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- // Copyright Paul A. Bristow 2015
- // Use, modification and distribution are subject to the
- // Boost Software License, Version 1.0.
- // (See accompanying file LICENSE_1_0.txt
- // or copy at http://www.boost.org/LICENSE_1_0.txt)
- // Comparison of finding roots using TOMS748, Newton-Raphson, Schroder & Halley algorithms.
- // Note that this file contains Quickbook mark-up as well as code
- // and comments, don't change any of the special comment mark-ups!
- // root_finding_algorithms.cpp
- #include <boost/cstdlib.hpp>
- #include <boost/config.hpp>
- #include <boost/array.hpp>
- #include <boost/type_traits/is_floating_point.hpp>
- #include <boost/type_traits/is_fundamental.hpp>
- #include "table_type.hpp"
- // Copy of i:\modular-boost\libs\math\test\table_type.hpp
- // #include "handle_test_result.hpp"
- // Copy of i:\modular - boost\libs\math\test\handle_test_result.hpp
- #include <boost/math/tools/roots.hpp>
- //using boost::math::policies::policy;
- //using boost::math::tools::newton_raphson_iterate;
- //using boost::math::tools::halley_iterate; //
- //using boost::math::tools::eps_tolerance; // Binary functor for specified number of bits.
- //using boost::math::tools::bracket_and_solve_root;
- //using boost::math::tools::toms748_solve;
- //using boost::math::tools::schroder_iterate;
- #include <boost/math/special_functions/next.hpp> // For float_distance.
- #include <tuple> // for tuple and make_tuple.
- #include <boost/math/special_functions/cbrt.hpp> // For boost::math::cbrt.
- #include <boost/multiprecision/cpp_bin_float.hpp> // is binary.
- //#include <boost/multiprecision/cpp_dec_float.hpp> // is decimal.
- using boost::multiprecision::cpp_bin_float_100;
- using boost::multiprecision::cpp_bin_float_50;
- #include <boost/timer/timer.hpp>
- #include <boost/system/error_code.hpp>
- #include <boost/multiprecision/cpp_bin_float/io.hpp>
- #include <boost/preprocessor/stringize.hpp>
- // STL
- #include <iostream>
- #include <iomanip>
- #include <string>
- #include <vector>
- #include <limits>
- #include <fstream> // std::ofstream
- #include <cmath>
- #include <typeinfo> // for type name using typid(thingy).name();
- #ifndef BOOST_ROOT
- # define BOOST_ROOT i:/modular-boost/
- #endif
- // Need to find this
- #ifdef __FILE__
- std::string sourcefilename = __FILE__;
- #endif
- std::string chop_last(std::string s)
- {
- std::string::size_type pos = s.find_last_of("\\/");
- if(pos != std::string::npos)
- s.erase(pos);
- else if(s.empty())
- abort();
- else
- s.erase();
- return s;
- }
- std::string make_root()
- {
- std::string result;
- if(sourcefilename.find_first_of(":") != std::string::npos)
- {
- result = chop_last(sourcefilename); // lose filename part
- result = chop_last(result); // lose /example/
- result = chop_last(result); // lose /math/
- result = chop_last(result); // lose /libs/
- }
- else
- {
- result = chop_last(sourcefilename); // lose filename part
- if(result.empty())
- result = ".";
- result += "/../../..";
- }
- return result;
- }
- std::string short_file_name(std::string s)
- {
- std::string::size_type pos = s.find_last_of("\\/");
- if(pos != std::string::npos)
- s.erase(0, pos + 1);
- return s;
- }
- std::string boost_root = make_root();
- #ifdef _MSC_VER
- std::string filename = boost_root.append("/libs/math/doc/roots/root_comparison_tables_msvc.qbk");
- #else // assume GCC
- std::string filename = boost_root.append("/libs/math/doc/roots/root_comparison_tables_gcc.qbk");
- #endif
- std::ofstream fout (filename.c_str(), std::ios_base::out);
- //std::array<std::string, 6> float_type_names =
- //{
- // "float", "double", "long double", "cpp_bin_128", "cpp_dec_50", "cpp_dec_100"
- //};
- std::vector<std::string> algo_names =
- {
- "cbrt", "TOMS748", "Newton", "Halley", "Schr'''ö'''der"
- };
- std::vector<int> max_digits10s;
- std::vector<std::string> typenames; // Full computer generated type name.
- std::vector<std::string> names; // short name.
- uintmax_t iters; // Global as iterations is not returned by rooting function.
- const int count = 1000000; // Number of iterations to average.
-
- struct root_info
- { // for a floating-point type, float, double ...
- std::size_t max_digits10; // for type.
- std::string full_typename; // for type from type_id.name().
- std::string short_typename; // for type "float", "double", "cpp_bin_float_50" ....
- std::size_t bin_digits; // binary in floating-point type numeric_limits<T>::digits;
- int get_digits; // fraction of maximum possible accuracy required.
- // = digits * digits_accuracy
- // Vector of values for each algorithm, std::cbrt, boost::math::cbrt, TOMS748, Newton, Halley.
- //std::vector< boost::int_least64_t> times; converted to int.
- std::vector<int> times;
- //boost::int_least64_t min_time = std::numeric_limits<boost::int_least64_t>::max(); // Used to normalize times (as int).
- std::vector<double> normed_times;
- boost::int_least64_t min_time = (std::numeric_limits<boost::int_least64_t>::max)(); // Used to normalize times.
- std::vector<uintmax_t> iterations;
- std::vector<long int> distances;
- std::vector<cpp_bin_float_100> full_results;
- }; // struct root_info
- std::vector<root_info> root_infos; // One element for each type used.
- int type_no = -1; // float = 0, double = 1, ... indexing root_infos.
- inline std::string build_test_name(const char* type_name, const char* test_name)
- {
- std::string result(BOOST_COMPILER);
- result += "|";
- result += BOOST_STDLIB;
- result += "|";
- result += BOOST_PLATFORM;
- result += "|";
- result += type_name;
- result += "|";
- result += test_name;
- #if defined(_DEBUG ) || !defined(NDEBUG)
- result += "|";
- result += " debug";
- #else
- result += "|";
- result += " release";
- #endif
- result += "|";
- return result;
- }
- // No derivatives - using TOMS748 internally.
- template <class T>
- struct cbrt_functor_noderiv
- { // cube root of x using only function - no derivatives.
- cbrt_functor_noderiv(T const& to_find_root_of) : a(to_find_root_of)
- { // Constructor just stores value a to find root of.
- }
- T operator()(T const& x)
- {
- T fx = x*x*x - a; // Difference (estimate x^3 - a).
- return fx;
- }
- private:
- T a; // to be 'cube_rooted'.
- }; // template <class T> struct cbrt_functor_noderiv
- template <class T>
- T cbrt_noderiv(T x)
- { // return cube root of x using bracket_and_solve (using NO derivatives).
- using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools; // For bracket_and_solve_root.
- // Maybe guess should be double, or use enable_if to avoid warning about conversion double to float here?
- T guess;
- if (boost::is_fundamental<T>::value)
- {
- int exponent;
- frexp(x, &exponent); // Get exponent of z (ignore mantissa).
- guess = ldexp((T)1., exponent / 3); // Rough guess is to divide the exponent by three.
- }
- else
- { // (boost::is_class<T>)
- double dx = static_cast<double>(x);
- guess = boost::math::cbrt<T>(dx); // Get guess using double.
- }
-
- T factor = 2; // How big steps to take when searching.
- const boost::uintmax_t maxit = 50; // Limit to maximum iterations.
- boost::uintmax_t it = maxit; // Initally our chosen max iterations, but updated with actual.
- bool is_rising = true; // So if result if guess^3 is too low, then try increasing guess.
- // Some fraction of digits is used to control how accurate to try to make the result.
- int get_digits = static_cast<int>(std::numeric_limits<T>::digits - 2);
- eps_tolerance<T> tol(get_digits); // Set the tolerance.
- std::pair<T, T> r =
- bracket_and_solve_root(cbrt_functor_noderiv<T>(x), guess, factor, is_rising, tol, it);
- iters = it;
- T result = r.first + (r.second - r.first) / 2; // Midway between brackets.
- return result;
- } // template <class T> T cbrt_noderiv(T x)
- // Using 1st derivative only Newton-Raphson
- template <class T>
- struct cbrt_functor_deriv
- { // Functor also returning 1st derviative.
- cbrt_functor_deriv(T const& to_find_root_of) : a(to_find_root_of)
- { // Constructor stores value a to find root of,
- // for example: calling cbrt_functor_deriv<T>(x) to use to get cube root of x.
- }
- std::pair<T, T> operator()(T const& x)
- { // Return both f(x) and f'(x).
- T fx = x*x*x - a; // Difference (estimate x^3 - value).
- T dx = 3 * x*x; // 1st derivative = 3x^2.
- return std::make_pair(fx, dx); // 'return' both fx and dx.
- }
- private:
- T a; // to be 'cube_rooted'.
- };
- template <class T>
- T cbrt_deriv(T x)
- { // return cube root of x using 1st derivative and Newton_Raphson.
- using namespace boost::math::tools;
- int exponent;
- T guess;
- if(boost::is_fundamental<T>::value)
- {
- 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.
- int get_digits = static_cast<int>(std::numeric_limits<T>::digits * 0.6);
- const boost::uintmax_t maxit = 20;
- boost::uintmax_t it = maxit;
- T result = newton_raphson_iterate(cbrt_functor_deriv<T>(x), guess, min, max, get_digits, it);
- iters = it;
- return result;
- }
- // Using 1st and 2nd derivatives with Halley algorithm.
- template <class T>
- struct cbrt_functor_2deriv
- { // Functor returning both 1st and 2nd derivatives.
- cbrt_functor_2deriv(T const& to_find_root_of) : a(to_find_root_of)
- { // Constructor stores value a to find root of, for example:
- // calling cbrt_functor_2deriv<T>(x) to get cube root of x,
- }
- std::tuple<T, T, T> operator()(T const& x)
- { // Return both f(x) and f'(x) and f''(x).
- T fx = x*x*x - a; // Difference (estimate x^3 - value).
- T dx = 3 * x*x; // 1st derivative = 3x^2.
- T d2x = 6 * x; // 2nd derivative = 6x.
- return std::make_tuple(fx, dx, d2x); // 'return' fx, dx and d2x.
- }
- private:
- T a; // to be 'cube_rooted'.
- };
- template <class T>
- T cbrt_2deriv(T x)
- { // return cube root of x using 1st and 2nd derivatives and Halley.
- //using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools;
- int exponent;
- T guess;
- if(boost::is_fundamental<T>::value)
- {
- 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.
- // 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);
- boost::uintmax_t maxit = 20;
- boost::uintmax_t it = maxit;
- T result = halley_iterate(cbrt_functor_2deriv<T>(x), guess, min, max, get_digits, it);
- iters = it;
- return result;
- }
- // Using 1st and 2nd derivatives using Schroder algorithm.
- template <class T>
- T cbrt_2deriv_s(T x)
- { // return cube root of x using 1st and 2nd derivatives and Schroder algorithm.
- //using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools;
- int exponent;
- T guess;
- if(boost::is_fundamental<T>::value)
- {
- 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.
- // 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();
- 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.
- test_root<float>(full_value, full_answer, "float");
- test_root<double>(full_value, full_answer, "double");
- test_root<long double>(full_value, full_answer, "long double");
- test_root<cpp_bin_float_50>(full_value, full_answer, "cpp_bin_float_50");
- //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;
- // Row for all algorithms.
- for (unsigned 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 (size_t 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 const& 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> ==================================================================
- */
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