ceph/src/boost/libs/math/test/test_igamma_inva.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 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
   8
   9 #include <boost/math/concepts/real_concept.hpp>
  10 #include <boost/math/special_functions/math_fwd.hpp>
  11 #define BOOST_TEST_MAIN
  12 #include <boost/test/unit_test.hpp>
  13 #include <boost/test/results_collector.hpp>
  14 #include <boost/test/unit_test.hpp>
  15 #include <boost/test/tools/floating_point_comparison.hpp>
  16 #include <boost/math/tools/stats.hpp>
  17 #include <boost/math/tools/test.hpp>
  18 #include <boost/math/constants/constants.hpp>
  19 #include <boost/type_traits/is_floating_point.hpp>
  20 #include <boost/array.hpp>
  21 #include "functor.hpp"
  22 #include "table_type.hpp"
  23 #include "handle_test_result.hpp"
  24
  25 #ifndef SC_
  26 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  27 #endif
  28
  29 #define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
  30    {\
  31       unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
  32       BOOST_CHECK_CLOSE(a, b, prec); \
  33       if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
  34       {\
  35          std::cerr << "Failure was at row " << i << std::endl;\
  36          std::cerr << std::setprecision(35); \
  37          std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
  38          std::cerr << " , " << data[i][3] << " , " << data[i][4] << " , " << data[i][5] << " } " << std::endl;\
  39       }\
  40    }
  41
  42 template <class Real, class T>
  43 void do_test_gamma_2(const T& data, const char* type_name, const char* test_name)
  44 {
  45    //
  46    // test gamma_p_inva(T, T) against data:
  47    //
  48    using namespace std;
  49    typedef Real                   value_type;
  50
  51    std::cout << test_name << " with type " << type_name << std::endl;
  52
  53    //
  54    // These sanity checks test for a round trip accuracy of one half
  55    // of the bits in T, unless T is type float, in which case we check
  56    // for just one decimal digit.  The problem here is the sensitivity
  57    // of the functions, not their accuracy.  This test data was generated
  58    // for the forward functions, which means that when it is used as
  59    // the input to the inverses then it is necessarily inexact.  This rounding
  60    // of the input is what makes the data unsuitable for use as an accuracy check,
  61    // and also demonstrates that you can't in general round-trip these functions.
  62    // It is however a useful sanity check.
  63    //
  64    value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
  65    if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
  66       precision = 1;   // 1% or two decimal digits, all we can hope for when the input is truncated to float
  67
  68    for(unsigned i = 0; i < data.size(); ++i)
  69    {
  70       //
  71       // These inverse tests are thrown off if the output of the
  72       // incomplete gamma is too close to 1: basically there is insuffient
  73       // information left in the value we're using as input to the inverse
  74       // to be able to get back to the original value.
  75       //
  76       if(Real(data[i][5]) == 0)
  77          BOOST_CHECK_EQUAL(boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5])), std::numeric_limits<value_type>::has_infinity ? std::numeric_limits<value_type>::infinity() : boost::math::tools::max_value<value_type>());
  78       else if((1 - Real(data[i][5]) > 0.001) && (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<value_type>()))
  79       {
  80          value_type inv = boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5]));
  81          BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, precision, i);
  82       }
  83       else if(1 == Real(data[i][5]))
  84          BOOST_CHECK_EQUAL(boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5])), boost::math::tools::min_value<value_type>());
  85       else if(Real(data[i][5]) > 2 * boost::math::tools::min_value<value_type>())
  86       {
  87          // not enough bits in our input to get back to x, but we should be in
  88          // the same ball park:
  89          value_type inv = boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5]));
  90          BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, 100, i);
  91       }
  92
  93       if(Real(data[i][3]) == 0)
  94          BOOST_CHECK_EQUAL(boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3])), boost::math::tools::min_value<value_type>());
  95       else if((1 - Real(data[i][3]) > 0.001)
  96          && (fabs(Real(data[i][3])) > 2 * boost::math::tools::min_value<value_type>())
  97          && (fabs(Real(data[i][3])) > 2 * boost::math::tools::min_value<double>()))
  98       {
  99          value_type inv = boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3]));
 100          BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, precision, i);
 101       }
 102       else if(1 == Real(data[i][3]))
 103          BOOST_CHECK_EQUAL(boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3])), std::numeric_limits<value_type>::has_infinity ? std::numeric_limits<value_type>::infinity() : boost::math::tools::max_value<value_type>());
 104       else if(Real(data[i][3]) > 2 * boost::math::tools::min_value<value_type>())
 105       {
 106          // not enough bits in our input to get back to x, but we should be in
 107          // the same ball park:
 108          value_type inv = boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3]));
 109          BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, 100, i);
 110       }
 111    }
 112    std::cout << std::endl;
 113 }
 114
 115 template <class Real, class T>
 116 void do_test_gamma_inva(const T& data, const char* type_name, const char* test_name)
 117 {
 118 #if !(defined(ERROR_REPORTING_MODE) && !defined(GAMMAP_INVA_FUNCTION_TO_TEST))
 119    typedef Real                   value_type;
 120
 121    typedef value_type (*pg)(value_type, value_type);
 122 #ifdef GAMMAP_INVA_FUNCTION_TO_TEST
 123    pg funcp = GAMMAP_INVA_FUNCTION_TO_TEST;
 124 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 125    pg funcp = boost::math::gamma_p_inva<value_type, value_type>;
 126 #else
 127    pg funcp = boost::math::gamma_p_inva;
 128 #endif
 129
 130    boost::math::tools::test_result<value_type> result;
 131
 132    std::cout << "Testing " << test_name << " with type " << type_name
 133       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
 134
 135    //
 136    // test gamma_p_inva(T, T) against data:
 137    //
 138    result = boost::math::tools::test_hetero<Real>(
 139       data,
 140       bind_func<Real>(funcp, 0, 1),
 141       extract_result<Real>(2));
 142    handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_p_inva", test_name);
 143    //
 144    // test gamma_q_inva(T, T) against data:
 145    //
 146 #ifdef GAMMAQ_INVA_FUNCTION_TO_TEST
 147    funcp = GAMMAQ_INVA_FUNCTION_TO_TEST;
 148 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 149    funcp = boost::math::gamma_q_inva<value_type, value_type>;
 150 #else
 151    funcp = boost::math::gamma_q_inva;
 152 #endif
 153    result = boost::math::tools::test_hetero<Real>(
 154       data,
 155       bind_func<Real>(funcp, 0, 1),
 156       extract_result<Real>(3));
 157    handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_q_inva", test_name);
 158 #endif
 159 }
 160
 161 template <class T>
 162 void test_gamma(T, const char* name)
 163 {
 164 #if !defined(TEST_UDT) && !defined(ERROR_REPORTING_MODE)
 165    //
 166    // The actual test data is rather verbose, so it's in a separate file
 167    //
 168    // First the data for the incomplete gamma function, each
 169    // row has the following 6 entries:
 170    // Parameter a, parameter z,
 171    // Expected tgamma(a, z), Expected gamma_q(a, z)
 172    // Expected tgamma_lower(a, z), Expected gamma_p(a, z)
 173    //
 174 #  include "igamma_med_data.ipp"
 175
 176    do_test_gamma_2<T>(igamma_med_data, name, "Running round trip sanity checks on incomplete gamma medium sized values");
 177
 178 #  include "igamma_small_data.ipp"
 179
 180    do_test_gamma_2<T>(igamma_small_data, name, "Running round trip sanity checks on incomplete gamma small values");
 181
 182 #  include "igamma_big_data.ipp"
 183
 184    do_test_gamma_2<T>(igamma_big_data, name, "Running round trip sanity checks on incomplete gamma large values");
 185
 186 #endif
 187
 188 #  include "igamma_inva_data.ipp"
 189
 190    do_test_gamma_inva<T>(igamma_inva_data, name, "Incomplete gamma inverses.");
 191 }
 192