ceph/src/boost/libs/math/test/test_ellint_1.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 #ifdef _MSC_VER
   8 #  pragma warning(disable : 4756) // overflow in constant arithmetic
   9 // Constants are too big for float case, but this doesn't matter for test.
  10 #endif
  11
  12 #include <boost/math/concepts/real_concept.hpp>
  13 #define BOOST_TEST_MAIN
  14 #include <boost/test/unit_test.hpp>
  15 #include <boost/test/tools/floating_point_comparison.hpp>
  16 #include <boost/math/special_functions/math_fwd.hpp>
  17 #include <boost/array.hpp>
  18 #include "functor.hpp"
  19
  20 #include "handle_test_result.hpp"
  21 #include "table_type.hpp"
  22
  23 #ifndef SC_
  24 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  25 #endif
  26
  27 template <class Real, typename T>
  28 void do_test_ellint_f(T& data, const char* type_name, const char* test)
  29 {
  30 #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_1_FUNCTION_TO_TEST))
  31    typedef Real                   value_type;
  32
  33    std::cout << "Testing: " << test << std::endl;
  34
  35 #ifdef ELLINT_1_FUNCTION_TO_TEST
  36    value_type(*fp2)(value_type, value_type) = ELLINT_1_FUNCTION_TO_TEST;
  37 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  38     value_type (*fp2)(value_type, value_type) = boost::math::ellint_1<value_type, value_type>;
  39 #else
  40     value_type (*fp2)(value_type, value_type) = boost::math::ellint_1;
  41 #endif
  42     boost::math::tools::test_result<value_type> result;
  43
  44     result = boost::math::tools::test_hetero<Real>(
  45       data,
  46       bind_func<Real>(fp2, 1, 0),
  47       extract_result<Real>(2));
  48     handle_test_result(result, data[result.worst()], result.worst(),
  49       type_name, "ellint_1", test);
  50
  51    std::cout << std::endl;
  52 #endif
  53 }
  54
  55 template <class Real, typename T>
  56 void do_test_ellint_k(T& data, const char* type_name, const char* test)
  57 {
  58 #if !(defined(ERROR_REPORTING_MODE) && !defined(ELLINT_1C_FUNCTION_TO_TEST))
  59    typedef Real                   value_type;
  60     boost::math::tools::test_result<value_type> result;
  61
  62    std::cout << "Testing: " << test << std::endl;
  63
  64 #ifdef ELLINT_1C_FUNCTION_TO_TEST
  65    value_type(*fp1)(value_type) = ELLINT_1C_FUNCTION_TO_TEST;
  66 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  67    value_type (*fp1)(value_type) = boost::math::ellint_1<value_type>;
  68 #else
  69    value_type (*fp1)(value_type) = boost::math::ellint_1;
  70 #endif
  71    result = boost::math::tools::test_hetero<Real>(
  72       data,
  73       bind_func<Real>(fp1, 0),
  74       extract_result<Real>(1));
  75    handle_test_result(result, data[result.worst()], result.worst(),
  76       type_name, "ellint_1 (complete)", test);
  77
  78    std::cout << std::endl;
  79 #endif
  80 }
  81
  82 template <typename T>
  83 void test_spots(T, const char* type_name)
  84 {
  85     // Function values calculated on http://functions.wolfram.com/
  86     // Note that Mathematica's EllipticF accepts k^2 as the second parameter.
  87     static const boost::array<boost::array<typename table_type<T>::type, 3>, 22> data1 = {{
  88         {{ SC_(0.0), SC_(0.0), SC_(0.0) }},
  89         {{ SC_(-10.0), SC_(0.0), SC_(-10.0) }},
  90         {{ SC_(-1.0), SC_(-1.0), SC_(-1.2261911708835170708130609674719067527242483502207) }},
  91         {{ SC_(-4.0), SC_(0.875), SC_(-5.3190556182262405182189463092940736859067548232647) }},
  92         {{ SC_(8.0), SC_(-0.625), SC_(9.0419973860310100524448893214394562615252527557062) }},
  93         {{ SC_(1e-05), SC_(0.875), SC_(0.000010000000000127604166668510945638036143355898993088) }},
  94         {{ SC_(1e+05), SC_(0.009765625) /*T(10)/1024*/, SC_(100002.38431454899771096037307519328741455615271038) }},
  95         {{ SC_(1e-20), SC_(1.0), SC_(1.0000000000000000000000000000000000000000166666667e-20) }},
  96         {{ SC_(1e-20), SC_(1e-20), SC_(1.000000000000000e-20) }},
  97         {{ SC_(1e+20), SC_(0.390625) /*T(400)/1024*/, SC_(1.0418143796499216839719289963154558027005142709763e20) }},
  98         {{ SC_(1e+50), SC_(0.875), SC_(1.3913251718238765549409892714295358043696028445944e50) }},
  99         {{ SC_(2.0), SC_(0.5), SC_(2.1765877052210673672479877957388515321497888026770) }},
 100         {{ SC_(4.0), SC_(0.5), SC_(4.2543274975235836861894752787874633017836785640477) }},
 101         {{ SC_(6.0), SC_(0.5), SC_(6.4588766202317746302999080620490579800463614807916) }},
 102         {{ SC_(10.0), SC_(0.5), SC_(10.697409951222544858346795279378531495869386960090) }},
 103         {{ SC_(-2.0), SC_(0.5), SC_(-2.1765877052210673672479877957388515321497888026770) }},
 104         {{ SC_(-4.0), SC_(0.5), SC_(-4.2543274975235836861894752787874633017836785640477) }},
 105         {{ SC_(-6.0), SC_(0.5), SC_(-6.4588766202317746302999080620490579800463614807916) }},
 106         {{ SC_(-10.0), SC_(0.5), SC_(-10.697409951222544858346795279378531495869386960090) }},
 107         // Some values where k is > 1:
 108         {{ SC_(0.1538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538), SC_(1.1538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538), SC_(0.154661869446904722070471580919758948531148566762183486996920)}},
 109         {{ SC_(0.1538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538), SC_(1.461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461), SC_(0.155166467455029577314314021156113481657713115640002027219)}},
 110         {{ SC_(0.1538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538), SC_(2.461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461538461), SC_(0.15776272074094290829870142225970052217542486917945444918)}},
 111     }};
 112
 113     do_test_ellint_f<T>(data1, type_name, "Elliptic Integral F: Mathworld Data");
 114
 115 #include "ellint_f_data.ipp"
 116
 117     do_test_ellint_f<T>(ellint_f_data, type_name, "Elliptic Integral F: Random Data");
 118
 119     // Function values calculated on http://functions.wolfram.com/
 120     // Note that Mathematica's EllipticK accepts k^2 as the second parameter.
 121     static const boost::array<boost::array<typename table_type<T>::type, 2>, 9> data2 = {{
 122         {{ SC_(0.0), SC_(1.5707963267948966192313216916397514420985846996876) }},
 123         {{ SC_(0.125), SC_(1.5769867712158131421244030532288080803822271060839) }},
 124         {{ SC_(0.25), SC_(1.5962422221317835101489690714979498795055744578951) }},
 125         {{ SC_(0.29296875) /*T(300)/1024*/, SC_(1.6062331054696636704261124078746600894998873503208) }},
 126         {{ SC_(0.390625) /*T(400)/1024*/, SC_(1.6364782007562008756208066125715722889067992997614) }},
 127         {{ SC_(-0.5), SC_(1.6857503548125960428712036577990769895008008941411) }},
 128         {{ SC_(-0.75), SC_(1.9109897807518291965531482187613425592531451316788) }},
 129         {{ SC_(0.875) /*1-T(1)/8*/, SC_(2.185488469278223686913080323730158689730428415766) }},
 130         {{ SC_(0.9990234375) /*1-T(1)/1024*/, SC_(4.5074135978990422666372495313621124487894807327687) }},
 131     }};
 132
 133     do_test_ellint_k<T>(data2, type_name, "Elliptic Integral K: Mathworld Data");
 134
 135 #include "ellint_k_data.ipp"
 136
 137     do_test_ellint_k<T>(ellint_k_data, type_name, "Elliptic Integral K: Random Data");
 138
 139     //
 140     // Test error handling:
 141     //
 142     BOOST_CHECK_GE(boost::math::ellint_1(T(1)), boost::math::tools::max_value<T>());
 143     BOOST_CHECK_GE(boost::math::ellint_1(T(-1)), boost::math::tools::max_value<T>());
 144     BOOST_CHECK_THROW(boost::math::ellint_1(T(1.0001)), std::domain_error);
 145     BOOST_CHECK_THROW(boost::math::ellint_1(T(-1.0001)), std::domain_error);
 146     BOOST_CHECK_THROW(boost::math::ellint_1(T(2.2), T(0.5)), std::domain_error);
 147     BOOST_CHECK_THROW(boost::math::ellint_1(T(-2.2), T(0.5)), std::domain_error);
 148 }
 149