// 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)

#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>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
#include "table_type.hpp"

#ifndef SC_
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#endif


template <class Real, typename T>
void do_test_ellint_pi3(T& data, const char* type_name, const char* test)
{
   typedef Real                   value_type;

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

#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
    value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3<value_type, value_type, value_type>;
#else
    value_type (*fp2)(value_type, value_type, value_type) = boost::math::ellint_3;
#endif
    boost::math::tools::test_result<value_type> result;

    result = boost::math::tools::test_hetero<Real>(
      data,
      bind_func<Real>(fp2, 2, 0, 1),
      extract_result<Real>(3));
   handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "boost::math::ellint_3", test);

   std::cout << std::endl;

}

template <class Real, typename T>
void do_test_ellint_pi2(T& data, const char* type_name, const char* test)
{
   typedef Real                   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_3<value_type, value_type>;
#else
    value_type (*fp2)(value_type, value_type) = boost::math::ellint_3;
#endif
    boost::math::tools::test_result<value_type> result;

    result = boost::math::tools::test_hetero<Real>(
      data,
      bind_func<Real>(fp2, 1, 0),
      extract_result<Real>(2));
   handle_test_result(result, data[result.worst()], result.worst(),
      type_name, "boost::math::ellint_3", test);

   std::cout << std::endl;

}

template <typename T>
void test_spots(T, const char* type_name)
{
    // function values calculated on http://functions.wolfram.com/
    static const boost::array<boost::array<T, 4>, 25> data1 = {{
        {{ SC_(1), SC_(-1), SC_(0), SC_(-1.557407724654902230506974807458360173087) }},
        {{ SC_(0), SC_(-4), SC_(0.4), SC_(-4.153623371196831087495427530365430979011) }},
        {{ SC_(0), SC_(8), SC_(-0.6), SC_(8.935930619078575123490612395578518914416) }},
        {{ SC_(0), SC_(0.5), SC_(0.25), SC_(0.501246705365439492445236118603525029757890291780157969500480) }},
        {{ SC_(0), SC_(0.5), SC_(0), SC_(0.5) }},
        {{ SC_(-2), SC_(0.5), SC_(0), SC_(0.437501067017546278595664813509803743009132067629603474488486) }},
        {{ SC_(0.25), SC_(0.5), SC_(0), SC_(0.510269830229213412212501938035914557628394166585442994564135) }},
        {{ SC_(0.75), SC_(0.5), SC_(0), SC_(0.533293253875952645421201146925578536430596894471541312806165) }},
        {{ SC_(0.75), SC_(0.75), SC_(0), SC_(0.871827580412760575085768367421866079353646112288567703061975) }},
        {{ SC_(1), SC_(0.25), SC_(0), SC_(0.255341921221036266504482236490473678204201638800822621740476) }},
        {{ SC_(2), SC_(0.25), SC_(0), SC_(0.261119051639220165094943572468224137699644963125853641716219) }},
        {{ T(1023)/1024, SC_(1.5), SC_(0), SC_(13.2821612239764190363647953338544569682942329604483733197131) }},
        {{ SC_(0.5), SC_(-1), SC_(0.5), SC_(-1.228014414316220642611298946293865487807) }},
        {{ SC_(0.5), SC_(1e+10), SC_(0.5), SC_(1.536591003599172091573590441336982730551e+10) }},
        {{ SC_(-1e+05), SC_(10), SC_(0.75), SC_(0.0347926099493147087821620459290460547131012904008557007934290) }},
        {{ SC_(-1e+10), SC_(10), SC_(0.875), SC_(0.000109956202759561502329123384755016959364346382187364656768212) }},
        {{ SC_(-1e+10), SC_(1e+20), SC_(0.875), SC_(1.00000626665567332602765201107198822183913978895904937646809e15) }},
        {{ SC_(-1e+10), T(1608)/1024, SC_(0.875), SC_(0.0000157080616044072676127333183571107873332593142625043567690379) }},
        {{ 1-T(1) / 1024, SC_(1e+20), SC_(0.875), SC_(6.43274293944380717581167058274600202023334985100499739678963e21) }},
        {{ SC_(50), SC_(0.125), SC_(0.25), SC_(0.196321043776719739372196642514913879497104766409504746018939) }},
        {{ SC_(1.125), SC_(1), SC_(0.25), SC_(1.77299767784815770192352979665283069318388205110727241629752) }},
        {{ SC_(1.125), SC_(10), SC_(0.25), SC_(0.662467818678976949597336360256848770217429434745967677192487) }},
        {{ SC_(1.125), SC_(3), SC_(0.25), SC_(-0.142697285116693775525461312178015106079842313950476205580178) }},
        {{ T(257)/256, SC_(1.5), SC_(0.125), SC_(22.2699300473528164111357290313578126108398839810535700884237) }},
        {{ T(257)/256, SC_(21.5), SC_(0.125), SC_(-0.535406081652313940727588125663856894154526187713506526799429) }},
    }};

    do_test_ellint_pi3<T>(data1, type_name, "Elliptic Integral PI: Mathworld Data");

#include "ellint_pi3_data.ipp"

    do_test_ellint_pi3<T>(ellint_pi3_data, type_name, "Elliptic Integral PI: Random Data");

#include "ellint_pi3_large_data.ipp"

    do_test_ellint_pi3<T>(ellint_pi3_large_data, type_name, "Elliptic Integral PI: Large Random Data");

    // function values calculated on http://functions.wolfram.com/
    static const boost::array<boost::array<T, 3>, 9> data2 = {{
        {{ SC_(0), SC_(0.2), SC_(1.586867847454166237308008033828114192951) }},
        {{ SC_(0), SC_(0.4), SC_(1.639999865864511206865258329748601457626) }},
        {{ SC_(0), SC_(0), SC_(1.57079632679489661923132169163975144209858469968755291048747) }},
        {{ SC_(0.5), SC_(0), SC_(2.221441469079183123507940495030346849307) }},
        {{ SC_(-4), SC_(0.3), SC_(0.712708870925620061597924858162260293305195624270730660081949) }},
        {{ SC_(-1e+05), SC_(-0.5), SC_(0.00496944596485066055800109163256108604615568144080386919012831) }},
        {{ SC_(-1e+10), SC_(-0.75), SC_(0.0000157080225184890546939710019277357161497407143903832703317801) }},
        {{ T(1) / 1024, SC_(-0.875), SC_(2.18674503176462374414944618968850352696579451638002110619287) }},
        {{ T(1023)/1024, SC_(-0.875), SC_(101.045289804941384100960063898569538919135722087486350366997) }},
    }};

    do_test_ellint_pi2<T>(data2, type_name, "Complete Elliptic Integral PI: Mathworld Data");

#include "ellint_pi2_data.ipp"

    do_test_ellint_pi2<T>(ellint_pi2_data, type_name, "Complete Elliptic Integral PI: Random Data");

    // Special cases, exceptions etc:
    BOOST_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1), T(0)), std::domain_error);
    BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(20), T(1.5)), std::domain_error);
    BOOST_CHECK_THROW(boost::math::ellint_3(T(1.0001), T(-1)), std::domain_error);
    BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(1)), std::domain_error);
    BOOST_CHECK_THROW(boost::math::ellint_3(T(0.5), T(2)), std::domain_error);
}