ceph/src/boost/libs/math/test/test_inv_hyp.cpp

   1 //  (C) Copyright John Maddock 2006.
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #include <pch.hpp>
   7
   8 #include <boost/math/concepts/real_concept.hpp>
   9 #include <boost/math/special_functions/acosh.hpp>
  10 #include <boost/math/special_functions/asinh.hpp>
  11 #include <boost/math/special_functions/atanh.hpp>
  12 #define BOOST_TEST_MAIN
  13 #include <boost/test/unit_test.hpp>
  14 #include <boost/test/tools/floating_point_comparison.hpp>
  15 #include <boost/math/tools/stats.hpp>
  16 #include <boost/math/tools/test.hpp>
  17 #include <boost/math/constants/constants.hpp>
  18 #include <boost/type_traits/is_floating_point.hpp>
  19 #include <boost/array.hpp>
  20 #include "functor.hpp"
  21
  22 #include "handle_test_result.hpp"
  23 #include "table_type.hpp"
  24
  25 #include <iostream>
  26 #include <iomanip>
  27 //
  28 // DESCRIPTION:
  29 // ~~~~~~~~~~~~
  30 //
  31 // This file tests the inverse hyperbolic functions. There are two sets of tests:
  32 // 1) Sanity checks: comparison to test values created with the
  33 // online calculator at functions.wolfram.com
  34 // 2) Accuracy tests use values generated with NTL::RR at
  35 // 1000-bit precision and our generic versions of these functions.
  36 //
  37 // Note that when this file is first run on a new platform many of
  38 // these tests will fail: the default accuracy is 1 epsilon which
  39 // is too tight for most platforms.  In this situation you will
  40 // need to cast a human eye over the error rates reported and make
  41 // a judgement as to whether they are acceptable.  Either way please
  42 // report the results to the Boost mailing list.  Acceptable rates of
  43 // error are marked up below as a series of regular expressions that
  44 // identify the compiler/stdlib/platform/data-type/test-data/test-function
  45 // along with the maximum expected peek and RMS mean errors for that
  46 // test.
  47 //
  48
  49 void expected_results()
  50 {
  51    //
  52    // Define the max and mean errors expected for
  53    // various compilers and platforms.
  54    //
  55    const char* largest_type;
  56 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  57    if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
  58    {
  59       largest_type = "(long\\s+)?double|real_concept";
  60    }
  61    else
  62    {
  63       largest_type = "long double|real_concept";
  64    }
  65 #else
  66    largest_type = "(long\\s+)?double";
  67 #endif
  68
  69    add_expected_result(
  70       ".*",                          // compiler
  71       ".*",                          // stdlib
  72       ".*",                          // platform
  73       largest_type,                  // test type(s)
  74       "atanh.*",                     // test data group
  75       ".*", 6, 1);                   // test function
  76    add_expected_result(
  77       ".*",                          // compiler
  78       ".*",                          // stdlib
  79       ".*",                          // platform
  80       "real_concept",                // test type(s)
  81       ".*",                          // test data group
  82       ".*", 4, 2);                   // test function
  83    add_expected_result(
  84       ".*",                          // compiler
  85       ".*",                          // stdlib
  86       ".*",                          // platform
  87       largest_type,                  // test type(s)
  88       ".*",                          // test data group
  89       ".*", 4, 1);                   // test function
  90
  91    std::cout << "Tests run with " << BOOST_COMPILER << ", "
  92       << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
  93 }
  94
  95 template <class Real, class T>
  96 void do_test_asinh(const T& data, const char* type_name, const char* test_name)
  97 {
  98    //
  99    // test asinh(T) against data:
 100    //
 101    using namespace std;
 102    typedef Real                   value_type;
 103
 104    std::cout << test_name << " with type " << type_name << std::endl;
 105
 106    typedef value_type (*pg)(value_type);
 107 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 108    pg funcp = boost::math::asinh<value_type>;
 109 #else
 110    pg funcp = boost::math::asinh;
 111 #endif
 112
 113    boost::math::tools::test_result<value_type> result;
 114    //
 115    // test asinh against data:
 116    //
 117    result = boost::math::tools::test_hetero<Real>(
 118       data,
 119       bind_func<Real>(funcp, 0),
 120       extract_result<Real>(1));
 121    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::asinh", test_name);
 122    std::cout << std::endl;
 123 }
 124
 125 template <class Real, class T>
 126 void do_test_acosh(const T& data, const char* type_name, const char* test_name)
 127 {
 128    //
 129    // test acosh(T) against data:
 130    //
 131    using namespace std;
 132    typedef Real                   value_type;
 133
 134    std::cout << test_name << " with type " << type_name << std::endl;
 135
 136    typedef value_type (*pg)(value_type);
 137 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 138    pg funcp = boost::math::acosh<value_type>;
 139 #else
 140    pg funcp = boost::math::acosh;
 141 #endif
 142
 143    boost::math::tools::test_result<value_type> result;
 144    //
 145    // test acosh against data:
 146    //
 147    result = boost::math::tools::test_hetero<Real>(
 148       data,
 149       bind_func<Real>(funcp, 0),
 150       extract_result<Real>(1));
 151    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::acosh", test_name);
 152    std::cout << std::endl;
 153 }
 154
 155 template <class Real, class T>
 156 void do_test_atanh(const T& data, const char* type_name, const char* test_name)
 157 {
 158    //
 159    // test atanh(T) against data:
 160    //
 161    using namespace std;
 162    typedef Real                   value_type;
 163
 164    std::cout << test_name << " with type " << type_name << std::endl;
 165
 166    typedef value_type (*pg)(value_type);
 167 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 168    pg funcp = boost::math::atanh<value_type>;
 169 #else
 170    pg funcp = boost::math::atanh;
 171 #endif
 172
 173    boost::math::tools::test_result<value_type> result;
 174    //
 175    // test atanh against data:
 176    //
 177    result = boost::math::tools::test_hetero<Real>(
 178       data,
 179       bind_func<Real>(funcp, 0),
 180       extract_result<Real>(1));
 181    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::atanh", test_name);
 182    std::cout << std::endl;
 183 }
 184
 185 template <class T>
 186 void test_inv_hyperbolics(T, const char* name)
 187 {
 188     // function values calculated on http://functions.wolfram.com/
 189     #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
 190     static const boost::array<boost::array<typename table_type<T>::type, 2>, 16> data1 = {{
 191         {{ SC_(1.0), SC_(0.0) }},
 192         {{ SC_(18014398509481985.0)/SC_(18014398509481984.0), (SC_(18014398509481985.0)/SC_(18014398509481984.0) == 1 ? 0 : SC_(1.05367121277235078980001569764860129317209081216314559121044e-8)) }},
 193         {{ SC_(140737488355329.0)/SC_(140737488355328.0), (SC_(140737488355329.0)/SC_(140737488355328.0) == 1 ? 0 : SC_(1.19209289550781179413921062141751258430803882725295121500042e-7)) }},
 194         {{ SC_(1073741825.0)/SC_(1073741824.0), (SC_(1073741825.0)/SC_(1073741824.0) == 1 ? 0 : SC_(0.0000431583728718059579720327225039166883356735150941350459126580)) }},
 195         {{ SC_(32769.0)/32768, (SC_(32769.0)/32768 == 1 ? 0 : SC_(0.00781248013192149783598227588546120945538554063153555218442060)) }},
 196         {{ SC_(1025.0)/1024, SC_(0.0441905780831100944299637635287994671116916497867872322058681) }},
 197         {{ SC_(513.0)/512, SC_(0.0624898319417098609694799246056217361555882834152944713872228) }},
 198         {{ SC_(129.0)/128, SC_(0.124918762511080617606418193883982155828039646714882611321039) }},
 199         {{ SC_(33.0)/32, SC_(0.249353493842885487851439075410018843027071727873456825299808) }},
 200         {{ SC_(5.0)/4, SC_(0.693147180559945309417232121458176568075500134360255254120680) }},
 201         {{ SC_(3.0)/2, SC_(0.962423650119206894995517826848736846270368668771321039322036) }},
 202         {{ SC_(1.75), SC_(1.15881036042994681173087299087873019318368454205435905403767) }},
 203         {{ SC_(2.0), SC_(1.31695789692481670862504634730796844402698197146751647976847) }},
 204         {{ SC_(20.0), SC_(3.68825386736129666761816757203235188783315569765587425882926) }},
 205         {{ SC_(200.0), SC_(5.99145829704938742305501213819154333467246121857058747847273) }},
 206         {{ SC_(2000.0), SC_(8.29404957760202181151262480475259799729149903827743516943515) }},
 207     }};
 208     #undef SC_
 209
 210    //
 211    // The actual test data is rather verbose, so it's in a separate file
 212    //
 213 #include "asinh_data.ipp"
 214    do_test_asinh<T>(asinh_data, name, "asinh");
 215 #include "acosh_data.ipp"
 216    do_test_acosh<T>(data1, name, "acosh: Mathworld Data");
 217    do_test_acosh<T>(acosh_data, name, "acosh");
 218 #include "atanh_data.ipp"
 219    do_test_atanh<T>(atanh_data, name, "atanh");
 220 }
 221
 222 extern "C" double zetac(double);
 223
 224 template <class T>
 225 void test_spots(T, const char* t)
 226 {
 227    std::cout << "Testing basic sanity checks for type " << t << std::endl;
 228    //
 229    // Basic sanity checks, tolerance is either 5 or 10 epsilon
 230    // expressed as a percentage:
 231    //
 232    T tolerance = boost::math::tools::epsilon<T>() * 100 *
 233       (boost::is_floating_point<T>::value ? 5 : 10);
 234    BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(262145)/262144L), static_cast<T>(0.00276213498595136093375633956331651432309750291610866833462649L), tolerance);
 235    BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(2)), static_cast<T>(1.31695789692481670862504634730796844402698197146751647976847L), tolerance);
 236    BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(40)), static_cast<T>(4.38187034804006698696313269586603717076961771721038534547948L), tolerance);
 237    BOOST_CHECK_CLOSE(::boost::math::acosh(static_cast<T>(262145L)), static_cast<T>(13.1698002453253126137651962522659827810753786944786303017757L), tolerance);
 238
 239    BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(0)), static_cast<T>(0), tolerance);
 240    BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(1)/262145L), static_cast<T>(3.81468271375603081996185039385472561751449912305225962381803e-6L), tolerance);
 241    BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(0.25)), static_cast<T>(0.247466461547263452944781549788359289253766903098567696469117L), tolerance);
 242    BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(1)), static_cast<T>(0.881373587019543025232609324979792309028160328261635410753296L), tolerance);
 243    BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(10)), static_cast<T>(2.99822295029796973884659553759645347660705805487730365573446L), tolerance);
 244    BOOST_CHECK_CLOSE(::boost::math::asinh(static_cast<T>(262145L)), static_cast<T>(13.1698002453325885158685460826511173257938039316922010439486L), tolerance);
 245
 246    BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(0)), static_cast<T>(0), tolerance);
 247    BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(1)/262145L), static_cast<T>(3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance);
 248    BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(-1)/262145L), static_cast<T>(-3.81468271378378607794264842456613940280945630999769224301574e-6L), tolerance);
 249    BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(0.5)), static_cast<T>(0.549306144334054845697622618461262852323745278911374725867347L), tolerance);
 250    BOOST_CHECK_CLOSE(::boost::math::atanh(static_cast<T>(-0.5)), static_cast<T>(-0.549306144334054845697622618461262852323745278911374725867347L), tolerance);
 251 }
 252
 253 BOOST_AUTO_TEST_CASE( test_main )
 254 {
 255    expected_results();
 256    BOOST_MATH_CONTROL_FP;
 257
 258    test_spots(0.0f, "float");
 259    test_spots(0.0, "double");
 260 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 261    test_spots(0.0L, "long double");
 262 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
 263    test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
 264 #endif
 265 #else
 266    std::cout << "<note>The long double tests have been disabled on this platform "
 267       "either because the long double overloads of the usual math functions are "
 268       "not available at all, or because they are too inaccurate for these tests "
 269       "to pass.</note>" << std::endl;
 270 #endif
 271
 272    test_inv_hyperbolics(0.1F, "float");
 273    test_inv_hyperbolics(0.1, "double");
 274 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 275    test_inv_hyperbolics(0.1L, "long double");
 276 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
 277    test_inv_hyperbolics(boost::math::concepts::real_concept(0.1), "real_concept");
 278 #endif
 279 #else
 280    std::cout << "<note>The long double tests have been disabled on this platform "
 281       "either because the long double overloads of the usual math functions are "
 282       "not available at all, or because they are too inaccurate for these tests "
 283       "to pass.</note>" << std::endl;
 284 #endif
 285
 286 }