test_bessel_i.cpp

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//  (C) Copyright John Maddock 2007.
//  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/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/bessel.hpp>
#include <boost/math/special_functions/trunc.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
#include "test_bessel_hooks.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the bessel I function.  There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at 
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms.  In this situation you will 
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable.  Either way please
// report the results to the Boost mailing list.  Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//

void expected_results()
{
   //
   // Define the max and mean errors expected for
   // various compilers and platforms.
   //
   const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
   {
      largest_type = "(long\\s+)?double";
   }
   else
   {
      largest_type = "long double";
   }
#else
   largest_type = "(long\\s+)?double";
#endif

   //
   // Mac OS has higher error rates, why?
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                  // test type(s)
      ".*",                          // test data group
      ".*", 100, 50);                 // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      "real_concept",                // test type(s)
      ".*",                          // test data group
      ".*", 100, 50);                 // test function

   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*",                          // test data group
      ".*", 15, 10);                 // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                // test type(s)
      ".*",                          // test data group
      ".*", 15, 10);                 // test function
   //
   // Finish off by printing out the compiler/stdlib/platform names,
   // we do this to make it easier to mark up expected error rates.
   //
   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}

template <class T>
T cyl_bessel_i_int_wrapper(T v, T x)
{
   return static_cast<T>(
      boost::math::cyl_bessel_i(
      boost::math::itrunc(v), x));
}

template <class T>
void do_test_cyl_bessel_i(const T& data, const char* type_name, const char* test_name)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   typedef value_type (*pg)(value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg funcp = boost::math::cyl_bessel_i<value_type, value_type>;
#else
   pg funcp = boost::math::cyl_bessel_i;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test cyl_bessel_i against data:
   //
   result = boost::math::tools::test(
      data, 
      bind_func(funcp, 0, 1), 
      extract_result(2));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_bessel_i", test_name);
   std::cout << std::endl;

#ifdef TEST_OTHER
   if(boost::is_floating_point<value_type>::value)
   {
      funcp = other::cyl_bessel_i;

      //
      // test other::cyl_bessel_i against data:
      //
      result = boost::math::tools::test(
         data, 
         boost::lambda::bind(funcp, 
            boost::lambda::ret<value_type>(boost::lambda::_1[0]),
            boost::lambda::ret<value_type>(boost::lambda::_1[1])), 
         boost::lambda::ret<value_type>(boost::lambda::_1[2]));
      print_test_result(result, data[result.worst()], result.worst(), type_name, "other::cyl_bessel_i");
      std::cout << std::endl;
   }
#endif
}

template <class T>
void do_test_cyl_bessel_i_int(const T& data, const char* type_name, const char* test_name)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   typedef value_type (*pg)(value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg funcp = cyl_bessel_i_int_wrapper<value_type>;
#else
   pg funcp = cyl_bessel_i_int_wrapper;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test cyl_bessel_i against data:
   //
   result = boost::math::tools::test(
      data, 
      bind_func(funcp, 0, 1), 
      extract_result(2));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_bessel_i", test_name);
   std::cout << std::endl;
}

template <class T>
void test_bessel(T, const char* name)
{
    // function values calculated on http://functions.wolfram.com/
    #define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
    static const boost::array<boost::array<T, 3>, 10> i0_data = {{
        SC_(0), SC_(0), SC_(1),
        SC_(0), SC_(1), SC_(1.26606587775200833559824462521471753760767031135496220680814),
        SC_(0), SC_(-2), SC_(2.27958530233606726743720444081153335328584110278545905407084),
        SC_(0), SC_(4), SC_(11.3019219521363304963562701832171024974126165944353377060065),
        SC_(0), SC_(-7), SC_(168.593908510289698857326627187500840376522679234531714193194),
        SC_(0), SC_(1) / 1024, SC_(1.00000023841859331241759166109699567801556273303717896447683),
        SC_(0), SC_(1) / (1024*1024), SC_(1.00000000000022737367544324498417583090700894607432256476338),
        SC_(0), SC_(-1), SC_(1.26606587775200833559824462521471753760767031135496220680814),
        SC_(0), SC_(100), SC_(1.07375170713107382351972085760349466128840319332527279540154e42),
        SC_(0), SC_(200), SC_(2.03968717340972461954167312677945962233267573614834337894328e85),
    }};
    static const boost::array<boost::array<T, 3>, 10> i1_data = {
        SC_(1), SC_(0), SC_(0),
        SC_(1), SC_(1), SC_(0.565159103992485027207696027609863307328899621621092009480294),
        SC_(1), SC_(-2), SC_(-1.59063685463732906338225442499966624795447815949553664713229),
        SC_(1), SC_(4), SC_(9.75946515370444990947519256731268090005597033325296730692753),
        SC_(1), SC_(-8), SC_(-399.873136782560098219083086145822754889628443904067647306574),
        SC_(1), SC_(1)/1024, SC_(0.000488281308207663226432087816784315537514225208473395063575150),
        SC_(1), SC_(1)/(1024*1024), SC_(4.76837158203179210108624277276025646653133998635956784292029E-7),
        SC_(1), SC_(-10), SC_(-2670.98830370125465434103196677215254914574515378753771310849),
        SC_(1), SC_(100), SC_(1.06836939033816248120614576322429526544612284405623226965918e42),
        SC_(1), SC_(200), SC_(2.03458154933206270342742797713906950389661161681122964159220e85),
    };
    static const boost::array<boost::array<T, 3>, 10> in_data = {
        SC_(-2), SC_(0), SC_(0),
        SC_(2), SC_(1)/(1024*1024), SC_(1.13686837721624646204093977095674566928522671779753217215467e-13),
        SC_(5), SC_(10), SC_(777.188286403259959907293484802339632852674154572666041953297),
        SC_(-5), SC_(100), SC_(9.47009387303558124618275555002161742321578485033007130107740e41),
        SC_(-5), SC_(-1), SC_(-0.000271463155956971875181073905153777342383564426758143634974124),
        SC_(10), SC_(20), SC_(3.54020020901952109905289138244985607057267103782948493874391e6),
        SC_(10), SC_(-5), SC_(0.00458004441917605126118647027872016953192323139337073320016447),
        SC_(1e+02), SC_(9), SC_(2.74306601746058997093587654668959071522869282506446891736820e-93),
        SC_(1e+02), SC_(80), SC_(4.65194832850610205318128191404145885093970505338730540776711e8),
        SC_(-100), SC_(-200), SC_(4.35275044972702191438729017441198257508190719030765213981307e74),
    };
    static const boost::array<boost::array<T, 3>, 10> iv_data = {
        SC_(2.25), SC_(1)/(1024*1024), SC_(2.34379212133481347189068464680335815256364262507955635911656e-15),
        SC_(5.5), SC_(3.125), SC_(0.0583514045989371500460946536220735787163510569634133670181210),
        SC_(-5) + T(1)/1024, SC_(2.125), SC_(0.0267920938009571023702933210070984416052633027166975342895062),
        SC_(-5.5), SC_(10), SC_(597.577606961369169607937419869926705730305175364662688426534),
        SC_(-5.5), SC_(100), SC_(9.22362906144706871737354069133813819358704200689067071415379e41),
        SC_(-10486074)/(1024*1024), SC_(1)/1024, SC_(1.41474005665181350367684623930576333542989766867888186478185e35),
        SC_(-10486074)/(1024*1024), SC_(50), SC_(1.07153277202900671531087024688681954238311679648319534644743e20),
        SC_(144794)/1024, SC_(100), SC_(2066.27694757392660413922181531984160871678224178890247540320),
        SC_(144794)/1024, SC_(200), SC_(2.23699739472246928794922868978337381373643889659337595319774e64),
        SC_(-144794)/1024, SC_(100), SC_(2066.27694672763190927440969155740243346136463461655104698748),
    };
    #undef SC_

    do_test_cyl_bessel_i(i0_data, name, "Bessel I0: Mathworld Data");
    do_test_cyl_bessel_i(i1_data, name, "Bessel I1: Mathworld Data");
    do_test_cyl_bessel_i(in_data, name, "Bessel In: Mathworld Data");

    do_test_cyl_bessel_i_int(i0_data, name, "Bessel I0: Mathworld Data (Integer Version)");
    do_test_cyl_bessel_i_int(i1_data, name, "Bessel I1: Mathworld Data (Integer Version)");
    do_test_cyl_bessel_i_int(in_data, name, "Bessel In: Mathworld Data (Integer Version)");

    do_test_cyl_bessel_i(iv_data, name, "Bessel Iv: Mathworld Data");

#include "bessel_i_int_data.ipp"
    do_test_cyl_bessel_i(bessel_i_int_data, name, "Bessel In: Random Data");
#include "bessel_i_data.ipp"
    do_test_cyl_bessel_i(bessel_i_data, name, "Bessel Iv: Random Data");
}

int test_main(int, char* [])
{
#ifdef TEST_GSL
   gsl_set_error_handler_off();
#endif
   expected_results();
   BOOST_MATH_CONTROL_FP;

#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
   test_bessel(0.1F, "float");
#endif
   test_bessel(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   test_bessel(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
   test_bessel(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#else
   std::cout << "<note>The long double tests have been disabled on this platform "
      "either because the long double overloads of the usual math functions are "
      "not available at all, or because they are too inaccurate for these tests "
      "to pass.</note>" << std::cout;
#endif
   return 0;
}