ceph/src/boost/libs/math/test/test_erf.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 #include <boost/math/concepts/real_concept.hpp>
   8 #define BOOST_TEST_MAIN
   9 #include <boost/test/unit_test.hpp>
  10 #include <boost/test/floating_point_comparison.hpp>
  11 #include <boost/math/special_functions/math_fwd.hpp>
  12 #include <boost/math/constants/constants.hpp>
  13 #include <boost/type_traits/is_floating_point.hpp>
  14 #include <boost/array.hpp>
  15 #include "functor.hpp"
  16
  17 #include "handle_test_result.hpp"
  18 #include "table_type.hpp"
  19
  20 #ifndef SC_
  21 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  22 #endif
  23
  24 template <class Real, class T>
  25 void do_test_erf(const T& data, const char* type_name, const char* test_name)
  26 {
  27    typedef Real                   value_type;
  28
  29    typedef value_type (*pg)(value_type);
  30 #ifdef ERF_FUNCTION_TO_TEST
  31    pg funcp = ERF_FUNCTION_TO_TEST;
  32 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  33    pg funcp = boost::math::erf<value_type>;
  34 #else
  35    pg funcp = boost::math::erf;
  36 #endif
  37
  38    boost::math::tools::test_result<value_type> result;
  39
  40    std::cout << "Testing " << test_name << " with type " << type_name
  41       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  42
  43    //
  44    // test erf against data:
  45    //
  46 #if !(defined(ERROR_REPORTING_MODE) && !defined(ERF_FUNCTION_TO_TEST))
  47    result = boost::math::tools::test_hetero<Real>(
  48       data,
  49       bind_func<Real>(funcp, 0),
  50       extract_result<Real>(1));
  51    handle_test_result(result, data[result.worst()], result.worst(), type_name, "erf", test_name);
  52 #endif
  53    //
  54    // test erfc against data:
  55    //
  56 #ifdef ERFC_FUNCTION_TO_TEST
  57    funcp = ERFC_FUNCTION_TO_TEST;
  58 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  59    funcp = boost::math::erfc<value_type>;
  60 #else
  61    funcp = boost::math::erfc;
  62 #endif
  63 #if !(defined(ERROR_REPORTING_MODE) && !defined(ERFC_FUNCTION_TO_TEST))
  64    result = boost::math::tools::test_hetero<Real>(
  65       data,
  66       bind_func<Real>(funcp, 0),
  67       extract_result<Real>(2));
  68    handle_test_result(result, data[result.worst()], result.worst(), type_name, "erfc", test_name);
  69    std::cout << std::endl;
  70 #endif
  71 }
  72
  73
  74 template <class Real, class T>
  75 void do_test_erf_inv(const T& data, const char* type_name, const char* test_name)
  76 {
  77 #if !(defined(ERROR_REPORTING_MODE) && !defined(ERF_INV_FUNCTION_TO_TEST))
  78    typedef Real                   value_type;
  79
  80    typedef value_type (*pg)(value_type);
  81
  82    boost::math::tools::test_result<value_type> result;
  83    std::cout << "Testing " << test_name << " with type " << type_name
  84       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  85    //
  86    // test erf_inv against data:
  87    //
  88 #ifdef ERF_INV_FUNCTION_TO_TEST
  89    pg funcp = ERF_INV_FUNCTION_TO_TEST;
  90 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  91    pg funcp = boost::math::erf_inv<value_type>;
  92 #else
  93    pg funcp = boost::math::erf_inv;
  94 #endif
  95    result = boost::math::tools::test_hetero<Real>(
  96       data,
  97       bind_func<Real>(funcp, 0),
  98       extract_result<Real>(1));
  99    handle_test_result(result, data[result.worst()], result.worst(), type_name, "erf_inv", test_name);
 100    std::cout << std::endl;
 101 #endif
 102 }
 103
 104 template <class Real, class T>
 105 void do_test_erfc_inv(const T& data, const char* type_name, const char* test_name)
 106 {
 107 #if !(defined(ERROR_REPORTING_MODE) && !defined(ERFC_INV_FUNCTION_TO_TEST))
 108    typedef Real                   value_type;
 109
 110    typedef value_type (*pg)(value_type);
 111
 112    boost::math::tools::test_result<value_type> result;
 113    std::cout << "Testing " << test_name << " with type " << type_name
 114       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
 115    //
 116    // test erfc_inv against data:
 117    //
 118 #ifdef ERFC_INV_FUNCTION_TO_TEST
 119    pg funcp = ERFC_INV_FUNCTION_TO_TEST;
 120 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 121    pg funcp = boost::math::erfc_inv<value_type>;
 122 #else
 123    pg funcp = boost::math::erfc_inv;
 124 #endif
 125    result = boost::math::tools::test_hetero<Real>(
 126       data,
 127       bind_func<Real>(funcp, 0),
 128       extract_result<Real>(1));
 129    handle_test_result(result, data[result.worst()], result.worst(), type_name, "erfc_inv", test_name);
 130    std::cout << std::endl;
 131 #endif
 132 }
 133
 134 template <class T>
 135 void test_erf(T, const char* name)
 136 {
 137    //
 138    // The actual test data is rather verbose, so it's in a separate file
 139    //
 140    // The contents are as follows, each row of data contains
 141    // three items, input value a, input value b and erf(a, b):
 142    //
 143 #  include "erf_small_data.ipp"
 144
 145    do_test_erf<T>(erf_small_data, name, "Erf Function: Small Values");
 146
 147 #  include "erf_data.ipp"
 148
 149    do_test_erf<T>(erf_data, name, "Erf Function: Medium Values");
 150
 151 #  include "erf_large_data.ipp"
 152
 153    do_test_erf<T>(erf_large_data, name, "Erf Function: Large Values");
 154
 155 #  include "erf_inv_data.ipp"
 156
 157    do_test_erf_inv<T>(erf_inv_data, name, "Inverse Erf Function");
 158
 159 #  include "erfc_inv_data.ipp"
 160
 161    do_test_erfc_inv<T>(erfc_inv_data, name, "Inverse Erfc Function");
 162
 163 #  include "erfc_inv_big_data.ipp"
 164
 165    if(std::numeric_limits<T>::min_exponent <= -4500)
 166    {
 167       do_test_erfc_inv<T>(erfc_inv_big_data, name, "Inverse Erfc Function: extreme values");
 168    }
 169 }
 170
 171 template <class T>
 172 void test_spots(T, const char* t)
 173 {
 174    std::cout << "Testing basic sanity checks for type " << t << std::endl;
 175    //
 176    // basic sanity checks, tolerance is 10 epsilon expressed as a percentage:
 177    //
 178    T tolerance = boost::math::tools::epsilon<T>() * 1000;
 179    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.125)), static_cast<T>(0.85968379519866618260697055347837660181302041685015L), tolerance);
 180    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.5)), static_cast<T>(0.47950012218695346231725334610803547126354842424204L), tolerance);
 181    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(1)), static_cast<T>(0.15729920705028513065877936491739074070393300203370L), tolerance);
 182    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(5)), static_cast<T>(1.5374597944280348501883434853833788901180503147234e-12L), tolerance);
 183    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.125)), static_cast<T>(1.1403162048013338173930294465216233981869795831498L), tolerance);
 184    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.5)), static_cast<T>(1.5204998778130465376827466538919645287364515757580L), tolerance);
 185    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0)), static_cast<T>(1), tolerance);
 186
 187    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.125)), static_cast<T>(0.14031620480133381739302944652162339818697958314985L), tolerance);
 188    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.5)), static_cast<T>(0.52049987781304653768274665389196452873645157575796L), tolerance);
 189    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(1)), static_cast<T>(0.84270079294971486934122063508260925929606699796630L), tolerance);
 190    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(5)), static_cast<T>(0.9999999999984625402055719651498116565146166211099L), tolerance);
 191    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.125)), static_cast<T>(-0.14031620480133381739302944652162339818697958314985L), tolerance);
 192    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.5)), static_cast<T>(-0.52049987781304653768274665389196452873645157575796L), tolerance);
 193    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0)), static_cast<T>(0), tolerance);
 194
 195    tolerance = boost::math::tools::epsilon<T>() * 100 * 200; // 200 eps %.
 196 #if defined(__CYGWIN__)
 197    // some platforms long double is only reliably accurate to double precision:
 198    if(sizeof(T) == sizeof(long double))
 199       tolerance = boost::math::tools::epsilon<double>() * 100 * 200; // 200 eps %.
 200 #endif
 201
 202    for(T i = -0.95f; i < 1; i += 0.125f)
 203    {
 204       T inv = boost::math::erf_inv(i);
 205       T b = boost::math::erf(inv);
 206       BOOST_CHECK_CLOSE(b, i, tolerance);
 207    }
 208    for(T j = 0.125f; j < 2; j += 0.125f)
 209    {
 210       T inv = boost::math::erfc_inv(j);
 211       T b = boost::math::erfc(inv);
 212       BOOST_CHECK_CLOSE(b, j, tolerance);
 213    }
 214 }
 215