]>
Commit | Line | Data |
---|---|---|
7c673cae FG |
1 | // Copyright Paul A. Bristow 2015 |
2 | ||
3 | // Use, modification and distribution are subject to the | |
4 | // Boost Software License, Version 1.0. | |
5 | // (See accompanying file LICENSE_1_0.txt | |
6 | // or copy at http://www.boost.org/LICENSE_1_0.txt) | |
7 | ||
8 | // Comparison of finding roots using TOMS748, Newton-Raphson, Halley & Schroder algorithms. | |
9 | // root_n_finding_algorithms.cpp Generalised for nth root version. | |
10 | ||
11 | // http://en.wikipedia.org/wiki/Cube_root | |
12 | ||
13 | // Note that this file contains Quickbook mark-up as well as code | |
14 | // and comments, don't change any of the special comment mark-ups! | |
15 | // This program also writes files in Quickbook tables mark-up format. | |
16 | ||
17 | #include <boost/cstdlib.hpp> | |
18 | #include <boost/config.hpp> | |
19 | #include <boost/array.hpp> | |
20 | #include <boost/type_traits/is_floating_point.hpp> | |
21 | #include <boost/math/concepts/real_concept.hpp> | |
22 | #include <boost/math/tools/roots.hpp> | |
23 | ||
24 | //using boost::math::policies::policy; | |
25 | //using boost::math::tools::eps_tolerance; // Binary functor for specified number of bits. | |
26 | //using boost::math::tools::bracket_and_solve_root; | |
27 | //using boost::math::tools::toms748_solve; | |
28 | //using boost::math::tools::halley_iterate; | |
29 | //using boost::math::tools::newton_raphson_iterate; | |
30 | //using boost::math::tools::schroder_iterate; | |
31 | ||
32 | #include <boost/math/special_functions/next.hpp> // For float_distance. | |
33 | #include <boost/math/special_functions/pow.hpp> // For pow<N>. | |
34 | #include <boost/math/tools/tuple.hpp> // for tuple and make_tuple. | |
35 | ||
36 | #include <boost/multiprecision/cpp_bin_float.hpp> // is binary. | |
37 | using boost::multiprecision::cpp_bin_float_100; | |
38 | using boost::multiprecision::cpp_bin_float_50; | |
39 | ||
40 | #include <boost/timer/timer.hpp> | |
41 | #include <boost/system/error_code.hpp> | |
42 | #include <boost/preprocessor/stringize.hpp> | |
43 | ||
44 | // STL | |
45 | #include <iostream> | |
46 | #include <iomanip> | |
47 | #include <string> | |
48 | #include <vector> | |
49 | #include <limits> | |
50 | #include <fstream> // std::ofstream | |
51 | #include <cmath> | |
52 | #include <typeinfo> // for type name using typid(thingy).name(); | |
53 | ||
54 | #ifdef __FILE__ | |
55 | std::string sourcefilename = __FILE__; | |
56 | #else | |
57 | std::string sourcefilename(""); | |
58 | #endif | |
59 | ||
60 | std::string chop_last(std::string s) | |
61 | { | |
62 | std::string::size_type pos = s.find_last_of("\\/"); | |
63 | if(pos != std::string::npos) | |
64 | s.erase(pos); | |
65 | else if(s.empty()) | |
66 | abort(); | |
67 | else | |
68 | s.erase(); | |
69 | return s; | |
70 | } | |
71 | ||
72 | std::string make_root() | |
73 | { | |
74 | std::string result; | |
75 | if(sourcefilename.find_first_of(":") != std::string::npos) | |
76 | { | |
77 | result = chop_last(sourcefilename); // lose filename part | |
78 | result = chop_last(result); // lose /example/ | |
79 | result = chop_last(result); // lose /math/ | |
80 | result = chop_last(result); // lose /libs/ | |
81 | } | |
82 | else | |
83 | { | |
84 | result = chop_last(sourcefilename); // lose filename part | |
85 | if(result.empty()) | |
86 | result = "."; | |
87 | result += "/../../.."; | |
88 | } | |
89 | return result; | |
90 | } | |
91 | ||
92 | std::string short_file_name(std::string s) | |
93 | { | |
94 | std::string::size_type pos = s.find_last_of("\\/"); | |
95 | if(pos != std::string::npos) | |
96 | s.erase(0, pos + 1); | |
97 | return s; | |
98 | } | |
99 | ||
100 | std::string boost_root = make_root(); | |
101 | ||
102 | ||
103 | std::string fp_hardware; // Any hardware features like SEE or AVX | |
104 | ||
105 | const std::string roots_name = "libs/math/doc/roots/"; | |
106 | ||
107 | const std::string full_roots_name(boost_root + "/libs/math/doc/roots/"); | |
108 | ||
109 | const std::size_t nooftypes = 4; | |
110 | const std::size_t noofalgos = 4; | |
7c673cae FG |
111 | |
112 | double digits_accuracy = 1.0; // 1 == maximum possible accuracy. | |
113 | ||
114 | std::stringstream ss; | |
115 | ||
116 | std::ofstream fout; | |
117 | ||
118 | std::vector<std::string> algo_names = | |
119 | { | |
120 | "TOMS748", "Newton", "Halley", "Schr'''ö'''der" | |
121 | }; | |
122 | ||
123 | std::vector<std::string> names = | |
124 | { | |
125 | "float", "double", "long double", "cpp_bin_float50" | |
126 | }; | |
127 | ||
128 | uintmax_t iters; // Global as value of iterations is not returned. | |
129 | ||
130 | struct root_info | |
131 | { // for a floating-point type, float, double ... | |
132 | std::size_t max_digits10; // for type. | |
133 | std::string full_typename; // for type from type_id.name(). | |
134 | std::string short_typename; // for type "float", "double", "cpp_bin_float_50" .... | |
135 | std::size_t bin_digits; // binary in floating-point type numeric_limits<T>::digits; | |
136 | int get_digits; // fraction of maximum possible accuracy required. | |
137 | // = digits * digits_accuracy | |
138 | // Vector of values (4) for each algorithm, TOMS748, Newton, Halley & Schroder. | |
139 | //std::vector< boost::int_least64_t> times; converted to int. | |
140 | std::vector<int> times; // arbirary units (ticks). | |
141 | //boost::int_least64_t min_time = std::numeric_limits<boost::int_least64_t>::max(); // Used to normalize times (as int). | |
142 | std::vector<double> normed_times; | |
143 | int min_time = (std::numeric_limits<int>::max)(); // Used to normalize times. | |
144 | std::vector<uintmax_t> iterations; | |
145 | std::vector<long int> distances; | |
146 | std::vector<cpp_bin_float_100> full_results; | |
147 | }; // struct root_info | |
148 | ||
149 | std::vector<root_info> root_infos; // One element for each floating-point type used. | |
150 | ||
151 | inline std::string build_test_name(const char* type_name, const char* test_name) | |
152 | { | |
153 | std::string result(BOOST_COMPILER); | |
154 | result += "|"; | |
155 | result += BOOST_STDLIB; | |
156 | result += "|"; | |
157 | result += BOOST_PLATFORM; | |
158 | result += "|"; | |
159 | result += type_name; | |
160 | result += "|"; | |
161 | result += test_name; | |
162 | #if defined(_DEBUG) || !defined(NDEBUG) | |
163 | result += "|"; | |
164 | result += " debug"; | |
165 | #else | |
166 | result += "|"; | |
167 | result += " release"; | |
168 | #endif | |
169 | result += "|"; | |
170 | return result; | |
171 | } // std::string build_test_name | |
172 | ||
173 | // Algorithms ////////////////////////////////////////////// | |
174 | ||
175 | // No derivatives - using TOMS748 internally. | |
176 | ||
177 | template <int N, typename T = double> | |
178 | struct nth_root_functor_noderiv | |
179 | { // Nth root of x using only function - no derivatives. | |
180 | nth_root_functor_noderiv(T const& to_find_root_of) : a(to_find_root_of) | |
181 | { // Constructor just stores value a to find root of. | |
182 | } | |
183 | T operator()(T const& x) | |
184 | { | |
185 | using boost::math::pow; | |
186 | T fx = pow<N>(x) -a; // Difference (estimate x^n - a). | |
187 | return fx; | |
188 | } | |
189 | private: | |
190 | T a; // to be 'cube_rooted'. | |
191 | }; // template <int N, class T> struct nth_root_functor_noderiv | |
192 | ||
193 | template <int N, class T = double> | |
194 | T nth_root_noderiv(T x) | |
195 | { // return Nth root of x using bracket_and_solve (using NO derivatives). | |
196 | using namespace std; // Help ADL of std functions. | |
197 | using namespace boost::math::tools; // For bracket_and_solve_root. | |
198 | ||
199 | typedef double guess_type; | |
200 | ||
201 | int exponent; | |
202 | frexp(static_cast<guess_type>(x), &exponent); // Get exponent of z (ignore mantissa). | |
203 | T guess = static_cast<T>(ldexp(static_cast<guess_type>(1.), exponent / N)); // Rough guess is to divide the exponent by n. | |
204 | //T min = static_cast<T>(ldexp(static_cast<guess_type>(1.) / 2, exponent / N)); // Minimum possible value is half our guess. | |
205 | //T max = static_cast<T>(ldexp(static_cast<guess_type>(2.), exponent / N)); // Maximum possible value is twice our guess. | |
206 | ||
207 | T factor = 2; // How big steps to take when searching. | |
208 | ||
209 | const boost::uintmax_t maxit = 50; // Limit to maximum iterations. | |
210 | boost::uintmax_t it = maxit; // Initally our chosen max iterations, but updated with actual. | |
211 | bool is_rising = true; // So if result if guess^3 is too low, then try increasing guess. | |
212 | // Some fraction of digits is used to control how accurate to try to make the result. | |
213 | int get_digits = std::numeric_limits<T>::digits - 2; | |
214 | eps_tolerance<T> tol(get_digits); // Set the tolerance. | |
215 | std::pair<T, T> r; | |
216 | r = bracket_and_solve_root(nth_root_functor_noderiv<N, T>(x), guess, factor, is_rising, tol, it); | |
217 | iters = it; | |
218 | T result = r.first + (r.second - r.first) / 2; // Midway between brackets. | |
219 | return result; | |
220 | } // template <class T> T nth_root_noderiv(T x) | |
221 | ||
222 | // Using 1st derivative only Newton-Raphson | |
223 | ||
224 | template <int N, class T = double> | |
225 | struct nth_root_functor_1deriv | |
226 | { // Functor also returning 1st derviative. | |
227 | BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!"); | |
228 | BOOST_STATIC_ASSERT_MSG((N > 0) == true, "root N must be > 0!"); | |
229 | ||
230 | nth_root_functor_1deriv(T const& to_find_root_of) : a(to_find_root_of) | |
231 | { // Constructor stores value a to find root of, for example: | |
232 | } | |
233 | std::pair<T, T> operator()(T const& x) | |
234 | { // Return both f(x) and f'(x). | |
235 | using boost::math::pow; // // Compile-time integral power. | |
236 | T p = pow<N - 1>(x); | |
237 | return std::make_pair(p * x - a, N * p); // 'return' both fx and dx. | |
238 | } | |
239 | ||
240 | private: | |
241 | T a; // to be 'nth_rooted'. | |
242 | }; // struct nthroot__functor_1deriv | |
243 | ||
244 | template <int N, class T = double> | |
245 | T nth_root_1deriv(T x) | |
246 | { // return nth root of x using 1st derivative and Newton_Raphson. | |
247 | using namespace std; // Help ADL of std functions. | |
248 | using namespace boost::math::tools; // For newton_raphson_iterate. | |
249 | ||
250 | BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!"); | |
251 | BOOST_STATIC_ASSERT_MSG((N > 0) == true, "root N must be > 0!"); | |
252 | BOOST_STATIC_ASSERT_MSG((N > 1000) == false, "root N is too big!"); | |
253 | ||
254 | typedef double guess_type; | |
255 | ||
256 | int exponent; | |
257 | frexp(static_cast<guess_type>(x), &exponent); // Get exponent of z (ignore mantissa). | |
258 | T guess = static_cast<T>(ldexp(static_cast<guess_type>(1.), exponent / N)); // Rough guess is to divide the exponent by n. | |
259 | T min = static_cast<T>(ldexp(static_cast<guess_type>(1.) / 2, exponent / N)); // Minimum possible value is half our guess. | |
260 | T max = static_cast<T>(ldexp(static_cast<guess_type>(2.), exponent / N)); // Maximum possible value is twice our guess. | |
261 | ||
262 | int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T. | |
263 | int get_digits = static_cast<int>(digits * 0.6); | |
264 | const boost::uintmax_t maxit = 20; | |
265 | boost::uintmax_t it = maxit; | |
266 | T result = newton_raphson_iterate(nth_root_functor_1deriv<N, T>(x), guess, min, max, get_digits, it); | |
267 | iters = it; | |
268 | return result; | |
269 | } // T nth_root_1_deriv Newton-Raphson | |
270 | ||
271 | // Using 1st and 2nd derivatives with Halley algorithm. | |
272 | ||
273 | template <int N, class T = double> | |
274 | struct nth_root_functor_2deriv | |
275 | { // Functor returning both 1st and 2nd derivatives. | |
276 | BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!"); | |
277 | BOOST_STATIC_ASSERT_MSG((N > 0) == true, "root N must be > 0!"); | |
278 | ||
279 | nth_root_functor_2deriv(T const& to_find_root_of) : a(to_find_root_of) | |
280 | { // Constructor stores value a to find root of, for example: | |
281 | } | |
282 | ||
283 | // using boost::math::tuple; // to return three values. | |
284 | std::tuple<T, T, T> operator()(T const& x) | |
285 | { // Return f(x), f'(x) and f''(x). | |
286 | using boost::math::pow; // Compile-time integral power. | |
287 | T p = pow<N - 2>(x); | |
288 | ||
289 | return std::make_tuple(p * x * x - a, p * x * N, p * N * (N - 1)); // 'return' fx, dx and d2x. | |
290 | } | |
291 | private: | |
292 | T a; // to be 'nth_rooted'. | |
293 | }; | |
294 | ||
295 | template <int N, class T = double> | |
296 | T nth_root_2deriv(T x) | |
297 | { // return nth root of x using 1st and 2nd derivatives and Halley. | |
298 | ||
299 | using namespace std; // Help ADL of std functions. | |
300 | using namespace boost::math::tools; // For halley_iterate. | |
301 | ||
302 | BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!"); | |
303 | BOOST_STATIC_ASSERT_MSG((N > 0) == true, "root N must be > 0!"); | |
304 | BOOST_STATIC_ASSERT_MSG((N > 1000) == false, "root N is too big!"); | |
305 | ||
306 | typedef double guess_type; | |
307 | ||
308 | int exponent; | |
309 | frexp(static_cast<guess_type>(x), &exponent); // Get exponent of z (ignore mantissa). | |
310 | T guess = static_cast<T>(ldexp(static_cast<guess_type>(1.), exponent / N)); // Rough guess is to divide the exponent by n. | |
311 | T min = static_cast<T>(ldexp(static_cast<guess_type>(1.) / 2, exponent / N)); // Minimum possible value is half our guess. | |
312 | T max = static_cast<T>(ldexp(static_cast<guess_type>(2.), exponent / N)); // Maximum possible value is twice our guess. | |
313 | ||
314 | int digits = std::numeric_limits<T>::digits; // Maximum possible binary digits accuracy for type T. | |
315 | int get_digits = static_cast<int>(digits * 0.4); | |
316 | const boost::uintmax_t maxit = 20; | |
317 | boost::uintmax_t it = maxit; | |
318 | T result = halley_iterate(nth_root_functor_2deriv<N, T>(x), guess, min, max, get_digits, it); | |
319 | iters = it; | |
320 | ||
321 | return result; | |
322 | } // nth_2deriv Halley | |
323 | ||
324 | template <int N, class T = double> | |
325 | T nth_root_2deriv_s(T x) | |
326 | { // return nth root of x using 1st and 2nd derivatives and Schroder. | |
327 | ||
328 | using namespace std; // Help ADL of std functions. | |
329 | using namespace boost::math::tools; // For schroder_iterate. | |
330 | ||
331 | BOOST_STATIC_ASSERT_MSG(boost::is_integral<T>::value == false, "Only floating-point type types can be used!"); | |
332 | BOOST_STATIC_ASSERT_MSG((N > 0) == true, "root N must be > 0!"); | |
333 | BOOST_STATIC_ASSERT_MSG((N > 1000) == false, "root N is too big!"); | |
334 | ||
335 | typedef double guess_type; | |
336 | ||
337 | int exponent; | |
338 | frexp(static_cast<guess_type>(x), &exponent); // Get exponent of z (ignore mantissa). | |
339 | T guess = static_cast<T>(ldexp(static_cast<guess_type>(1.), exponent / N)); // Rough guess is to divide the exponent by n. | |
340 | T min = static_cast<T>(ldexp(static_cast<guess_type>(1.) / 2, exponent / N)); // Minimum possible value is half our guess. | |
341 | T max = static_cast<T>(ldexp(static_cast<guess_type>(2.), exponent / N)); // Maximum possible value is twice our guess. | |
342 | ||
343 | int get_digits = static_cast<int>(std::numeric_limits<T>::digits * 0.4); | |
344 | const boost::uintmax_t maxit = 20; | |
345 | boost::uintmax_t it = maxit; | |
346 | T result = schroder_iterate(nth_root_functor_2deriv<N, T>(x), guess, min, max, get_digits, it); | |
347 | iters = it; | |
348 | ||
349 | return result; | |
350 | } // T nth_root_2deriv_s Schroder | |
351 | ||
352 | //////////////////////////////////////////////////////// end of algorithms - perhaps in a separate .hpp? | |
353 | ||
354 | //! Print 4 floating-point types info: max_digits10, digits and required accuracy digits as a Quickbook table. | |
355 | int table_type_info(double digits_accuracy) | |
356 | { | |
357 | std::string qbk_name = full_roots_name; // Prefix by boost_root file. | |
358 | ||
359 | qbk_name += "type_info_table"; | |
360 | std::stringstream ss; | |
361 | ss.precision(3); | |
362 | ss << "_" << digits_accuracy * 100; | |
363 | qbk_name += ss.str(); | |
364 | ||
365 | #ifdef _MSC_VER | |
366 | qbk_name += "_msvc.qbk"; | |
367 | #else // assume GCC | |
368 | qbk_name += "_gcc.qbk"; | |
369 | #endif | |
370 | ||
371 | // Example: type_info_table_100_msvc.qbk | |
372 | fout.open(qbk_name, std::ios_base::out); | |
373 | ||
374 | if (fout.is_open()) | |
375 | { | |
376 | std::cout << "Output type table to " << qbk_name << std::endl; | |
377 | } | |
378 | else | |
379 | { // Failed to open. | |
380 | std::cout << " Open file " << qbk_name << " for output failed!" << std::endl; | |
381 | std::cout << "errno " << errno << std::endl; | |
382 | return errno; | |
383 | } | |
384 | ||
385 | fout << | |
386 | "[/" | |
387 | << qbk_name | |
388 | << "\n" | |
389 | "Copyright 2015 Paul A. Bristow.""\n" | |
390 | "Copyright 2015 John Maddock.""\n" | |
391 | "Distributed under the Boost Software License, Version 1.0.""\n" | |
392 | "(See accompanying file LICENSE_1_0.txt or copy at""\n" | |
393 | "http://www.boost.org/LICENSE_1_0.txt).""\n" | |
394 | "]""\n" | |
395 | << std::endl; | |
396 | ||
397 | fout << "[h6 Fraction of maximum possible bits of accuracy required is " << digits_accuracy << ".]\n" << std::endl; | |
398 | ||
399 | std::string table_id("type_info"); | |
400 | table_id += ss.str(); // Fraction digits accuracy. | |
401 | ||
402 | #ifdef _MSC_VER | |
403 | table_id += "_msvc"; | |
404 | #else // assume GCC | |
405 | table_id += "_gcc"; | |
406 | #endif | |
407 | ||
408 | fout << "[table:" << table_id << " Digits for float, double, long double and cpp_bin_float_50\n" | |
409 | << "[[type name] [max_digits10] [binary digits] [required digits]]\n";// header. | |
410 | ||
411 | // For all fout types: | |
412 | ||
413 | fout << "[[" << "float" << "]" | |
414 | << "[" << std::numeric_limits<float>::max_digits10 << "]" // max_digits10 | |
415 | << "[" << std::numeric_limits<float>::digits << "]"// < "Binary digits | |
416 | << "[" << static_cast<int>(std::numeric_limits<float>::digits * digits_accuracy) << "]]\n"; // Accuracy digits. | |
417 | ||
418 | fout << "[[" << "float" << "]" | |
419 | << "[" << std::numeric_limits<double>::max_digits10 << "]" // max_digits10 | |
420 | << "[" << std::numeric_limits<double>::digits << "]"// < "Binary digits | |
421 | << "[" << static_cast<int>(std::numeric_limits<double>::digits * digits_accuracy) << "]]\n"; // Accuracy digits. | |
422 | ||
423 | fout << "[[" << "long double" << "]" | |
424 | << "[" << std::numeric_limits<long double>::max_digits10 << "]" // max_digits10 | |
425 | << "[" << std::numeric_limits<long double>::digits << "]"// < "Binary digits | |
426 | << "[" << static_cast<int>(std::numeric_limits<long double>::digits * digits_accuracy) << "]]\n"; // Accuracy digits. | |
427 | ||
428 | fout << "[[" << "cpp_bin_float_50" << "]" | |
429 | << "[" << std::numeric_limits<cpp_bin_float_50>::max_digits10 << "]" // max_digits10 | |
430 | << "[" << std::numeric_limits<cpp_bin_float_50>::digits << "]"// < "Binary digits | |
431 | << "[" << static_cast<int>(std::numeric_limits<cpp_bin_float_50>::digits * digits_accuracy) << "]]\n"; // Accuracy digits. | |
432 | ||
433 | fout << "] [/table table_id_msvc] \n" << std::endl; // End of table. | |
434 | ||
435 | fout.close(); | |
436 | return 0; | |
437 | } // type_table | |
438 | ||
439 | //! Evaluate root N timing for each algorithm, and for one floating-point type T. | |
440 | template <int N, typename T> | |
441 | int test_root(cpp_bin_float_100 big_value, cpp_bin_float_100 answer, const char* type_name, std::size_t type_no) | |
442 | { | |
443 | std::size_t max_digits = 2 + std::numeric_limits<T>::digits * 3010 / 10000; | |
444 | // For new versions use max_digits10 | |
445 | // std::cout.precision(std::numeric_limits<T>::max_digits10); | |
446 | std::cout.precision(max_digits); | |
447 | std::cout << std::showpoint << std::endl; // Show trailing zeros too. | |
448 | ||
449 | root_infos.push_back(root_info()); | |
450 | ||
451 | root_infos[type_no].max_digits10 = max_digits; | |
452 | root_infos[type_no].full_typename = typeid(T).name(); // Full typename. | |
453 | root_infos[type_no].short_typename = type_name; // Short typename. | |
454 | root_infos[type_no].bin_digits = std::numeric_limits<T>::digits; | |
455 | root_infos[type_no].get_digits = static_cast<int>(std::numeric_limits<T>::digits * digits_accuracy); | |
456 | ||
457 | T to_root = static_cast<T>(big_value); | |
458 | ||
459 | T result; // root | |
460 | T sum = 0; | |
461 | T ans = static_cast<T>(answer); | |
462 | ||
463 | using boost::timer::nanosecond_type; | |
464 | using boost::timer::cpu_times; | |
465 | using boost::timer::cpu_timer; | |
466 | ||
467 | int eval_count = boost::is_floating_point<T>::value ? 10000000 : 100000; // To give a sufficiently stable timing for the fast built-in types, | |
468 | //int eval_count = 1000000; // To give a sufficiently stable timing for the fast built-in types, | |
469 | // This takes an inconveniently long time for multiprecision cpp_bin_float_50 etc types. | |
470 | ||
471 | cpu_times now; // Holds wall, user and system times. | |
472 | ||
473 | { // Evaluate times etc for each algorithm. | |
474 | //algorithm_names.push_back("TOMS748"); // | |
475 | cpu_timer ti; // Can start, pause, resume and stop, and read elapsed. | |
476 | ti.start(); | |
477 | for (long i = 0; i < eval_count; ++i) | |
478 | { | |
479 | result = nth_root_noderiv<N, T>(to_root); // | |
480 | sum += result; | |
481 | } | |
482 | now = ti.elapsed(); | |
483 | int time = static_cast<int>(now.user / eval_count); | |
484 | root_infos[type_no].times.push_back(time); // CPU time taken. | |
485 | if (time < root_infos[type_no].min_time) | |
486 | { | |
487 | root_infos[type_no].min_time = time; | |
488 | } | |
489 | ti.stop(); | |
490 | long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans)); | |
491 | root_infos[type_no].distances.push_back(distance); | |
492 | root_infos[type_no].iterations.push_back(iters); // | |
493 | root_infos[type_no].full_results.push_back(result); | |
494 | } | |
495 | { | |
496 | // algorithm_names.push_back("Newton"); // algorithm | |
497 | cpu_timer ti; // Can start, pause, resume and stop, and read elapsed. | |
498 | ti.start(); | |
499 | for (long i = 0; i < eval_count; ++i) | |
500 | { | |
501 | result = nth_root_1deriv<N, T>(to_root); // | |
502 | sum += result; | |
503 | } | |
504 | now = ti.elapsed(); | |
505 | int time = static_cast<int>(now.user / eval_count); | |
506 | root_infos[type_no].times.push_back(time); // CPU time taken. | |
507 | if (time < root_infos[type_no].min_time) | |
508 | { | |
509 | root_infos[type_no].min_time = time; | |
510 | } | |
511 | ||
512 | ti.stop(); | |
513 | long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans)); | |
514 | root_infos[type_no].distances.push_back(distance); | |
515 | root_infos[type_no].iterations.push_back(iters); // | |
516 | root_infos[type_no].full_results.push_back(result); | |
517 | } | |
518 | { | |
519 | //algorithm_names.push_back("Halley"); // algorithm | |
520 | cpu_timer ti; // Can start, pause, resume and stop, and read elapsed. | |
521 | ti.start(); | |
522 | for (long i = 0; i < eval_count; ++i) | |
523 | { | |
524 | result = nth_root_2deriv<N>(to_root); // | |
525 | sum += result; | |
526 | } | |
527 | now = ti.elapsed(); | |
528 | int time = static_cast<int>(now.user / eval_count); | |
529 | root_infos[type_no].times.push_back(time); // CPU time taken. | |
530 | ti.stop(); | |
531 | if (time < root_infos[type_no].min_time) | |
532 | { | |
533 | root_infos[type_no].min_time = time; | |
534 | } | |
535 | long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans)); | |
536 | root_infos[type_no].distances.push_back(distance); | |
537 | root_infos[type_no].iterations.push_back(iters); // | |
538 | root_infos[type_no].full_results.push_back(result); | |
539 | } | |
540 | { | |
541 | // algorithm_names.push_back("Schroder"); // algorithm | |
542 | cpu_timer ti; // Can start, pause, resume and stop, and read elapsed. | |
543 | ti.start(); | |
544 | for (long i = 0; i < eval_count; ++i) | |
545 | { | |
546 | result = nth_root_2deriv_s<N>(to_root); // | |
547 | sum += result; | |
548 | } | |
549 | now = ti.elapsed(); | |
550 | int time = static_cast<int>(now.user / eval_count); | |
551 | root_infos[type_no].times.push_back(time); // CPU time taken. | |
552 | if (time < root_infos[type_no].min_time) | |
553 | { | |
554 | root_infos[type_no].min_time = time; | |
555 | } | |
556 | ti.stop(); | |
557 | long int distance = static_cast<int>(boost::math::float_distance<T>(result, ans)); | |
558 | root_infos[type_no].distances.push_back(distance); | |
559 | root_infos[type_no].iterations.push_back(iters); // | |
560 | root_infos[type_no].full_results.push_back(result); | |
561 | } | |
562 | for (size_t i = 0; i != root_infos[type_no].times.size(); i++) // For each time. | |
563 | { // Normalize times. | |
564 | root_infos[type_no].normed_times.push_back(static_cast<double>(root_infos[type_no].times[i]) / root_infos[type_no].min_time); | |
565 | } | |
566 | ||
567 | std::cout << "Accumulated result was: " << sum << std::endl; | |
568 | ||
569 | return 4; // eval_count of how many algorithms used. | |
570 | } // test_root | |
571 | ||
572 | /*! Fill array of times, interations, etc for Nth root for all 4 types, | |
573 | and write a table of results in Quickbook format. | |
574 | */ | |
575 | template <int N> | |
576 | void table_root_info(cpp_bin_float_100 full_value) | |
577 | { | |
578 | using std::abs; | |
579 | std::cout << nooftypes << " floating-point types tested:" << std::endl; | |
580 | #if defined(_DEBUG) || !defined(NDEBUG) | |
581 | std::cout << "Compiled in debug mode." << std::endl; | |
582 | #else | |
583 | std::cout << "Compiled in optimise mode." << std::endl; | |
584 | #endif | |
585 | std::cout << "FP hardware " << fp_hardware << std::endl; | |
586 | // Compute the 'right' answer for root N at 100 decimal digits. | |
587 | cpp_bin_float_100 full_answer = nth_root_noderiv<N, cpp_bin_float_100>(full_value); | |
588 | ||
7c673cae FG |
589 | root_infos.clear(); // Erase any previous data. |
590 | // Fill the elements of the array for each floating-point type. | |
591 | ||
92f5a8d4 TL |
592 | test_root<N, float>(full_value, full_answer, "float", 0); |
593 | test_root<N, double>(full_value, full_answer, "double", 1); | |
594 | test_root<N, long double>(full_value, full_answer, "long double", 2); | |
595 | test_root<N, cpp_bin_float_50>(full_value, full_answer, "cpp_bin_float_50", 3); | |
7c673cae FG |
596 | |
597 | // Use info from 4 floating point types to | |
598 | ||
599 | // Prepare Quickbook table for a single root | |
600 | // with columns of times, iterations, distances repeated for various floating-point types, | |
601 | // and 4 rows for each algorithm. | |
602 | ||
603 | std::stringstream table_info; | |
604 | table_info.precision(3); | |
605 | table_info << "[table:root_" << N << " " << N << "th root(" << static_cast<float>(full_value) << ") for float, double, long double and cpp_bin_float_50 types"; | |
606 | if (fp_hardware != "") | |
607 | { | |
608 | table_info << ", using " << fp_hardware; | |
609 | } | |
610 | table_info << std::endl; | |
611 | ||
612 | fout << table_info.str() | |
613 | << "[[][float][][][] [][double][][][] [][long d][][][] [][cpp50][][]]\n" | |
614 | << "[[Algo ]"; | |
615 | for (size_t tp = 0; tp != nooftypes; tp++) | |
616 | { // For all types: | |
617 | fout << "[Its]" << "[Times]" << "[Norm]" << "[Dis]" << "[ ]"; | |
618 | } | |
619 | fout << "]" << std::endl; | |
620 | ||
621 | // Row for all algorithms. | |
622 | for (std::size_t algo = 0; algo != noofalgos; algo++) | |
623 | { | |
624 | fout << "[[" << std::left << std::setw(9) << algo_names[algo] << "]"; | |
625 | for (size_t tp = 0; tp != nooftypes; tp++) | |
626 | { // For all types: | |
627 | fout | |
628 | << "[" << std::right << std::showpoint | |
629 | << std::setw(3) << std::setprecision(2) << root_infos[tp].iterations[algo] << "][" | |
630 | << std::setw(5) << std::setprecision(5) << root_infos[tp].times[algo] << "]["; | |
631 | fout << std::setw(3) << std::setprecision(3); | |
632 | double normed_time = root_infos[tp].normed_times[algo]; | |
633 | if (abs(normed_time - 1.00) <= 0.05) | |
634 | { // At or near the best time, so show as blue. | |
635 | fout << "[role blue " << normed_time << "]"; | |
636 | } | |
637 | else if (abs(normed_time) > 4.) | |
638 | { // markedly poor so show as red. | |
639 | fout << "[role red " << normed_time << "]"; | |
640 | } | |
641 | else | |
642 | { // Not the best, so normal black. | |
643 | fout << normed_time; | |
644 | } | |
645 | fout << "][" | |
646 | << std::setw(3) << std::setprecision(2) << root_infos[tp].distances[algo] << "][ ]"; | |
647 | } // tp | |
648 | fout << "]" << std::endl; | |
649 | } // for algo | |
650 | fout << "] [/end of table root]\n"; | |
651 | } // void table_root_info | |
652 | ||
653 | /*! Output program header, table of type info, and tables for 4 algorithms and 4 floating-point types, | |
654 | for Nth root required digits_accuracy. | |
655 | */ | |
656 | ||
657 | int roots_tables(cpp_bin_float_100 full_value, double digits_accuracy) | |
658 | { | |
659 | ::digits_accuracy = digits_accuracy; | |
660 | // Save globally so that it is available to root-finding algorithms. Ugly :-( | |
661 | ||
662 | #if defined(_DEBUG) || !defined(NDEBUG) | |
663 | std::string debug_or_optimize("Compiled in debug mode."); | |
664 | #else | |
665 | std::string debug_or_optimize("Compiled in optimise mode."); | |
666 | #endif | |
667 | ||
668 | // Create filename for roots_table | |
669 | std::string qbk_name = full_roots_name; | |
670 | qbk_name += "roots_table"; | |
671 | ||
672 | std::stringstream ss; | |
673 | ss.precision(3); | |
674 | // ss << "_" << N // now put all the tables in one .qbk file? | |
675 | ss << "_" << digits_accuracy * 100 | |
676 | << std::flush; | |
677 | // Assume only save optimize mode runs, so don't add any _DEBUG info. | |
678 | qbk_name += ss.str(); | |
679 | ||
680 | #ifdef _MSC_VER | |
681 | qbk_name += "_msvc"; | |
682 | #else // assume GCC | |
683 | qbk_name += "_gcc"; | |
684 | #endif | |
685 | if (fp_hardware != "") | |
686 | { | |
687 | qbk_name += fp_hardware; | |
688 | } | |
689 | qbk_name += ".qbk"; | |
690 | ||
691 | fout.open(qbk_name, std::ios_base::out); | |
692 | ||
693 | if (fout.is_open()) | |
694 | { | |
695 | std::cout << "Output root table to " << qbk_name << std::endl; | |
696 | } | |
697 | else | |
698 | { // Failed to open. | |
699 | std::cout << " Open file " << qbk_name << " for output failed!" << std::endl; | |
700 | std::cout << "errno " << errno << std::endl; | |
701 | return errno; | |
702 | } | |
703 | ||
704 | fout << | |
705 | "[/" | |
706 | << qbk_name | |
707 | << "\n" | |
708 | "Copyright 2015 Paul A. Bristow.""\n" | |
709 | "Copyright 2015 John Maddock.""\n" | |
710 | "Distributed under the Boost Software License, Version 1.0.""\n" | |
711 | "(See accompanying file LICENSE_1_0.txt or copy at""\n" | |
712 | "http://www.boost.org/LICENSE_1_0.txt).""\n" | |
713 | "]""\n" | |
714 | << std::endl; | |
715 | ||
716 | // Print out the program/compiler/stdlib/platform names as a Quickbook comment: | |
717 | fout << "\n[h6 Program " << sourcefilename << ",\n " | |
718 | << BOOST_COMPILER << ", " | |
719 | << BOOST_STDLIB << ", " | |
720 | << BOOST_PLATFORM << "\n" | |
721 | << debug_or_optimize | |
722 | << ((fp_hardware != "") ? ", " + fp_hardware : "") | |
723 | << "]" // [h6 close]. | |
724 | << std::endl; | |
725 | ||
726 | fout << "Fraction of full accuracy " << digits_accuracy << std::endl; | |
727 | ||
728 | table_root_info<5>(full_value); | |
729 | table_root_info<7>(full_value); | |
730 | table_root_info<11>(full_value); | |
731 | ||
732 | fout.close(); | |
733 | ||
734 | // table_type_info(digits_accuracy); | |
735 | ||
736 | return 0; | |
737 | } // roots_tables | |
738 | ||
739 | ||
740 | int main() | |
741 | { | |
742 | using namespace boost::multiprecision; | |
743 | using namespace boost::math; | |
744 | ||
745 | ||
746 | try | |
747 | { | |
748 | std::cout << "Tests run with " << BOOST_COMPILER << ", " | |
749 | << BOOST_STDLIB << ", " << BOOST_PLATFORM << ", "; | |
750 | ||
751 | // How to: Configure Visual C++ Projects to Target 64-Bit Platforms | |
752 | // https://msdn.microsoft.com/en-us/library/9yb4317s.aspx | |
753 | ||
754 | #ifdef _M_X64 // Defined for compilations that target x64 processors. | |
755 | std::cout << "X64 " << std::endl; | |
756 | fp_hardware += "_X64"; | |
757 | #else | |
758 | # ifdef _M_IX86 | |
759 | std::cout << "X32 " << std::endl; | |
760 | fp_hardware += "_X86"; | |
761 | # endif | |
762 | #endif | |
763 | ||
764 | #ifdef _M_AMD64 | |
765 | std::cout << "AMD64 " << std::endl; | |
766 | // fp_hardware += "_AMD64"; | |
767 | #endif | |
768 | ||
769 | // https://msdn.microsoft.com/en-us/library/7t5yh4fd.aspx | |
770 | // /arch (x86) options /arch:[IA32|SSE|SSE2|AVX|AVX2] | |
771 | // default is to use SSE and SSE2 instructions by default. | |
772 | // https://msdn.microsoft.com/en-us/library/jj620901.aspx | |
773 | // /arch (x64) options /arch:AVX and /arch:AVX2 | |
774 | ||
775 | // MSVC doesn't bother to set these SSE macros! | |
776 | // http://stackoverflow.com/questions/18563978/sse-sse2-is-enabled-control-in-visual-studio | |
777 | // https://msdn.microsoft.com/en-us/library/b0084kay.aspx predefined macros. | |
778 | ||
779 | // But some of these macros are *not* defined by MSVC, | |
780 | // unlike AVX (but *are* defined by GCC and Clang). | |
781 | // So the macro code above does define them. | |
782 | #if (defined(_M_AMD64) || defined (_M_X64)) | |
783 | #ifndef _M_X64 | |
784 | # define _M_X64 | |
785 | #endif | |
786 | #ifndef __SSE2__ | |
787 | # define __SSE2__ | |
788 | #endif | |
789 | #else | |
790 | # ifdef _M_IX86_FP // Expands to an integer literal value indicating which /arch compiler option was used: | |
791 | std::cout << "Floating-point _M_IX86_FP = " << _M_IX86_FP << std::endl; | |
792 | # if (_M_IX86_FP == 2) // 2 if /arch:SSE2, /arch:AVX or /arch:AVX2 | |
793 | # define __SSE2__ // x32 | |
794 | # elif (_M_IX86_FP == 1) // 1 if /arch:SSE was used. | |
795 | # define __SSE__ // x32 | |
796 | # elif (_M_IX86_FP == 0) // 0 if /arch:IA32 was used. | |
797 | # define _X32 // No special FP instructions. | |
798 | # endif | |
799 | # endif | |
800 | #endif | |
801 | // Set the fp_hardware that is used in the .qbk filename. | |
802 | #ifdef __AVX2__ | |
803 | std::cout << "Floating-point AVX2 " << std::endl; | |
804 | fp_hardware += "_AVX2"; | |
805 | # else | |
806 | # ifdef __AVX__ | |
807 | std::cout << "Floating-point AVX " << std::endl; | |
808 | fp_hardware += "_AVX"; | |
809 | # else | |
810 | # ifdef __SSE2__ | |
811 | std::cout << "Floating-point SSE2 " << std::endl; | |
812 | fp_hardware += "_SSE2"; | |
813 | # else | |
814 | # ifdef __SSE__ | |
815 | std::cout << "Floating-point SSE " << std::endl; | |
816 | fp_hardware += "_SSE"; | |
817 | # endif | |
818 | # endif | |
819 | # endif | |
820 | # endif | |
821 | ||
822 | #ifdef _M_IX86 | |
823 | std::cout << "Floating-point X86 _M_IX86 = " << _M_IX86 << std::endl; | |
824 | // https://msdn.microsoft.com/en-us/library/aa273918%28v=vs.60%29.aspx#_predir_table_1..3 | |
825 | // 600 = Pentium Pro | |
826 | #endif | |
827 | ||
828 | #ifdef _MSC_FULL_VER | |
829 | std::cout << "Floating-point _MSC_FULL_VER " << _MSC_FULL_VER << std::endl; | |
830 | #endif | |
831 | ||
832 | #ifdef __MSVC_RUNTIME_CHECKS | |
833 | std::cout << "Runtime __MSVC_RUNTIME_CHECKS " << std::endl; | |
834 | #endif | |
835 | ||
836 | BOOST_MATH_CONTROL_FP; | |
837 | ||
838 | cpp_bin_float_100 full_value("28."); | |
839 | // Compute full answer to more than precision of tests. | |
840 | //T value = 28.; // integer (exactly representable as floating-point) | |
841 | // whose cube root is *not* exactly representable. | |
842 | // Wolfram Alpha command N[28 ^ (1 / 3), 100] computes cube root to 100 decimal digits. | |
843 | // 3.036588971875662519420809578505669635581453977248111123242141654169177268411884961770250390838097895 | |
844 | ||
845 | std::cout.precision(100); | |
846 | std::cout << "value " << full_value << std::endl; | |
847 | // std::cout << ",\n""answer = " << full_answer << std::endl; | |
848 | std::cout.precision(6); | |
849 | // cbrt cpp_bin_float_100 full_answer("3.036588971875662519420809578505669635581453977248111123242141654169177268411884961770250390838097895"); | |
850 | ||
851 | // Output the table of types, maxdigits10 and digits and required digits for some accuracies. | |
852 | ||
853 | // Output tables for some roots at full accuracy. | |
854 | roots_tables(full_value, 1.); | |
855 | ||
856 | // Output tables for some roots at less accuracy. | |
857 | //roots_tables(full_value, 0.75); | |
858 | ||
859 | return boost::exit_success; | |
860 | } | |
92f5a8d4 | 861 | catch (std::exception const& ex) |
7c673cae FG |
862 | { |
863 | std::cout << "exception thrown: " << ex.what() << std::endl; | |
864 | return boost::exit_failure; | |
865 | } | |
866 | } // int main() | |
867 | ||
868 | /* | |
869 | ||
870 | */ |