ceph/src/boost/libs/math/test/test_bernoulli_constants.cpp

   1 //  (C) Copyright John Maddock 2013.
   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_TEST_MAIN
   7 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
   8
   9 #include <boost/test/unit_test.hpp>
  10 #include <boost/math/concepts/real_concept.hpp>
  11 #include <boost/math/special_functions/bernoulli.hpp>
  12 #include <libs/math/test/table_type.hpp>
  13 #include <boost/math/tools/test.hpp>
  14 #include <iostream>
  15 #include <iomanip>
  16
  17 #define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  18
  19 template <class T>
  20 void test(const char* name)
  21 {
  22    std::cout << "Testing type " << name << ":\n";
  23
  24    static const typename table_type<T>::type data[] =
  25    {
  26       /* First 50 from 2 to 100 inclusive: */
  27       /* TABLE[N[BernoulliB[n], 200], {n,2,100,2}] */
  28
  29       SC_(0.1666666666666666666666666666666666666666),
  30       SC_(-0.0333333333333333333333333333333333333333),
  31       SC_(0.0238095238095238095238095238095238095238),
  32       SC_(-0.0333333333333333333333333333333333333333),
  33       SC_(0.0757575757575757575757575757575757575757),
  34       SC_(-0.2531135531135531135531135531135531135531),
  35       SC_(1.1666666666666666666666666666666666666666),
  36       SC_(-7.0921568627450980392156862745098039215686),
  37       SC_(54.9711779448621553884711779448621553884711),
  38       SC_(-529.1242424242424242424242424242424242424242),
  39       SC_(6192.1231884057971014492753623188405797101449),
  40       SC_(-86580.2531135531135531135531135531135531135531),
  41       SC_(1.4255171666666666666666666666666666666666e6),
  42       SC_(-2.7298231067816091954022988505747126436781e7),
  43       SC_(6.0158087390064236838430386817483591677140e8),
  44       SC_(-1.5116315767092156862745098039215686274509e10),
  45       SC_(4.2961464306116666666666666666666666666666e11),
  46       SC_(-1.3711655205088332772159087948561632772159e13),
  47       SC_(4.8833231897359316666666666666666666666666e14),
  48       SC_(-1.9296579341940068148632668144863266814486e16),
  49       SC_(8.4169304757368261500055370985603543743078e17),
  50       SC_(-4.0338071854059455413076811594202898550724e19),
  51       SC_(2.1150748638081991605601453900709219858156e21),
  52       SC_(-1.2086626522296525934602731193708252531781e23),
  53       SC_(7.5008667460769643668557200757575757575757e24),
  54       SC_(-5.0387781014810689141378930305220125786163e26),
  55       SC_(3.6528776484818123335110430842971177944862e28),
  56       SC_(-2.8498769302450882226269146432910678160919e30),
  57       SC_(2.3865427499683627644645981919219214971751e32),
  58       SC_(-2.1399949257225333665810744765191097392674e34),
  59       SC_(2.0500975723478097569921733095672310251666e36),
  60       SC_(-2.0938005911346378409095185290027970184709e38),
  61       SC_(2.2752696488463515559649260352769264581469e40),
  62       SC_(-2.6257710286239576047303049736158202081449e42),
  63       SC_(3.2125082102718032518204792304264985243521e44),
  64       SC_(-4.1598278166794710913917074495262358936689e46),
  65       SC_(5.6920695482035280023883456219121058644480e48),
  66       SC_(-8.2183629419784575692290653468617333014550e50),
  67       SC_(1.2502904327166993016732339829702895524177e53),
  68       SC_(-2.0015583233248370274925329198813298768724e55),
  69       SC_(3.3674982915364374233396676903338753016219e57),
  70       SC_(-5.9470970503135447718660496844051540840579e59),
  71       SC_(1.1011910323627977559564130790437691604630e62),
  72       SC_(-2.1355259545253501188658385019041065678973e64),
  73       SC_(4.3328896986641192419616613059379206218451e66),
  74       SC_(-9.1885528241669328226200555215501897138960e68),
  75       SC_(2.0346896776329074493455027990220020065975e71),
  76       SC_(-4.7003833958035731078575255535006060654596e73),
  77       SC_(1.1318043445484249270675186257733934267890e76),
  78       SC_(-2.8382249570693706959264156336481764738284e78),
  79
  80       /* next 50 from 102 to 200: */
  81       /* TABLE[N[BernoulliB[n], 200], {n,102,200,2}] */
  82
  83       SC_(7.4064248979678850629750827140920984176879e80),
  84       SC_(-2.0096454802756604483465619672715363186867e83),
  85       SC_(5.6657170050805941445719346030519356961419e85),
  86       SC_(-1.6584511154136216915823713374319912301494e88),
  87       SC_(5.0368859950492377419289421915180154812442e90),
  88       SC_(-1.5861468237658186369363401572966438782740e93),
  89       SC_(5.1756743617545626984073240682507122561240e95),
  90       SC_(-1.7488921840217117339690025877618159145141e98),
  91       SC_(6.1160519994952185255824525264264167780767e100),
  92       SC_(-2.2122776912707834942288323456712932445573e103),
  93       SC_(8.2722776798770969854221062459984595731204e105),
  94       SC_(-3.1958925111415709583591634369180814873526e108),
  95       SC_(1.2750082223387792982310024302926679866957e111),
  96       SC_(-5.2500923086774133899402824624565175446919e113),
  97       SC_(2.2301817894241625209869298198838728143738e116),
  98       SC_(-9.7684521930955204438633513398980239301166e118),
  99       SC_(4.4098361978452954272272622874813169191875e121),
 100       SC_(-2.0508570886464088839729337727583015486456e124),
 101       SC_(9.8214433279791277107572969602097521041491e126),
 102       SC_(-4.8412600798208880508789196709963412761130e129),
 103       SC_(2.4553088801480982609783467404088690399673e132),
 104       SC_(-1.2806926804084747548782513278601785721811e135),
 105       SC_(6.8676167104668581192101888598464400436092e137),
 106       SC_(-3.7846468581969104694978995416379556814489e140),
 107       SC_(2.1426101250665291550871323135148272096660e143),
 108       SC_(-1.2456727137183695007019642961637607219458e146),
 109       SC_(7.4345787551000152543679668394052061311780e148),
 110       SC_(-4.5535795304641704894063333223321274876772e151),
 111       SC_(2.8612112816858868345363847251017232522918e154),
 112       SC_(-1.8437723552033869727688202653628785487541e157),
 113       SC_(1.2181154536221046699501316506599521355817e160),
 114       SC_(-8.2482187185314121548481845729689344730141e162),
 115       SC_(5.7225877937832943329651649814297861591868e165),
 116       SC_(-4.0668530525059104726767969383115865560219e168),
 117       SC_(2.9596092064642050062875269581585187042637e171),
 118       SC_(-2.2049522565189457509031175227344598483637e174),
 119       SC_(1.6812597072889599805831152515136066575446e177),
 120       SC_(-1.3116736213556957648645280635581715300443e180),
 121       SC_(1.0467894009478038082183285392982308964382e183),
 122       SC_(-8.5432893578833707718598254629908277459327e185),
 123       SC_(7.1287821322486542352288406677143822472124e188),
 124       SC_(-6.0802931455535899300084711868647745846198e191),
 125       SC_(5.2996776424849923930094291004324726622848e194),
 126       SC_(-4.7194259168745862644364622901337991110376e197),
 127       SC_(4.2928413791402981089416829654107466904552e200),
 128       SC_(-3.9876744968232207443447765554293879510665e203),
 129       SC_(3.7819780419358882713894418116139332789822e206),
 130       SC_(-3.6614233683681191243685808215119734875519e209),
 131       SC_(3.6176090272372862348855460929891408947754e212),
 132       SC_(-3.6470772645191354362138308865549944904868e215),
 133    };
 134
 135    T tol = boost::math::tools::epsilon<T>() * 20;
 136    for(unsigned i = 1; i <= 100; ++i)
 137    {
 138       T b2n = boost::math::bernoulli_b2n<T>(i);
 139       T t2n = boost::math::tangent_t2n<T>(i);
 140       if((boost::math::isinf)(b2n))
 141       {
 142          if(!(boost::math::isinf)(data[i - 1]))
 143          {
 144             std::cout << "When calculating B2N(" << i << ")\n";
 145             BOOST_ERROR("Got an infinity when one wasn't expected");
 146          }
 147          else if((b2n > 0) != (data[i - 1] > 0))
 148          {
 149             std::cout << "When calculating B2N(" << i << ")\n";
 150             BOOST_ERROR("Sign of infinity was incorrect");
 151          }
 152       }
 153       else if((boost::math::isnan)(b2n))
 154       {
 155          std::cout << "When calculating B2N(" << i << ")\n";
 156          BOOST_ERROR("Result of B2n was a NaN, and that should never happen!");
 157       }
 158       else
 159       {
 160          BOOST_CHECK_CLOSE_FRACTION(b2n, data[i - 1], tol);
 161       }
 162       if(i <= boost::math::max_bernoulli_b2n<T>::value)
 163       {
 164          BOOST_CHECK_EQUAL(b2n, boost::math::unchecked_bernoulli_b2n<T>(i));
 165       }
 166       if((boost::math::isfinite)(t2n) && (t2n < boost::math::tools::max_value<T>()))
 167       {
 168          T p = ldexp(T(1), 2 * i);
 169          int s = i & 1 ? 1 : -1;
 170          p = t2n / (s * p * (p - 1));
 171          p *= 2 * i;
 172          BOOST_CHECK_CLOSE_FRACTION(p, b2n, tol);
 173       }
 174    }
 175    //
 176    // Test consistency of array interface:
 177    //
 178    T bn[boost::math::max_bernoulli_b2n<T>::value + 20];
 179    boost::math::bernoulli_b2n<T>(0, boost::math::max_bernoulli_b2n<T>::value + 20, bn);
 180
 181    for(unsigned i = 0; i < boost::math::max_bernoulli_b2n<T>::value + 20; ++i)
 182    {
 183       BOOST_CHECK_EQUAL(bn[i], boost::math::bernoulli_b2n<T>(i));
 184    }
 185
 186    boost::math::tangent_t2n<T>(0, boost::math::max_bernoulli_b2n<T>::value + 20, bn);
 187
 188    for(unsigned i = 0; i < boost::math::max_bernoulli_b2n<T>::value + 20; ++i)
 189    {
 190       BOOST_CHECK_EQUAL(bn[i], boost::math::tangent_t2n<T>(i));
 191    }
 192    //
 193    // Some spot tests for things that should throw exceptions:
 194    //
 195    static unsigned overflow_index = boost::is_same<T, boost::math::concepts::real_concept>::value ?
 196       boost::math::max_bernoulli_b2n<long double>::value + 5 : boost::math::max_bernoulli_b2n<T>::value + 5;
 197 #ifndef BOOST_NO_EXCEPTIONS
 198    BOOST_MATH_CHECK_THROW(boost::math::bernoulli_b2n<T>(overflow_index, boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::throw_on_error>())), std::overflow_error);
 199    BOOST_MATH_CHECK_THROW(boost::math::tangent_t2n<T>(overflow_index, boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::throw_on_error>())), std::overflow_error);
 200 #endif
 201 }
 202
 203 void test_real_concept_extra()
 204 {
 205    boost::math::concepts::real_concept tol = boost::math::tools::epsilon<boost::math::concepts::real_concept>() * 20;
 206    for(unsigned i = 0; i <= boost::math::max_bernoulli_b2n<long double>::value; ++i)
 207    {
 208       BOOST_CHECK_CLOSE_FRACTION(static_cast<boost::math::concepts::real_concept>(boost::math::bernoulli_b2n<long double>(i)), boost::math::bernoulli_b2n<boost::math::concepts::real_concept>(i), tol);
 209    }
 210    for(unsigned i = 1; i < 500; ++i)
 211    {
 212       boost::math::concepts::real_concept r = boost::math::bernoulli_b2n<long double>(i + boost::math::max_bernoulli_b2n<long double>::value);
 213       if((i + boost::math::max_bernoulli_b2n<long double>::value) & 1)
 214       {
 215          BOOST_CHECK(r >= boost::math::tools::max_value<boost::math::concepts::real_concept>());
 216       }
 217       else
 218       {
 219          BOOST_CHECK(r <= -boost::math::tools::max_value<boost::math::concepts::real_concept>());
 220       }
 221    }
 222 }
 223
 224
 225 BOOST_AUTO_TEST_CASE( test_main )
 226 {
 227    test<float>("float");
 228    test<double>("double");
 229 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 230    test<long double>("long double");
 231    test<boost::math::concepts::real_concept>("real_concept");
 232    test_real_concept_extra();
 233 #endif
 234 }
 235
 236