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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, Halley & Schroder algorithms.
- // root_n_finding_algorithms.cpp Generalised for nth root version.
- // http://en.wikipedia.org/wiki/Cube_root
- // Note that this file contains Quickbook mark-up as well as code
- // and comments, don't change any of the special comment mark-ups!
- // This program also writes files in Quickbook tables mark-up format.
- #include <boost/cstdlib.hpp>
- #include <boost/config.hpp>
- #include <boost/array.hpp>
- #include <boost/type_traits/is_floating_point.hpp>
- #include <boost/math/tools/roots.hpp>
- #include <boost/math/special_functions/ellint_1.hpp>
- #include <boost/math/special_functions/ellint_2.hpp>
- //using boost::math::policies::policy;
- //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::halley_iterate;
- //using boost::math::tools::newton_raphson_iterate;
- //using boost::math::tools::schroder_iterate;
- #include <boost/math/special_functions/next.hpp> // For float_distance.
- #include <boost/multiprecision/cpp_bin_float.hpp> // is binary.
- 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/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();
- #ifdef __FILE__
- std::string sourcefilename = __FILE__;
- #else
- std::string sourcefilename("");
- #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();
- std::string fp_hardware; // Any hardware features like SEE or AVX
- const std::string roots_name = "libs/math/doc/roots/";
- const std::string full_roots_name(boost_root + "/libs/math/doc/roots/");
- const std::size_t nooftypes = 4;
- const std::size_t noofalgos = 4;
- double digits_accuracy = 1.0; // 1 == maximum possible accuracy.
- std::stringstream ss;
- std::ofstream fout;
- std::vector<std::string> algo_names =
- {
- "TOMS748", "Newton", "Halley", "Schr'''ö'''der"
- };
- std::vector<std::string> names =
- {
- "float", "double", "long double", "cpp_bin_float50"
- };
- uintmax_t iters; // Global as value of iterations is not returned.
- 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 (4) for each algorithm, TOMS748, Newton, Halley & Schroder.
- //std::vector< boost::int_least64_t> times; converted to int.
- std::vector<int> times; // arbirary units (ticks).
- //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;
- int min_time = (std::numeric_limits<int>::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 floating-point type used.
- 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;
- } // std::string build_test_name
- // Algorithms //////////////////////////////////////////////
- // No derivatives - using TOMS748 internally.
- //[elliptic_noderv_func
- template <typename T = double>
- struct elliptic_root_functor_noderiv
- { // Nth root of x using only function - no derivatives.
- elliptic_root_functor_noderiv(T const& arc, T const& radius) : m_arc(arc), m_radius(radius)
- { // Constructor just stores value a to find root of.
- }
- T operator()(T const& x)
- {
- using std::sqrt;
- // return the difference between required arc-length, and the calculated arc-length for an
- // ellipse with radii m_radius and x:
- T a = (std::max)(m_radius, x);
- T b = (std::min)(m_radius, x);
- T k = sqrt(1 - b * b / (a * a));
- return 4 * a * boost::math::ellint_2(k) - m_arc;
- }
- private:
- T m_arc; // length of arc.
- T m_radius; // one of the two radii of the ellipse
- }; // template <class T> struct elliptic_root_functor_noderiv
- //]
- //[elliptic_root_noderiv
- template <class T = double>
- T elliptic_root_noderiv(T radius, T arc)
- { // return the other radius of an ellipse, given one radii and the arc-length
- using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools; // For bracket_and_solve_root.
- T guess = sqrt(arc * arc / 16 - radius * radius);
- T factor = 1.2; // 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; // arc-length increases if one radii increases, so function is rising
- // Define a termination condition, stop when nearly all digits are correct, but allow for
- // the fact that we are returning a range, and must have some inaccuracy in the elliptic integral:
- eps_tolerance<T> tol(std::numeric_limits<T>::digits - 2);
- // Call bracket_and_solve_root to find the solution, note that this is a rising function:
- std::pair<T, T> r = bracket_and_solve_root(elliptic_root_functor_noderiv<T>(arc, radius), guess, factor, is_rising, tol, it);
- //<-
- iters = it;
- //->
- // Result is midway between the endpoints of the range:
- return r.first + (r.second - r.first) / 2;
- } // template <class T> T elliptic_root_noderiv(T x)
- //]
- // Using 1st derivative only Newton-Raphson
- //[elliptic_1deriv_func
- template <class T = double>
- struct elliptic_root_functor_1deriv
- { // Functor also returning 1st derviative.
- BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!");
- elliptic_root_functor_1deriv(T const& arc, T const& radius) : m_arc(arc), m_radius(radius)
- { // Constructor just stores value a to find root of.
- }
- std::pair<T, T> operator()(T const& x)
- {
- using std::sqrt;
- // Return the difference between required arc-length, and the calculated arc-length for an
- // ellipse with radii m_radius and x, plus it's derivative.
- // See http://www.wolframalpha.com/input/?i=d%2Fda+[4+*+a+*+EllipticE%281+-+b^2%2Fa^2%29]
- // We require two elliptic integral calls, but from these we can calculate both
- // the function and it's derivative:
- T a = (std::max)(m_radius, x);
- T b = (std::min)(m_radius, x);
- T a2 = a * a;
- T b2 = b * b;
- T k = sqrt(1 - b2 / a2);
- T Ek = boost::math::ellint_2(k);
- T Kk = boost::math::ellint_1(k);
- T fx = 4 * a * Ek - m_arc;
- T dfx = 4 * (a2 * Ek - b2 * Kk) / (a2 - b2);
- return std::make_pair(fx, dfx);
- }
- private:
- T m_arc; // length of arc.
- T m_radius; // one of the two radii of the ellipse
- }; // struct elliptic_root__functor_1deriv
- //]
- //[elliptic_1deriv
- template <class T = double>
- T elliptic_root_1deriv(T radius, T arc)
- {
- using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools; // For newton_raphson_iterate.
- BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!");
- T guess = sqrt(arc * arc / 16 - radius * radius);
- T min = 0; // Minimum possible value is zero.
- T max = arc; // Maximum possible value is the arc length.
- // Accuracy doubles at each step, so stop when just over half of the digits are
- // correct, and rely on that step to polish off the remainder:
- 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(elliptic_root_functor_1deriv<T>(arc, radius), guess, min, max, get_digits, it);
- //<-
- iters = it;
- //->
- return result;
- } // T elliptic_root_1_deriv Newton-Raphson
- //]
- // Using 1st and 2nd derivatives with Halley algorithm.
- //[elliptic_2deriv_func
- template <class T = double>
- struct elliptic_root_functor_2deriv
- { // Functor returning both 1st and 2nd derivatives.
- BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!");
- elliptic_root_functor_2deriv(T const& arc, T const& radius) : m_arc(arc), m_radius(radius) {}
- std::tuple<T, T, T> operator()(T const& x)
- {
- using std::sqrt;
- // Return the difference between required arc-length, and the calculated arc-length for an
- // ellipse with radii m_radius and x, plus it's derivative.
- // See http://www.wolframalpha.com/input/?i=d^2%2Fda^2+[4+*+a+*+EllipticE%281+-+b^2%2Fa^2%29]
- // for the second derivative.
- T a = (std::max)(m_radius, x);
- T b = (std::min)(m_radius, x);
- T a2 = a * a;
- T b2 = b * b;
- T k = sqrt(1 - b2 / a2);
- T Ek = boost::math::ellint_2(k);
- T Kk = boost::math::ellint_1(k);
- T fx = 4 * a * Ek - m_arc;
- T dfx = 4 * (a2 * Ek - b2 * Kk) / (a2 - b2);
- T dfx2 = 4 * b2 * ((a2 + b2) * Kk - 2 * a2 * Ek) / (a * (a2 - b2) * (a2 - b2));
- return std::make_tuple(fx, dfx, dfx2);
- }
- private:
- T m_arc; // length of arc.
- T m_radius; // one of the two radii of the ellipse
- };
- //]
- //[elliptic_2deriv
- template <class T = double>
- T elliptic_root_2deriv(T radius, T arc)
- {
- using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools; // For halley_iterate.
- BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!");
- T guess = sqrt(arc * arc / 16 - radius * radius);
- T min = 0; // Minimum possible value is zero.
- T max = arc; // radius can't be larger than the arc length.
- // Accuracy triples at each step, so stop when just over one-third of the digits
- // are correct, and the last iteration will polish off the remaining digits:
- 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 = halley_iterate(elliptic_root_functor_2deriv<T>(arc, radius), guess, min, max, get_digits, it);
- //<-
- iters = it;
- //->
- return result;
- } // nth_2deriv Halley
- //]
- // Using 1st and 2nd derivatives using Schroder algorithm.
- template <class T = double>
- T elliptic_root_2deriv_s(T arc, T radius)
- { // return nth root of x using 1st and 2nd derivatives and Schroder.
- using namespace std; // Help ADL of std functions.
- using namespace boost::math::tools; // For schroder_iterate.
- BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!");
- T guess = sqrt(arc * arc / 16 - radius * radius);
- T min = 0; // Minimum possible value is zero.
- T max = arc; // radius can't be larger than the arc length.
- int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T.
- int get_digits = static_cast<int>(digits * digits_accuracy);
- const boost::uintmax_t maxit = 20;
- boost::uintmax_t it = maxit;
- T result = schroder_iterate(elliptic_root_functor_2deriv<T>(arc, radius), guess, min, max, get_digits, it);
- iters = it;
- return result;
- } // T elliptic_root_2deriv_s Schroder
- //////////////////////////////////////////////////////// end of algorithms - perhaps in a separate .hpp?
- //! Print 4 floating-point types info: max_digits10, digits and required accuracy digits as a Quickbook table.
- int table_type_info(double digits_accuracy)
- {
- std::string qbk_name = full_roots_name; // Prefix by boost_root file.
- qbk_name += "type_info_table";
- std::stringstream ss;
- ss.precision(3);
- ss << "_" << digits_accuracy * 100;
- qbk_name += ss.str();
- #ifdef _MSC_VER
- qbk_name += "_msvc.qbk";
- #else // assume GCC
- qbk_name += "_gcc.qbk";
- #endif
- // Example: type_info_table_100_msvc.qbk
- fout.open(qbk_name, std::ios_base::out);
- if (fout.is_open())
- {
- std::cout << "Output type table to " << qbk_name << std::endl;
- }
- else
- { // Failed to open.
- std::cout << " Open file " << qbk_name << " for output failed!" << std::endl;
- std::cout << "errno " << errno << std::endl;
- return errno;
- }
- fout <<
- "[/"
- << qbk_name
- << "\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;
- fout << "[h6 Fraction of maximum possible bits of accuracy required is " << digits_accuracy << ".]\n" << std::endl;
- std::string table_id("type_info");
- table_id += ss.str(); // Fraction digits accuracy.
- #ifdef _MSC_VER
- table_id += "_msvc";
- #else // assume GCC
- table_id += "_gcc";
- #endif
- fout << "[table:" << table_id << " Digits for float, double, long double and cpp_bin_float_50\n"
- << "[[type name] [max_digits10] [binary digits] [required digits]]\n";// header.
- // For all fout types:
- fout << "[[" << "float" << "]"
- << "[" << std::numeric_limits<float>::max_digits10 << "]" // max_digits10
- << "[" << std::numeric_limits<float>::digits << "]"// < "Binary digits
- << "[" << static_cast<int>(std::numeric_limits<float>::digits * digits_accuracy) << "]]\n"; // Accuracy digits.
- fout << "[[" << "float" << "]"
- << "[" << std::numeric_limits<double>::max_digits10 << "]" // max_digits10
- << "[" << std::numeric_limits<double>::digits << "]"// < "Binary digits
- << "[" << static_cast<int>(std::numeric_limits<double>::digits * digits_accuracy) << "]]\n"; // Accuracy digits.
- fout << "[[" << "long double" << "]"
- << "[" << std::numeric_limits<long double>::max_digits10 << "]" // max_digits10
- << "[" << std::numeric_limits<long double>::digits << "]"// < "Binary digits
- << "[" << static_cast<int>(std::numeric_limits<long double>::digits * digits_accuracy) << "]]\n"; // Accuracy digits.
- fout << "[[" << "cpp_bin_float_50" << "]"
- << "[" << std::numeric_limits<cpp_bin_float_50>::max_digits10 << "]" // max_digits10
- << "[" << std::numeric_limits<cpp_bin_float_50>::digits << "]"// < "Binary digits
- << "[" << static_cast<int>(std::numeric_limits<cpp_bin_float_50>::digits * digits_accuracy) << "]]\n"; // Accuracy digits.
- fout << "] [/table table_id_msvc] \n" << std::endl; // End of table.
- fout.close();
- return 0;
- } // type_table
- //! Evaluate root N timing for each algorithm, and for one floating-point type T.
- template <typename T>
- int test_root(cpp_bin_float_100 big_radius, cpp_bin_float_100 big_arc, cpp_bin_float_100 answer, const char* type_name, std::size_t type_no)
- {
- 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; // Show trailing zeros too.
- root_infos.push_back(root_info());
- 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 = static_cast<int>(std::numeric_limits<T>::digits * digits_accuracy);
- T radius = static_cast<T>(big_radius);
- T arc = static_cast<T>(big_arc);
- T result; // root
- T sum = 0;
- T ans = static_cast<T>(answer);
- using boost::timer::nanosecond_type;
- using boost::timer::cpu_times;
- using boost::timer::cpu_timer;
- long eval_count = boost::is_floating_point<T>::value ? 1000000 : 10000; // To give a sufficiently stable timing for the fast built-in types,
- // This takes an inconveniently long time for multiprecision cpp_bin_float_50 etc types.
- cpu_times now; // Holds wall, user and system times.
- { // Evaluate times etc for each algorithm.
- //algorithm_names.push_back("TOMS748"); //
- cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
- ti.start();
- for(long i = eval_count; i >= 0; --i)
- {
- result = elliptic_root_noderiv(radius, arc); //
- sum += result;
- }
- now = ti.elapsed();
- int time = static_cast<int>(now.user / eval_count);
- 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 = eval_count; i >= 0; --i)
- {
- result = elliptic_root_1deriv(radius, arc); //
- sum += result;
- }
- now = ti.elapsed();
- int time = static_cast<int>(now.user / eval_count);
- 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 = eval_count; i >= 0; --i)
- {
- result = elliptic_root_2deriv(radius, arc); //
- sum += result;
- }
- now = ti.elapsed();
- int time = static_cast<int>(now.user / eval_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(iters); //
- root_infos[type_no].full_results.push_back(result);
- }
- {
- // algorithm_names.push_back("Schr'''ö'''der"); // algorithm
- cpu_timer ti; // Can start, pause, resume and stop, and read elapsed.
- ti.start();
- for(long i = eval_count; i >= 0; --i)
- {
- result = elliptic_root_2deriv_s(arc, radius); //
- sum += result;
- }
- now = ti.elapsed();
- int time = static_cast<int>(now.user / eval_count);
- 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++) // For each time.
- { // Normalize times.
- root_infos[type_no].normed_times.push_back(static_cast<double>(root_infos[type_no].times[i]) / root_infos[type_no].min_time);
- }
- std::cout << "Accumulated result was: " << sum << std::endl;
- return 4; // eval_count of how many algorithms used.
- } // test_root
- /*! Fill array of times, interations, etc for Nth root for all 4 types,
- and write a table of results in Quickbook format.
- */
- void table_root_info(cpp_bin_float_100 radius, cpp_bin_float_100 arc)
- {
- using std::abs;
- std::cout << nooftypes << " floating-point types tested:" << std::endl;
- #if defined(_DEBUG) || !defined(NDEBUG)
- std::cout << "Compiled in debug mode." << std::endl;
- #else
- std::cout << "Compiled in optimise mode." << std::endl;
- #endif
- std::cout << "FP hardware " << fp_hardware << std::endl;
- // Compute the 'right' answer for root N at 100 decimal digits.
- cpp_bin_float_100 full_answer = elliptic_root_noderiv(radius, arc);
- root_infos.clear(); // Erase any previous data.
- // Fill the elements of the array for each floating-point type.
- test_root<float>(radius, arc, full_answer, "float", 0);
- test_root<double>(radius, arc, full_answer, "double", 1);
- test_root<long double>(radius, arc, full_answer, "long double", 2);
- test_root<cpp_bin_float_50>(radius, arc, full_answer, "cpp_bin_float_50", 3);
- // Use info from 4 floating point types to
- // Prepare Quickbook table for a single root
- // with columns of times, iterations, distances repeated for various floating-point types,
- // and 4 rows for each algorithm.
- std::stringstream table_info;
- table_info.precision(3);
- table_info << "[table:elliptic root with radius " << radius << " and arc length " << arc << ") for float, double, long double and cpp_bin_float_50 types";
- if (fp_hardware != "")
- {
- table_info << ", using " << fp_hardware;
- }
- table_info << std::endl;
- fout << table_info.str()
- << "[[][float][][][] [][double][][][] [][long d][][][] [][cpp50][][]]\n"
- << "[[Algo ]";
- for (size_t tp = 0; tp != nooftypes; tp++)
- { // For all types:
- fout << "[Its]" << "[Times]" << "[Norm]" << "[Dis]" << "[ ]";
- }
- fout << "]" << std::endl;
- // Row for all algorithms.
- for (std::size_t algo = 0; algo != noofalgos; algo++)
- {
- fout << "[[" << std::left << std::setw(9) << algo_names[algo] << "]";
- for (size_t tp = 0; tp != nooftypes; 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] << "][";
- fout << std::setw(3) << std::setprecision(3);
- double normed_time = root_infos[tp].normed_times[algo];
- if (abs(normed_time - 1.00) <= 0.05)
- { // At or near the best time, so show as blue.
- fout << "[role blue " << normed_time << "]";
- }
- else if (abs(normed_time) > 4.)
- { // markedly poor so show as red.
- fout << "[role red " << normed_time << "]";
- }
- else
- { // Not the best, so normal black.
- fout << normed_time;
- }
- fout << "]["
- << std::setw(3) << std::setprecision(2) << root_infos[tp].distances[algo] << "][ ]";
- } // tp
- fout << "]" << std::endl;
- } // for algo
- fout << "] [/end of table root]\n";
- } // void table_root_info
- /*! Output program header, table of type info, and tables for 4 algorithms and 4 floating-point types,
- for Nth root required digits_accuracy.
- */
- int roots_tables(cpp_bin_float_100 radius, cpp_bin_float_100 arc, double digits_accuracy)
- {
- ::digits_accuracy = digits_accuracy;
- // Save globally so that it is available to root-finding algorithms. Ugly :-(
- #if defined(_DEBUG) || !defined(NDEBUG)
- std::string debug_or_optimize("Compiled in debug mode.");
- #else
- std::string debug_or_optimize("Compiled in optimise mode.");
- #endif
- // Create filename for roots_table
- std::string qbk_name = full_roots_name;
- qbk_name += "elliptic_table";
- std::stringstream ss;
- ss.precision(3);
- // ss << "_" << N // now put all the tables in one .qbk file?
- ss << "_" << digits_accuracy * 100
- << std::flush;
- // Assume only save optimize mode runs, so don't add any _DEBUG info.
- qbk_name += ss.str();
- #ifdef _MSC_VER
- qbk_name += "_msvc";
- #else // assume GCC
- qbk_name += "_gcc";
- #endif
- if (fp_hardware != "")
- {
- qbk_name += fp_hardware;
- }
- qbk_name += ".qbk";
- fout.open(qbk_name, std::ios_base::out);
- if (fout.is_open())
- {
- std::cout << "Output root table to " << qbk_name << std::endl;
- }
- else
- { // Failed to open.
- std::cout << " Open file " << qbk_name << " for output failed!" << std::endl;
- std::cout << "errno " << errno << std::endl;
- return errno;
- }
- fout <<
- "[/"
- << qbk_name
- << "\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;
- // Print out the program/compiler/stdlib/platform names as a Quickbook comment:
- fout << "\n[h6 Program [@../../example/" << short_file_name(sourcefilename) << " " << short_file_name(sourcefilename) << "],\n "
- << BOOST_COMPILER << ", "
- << BOOST_STDLIB << ", "
- << BOOST_PLATFORM << "\n"
- << debug_or_optimize
- << ((fp_hardware != "") ? ", " + fp_hardware : "")
- << "]" // [h6 close].
- << std::endl;
- //fout << "Fraction of full accuracy " << digits_accuracy << std::endl;
- table_root_info(radius, arc);
- fout.close();
- // table_type_info(digits_accuracy);
- return 0;
- } // roots_tables
- int main()
- {
- using namespace boost::multiprecision;
- using namespace boost::math;
- try
- {
- std::cout << "Tests run with " << BOOST_COMPILER << ", "
- << BOOST_STDLIB << ", " << BOOST_PLATFORM << ", ";
- // How to: Configure Visual C++ Projects to Target 64-Bit Platforms
- // https://msdn.microsoft.com/en-us/library/9yb4317s.aspx
- #ifdef _M_X64 // Defined for compilations that target x64 processors.
- std::cout << "X64 " << std::endl;
- fp_hardware += "_X64";
- #else
- # ifdef _M_IX86
- std::cout << "X32 " << std::endl;
- fp_hardware += "_X86";
- # endif
- #endif
- #ifdef _M_AMD64
- std::cout << "AMD64 " << std::endl;
- // fp_hardware += "_AMD64";
- #endif
- // https://msdn.microsoft.com/en-us/library/7t5yh4fd.aspx
- // /arch (x86) options /arch:[IA32|SSE|SSE2|AVX|AVX2]
- // default is to use SSE and SSE2 instructions by default.
- // https://msdn.microsoft.com/en-us/library/jj620901.aspx
- // /arch (x64) options /arch:AVX and /arch:AVX2
- // MSVC doesn't bother to set these SSE macros!
- // http://stackoverflow.com/questions/18563978/sse-sse2-is-enabled-control-in-visual-studio
- // https://msdn.microsoft.com/en-us/library/b0084kay.aspx predefined macros.
- // But some of these macros are *not* defined by MSVC,
- // unlike AVX (but *are* defined by GCC and Clang).
- // So the macro code above does define them.
- #if (defined(_M_AMD64) || defined (_M_X64))
- # define _M_X64
- # define __SSE2__
- #else
- # ifdef _M_IX86_FP // Expands to an integer literal value indicating which /arch compiler option was used:
- std::cout << "Floating-point _M_IX86_FP = " << _M_IX86_FP << std::endl;
- # if (_M_IX86_FP == 2) // 2 if /arch:SSE2, /arch:AVX or /arch:AVX2
- # define __SSE2__ // x32
- # elif (_M_IX86_FP == 1) // 1 if /arch:SSE was used.
- # define __SSE__ // x32
- # elif (_M_IX86_FP == 0) // 0 if /arch:IA32 was used.
- # define _X32 // No special FP instructions.
- # endif
- # endif
- #endif
- // Set the fp_hardware that is used in the .qbk filename.
- #ifdef __AVX2__
- std::cout << "Floating-point AVX2 " << std::endl;
- fp_hardware += "_AVX2";
- # else
- # ifdef __AVX__
- std::cout << "Floating-point AVX " << std::endl;
- fp_hardware += "_AVX";
- # else
- # ifdef __SSE2__
- std::cout << "Floating-point SSE2 " << std::endl;
- fp_hardware += "_SSE2";
- # else
- # ifdef __SSE__
- std::cout << "Floating-point SSE " << std::endl;
- fp_hardware += "_SSE";
- # endif
- # endif
- # endif
- # endif
- #ifdef _M_IX86
- std::cout << "Floating-point X86 _M_IX86 = " << _M_IX86 << std::endl;
- // https://msdn.microsoft.com/en-us/library/aa273918%28v=vs.60%29.aspx#_predir_table_1..3
- // 600 = Pentium Pro
- #endif
- #ifdef _MSC_FULL_VER
- std::cout << "Floating-point _MSC_FULL_VER " << _MSC_FULL_VER << std::endl;
- #endif
- #ifdef __MSVC_RUNTIME_CHECKS
- std::cout << "Runtime __MSVC_RUNTIME_CHECKS " << std::endl;
- #endif
- BOOST_MATH_CONTROL_FP;
- cpp_bin_float_100 radius("28.");
- cpp_bin_float_100 arc("300.");
- // Compute full answer to more than precision of tests.
- //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::cout.precision(100);
- std::cout << "radius 1" << radius << std::endl;
- std::cout << "arc length" << arc << std::endl;
- // std::cout << ",\n""answer = " << full_answer << std::endl;
- std::cout.precision(6);
- // cbrt cpp_bin_float_100 full_answer("3.036588971875662519420809578505669635581453977248111123242141654169177268411884961770250390838097895");
- // Output the table of types, maxdigits10 and digits and required digits for some accuracies.
- // Output tables for some roots at full accuracy.
- roots_tables(radius, arc, 1.);
- // Output tables for some roots at less accuracy.
- //roots_tables(full_value, 0.75);
- return boost::exit_success;
- }
- catch (std::exception const& ex)
- {
- std::cout << "exception thrown: " << ex.what() << std::endl;
- return boost::exit_failure;
- }
- } // int main()
- /*
- */
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