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+// Copyright John Maddock 2006.
+// Copyright Paul A. Bristow 2007, 2009
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+
+#include <boost/math/concepts/real_concept.hpp>
+#include <boost/math/special_functions/math_fwd.hpp>
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp>
+#include <boost/test/results_collector.hpp>
+#include <boost/test/unit_test.hpp>
+#include <boost/test/tools/floating_point_comparison.hpp>
+#include <boost/math/tools/stats.hpp>
+#include <boost/math/tools/test.hpp>
+#include <boost/math/constants/constants.hpp>
+#include <boost/type_traits/is_floating_point.hpp>
+#include <boost/array.hpp>
+#include "functor.hpp"
+#include "table_type.hpp"
+#include "handle_test_result.hpp"
+
+#ifndef SC_
+#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
+#endif
+
+#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
+ {\
+ unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+ BOOST_CHECK_CLOSE(a, b, prec); \
+ if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+ {\
+ std::cerr << "Failure was at row " << i << std::endl;\
+ std::cerr << std::setprecision(35); \
+ std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+ std::cerr << " , " << data[i][3] << " , " << data[i][4] << " , " << data[i][5] << " } " << std::endl;\
+ }\
+ }
+
+template <class Real, class T>
+void do_test_gamma_2(const T& data, const char* type_name, const char* test_name)
+{
+ //
+ // test gamma_p_inva(T, T) against data:
+ //
+ using namespace std;
+ typedef Real value_type;
+
+ std::cout << test_name << " with type " << type_name << std::endl;
+
+ //
+ // These sanity checks test for a round trip accuracy of one half
+ // of the bits in T, unless T is type float, in which case we check
+ // for just one decimal digit. The problem here is the sensitivity
+ // of the functions, not their accuracy. This test data was generated
+ // for the forward functions, which means that when it is used as
+ // the input to the inverses then it is necessarily inexact. This rounding
+ // of the input is what makes the data unsuitable for use as an accuracy check,
+ // and also demonstrates that you can't in general round-trip these functions.
+ // It is however a useful sanity check.
+ //
+ value_type precision = static_cast<value_type>(ldexp(1.0, 1-boost::math::policies::digits<value_type, boost::math::policies::policy<> >()/2)) * 100;
+ if(boost::math::policies::digits<value_type, boost::math::policies::policy<> >() < 50)
+ precision = 1; // 1% or two decimal digits, all we can hope for when the input is truncated to float
+
+ for(unsigned i = 0; i < data.size(); ++i)
+ {
+ //
+ // These inverse tests are thrown off if the output of the
+ // incomplete gamma is too close to 1: basically there is insuffient
+ // information left in the value we're using as input to the inverse
+ // to be able to get back to the original value.
+ //
+ if(Real(data[i][5]) == 0)
+ 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>());
+ else if((1 - Real(data[i][5]) > 0.001) && (fabs(Real(data[i][5])) > 2 * boost::math::tools::min_value<value_type>()))
+ {
+ value_type inv = boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5]));
+ BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, precision, i);
+ }
+ else if(1 == Real(data[i][5]))
+ BOOST_CHECK_EQUAL(boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5])), boost::math::tools::min_value<value_type>());
+ else if(Real(data[i][5]) > 2 * boost::math::tools::min_value<value_type>())
+ {
+ // not enough bits in our input to get back to x, but we should be in
+ // the same ball park:
+ value_type inv = boost::math::gamma_p_inva(Real(data[i][1]), Real(data[i][5]));
+ BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, 100, i);
+ }
+
+ if(Real(data[i][3]) == 0)
+ BOOST_CHECK_EQUAL(boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3])), boost::math::tools::min_value<value_type>());
+ else if((1 - Real(data[i][3]) > 0.001)
+ && (fabs(Real(data[i][3])) > 2 * boost::math::tools::min_value<value_type>())
+ && (fabs(Real(data[i][3])) > 2 * boost::math::tools::min_value<double>()))
+ {
+ value_type inv = boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3]));
+ BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, precision, i);
+ }
+ else if(1 == Real(data[i][3]))
+ 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>());
+ else if(Real(data[i][3]) > 2 * boost::math::tools::min_value<value_type>())
+ {
+ // not enough bits in our input to get back to x, but we should be in
+ // the same ball park:
+ value_type inv = boost::math::gamma_q_inva(Real(data[i][1]), Real(data[i][3]));
+ BOOST_CHECK_CLOSE_EX(Real(data[i][0]), inv, 100, i);
+ }
+ }
+ std::cout << std::endl;
+}
+
+template <class Real, class T>
+void do_test_gamma_inva(const T& data, const char* type_name, const char* test_name)
+{
+#if !(defined(ERROR_REPORTING_MODE) && !defined(GAMMAP_INVA_FUNCTION_TO_TEST))
+ typedef Real value_type;
+
+ typedef value_type (*pg)(value_type, value_type);
+#ifdef GAMMAP_INVA_FUNCTION_TO_TEST
+ pg funcp = GAMMAP_INVA_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+ pg funcp = boost::math::gamma_p_inva<value_type, value_type>;
+#else
+ pg funcp = boost::math::gamma_p_inva;
+#endif
+
+ boost::math::tools::test_result<value_type> result;
+
+ std::cout << "Testing " << test_name << " with type " << type_name
+ << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
+
+ //
+ // test gamma_p_inva(T, T) against data:
+ //
+ result = boost::math::tools::test_hetero<Real>(
+ data,
+ bind_func<Real>(funcp, 0, 1),
+ extract_result<Real>(2));
+ handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_p_inva", test_name);
+ //
+ // test gamma_q_inva(T, T) against data:
+ //
+#ifdef GAMMAQ_INVA_FUNCTION_TO_TEST
+ funcp = GAMMAQ_INVA_FUNCTION_TO_TEST;
+#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
+ funcp = boost::math::gamma_q_inva<value_type, value_type>;
+#else
+ funcp = boost::math::gamma_q_inva;
+#endif
+ result = boost::math::tools::test_hetero<Real>(
+ data,
+ bind_func<Real>(funcp, 0, 1),
+ extract_result<Real>(3));
+ handle_test_result(result, data[result.worst()], result.worst(), type_name, "gamma_q_inva", test_name);
+#endif
+}
+
+template <class T>
+void test_gamma(T, const char* name)
+{
+#if !defined(TEST_UDT) && !defined(ERROR_REPORTING_MODE)
+ //
+ // The actual test data is rather verbose, so it's in a separate file
+ //
+ // First the data for the incomplete gamma function, each
+ // row has the following 6 entries:
+ // Parameter a, parameter z,
+ // Expected tgamma(a, z), Expected gamma_q(a, z)
+ // Expected tgamma_lower(a, z), Expected gamma_p(a, z)
+ //
+# include "igamma_med_data.ipp"
+
+ do_test_gamma_2<T>(igamma_med_data, name, "Running round trip sanity checks on incomplete gamma medium sized values");
+
+# include "igamma_small_data.ipp"
+
+ do_test_gamma_2<T>(igamma_small_data, name, "Running round trip sanity checks on incomplete gamma small values");
+
+# include "igamma_big_data.ipp"
+
+ do_test_gamma_2<T>(igamma_big_data, name, "Running round trip sanity checks on incomplete gamma large values");
+
+#endif
+
+# include "igamma_inva_data.ipp"
+
+ do_test_gamma_inva<T>(igamma_inva_data, name, "Incomplete gamma inverses.");
+}
+
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