ceph/src/boost/libs/math/test/test_legendre.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_light.hpp>
   7 #include "test_legendre.hpp"
   8
   9 //
  10 // DESCRIPTION:
  11 // ~~~~~~~~~~~~
  12 //
  13 // This file tests the legendre polynomials.
  14 // There are two sets of tests, spot
  15 // tests which compare our results with selected values computed
  16 // using the online special function calculator at
  17 // functions.wolfram.com, while the bulk of the accuracy tests
  18 // use values generated with NTL::RR at 1000-bit precision
  19 // and our generic versions of these functions.
  20 //
  21 // Note that when this file is first run on a new platform many of
  22 // these tests will fail: the default accuracy is 1 epsilon which
  23 // is too tight for most platforms.  In this situation you will
  24 // need to cast a human eye over the error rates reported and make
  25 // a judgement as to whether they are acceptable.  Either way please
  26 // report the results to the Boost mailing list.  Acceptable rates of
  27 // error are marked up below as a series of regular expressions that
  28 // identify the compiler/stdlib/platform/data-type/test-data/test-function
  29 // along with the maximum expected peek and RMS mean errors for that
  30 // test.
  31 //
  32
  33 void expected_results()
  34 {
  35    //
  36    // Define the max and mean errors expected for
  37    // various compilers and platforms.
  38    //
  39    const char* largest_type;
  40 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  41    if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
  42    {
  43       largest_type = "(long\\s+)?double";
  44    }
  45    else
  46    {
  47       largest_type = "long double";
  48    }
  49 #else
  50    largest_type = "(long\\s+)?double";
  51 #endif
  52    //
  53    // Linux:
  54    //
  55    if((std::numeric_limits<long double>::digits <= 64)
  56       && (std::numeric_limits<long double>::digits != std::numeric_limits<double>::digits))
  57    {
  58 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  59       add_expected_result(
  60          ".*",                          // compiler
  61          ".*",                          // stdlib
  62          ".*",                          // platform
  63          "double",                      // test type(s)
  64          ".*",                          // test data group
  65          ".*", 10, 5);                  // test function
  66 #endif
  67    }
  68    if(std::numeric_limits<long double>::digits == 64)
  69    {
  70       add_expected_result(
  71          ".*",                          // compiler
  72          ".*",                          // stdlib
  73          ".*",                          // platform
  74          largest_type,                  // test type(s)
  75          "Legendre Polynomials.*Large.*",      // test data group
  76          "legendre_p", 1000, 200);  // test function
  77       add_expected_result(
  78          "Intel.*",                          // compiler
  79          ".*",                          // stdlib
  80          ".*",                          // platform
  81          largest_type,                  // test type(s)
  82          "Legendre Polynomials.*Large.*",      // test data group
  83          "legendre_q", 10000, 1000);  // test function
  84       add_expected_result(
  85          ".*",                          // compiler
  86          ".*",                          // stdlib
  87          ".*",                          // platform
  88          largest_type,                  // test type(s)
  89          "Legendre Polynomials.*Large.*",      // test data group
  90          "legendre_q", 7000, 1000);  // test function
  91       add_expected_result(
  92          ".*",                          // compiler
  93          ".*",                          // stdlib
  94          ".*",                          // platform
  95          "real_concept",                  // test type(s)
  96          "Legendre Polynomials.*Large.*",      // test data group
  97          "legendre_p", 1000, 200);  // test function
  98       add_expected_result(
  99          ".*",                          // compiler
 100          ".*",                          // stdlib
 101          ".*",                          // platform
 102          "real_concept",                  // test type(s)
 103          "Legendre Polynomials.*Large.*",      // test data group
 104          "legendre_q", 7000, 1000);  // test function
 105    }
 106    //
 107    // Catch all cases come last:
 108    //
 109    add_expected_result(
 110       ".*",                          // compiler
 111       ".*",                          // stdlib
 112       ".*",                          // platform
 113       largest_type,                  // test type(s)
 114       "Legendre Polynomials.*Large.*",      // test data group
 115       "legendre_p", 500, 200);  // test function
 116    add_expected_result(
 117       ".*",                          // compiler
 118       ".*",                          // stdlib
 119       ".*",                          // platform
 120       largest_type,                  // test type(s)
 121       "Legendre Polynomials.*Large.*",      // test data group
 122       "legendre_q", 5400, 500);  // test function
 123    add_expected_result(
 124       ".*",                          // compiler
 125       ".*",                          // stdlib
 126       ".*",                          // platform
 127       largest_type,                  // test type(s)
 128       "Legendre Polynomials.*",      // test data group
 129       "legendre_p", 300, 80);  // test function
 130    add_expected_result(
 131       ".*",                          // compiler
 132       ".*",                          // stdlib
 133       ".*",                          // platform
 134       largest_type,                  // test type(s)
 135       "Legendre Polynomials.*",      // test data group
 136       "legendre_q", 100, 50);  // test function
 137    add_expected_result(
 138       "Intel.*",                          // compiler
 139       ".*",                          // stdlib
 140       ".*",                          // platform
 141       largest_type,                  // test type(s)
 142       "Associated Legendre Polynomials.*",      // test data group
 143       ".*", 300, 20);  // test function
 144    add_expected_result(
 145       ".*",                          // compiler
 146       ".*",                          // stdlib
 147       ".*",                          // platform
 148       largest_type,                  // test type(s)
 149       "Associated Legendre Polynomials.*",      // test data group
 150       ".*", 200, 20);  // test function
 151
 152    add_expected_result(
 153       ".*",                          // compiler
 154       ".*",                          // stdlib
 155       ".*",                          // platform
 156       "real_concept",                  // test type(s)
 157       "Legendre Polynomials.*Large.*",      // test data group
 158       "legendre_p", 500, 200);  // test function
 159    add_expected_result(
 160       ".*",                          // compiler
 161       ".*",                          // stdlib
 162       ".*",                          // platform
 163       "real_concept",                  // test type(s)
 164       "Legendre Polynomials.*Large.*",      // test data group
 165       "legendre_q", 5400, 500);  // test function
 166    add_expected_result(
 167       ".*",                          // compiler
 168       ".*",                          // stdlib
 169       ".*",                          // platform
 170       "real_concept",                  // test type(s)
 171       "Legendre Polynomials.*",      // test data group
 172       "legendre_p", 300, 80);  // test function
 173    add_expected_result(
 174       ".*",                          // compiler
 175       ".*",                          // stdlib
 176       ".*",                          // platform
 177       "real_concept",                  // test type(s)
 178       "Legendre Polynomials.*",      // test data group
 179       "legendre_q", 100, 50);  // test function
 180    add_expected_result(
 181       ".*",                          // compiler
 182       ".*",                          // stdlib
 183       ".*",                          // platform
 184       "real_concept",                  // test type(s)
 185       "Associated Legendre Polynomials.*",      // test data group
 186       ".*", 200, 20);  // test function
 187    //
 188    // Finish off by printing out the compiler/stdlib/platform names,
 189    // we do this to make it easier to mark up expected error rates.
 190    //
 191    std::cout << "Tests run with " << BOOST_COMPILER << ", "
 192       << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
 193 }
 194
 195
 196 BOOST_AUTO_TEST_CASE( test_main )
 197 {
 198    BOOST_MATH_CONTROL_FP;
 199    test_spots(0.0F, "float");
 200    test_spots(0.0, "double");
 201 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 202    test_spots(0.0L, "long double");
 203    test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
 204 #endif
 205
 206    expected_results();
 207
 208    test_legendre_p(0.1F, "float");
 209    test_legendre_p(0.1, "double");
 210 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 211    test_legendre_p(0.1L, "long double");
 212 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
 213    test_legendre_p(boost::math::concepts::real_concept(0.1), "real_concept");
 214 #endif
 215 #else
 216    std::cout << "<note>The long double tests have been disabled on this platform "
 217       "either because the long double overloads of the usual math functions are "
 218       "not available at all, or because they are too inaccurate for these tests "
 219       "to pass.</note>" << std::endl;
 220 #endif
 221
 222    test_legendre_p_prime<float>();
 223    test_legendre_p_prime<double>();
 224    test_legendre_p_prime<long double>();
 225
 226    int ulp_distance = test_legendre_p_zeros_double_ulp(1, 100);
 227    BOOST_CHECK(ulp_distance <= 2);
 228    test_legendre_p_zeros<float>();
 229    test_legendre_p_zeros<double>();
 230    test_legendre_p_zeros<long double>();
 231 }