test_ellint_1.cpp

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//  Copyright Xiaogang Zhang 2006
//  Copyright John Maddock 2006, 2007
//  Copyright Paul A. Bristow 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)

#ifdef _MSC_VER
#  pragma warning(disable : 4756) // overflow in constant arithmetic
// Constants are too big for float case, but this doesn't matter for test.
#endif

#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/ellint_1.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the Elliptic Integrals of the first kind.
// 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

   //
   // Catch all cases come last:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*",      // test data group
      ".*", 5, 3);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                  // test type(s)
      ".*",      // test data group
      ".*", 5, 3);  // 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 <typename T>
void do_test_ellint_f(T& data, const char* type_name, const char* test)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   std::cout << "Testing: " << test << std::endl;

#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
    value_type (*fp2)(value_type, value_type) = boost::math::ellint_1<value_type, value_type>;
#else
    value_type (*fp2)(value_type, value_type) = boost::math::ellint_1;
#endif
    boost::math::tools::test_result<value_type> result;

    result = boost::math::tools::test(
      data,
      bind_func(fp2, 1, 0),
      extract_result(2));
    handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "boost::math::ellint_1", test);

   std::cout << std::endl;

}

template <typename T>
void do_test_ellint_k(T& data, const char* type_name, const char* test)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;
    boost::math::tools::test_result<value_type> result;

   std::cout << "Testing: " << test << std::endl;

#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   value_type (*fp1)(value_type) = boost::math::ellint_1<value_type>;
#else
   value_type (*fp1)(value_type) = boost::math::ellint_1;
#endif
   result = boost::math::tools::test(
      data,
      bind_func(fp1, 0),
      extract_result(1));
   handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "boost::math::ellint_1", test);

   std::cout << std::endl;
}

template <typename T>
void test_spots(T, const char* type_name)
{
    // Function values calculated on http://functions.wolfram.com/
    // Note that Mathematica's EllipticF accepts k^2 as the second parameter.
    #define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
    static const boost::array<boost::array<T, 3>, 19> data1 = {
        SC_(0), SC_(0), SC_(0),
        SC_(-10), SC_(0), SC_(-10),
        SC_(-1), SC_(-1), SC_(-1.2261911708835170708130609674719067527242483502207),
        SC_(-4), SC_(0.875), SC_(-5.3190556182262405182189463092940736859067548232647),
        SC_(8), SC_(-0.625), SC_(9.0419973860310100524448893214394562615252527557062),
        SC_(1e-05), SC_(0.875), SC_(0.000010000000000127604166668510945638036143355898993088),
        SC_(1e+05), SC_(10)/1024, SC_(100002.38431454899771096037307519328741455615271038),
        SC_(1e-20), SC_(1), SC_(1.0000000000000000000000000000000000000000166666667e-20),
        SC_(1e-20), SC_(1e-20), SC_(1.000000000000000e-20),
        SC_(1e+20), SC_(400)/1024, SC_(1.0418143796499216839719289963154558027005142709763e20),
        SC_(1e+50), SC_(0.875), SC_(1.3913251718238765549409892714295358043696028445944e50),
        SC_(2), SC_(0.5), SC_(2.1765877052210673672479877957388515321497888026770),
        SC_(4), SC_(0.5), SC_(4.2543274975235836861894752787874633017836785640477),
        SC_(6), SC_(0.5), SC_(6.4588766202317746302999080620490579800463614807916),
        SC_(10), SC_(0.5), SC_(10.697409951222544858346795279378531495869386960090),
        SC_(-2), SC_(0.5), SC_(-2.1765877052210673672479877957388515321497888026770),
        SC_(-4), SC_(0.5), SC_(-4.2543274975235836861894752787874633017836785640477),
        SC_(-6), SC_(0.5), SC_(-6.4588766202317746302999080620490579800463614807916),
        SC_(-10), SC_(0.5), SC_(-10.697409951222544858346795279378531495869386960090),
    };
    #undef SC_

    do_test_ellint_f(data1, type_name, "Elliptic Integral F: Mathworld Data");

#include "ellint_f_data.ipp"

    do_test_ellint_f(ellint_f_data, type_name, "Elliptic Integral F: Random Data");

    // Function values calculated on http://functions.wolfram.com/
    // Note that Mathematica's EllipticK accepts k^2 as the second parameter.
    #define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
    static const boost::array<boost::array<T, 2>, 9> data2 = {
        SC_(0), SC_(1.5707963267948966192313216916397514420985846996876),
        SC_(0.125), SC_(1.5769867712158131421244030532288080803822271060839),
        SC_(0.25), SC_(1.5962422221317835101489690714979498795055744578951),
        SC_(300)/1024, SC_(1.6062331054696636704261124078746600894998873503208),
        SC_(400)/1024, SC_(1.6364782007562008756208066125715722889067992997614),
        SC_(-0.5), SC_(1.6857503548125960428712036577990769895008008941411),
        SC_(-0.75), SC_(1.9109897807518291965531482187613425592531451316788),
        1-SC_(1)/8, SC_(2.185488469278223686913080323730158689730428415766),
        1-SC_(1)/1024, SC_(4.5074135978990422666372495313621124487894807327687),
    };
    #undef SC_

    do_test_ellint_k(data2, type_name, "Elliptic Integral K: Mathworld Data");

#include "ellint_k_data.ipp"

    do_test_ellint_k(ellint_k_data, type_name, "Elliptic Integral K: Random Data");
}

int test_main(int, char* [])
{
    expected_results();
    BOOST_MATH_CONTROL_FP;

    test_spots(0.0F, "float");
    test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
    test_spots(0.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
    test_spots(boost::math::concepts::real_concept(0), "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;
}