ceph/src/boost/libs/math/test/test_legendre.hpp

   1 // Copyright John Maddock 2006.
   2 // Copyright Paul A. Bristow 2007, 2009
   3 //  Use, modification and distribution are subject to the
   4 //  Boost Software License, Version 1.0. (See accompanying file
   5 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   6
   7 #ifdef _MSC_VER
   8 #  pragma warning (disable : 4756) // overflow in constant arithmetic
   9 #endif
  10
  11 #include <boost/math/concepts/real_concept.hpp>
  12 #define BOOST_TEST_MAIN
  13 #include <boost/test/unit_test.hpp>
  14 #include <boost/test/floating_point_comparison.hpp>
  15 #include <boost/math/special_functions/math_fwd.hpp>
  16 #include <boost/math/constants/constants.hpp>
  17 #include <boost/array.hpp>
  18 #include "functor.hpp"
  19
  20 #include "handle_test_result.hpp"
  21 #include "table_type.hpp"
  22
  23 #ifndef SC_
  24 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  25 #endif
  26
  27 template <class Real, class T>
  28 void do_test_legendre_p(const T& data, const char* type_name, const char* test_name)
  29 {
  30    typedef Real                   value_type;
  31
  32    typedef value_type (*pg)(int, value_type);
  33    pg funcp;
  34
  35 #if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_P_FUNCTION_TO_TEST))
  36 #ifdef LEGENDRE_P_FUNCTION_TO_TEST
  37    funcp = LEGENDRE_P_FUNCTION_TO_TEST;
  38 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  39    funcp = boost::math::legendre_p<value_type>;
  40 #else
  41    funcp = boost::math::legendre_p;
  42 #endif
  43
  44    boost::math::tools::test_result<value_type> result;
  45
  46    std::cout << "Testing " << test_name << " with type " << type_name
  47       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  48
  49    //
  50    // test legendre_p against data:
  51    //
  52    result = boost::math::tools::test_hetero<Real>(
  53       data,
  54       bind_func_int1<Real>(funcp, 0, 1),
  55       extract_result<Real>(2));
  56    handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_p", test_name);
  57 #endif
  58
  59    typedef value_type (*pg2)(unsigned, value_type);
  60 #if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_Q_FUNCTION_TO_TEST))
  61 #ifdef LEGENDRE_Q_FUNCTION_TO_TEST
  62    pg2 funcp2 = LEGENDRE_Q_FUNCTION_TO_TEST;
  63 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  64    pg2 funcp2 = boost::math::legendre_q<value_type>;
  65 #else
  66    pg2 funcp2 = boost::math::legendre_q;
  67 #endif
  68
  69    //
  70    // test legendre_q against data:
  71    //
  72    result = boost::math::tools::test_hetero<Real>(
  73       data,
  74       bind_func_int1<Real>(funcp2, 0, 1),
  75       extract_result<Real>(3));
  76    handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_q", test_name);
  77
  78    std::cout << std::endl;
  79 #endif
  80 }
  81
  82 template <class Real, class T>
  83 void do_test_assoc_legendre_p(const T& data, const char* type_name, const char* test_name)
  84 {
  85 #if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_PA_FUNCTION_TO_TEST))
  86    typedef Real                   value_type;
  87
  88    typedef value_type (*pg)(int, int, value_type);
  89 #ifdef LEGENDRE_PA_FUNCTION_TO_TEST
  90    pg funcp = LEGENDRE_PA_FUNCTION_TO_TEST;
  91 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  92    pg funcp = boost::math::legendre_p<value_type>;
  93 #else
  94    pg funcp = boost::math::legendre_p;
  95 #endif
  96
  97    boost::math::tools::test_result<value_type> result;
  98
  99    std::cout << "Testing " << test_name << " with type " << type_name
 100       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
 101
 102    //
 103    // test legendre_p against data:
 104    //
 105    result = boost::math::tools::test_hetero<Real>(
 106       data,
 107       bind_func_int2<Real>(funcp, 0, 1, 2),
 108       extract_result<Real>(3));
 109    handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_p (associated)", test_name);
 110    std::cout << std::endl;
 111 #endif
 112 }
 113
 114 template <class T>
 115 void test_legendre_p(T, const char* name)
 116 {
 117    //
 118    // The actual test data is rather verbose, so it's in a separate file
 119    //
 120    // The contents are as follows, each row of data contains
 121    // three items, input value a, input value b and erf(a, b):
 122    //
 123 #  include "legendre_p.ipp"
 124
 125    do_test_legendre_p<T>(legendre_p, name, "Legendre Polynomials: Small Values");
 126
 127 #  include "legendre_p_large.ipp"
 128
 129    do_test_legendre_p<T>(legendre_p_large, name, "Legendre Polynomials: Large Values");
 130
 131 #  include "assoc_legendre_p.ipp"
 132
 133    do_test_assoc_legendre_p<T>(assoc_legendre_p, name, "Associated Legendre Polynomials: Small Values");
 134
 135 }
 136
 137 template <class T>
 138 void test_spots(T, const char* t)
 139 {
 140    std::cout << "Testing basic sanity checks for type " << t << std::endl;
 141    //
 142    // basic sanity checks, tolerance is 100 epsilon:
 143    //
 144    T tolerance = boost::math::tools::epsilon<T>() * 100;
 145    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance);
 146    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-1, static_cast<T>(0.5L)), static_cast<T>(1L), tolerance);
 147    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, static_cast<T>(0.5L)), static_cast<T>(-0.2890625000000000000000000000000000000000L), tolerance);
 148    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, static_cast<T>(0.5L)), static_cast<T>(-0.4375000000000000000000000000000000000000L), tolerance);
 149    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, static_cast<T>(0.5L)), static_cast<T>(0.2231445312500000000000000000000000000000L), tolerance);
 150    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, static_cast<T>(0.5L)), static_cast<T>(0.3232421875000000000000000000000000000000L), tolerance);
 151    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, static_cast<T>(0.5L)), static_cast<T>(-0.09542943523261546936538467572384923220258L), tolerance);
 152    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, static_cast<T>(0.5L)), static_cast<T>(-0.1316993126940266257030910566308990611306L), tolerance);
 153
 154    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
 155    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(0.5L)), static_cast<T>(5.625000000000000000000000000000000000000L), tolerance);
 156    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
 157    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
 158    if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
 159    {
 160       BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
 161    }
 162    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(0.5L)), static_cast<T>(4.966634149702370788037088925152355134665e30L), tolerance);
 163    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(-0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
 164    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(-0.5L)), static_cast<T>(-5.625000000000000000000000000000000000000L), tolerance);
 165    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(-0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
 166    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(-0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
 167    if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
 168    {
 169       BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(-0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
 170    }
 171    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(-0.5L)), static_cast<T>(-4.966634149702370788037088925152355134665e30L), tolerance);
 172    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, -2, static_cast<T>(0.5L)), static_cast<T>(0.01171875000000000000000000000000000000000L), tolerance);
 173    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, -2, static_cast<T>(0.5L)), static_cast<T>(0.04687500000000000000000000000000000000000L), tolerance);
 174    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, -5, static_cast<T>(0.5L)), static_cast<T>(0.00002378609812640364935569308025139290054701L), tolerance);
 175    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, -4, static_cast<T>(0.5L)), static_cast<T>(0.0002563476562500000000000000000000000000000L), tolerance);
 176    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, -30, static_cast<T>(0.5L)), static_cast<T>(-2.379819988646847616996471299410611801239e-48L), tolerance);
 177    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, -20, static_cast<T>(0.5L)), static_cast<T>(4.356454600748202401657099008867502679122e-33L), tolerance);
 178
 179    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(1, static_cast<T>(0.5L)), static_cast<T>(-0.7253469278329725771511886907693685738381L), tolerance);
 180    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(4, static_cast<T>(0.5L)), static_cast<T>(0.4401745259867706044988642951843745400835L), tolerance);
 181    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(7, static_cast<T>(0.5L)), static_cast<T>(-0.3439152932669753451878700644212067616780L), tolerance);
 182    BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(40, static_cast<T>(0.5L)), static_cast<T>(0.1493671665503550095010454949479907886011L), tolerance);
 183 }
 184