ceph/src/boost/libs/math/test/test_bessel_i_prime.hpp

   1 //  Copyright (c) 2013 Anton Bikineev
   2 //  Use, modification and distribution are subject to the
   3 //  Boost Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   5
   6 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
   7 #include <boost/math/concepts/real_concept.hpp>
   8 #define BOOST_TEST_MAIN
   9 #include <boost/test/unit_test.hpp>
  10 #include <boost/test/tools/floating_point_comparison.hpp>
  11 #include <boost/math/special_functions/math_fwd.hpp>
  12 #include <boost/type_traits/is_floating_point.hpp>
  13 #include <boost/array.hpp>
  14 #include "functor.hpp"
  15
  16 #include "handle_test_result.hpp"
  17 #include "table_type.hpp"
  18
  19 #ifndef SC_
  20 #  define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  21 #endif
  22
  23 template <class T>
  24 T cyl_bessel_i_prime_int_wrapper(T v, T x)
  25 {
  26 #ifdef BESSEL_IPN_FUNCTION_TO_TEST
  27    return static_cast<T>(
  28       BESSEL_IPN_FUNCTION_TO_TEST(
  29       boost::math::itrunc(v), x));
  30 #else
  31    return static_cast<T>(
  32       boost::math::cyl_bessel_i_prime(
  33       boost::math::itrunc(v), x));
  34 #endif
  35 }
  36
  37 template <class Real, class T>
  38 void do_test_cyl_bessel_i_prime(const T& data, const char* type_name, const char* test_name)
  39 {
  40 #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_IP_FUNCTION_TO_TEST))
  41    typedef Real                   value_type;
  42
  43    typedef value_type (*pg)(value_type, value_type);
  44 #ifdef BESSEL_IP_FUNCTION_TO_TEST
  45    pg funcp = BESSEL_IP_FUNCTION_TO_TEST;
  46 #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  47    pg funcp = boost::math::cyl_bessel_i_prime<value_type, value_type>;
  48 #else
  49    pg funcp = boost::math::cyl_bessel_i_prime;
  50 #endif
  51
  52    boost::math::tools::test_result<value_type> result;
  53
  54    std::cout << "Testing " << test_name << " with type " << type_name
  55       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  56
  57    //
  58    // test cyl_bessel_i_prime against data:
  59    //
  60    result = boost::math::tools::test_hetero<Real>(
  61       data,
  62       bind_func<Real>(funcp, 0, 1),
  63       extract_result<Real>(2));
  64    handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_i_prime", test_name);
  65    std::cout << std::endl;
  66 #endif
  67 }
  68
  69 template <class Real, class T>
  70 void do_test_cyl_bessel_i_prime_int(const T& data, const char* type_name, const char* test_name)
  71 {
  72 #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_IPN_FUNCTION_TO_TEST))
  73    typedef Real                   value_type;
  74
  75    typedef value_type (*pg)(value_type, value_type);
  76 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
  77    pg funcp = cyl_bessel_i_prime_int_wrapper<value_type>;
  78 #else
  79    pg funcp = cyl_bessel_i_prime_int_wrapper;
  80 #endif
  81
  82    boost::math::tools::test_result<value_type> result;
  83
  84    std::cout << "Testing " << test_name << " with type " << type_name
  85       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  86
  87    //
  88    // test cyl_bessel_i_prime against data:
  89    //
  90    result = boost::math::tools::test_hetero<Real>(
  91       data,
  92       bind_func<Real>(funcp, 0, 1),
  93       extract_result<Real>(2));
  94    handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_i_prime (integer orders)", test_name);
  95    std::cout << std::endl;
  96 #endif
  97 }
  98
  99 template <class T>
 100 void test_bessel(T, const char* name)
 101 {
 102     BOOST_MATH_STD_USING
 103     // function values calculated on wolframalpha.com
 104     static const boost::array<boost::array<T, 3>, 10> i0_prime_data = {{
 105         {{ SC_(0.0), SC_(0.0), SC_(0.0) }},
 106         {{ SC_(0.0), SC_(1.0), SC_(0.565159103992485027207696027609863307328899621621) }},
 107         {{ SC_(0.0), SC_(-2.0), SC_(-1.590636854637329063382254424999666247954478159496) }},
 108         {{ SC_(0.0), SC_(4.0), SC_(9.75946515370444990947519256731268090005597033325) }},
 109         {{ SC_(0.0), SC_(-7.0), SC_(-156.039092869955453462390580660711155630031052042) }},
 110         {{ SC_(0.0), T(1) / 1024, SC_(0.000488281308207663226432087816784315537514225208473395) }},
 111         {{ SC_(0.0), T(SC_(1.0)) / (1024*1024), SC_(4.76837158203179210108624277276025646653133998635957e-7) }},
 112         {{ SC_(0.0), SC_(-1.0), SC_(-0.565159103992485027207696027609863307328899621621) }},
 113         {{ SC_(0.0), SC_(100.0), SC_(1.068369390338162481206145763224295265446122844056e42) }},
 114         {{ SC_(0.0), SC_(200.0), SC_(2.034581549332062703427427977139069503896611616811e85) }},
 115     }};
 116     static const boost::array<boost::array<T, 3>, 10> i1_prime_data = {{
 117         {{ SC_(1.0), SC_(0.0), SC_(0.5) }},
 118         {{ SC_(1.0), SC_(1.0), SC_(0.700906773759523308390548597604854230278770689734) }},
 119         {{ SC_(1.0), SC_(-2.0), SC_(1.484266875017402735746077228311700229308602023038) }},
 120         {{ SC_(1.0), SC_(4.0), SC_(8.86205566371021801898747204138893227239862401112) }},
 121         {{ SC_(1.0), SC_(-8.0), SC_(377.579973623984772900011405549855040764360549303) }},
 122         {{ SC_(1.0), T(SC_(1.0))/1024, SC_(0.500000178813946168551133736709856567600996119560422) }},
 123         {{ SC_(1.0), T(SC_(1.0))/(1024*1024), SC_(0.500000000000170530256582434815189962442052310320626) }},
 124         {{ SC_(1.0), SC_(-10.0), SC_(2548.6177980961290060357079567493748381638767230173) }},
 125         {{ SC_(1.0), SC_(100.0), SC_(1.063068013227692198707659399971251708633941964885e42) }},
 126         {{ SC_(1.0), SC_(200.0), SC_(2.029514265663064306024535986893764274813192678064e85) }},
 127     }};
 128     static const boost::array<boost::array<T, 3>, 11> in_prime_data = {{
 129         {{ SC_(-2.0), SC_(0.0), SC_(0.0) }},
 130         {{ SC_(2.0), T(SC_(1.0))/(1024*1024), SC_(2.38418579101598640072416185021877537269848820467704e-7) }},
 131         {{ SC_(5.0), SC_(10.0), SC_(837.8963945578616177877239800250165373153505679130) }},
 132         {{ SC_(-5.0), SC_(100.0), SC_(9.434574089052212641696648538570565739509851953166e41) }},
 133         {{ SC_(-5.0), SC_(-1.0), SC_(0.001379804441262006949232714689824343061461150959112) }},
 134         {{ SC_(10.0), SC_(20.0), SC_(3.887291476282816593964936516887942731146400030466e6) }},
 135         {{ SC_(10.0), SC_(-5.0), SC_(-0.0101556299784624552653083645193223022003797137770) }},
 136         {{ SC_(1e+02), SC_(9.0), SC_(3.0600487816519872979909028718737622834061708443e-92) }},
 137         {{ SC_(1e+02), SC_(80.0), SC_(7.43545006374466980237328068214707549314834217923e8) }},
 138         {{ SC_(-100.0), SC_(-200.0), SC_(-4.8578174816088978115191937982677942557681326349558e74) }},
 139         {{ SC_(10.0), SC_(1e-100), SC_(2.6911444554673721340388007054673721340e-909) }},
 140     }};
 141     static const boost::array<boost::array<T, 3>, 10> iv_prime_data = {{
 142         {{ SC_(2.25), T(1)/(1024*1024), SC_(5.5296993766970839641084373853875345330202883e-9) }},
 143         {{ SC_(5.5), SC_(3.125), SC_(0.11607917746126037030394881599790144677553715606) }},
 144         {{ T(-5) + T(1)/1024, SC_(2.125), SC_(0.0001131925559871199041270456478317398625046249903864372470342210384462922281) }},
 145         {{ SC_(-5.5), SC_(10.0), SC_(659.1902595786901927596924259811320437384361101) }},
 146         {{ SC_(-5.5), SC_(100.0), SC_(9.191476042191556775282339209385028823905941708e41) }},
 147         {{ T(-10486074)/(1024*1024), T(1)/1024, SC_(-1.44873720736417608945635957884937466861026978539e39) }},
 148         {{ T(-10486074)/(1024*1024), SC_(50.0), SC_(1.082410021443599516897183930739816215073642812109e20) }},
 149         {{ T(144794)/1024, SC_(100.0), SC_(3575.11008553328328036816705258135747714241715202) }},
 150         {{ T(144794)/1024, SC_(200.0), SC_(2.7358895637426974377937620224627094172800852276956e64) }},
 151         {{ T(-144794)/1024, SC_(100.0), SC_(3575.11008700037933897402396449269857968451879323) }},
 152     }};
 153     static const boost::array<boost::array<T, 3>, 5> iv_prime_large_data = {{
 154         {{ SC_(-1.0), static_cast<T>(ldexp(0.5, -512)), SC_(0.5) }},
 155         {{ SC_(1.0),  static_cast<T>(ldexp(0.5, -512)), SC_(0.5) }},
 156         {{ SC_(1.125),  static_cast<T>(ldexp(0.5, -512)), SC_(2.42025162605150606399395900489934587657244145536315936432966315563638e-20) }},
 157         {{ SC_(0.5), static_cast<T>(ldexp(0.5, -683)), SC_(3.5741154998461284276309443770923823816821202344841143399486401387635e102) }},
 158 #if LDBL_MAX_10_EXP > 326
 159         {{ SC_(-1.125), static_cast<T>(ldexp(0.5, -512)), SC_(4.0715272050947359203430409041001937149343363573066460226173390878707e327) }},
 160 #else
 161         { { SC_(-1.125), static_cast<T>(ldexp(0.5, -512)), std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : boost::math::tools::max_value<T>() } },
 162 #endif
 163     }};
 164
 165     do_test_cyl_bessel_i_prime<T>(i0_prime_data, name, "Bessel I'0: Mathworld Data");
 166     do_test_cyl_bessel_i_prime<T>(i1_prime_data, name, "Bessel I'1: Mathworld Data");
 167     do_test_cyl_bessel_i_prime<T>(in_prime_data, name, "Bessel I'n: Mathworld Data");
 168
 169     do_test_cyl_bessel_i_prime_int<T>(i0_prime_data, name, "Bessel I'0: Mathworld Data (Integer Version)");
 170     do_test_cyl_bessel_i_prime_int<T>(i1_prime_data, name, "Bessel I'1: Mathworld Data (Integer Version)");
 171     do_test_cyl_bessel_i_prime_int<T>(in_prime_data, name, "Bessel I'n: Mathworld Data (Integer Version)");
 172
 173     do_test_cyl_bessel_i_prime<T>(iv_prime_data, name, "Bessel I'v: Mathworld Data");
 174
 175 #include "bessel_i_prime_int_data.ipp"
 176     do_test_cyl_bessel_i_prime<T>(bessel_i_prime_int_data, name, "Bessel I'n: Random Data");
 177 #include "bessel_i_prime_data.ipp"
 178     do_test_cyl_bessel_i_prime<T>(bessel_i_prime_data, name, "Bessel I'v: Random Data");
 179
 180     if(0 != static_cast<T>(ldexp(static_cast<T>(0.5), -700)))
 181       do_test_cyl_bessel_i_prime<T>(iv_prime_large_data, name, "Bessel I'v: Mathworld Data (large values)");
 182 }
 183