658891 3.03658891 3.03658891
|
||
|
|
|
||
|
|
|
||
|
|
1>
|
||
|
|
1> 5 algorithms used:
|
||
|
|
1> 10 algorithms used:
|
||
|
|
1> boost::math::cbrt TOMS748 Newton Halley Shroeder boost::math::cbrt TOMS748 Newton Halley Shroeder
|
||
|
|
1> 2 types compared.
|
||
|
|
1> Precision of full type = 102 decimal digits
|
||
|
|
1> Find root of 28.000000000000000,
|
||
|
|
1> Expected answer = 3.0365889718756625
|
||
|
|
1> typeid(T).name()float, maxdigits10 = 9
|
||
|
|
1> find root of 28.0000000, expected answer = 3.03658897
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 8 6 4 5
|
||
|
|
1> Times 468 8437 4375 3593 4062
|
||
|
|
1> Min Time 468
|
||
|
|
1> Normalized Times 1.00 18.0 9.35 7.68 8.68
|
||
|
|
1> Distance: 0 -1 0 0 0
|
||
|
|
1> Roots: 3.03658891 3.03658915 3.03658891 3.03658891 3.03658891
|
||
|
|
1> ==================================================================
|
||
|
|
1> typeid(T).name()double, maxdigits10 = 17
|
||
|
|
1> find root of 28.000000000000000, expected answer = 3.0365889718756625
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 11 7 5 6
|
||
|
|
1> Times 312 15000 4531 3906 4375
|
||
|
|
1> Min Time 312
|
||
|
|
1> Normalized Times 1.00 48.1 14.5 12.5 14.0
|
||
|
|
1> Distance: 1 2 0 0 0
|
||
|
|
1> Roots: 3.0365889718756622 3.0365889718756618 3.0365889718756627 3.0365889718756627 3.0365889718756627
|
||
|
|
1> ==================================================================
|
||
|
|
|
||
|
|
|
||
|
|
Release
|
||
|
|
|
||
|
|
1> 5 algorithms used:
|
||
|
|
1> 10 algorithms used:
|
||
|
|
1> boost::math::cbrt TOMS748 Newton Halley Shroeder boost::math::cbrt TOMS748 Newton Halley Shroeder
|
||
|
|
1> 2 types compared.
|
||
|
|
1> Precision of full type = 102 decimal digits
|
||
|
|
1> Find root of 28.000000000000000,
|
||
|
|
1> Expected answer = 3.0365889718756625
|
||
|
|
1> typeid(T).name()float, maxdigits10 = 9
|
||
|
|
1> find root of 28.0000000, expected answer = 3.03658897
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 8 6 4 5
|
||
|
|
1> Times 312 781 937 937 937
|
||
|
|
1> Min Time 312
|
||
|
|
1> Normalized Times 1.00 2.50 3.00 3.00 3.00
|
||
|
|
1> Distance: 0 -1 0 0 0
|
||
|
|
1> Roots: 3.03658891 3.03658915 3.03658891 3.03658891 3.03658891
|
||
|
|
1> ==================================================================
|
||
|
|
1> typeid(T).name()double, maxdigits10 = 17
|
||
|
|
1> find root of 28.000000000000000, expected answer = 3.0365889718756625
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 11 7 5 6
|
||
|
|
1> Times 312 1093 937 937 937
|
||
|
|
1> Min Time 312
|
||
|
|
1> Normalized Times 1.00 3.50 3.00 3.00 3.00
|
||
|
|
1> Distance: 1 2 0 0 0
|
||
|
|
1> Roots: 3.0365889718756622 3.0365889718756618 3.0365889718756627 3.0365889718756627 3.0365889718756627
|
||
|
|
1> ==================================================================
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
1> 5 algorithms used:
|
||
|
|
1> 15 algorithms used:
|
||
|
|
1> boost::math::cbrt TOMS748 Newton Halley Shroeder boost::math::cbrt TOMS748 Newton Halley Shroeder boost::math::cbrt TOMS748 Newton Halley Shroeder
|
||
|
|
1> 3 types compared.
|
||
|
|
1> Precision of full type = 102 decimal digits
|
||
|
|
1> Find root of 28.00000000000000000000000000000000000000000000000000,
|
||
|
|
1> Expected answer = 3.036588971875662519420809578505669635581453977248111
|
||
|
|
1> typeid(T).name()float, maxdigits10 = 9
|
||
|
|
1> find root of 28.0000000, expected answer = 3.03658897
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 8 6 4 5
|
||
|
|
1> Times 156 781 937 1093 937
|
||
|
|
1> Min Time 156
|
||
|
|
1> Normalized Times 1.00 5.01 6.01 7.01 6.01
|
||
|
|
1> Distance: 0 -1 0 0 0
|
||
|
|
1> Roots: 3.03658891 3.03658915 3.03658891 3.03658891 3.03658891
|
||
|
|
1> ==================================================================
|
||
|
|
1> typeid(T).name()double, maxdigits10 = 17
|
||
|
|
1> find root of 28.000000000000000, expected answer = 3.0365889718756625
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 11 7 5 6
|
||
|
|
1> Times 312 1093 937 937 937
|
||
|
|
1> Min Time 312
|
||
|
|
1> Normalized Times 1.00 3.50 3.00 3.00 3.00
|
||
|
|
1> Distance: 1 2 0 0 0
|
||
|
|
1> Roots: 3.0365889718756622 3.0365889718756618 3.0365889718756627 3.0365889718756627 3.0365889718756627
|
||
|
|
1> ==================================================================
|
||
|
|
1> typeid(T).name()class boost::multiprecision::number<class boost::multiprecision::backends::cpp_bin_float<50,10,void,int,0,0>,0>, maxdigits10 = 52
|
||
|
|
1> find root of 28.00000000000000000000000000000000000000000000000000, expected answer = 3.036588971875662519420809578505669635581453977248111
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 13 9 6 7
|
||
|
|
1> Times 8750 177343 30312 52968 58125
|
||
|
|
1> Min Time 8750
|
||
|
|
1> Normalized Times 1.00 20.3 3.46 6.05 6.64
|
||
|
|
1> Distance: 0 0 -1 0 0
|
||
|
|
1> Roots: 3.036588971875662519420809578505669635581453977248106 3.036588971875662519420809578505669635581453977248106 3.036588971875662519420809578505669635581453977248117 3.036588971875662519420809578505669635581453977248106 3.036588971875662519420809578505669635581453977248106
|
||
|
|
1> ==================================================================
|
||
|
|
|
||
|
|
Reduce accuracy required to 0.5
|
||
|
|
|
||
|
|
1> 5 algorithms used:
|
||
|
|
1> 15 algorithms used:
|
||
|
|
1> boost::math::cbrt TOMS748 Newton Halley Shroeder
|
||
|
|
1> 3 floating_point types compared.
|
||
|
|
1> Precision of full type = 102 decimal digits
|
||
|
|
1> Find root of 28.00000000000000000000000000000000000000000000000000,
|
||
|
|
1> Expected answer = 3.036588971875662519420809578505669635581453977248111
|
||
|
|
1> typeid(T).name() = float, maxdigits10 = 9
|
||
|
|
1> Digits accuracy fraction required = 0.500000000
|
||
|
|
1> find root of 28.0000000, expected answer = 3.03658897
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 8 5 3 4
|
||
|
|
1> Times 156 5937 1406 1250 1250
|
||
|
|
1> Min Time 156
|
||
|
|
1> Normalized Times 1.0 38. 9.0 8.0 8.0
|
||
|
|
1> Distance: 0 -1 0 0 0
|
||
|
|
1> Roots: 3.03658891 3.03658915 3.03658891 3.03658891 3.03658891
|
||
|
|
1> ==================================================================
|
||
|
|
1> typeid(T).name() = double, maxdigits10 = 17
|
||
|
|
1> Digits accuracy fraction required = 0.50000000000000000
|
||
|
|
1> find root of 28.000000000000000, expected answer = 3.0365889718756625
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 8 6 4 5
|
||
|
|
1> Times 156 6250 1406 1406 1250
|
||
|
|
1> Min Time 156
|
||
|
|
1> Normalized Times 1.0 40. 9.0 9.0 8.0
|
||
|
|
1> Distance: 1 3695766 0 0 0
|
||
|
|
1> Roots: 3.0365889718756622 3.0365889702344129 3.0365889718756627 3.0365889718756627 3.0365889718756627
|
||
|
|
1> ==================================================================
|
||
|
|
1> typeid(T).name() = class boost::multiprecision::number<class boost::multiprecision::backends::cpp_bin_float<50,10,void,int,0,0>,0>, maxdigits10 = 52
|
||
|
|
1> Digits accuracy fraction required = 0.5000000000000000000000000000000000000000000000000000
|
||
|
|
1> find root of 28.00000000000000000000000000000000000000000000000000, expected answer = 3.036588971875662519420809578505669635581453977248111
|
||
|
|
1>
|
||
|
|
1> Iterations: 0 11 8 5 6
|
||
|
|
1> Times 11562 239843 34843 47500 47812
|
||
|
|
1> Min Time 11562
|
||
|
|
1> Normalized Times 1.0 21. 3.0 4.1 4.1
|
||
|
|
1> Distance: 0 0 -1 0 0
|
||
|
|
1> Roots: 3.036588971875662519420809578505669635581453977248106 3.036588971875662519420809578505669635581453977248106 3.036588971875662519420809578505669635581453977248117 3.036588971875662519420809578505669635581453977248106 3.036588971875662519420809578505669635581453977248106
|
||
|
|
1> ==================================================================
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
*/
|