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

   1 // test_arcsine_dist.cpp
   2
   3 // Copyright John Maddock 2014.
   4 // Copyright  Paul A. Bristow 2014.
   5
   6 // Use, modification and distribution are subject to the
   7 // Boost Software License, Version 1.0.
   8 // (See accompanying file LICENSE_1_0.txt
   9 // or copy at http://www.boost.org/LICENSE_1_0.txt)
  10
  11 // Tests for the arcsine Distribution.
  12
  13 #include <pch.hpp> // Must be 1st include, and include_directory /libs/math/src/tr1/ is needed.
  14
  15 #ifdef _MSC_VER
  16 #  pragma warning(disable: 4127) // Conditional expression is constant.
  17 #  pragma warning (disable : 4996) // POSIX name for this item is deprecated.
  18 #  pragma warning (disable : 4224) // Nonstandard extension used : formal parameter 'arg' was previously defined as a type.
  19 #endif
  20
  21 #include <boost/math/concepts/real_concept.hpp> // for real_concept.
  22 using ::boost::math::concepts::real_concept;
  23 #include <boost/math/tools/test.hpp> // for real_concept.
  24
  25 #include <boost/math/distributions/arcsine.hpp> // for arcsine_distribution.
  26 using boost::math::arcsine_distribution;
  27
  28 #include <boost/math/constants/constants.hpp>
  29 using boost::math::constants::one_div_root_two;
  30
  31 #define BOOST_TEST_MAIN
  32 #include <boost/test/unit_test.hpp> // for test_main
  33 #include <boost/test/tools/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION
  34
  35 #include <cmath>
  36
  37 #include "test_out_of_range.hpp"
  38
  39 #include <iostream>
  40 using std::cout;
  41 using std::endl;
  42 #include <limits>
  43 using std::numeric_limits;
  44
  45
  46 template <class RealType>
  47 void test_ignore_policy(RealType)
  48 {
  49   // Check on returns when errors are ignored.
  50   if ((typeid(RealType) != typeid(boost::math::concepts::real_concept))
  51     && std::numeric_limits<RealType>::has_infinity
  52     && std::numeric_limits<RealType>::has_quiet_NaN
  53     )
  54   { // Ordinary floats only.
  55
  56     using namespace boost::math;
  57     //   RealType inf = std::numeric_limits<RealType>::infinity();
  58     RealType nan = std::numeric_limits<RealType>::quiet_NaN();
  59
  60     using boost::math::policies::policy;
  61     // Types of error whose action can be altered by policies:.
  62     //using boost::math::policies::evaluation_error;
  63     //using boost::math::policies::domain_error;
  64     //using boost::math::policies::overflow_error;
  65     //using boost::math::policies::underflow_error;
  66     //using boost::math::policies::domain_error;
  67     //using boost::math::policies::pole_error;
  68
  69     //// Actions on error (in enum error_policy_type):
  70     //using boost::math::policies::errno_on_error;
  71     //using boost::math::policies::ignore_error;
  72     //using boost::math::policies::throw_on_error;
  73     //using boost::math::policies::denorm_error;
  74     //using boost::math::policies::pole_error;
  75     //using boost::math::policies::user_error;
  76
  77     typedef policy<
  78       boost::math::policies::domain_error<boost::math::policies::ignore_error>,
  79       boost::math::policies::overflow_error<boost::math::policies::ignore_error>,
  80       boost::math::policies::underflow_error<boost::math::policies::ignore_error>,
  81       boost::math::policies::denorm_error<boost::math::policies::ignore_error>,
  82       boost::math::policies::pole_error<boost::math::policies::ignore_error>,
  83       boost::math::policies::evaluation_error<boost::math::policies::ignore_error>
  84     > ignore_all_policy;
  85
  86     typedef arcsine_distribution<RealType, ignore_all_policy> ignore_error_arcsine;
  87
  88     // Only test NaN and infinity if type has these features (realconcept returns zero).
  89     // Integers are always converted to RealType,
  90     // others requires static cast to RealType from long double.
  91
  92     if (std::numeric_limits<RealType>::has_quiet_NaN)
  93     {
  94       // Demonstrate output of PDF with infinity,
  95       // but strin goutput from NaN is platform dependent, so can't use BOOST_CHECK.
  96       if (std::numeric_limits<RealType>::has_infinity)
  97       {
  98         //std::cout << "pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) = " << pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) << std::endl;
  99         //  Outputs:  pdf(ignore_error_arcsine(-1, +1), std::numeric_limits<RealType>::infinity()) = 1.#QNAN
 100       }
 101       BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity
 102       BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), std::numeric_limits<RealType>::infinity()))); // x == infinity
 103       BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(-2))));  // x < xmin
 104       BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(-2))));  // x < xmin
 105       BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(0, 1), static_cast <RealType>(+2))));  // x > x_max
 106       BOOST_CHECK((boost::math::isnan)(pdf(ignore_error_arcsine(-1, 1), static_cast <RealType>(+2)))); // x > x_max
 107
 108       // Mean
 109       BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-nan, 0))));
 110       BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(+nan, 0))));
 111
 112       if (std::numeric_limits<RealType>::has_infinity)
 113       {
 114         //BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity(), 0))));
 115         // std::cout << "arcsine(-inf,+1) mean " << mean(ignore_error_arcsine(-std::numeric_limits<RealType>::infinity())) << std::endl;
 116         //BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(std::numeric_limits<RealType>::infinity(), 0))));
 117       }
 118
 119       // NaN constructors.
 120       BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(2, nan))));
 121       BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, nan))));
 122       BOOST_CHECK((boost::math::isnan)(mean(ignore_error_arcsine(nan, 2))));
 123
 124       // Variance
 125       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(nan, 0))));
 126       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, nan))));
 127       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, nan))));
 128       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(0, 0))));
 129       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(1, 0))));
 130       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(static_cast<RealType>(1.7L), 0))));
 131       BOOST_CHECK((boost::math::isnan)(variance(ignore_error_arcsine(2, 0))));
 132
 133       // Skewness
 134       BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(nan, 0))));
 135       BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(-1, nan))));
 136       BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(0, 0))));
 137       BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(1, 0))));
 138       BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(2, 0))));
 139       BOOST_CHECK((boost::math::isnan)(skewness(ignore_error_arcsine(3, 0))));
 140
 141       // Kurtosis
 142       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(nan, 0))));
 143       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(-1, nan))));
 144       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(0, 0))));
 145       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(1, 0))));
 146       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(2, 0))));
 147       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0))));
 148       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(3, 0))));
 149       BOOST_CHECK((boost::math::isnan)(kurtosis(ignore_error_arcsine(4, 0))));
 150
 151       // Kurtosis excess
 152       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(nan, 0))));
 153       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(-1, nan))));
 154       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(0, 0))));
 155       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(1, 0))));
 156       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(2, 0))));
 157       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(static_cast<RealType>(2.0001L), 0))));
 158       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(3, 0))));
 159       BOOST_CHECK((boost::math::isnan)(kurtosis_excess(ignore_error_arcsine(4, 0))));
 160     } // has_quiet_NaN
 161
 162     //
 163     BOOST_CHECK(boost::math::isfinite(mean(ignore_error_arcsine(0, std::numeric_limits<RealType>::epsilon()))));
 164
 165     check_support<arcsine_distribution<RealType> >(arcsine_distribution<RealType>(0, 1));
 166   } // ordinary floats.
 167 } // template <class RealType> void test_ignore_policy(RealType)
 168
 169
 170 template <class RealType>
 171 RealType informax()
 172 { //! \return Infinity else max_value.
 173   return ((std::numeric_limits<RealType>::has_infinity) ?
 174      std::numeric_limits<RealType>::infinity() : boost::math::tools::max_value<RealType>());
 175 }
 176
 177 template <class RealType>
 178 void test_spot(
 179   RealType a,    // alpha a or lo or x_min
 180   RealType b,    // arcsine b or hi or x_maz
 181   RealType x,    // Probability
 182   RealType P,    // CDF of arcsine(a, b)
 183   RealType Q,    // Complement of CDF of arcsine (a, b)
 184   RealType tol)  // Test tolerance.
 185 {
 186   boost::math::arcsine_distribution<RealType> anarcsine(a, b);
 187   BOOST_CHECK_CLOSE_FRACTION(cdf(anarcsine, x), P, tol);
 188   if ((P < 0.99) && (Q < 0.99))
 189   { // We can only check this if P is not too close to 1,
 190     // so that we can guarantee that Q is free of error,
 191     // (and similarly for Q).
 192     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(anarcsine, x)), Q, tol);
 193     if (x != 0)
 194     {
 195       BOOST_CHECK_CLOSE_FRACTION(
 196         quantile(anarcsine, P), x, tol);
 197     }
 198     else
 199     {
 200       // Just check quantile is very small:
 201       if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent)
 202         && (boost::is_floating_point<RealType>::value))
 203       {
 204         // Limit where this is checked: if exponent range is very large we may
 205         // run out of iterations in our root finding algorithm.
 206         BOOST_CHECK(quantile(anarcsine, P) < boost::math::tools::epsilon<RealType>() * 10);
 207       }
 208     } // if k
 209     if (x != 0)
 210     {
 211       BOOST_CHECK_CLOSE_FRACTION(quantile(complement(anarcsine, Q)), x, tol * 10);
 212     }
 213     else
 214     {  // Just check quantile is very small:
 215       if ((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
 216       { // Limit where this is checked: if exponent range is very large we may
 217         // run out of iterations in our root finding algorithm.
 218         BOOST_CHECK(quantile(complement(anarcsine, Q)) < boost::math::tools::epsilon<RealType>() * 10);
 219       }
 220     } // if x
 221   }
 222 } // template <class RealType> void test_spot
 223
 224 template <class RealType> // Any floating-point type RealType.
 225 void test_spots(RealType)
 226 {
 227     // Basic sanity checks with 'known good' values.
 228     // so set tolerance to a few eps expressed as a fraction, or
 229     // few eps of type double expressed as a fraction,
 230     // whichever is the larger.
 231
 232     RealType tolerance = (std::max)
 233       (boost::math::tools::epsilon<RealType>(),
 234       static_cast<RealType>(std::numeric_limits<double>::epsilon())); // 0 if real_concept.
 235
 236     tolerance *= 2; // Note: NO * 100 because tolerance is a fraction, NOT %.
 237     cout << "tolerance = " << tolerance << endl;
 238
 239     using boost::math::arcsine_distribution;
 240     using  ::boost::math::cdf;
 241     using  ::boost::math::pdf;
 242     using  ::boost::math::complement;
 243     using  ::boost::math::quantile;
 244
 245     // Basic sanity-check spot values.
 246
 247     // Test values from Wolfram alpha, for example:
 248     // http://www.wolframalpha.com/input/?i=+N%5BPDF%5Barcsinedistribution%5B0%2C+1%5D%2C+0.5%5D%2C+50%5D
 249     // N[PDF[arcsinedistribution[0, 1], 0.5], 50]
 250     // 0.63661977236758134307553505349005744813783858296183
 251
 252     arcsine_distribution<RealType> arcsine_01; // (Our) Standard arcsine.
 253     // Member functions.
 254     BOOST_CHECK_EQUAL(arcsine_01.x_min(), 0);
 255     BOOST_CHECK_EQUAL(arcsine_01.x_max(), 1);
 256
 257     // Derived functions.
 258     BOOST_CHECK_EQUAL(mean(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly.
 259     BOOST_CHECK_EQUAL(median(arcsine_01), 0.5); // 1 / (1 + 1) = 1/2 exactly.
 260     BOOST_CHECK_EQUAL(variance(arcsine_01), 0.125); // 1/8 = 0.125
 261     BOOST_CHECK_CLOSE_FRACTION(standard_deviation(arcsine_01), one_div_root_two<double>() / 2, tolerance); // 1/ sqrt(s) = 0.35355339059327379
 262     BOOST_CHECK_EQUAL(skewness(arcsine_01), 0); //
 263     BOOST_CHECK_EQUAL(kurtosis_excess(arcsine_01), -1.5); // 3/2
 264     BOOST_CHECK_EQUAL(support(arcsine_01).first, 0); //
 265     BOOST_CHECK_EQUAL(range(arcsine_01).first, 0); //
 266     BOOST_MATH_CHECK_THROW(mode(arcsine_01), std::domain_error); //  Two modes at x_min and x_max, so throw instead.
 267
 268     // PDF
 269     // pdf of x = 1/4 is same as reflected value at x = 3/4.
 270     // N[PDF[arcsinedistribution[0, 1], 0.25], 50]
 271     // N[PDF[arcsinedistribution[0, 1], 0.75], 50]
 272     // 0.73510519389572273268176866441729258852984864048885
 273
 274     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000001), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), tolerance);
 275     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.000005), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), tolerance);
 276     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.05), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), tolerance);
 277     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.5), static_cast<RealType>(0.63661977236758134307553505349005744813783858296183L), tolerance);
 278     // Note loss of significance when x is near x_max.
 279     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.95), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 8 * tolerance); // Less accurate.
 280     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.999995), static_cast<RealType>(142.35286456604168061345817902422241622116338936911L), 50000 * tolerance); // Much less accurate.
 281     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, 0.999999), static_cast<RealType>(318.31004533885312973989414360099118178698415543136L), 100000 * tolerance);// Even less accurate.
 282
 283     // Extreme x.
 284     if (std::numeric_limits<RealType>::has_infinity)
 285     { //
 286       BOOST_CHECK_EQUAL(pdf(arcsine_01, 0), informax<RealType>()); //
 287       BOOST_CHECK_EQUAL(pdf(arcsine_01, 1), informax<RealType>()); //
 288     }
 289
 290     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, tolerance),
 291       1 /(sqrt(tolerance) * boost::math::constants::pi<RealType>()), 2 * tolerance); //
 292     BOOST_CHECK_CLOSE_FRACTION(pdf(arcsine_01, static_cast<RealType>(1) - tolerance),
 293       1 /(sqrt(tolerance) * boost::math::constants::pi<RealType>()), 2 * tolerance); //
 294
 295     // CDF
 296     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.000001), static_cast<RealType>(0.00063661987847092448418377367957384866092127786060574L), tolerance);
 297     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.000005), static_cast<RealType>(0.0014235262731079289297302426454125318201831474507326L), tolerance);
 298     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.05), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), tolerance);
 299     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.5), static_cast<RealType>(0.5L), tolerance); // Exact.
 300     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.95), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), 2 * tolerance);
 301     // Values near unity should use the cdf complemented for better accuracy,
 302     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.999995), static_cast<RealType>(0.99857647372689207107026975735458746817981685254927L), 100 * tolerance); // Less accurate.
 303     BOOST_CHECK_CLOSE_FRACTION(cdf(arcsine_01, 0.999999), static_cast<RealType>(0.99936338012152907551581622632042615133907872213939L), 1000 * tolerance); // Less accurate.
 304
 305     //  Complement CDF
 306     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.000001)), static_cast<RealType>(1 - 0.00063661987847092448418377367957384866092127786060574L), 2 * tolerance);
 307     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.000001)), static_cast<RealType>(0.99936338012152907551581622632043L), 2 * tolerance); //
 308     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.05)), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), tolerance);
 309     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.5)), static_cast<RealType>(0.5L), tolerance); // Exact.
 310     // Some values near unity when complement is expected to be less accurate.
 311     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.95)), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), 8 * tolerance); // 2 for asin
 312     BOOST_CHECK_CLOSE_FRACTION(cdf(complement(arcsine_01, 0.999999)), static_cast<RealType>(1 - 0.99936338012152907551581622632042615133907872213939L), 1000000 * tolerance); // 10000 for asin, 1000000 for acos.
 313
 314     // Quantile.
 315
 316     // Check 1st, 2nd and 3rd quartiles.
 317     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.25L)), static_cast<RealType>(0.14644660940672624L), tolerance);
 318     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance);  // probability = 0.5, x = 0.5
 319     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.75L)), static_cast<RealType>(0.85355339059327373L), tolerance);
 320
 321     // N[CDF[arcsinedistribution[0, 1], 0.05], 50]  == 0.14356629312870627075094188477505571882161519989741
 322     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), 0.05, tolerance);
 323
 324     // Quantile of complement.
 325     // N[1-CDF[arcsinedistribution[0, 1], 0.05], 50] == 0.85643370687129372924905811522494428117838480010259
 326     BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L))), 0.05, tolerance * 2);
 327     // N[sin^2[0.75 * pi/2],50] == 0.85355339059327376220042218105242451964241796884424
 328     BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.25L))), static_cast<RealType>(0.85355339059327376220042218105242451964241796884424L), tolerance);
 329     BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.5L))), 0.5, 2 * tolerance);  // probability = 0.5, x = 0.5
 330     BOOST_CHECK_CLOSE_FRACTION(quantile(complement(arcsine_01, static_cast<RealType>(0.75L))), static_cast<RealType>(0.14644660940672623779957781894757548035758203115576L), 2 * tolerance); // Less accurate.
 331
 332     // N[CDF[arcsinedistribution[0, 1], 0.25], 5
 333     // 0.33333333333333333333333333333333333333333333333333
 334     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(1) / 3), static_cast<RealType>(0.25L), 2 * tolerance);
 335     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(0.5L)), 0.5, 2 * tolerance);  // probability = 0.5, x = 0.5
 336     BOOST_CHECK_CLOSE_FRACTION(quantile(arcsine_01, static_cast<RealType>(2) / 3), static_cast<RealType>(0.75L), tolerance);
 337
 338     // Arcsine(-1, +1)    xmin = -1, x_max = +1  symmetric about zero.
 339     arcsine_distribution<RealType> as_m11(-1, +1);
 340
 341     BOOST_CHECK_EQUAL(as_m11.x_min(), -1); //
 342     BOOST_CHECK_EQUAL(as_m11.x_max(), +1);
 343     BOOST_CHECK_EQUAL(mean(as_m11), 0); //
 344     BOOST_CHECK_EQUAL(median(as_m11), 0); //
 345     BOOST_CHECK_CLOSE_FRACTION(standard_deviation(as_m11), one_div_root_two<RealType>(),  tolerance * 2); //
 346
 347     BOOST_CHECK_EQUAL(variance(as_m11), 0.5); // 1 - (-1) = 2 ^ 2 = 4 /8 = 0.5
 348     BOOST_CHECK_EQUAL(skewness(as_m11), 0); //
 349     BOOST_CHECK_EQUAL(kurtosis_excess(as_m11), -1.5); // 3/2
 350
 351
 352     BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.05), static_cast<RealType>(0.31870852113797122803869876869296281629727218095644L), tolerance);
 353     BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.5), static_cast<RealType>(0.36755259694786136634088433220864629426492432024443L), tolerance);
 354     BOOST_CHECK_CLOSE_FRACTION(pdf(as_m11, 0.95), static_cast<RealType>(1.0194074882503562519812229448639426942621591013381L), 2 * tolerance); // Less accurate.
 355
 356     BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.05), static_cast<RealType>(0.51592213323666034437274347433261364289389772737836L), tolerance);
 357     BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.5), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), 2 * tolerance);
 358     BOOST_CHECK_CLOSE_FRACTION(cdf(as_m11, 0.95), static_cast<RealType>(0.89891737589574013042121018491729701360300248368629L), tolerance); //  Not less accurate.
 359
 360     // Quantile
 361     BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(1) / 3), -static_cast<RealType>(0.5L), 2 * tolerance); // p = 1/3 x = -0.5
 362     BOOST_CHECK_SMALL(quantile(as_m11, static_cast<RealType>(0.5L)), 2 * tolerance);                             // p = 0.5, x = 0
 363     BOOST_CHECK_CLOSE_FRACTION(quantile(as_m11, static_cast<RealType>(2) / 3), +static_cast<RealType>(0.5L), 4 * tolerance);     // p = 2/3, x = +0.5
 364
 365     //  Loop back tests.
 366     test_spot(
 367       static_cast<RealType>(0),   // lo or a
 368       static_cast<RealType>(1),   // hi or b
 369       static_cast<RealType>(0.05), // Random variate  x
 370       static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), // Probability of result (CDF of arcsine), P
 371       static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L),  // Complement of CDF Q = 1 - P
 372       tolerance); // Test tolerance.
 373
 374     test_spot(
 375       static_cast<RealType>(0),   // lo or a
 376       static_cast<RealType>(1),   // hi or b
 377       static_cast<RealType>(0.95), // Random variate  x
 378       static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), // Probability of result (CDF of arcsine), P
 379       static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L),  // Complement of CDF Q = 1 - P
 380       tolerance * 4); // Test tolerance (slightly inceased compared to x < 0.5 above).
 381
 382     test_spot(
 383       static_cast<RealType>(0),   // lo or a
 384       static_cast<RealType>(1),   // hi or b
 385       static_cast<RealType>(static_cast<RealType>(0.5L)), // Random variate  x
 386       static_cast<RealType>(static_cast<RealType>(0.5L)), // Probability of result (CDF of arcsine), P
 387       static_cast<RealType>(static_cast<RealType>(0.5L)),  // Complement of CDF Q = 1 - P
 388       tolerance * 4); // Test tolerance.
 389
 390     // Arcsine(-2, -1) xmin = -2, x_max = -1  - Asymmetric both negative.
 391     arcsine_distribution<RealType> as_m2m1(-2, -1);
 392
 393     BOOST_CHECK_EQUAL(as_m2m1.x_min(), -2); //
 394     BOOST_CHECK_EQUAL(as_m2m1.x_max(), -1);
 395     BOOST_CHECK_EQUAL(mean(as_m2m1), -1.5); // 1 / (1 + 1) = 1/2 exactly.
 396     BOOST_CHECK_EQUAL(median(as_m2m1), -1.5); // 1 / (1 + 1) = 1/2 exactly.
 397     BOOST_CHECK_EQUAL(variance(as_m2m1), 0.125);
 398     BOOST_CHECK_EQUAL(skewness(as_m2m1), 0); //
 399     BOOST_CHECK_EQUAL(kurtosis_excess(as_m2m1), -1.5); // 3/2
 400
 401     BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.95), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 4 * tolerance);
 402     BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.5), static_cast<RealType>(0.63661977236758134307553505349005744813783858296183L), tolerance);
 403     BOOST_CHECK_CLOSE_FRACTION(pdf(as_m2m1, -1.05), static_cast<RealType>(1.4605059227421865250256574657088244053723856445614L), 4 * tolerance); // Less accurate.
 404
 405     BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.05), static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L), tolerance);
 406     BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.5), static_cast<RealType>(0.5L), tolerance);
 407     BOOST_CHECK_CLOSE_FRACTION(cdf(as_m2m1, -1.95), static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L), 8 * tolerance); //  Not much less accurate.
 408
 409     // Quantile
 410     BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L)), -static_cast<RealType>(1.05L), 2 * tolerance); //
 411     BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.5L)), -static_cast<RealType>(1.5L), 2 * tolerance);                             //
 412     BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L)), -static_cast<RealType>(1.95L), 4 * tolerance);     //
 413
 414     BOOST_CHECK_CLOSE_FRACTION(quantile(complement(as_m2m1, static_cast<RealType>(0.14356629312870627075094188477505571882161519989741L))), -static_cast<RealType>(1.05L), 2 * tolerance); //
 415     BOOST_CHECK_CLOSE_FRACTION(quantile(as_m2m1, static_cast<RealType>(0.5L)), -static_cast<RealType>(1.5L), 2 * tolerance);                             //
 416     BOOST_CHECK_CLOSE_FRACTION(quantile(complement(as_m2m1, static_cast<RealType>(0.85643370687129372924905811522494428117838480010259L))), -static_cast<RealType>(1.95L), 4 * tolerance);
 417
 418     // Tests that should throw:
 419     BOOST_MATH_CHECK_THROW(mode(arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1))), std::domain_error);
 420     // mode is undefined, and must throw domain_error!
 421
 422
 423     BOOST_MATH_CHECK_THROW( // For various bad arguments.
 424       pdf(
 425       arcsine_distribution<RealType>(static_cast<RealType>(+1), static_cast<RealType>(-1)), // min_x > max_x
 426       static_cast<RealType>(1)), std::domain_error);
 427
 428     BOOST_MATH_CHECK_THROW(
 429       pdf(
 430       arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(0)), // bad constructor parameters.
 431       static_cast<RealType>(1)), std::domain_error);
 432
 433     BOOST_MATH_CHECK_THROW(
 434       pdf(
 435       arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(-1)), // bad constructor parameters.
 436       static_cast<RealType>(1)), std::domain_error);
 437
 438     BOOST_MATH_CHECK_THROW(
 439       pdf(
 440       arcsine_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // equal constructor parameters.
 441       static_cast<RealType>(-1)), std::domain_error);
 442
 443     BOOST_MATH_CHECK_THROW(
 444       pdf(
 445       arcsine_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1)), // bad x > 1.
 446       static_cast<RealType>(999)), std::domain_error);
 447
 448     // Checks on things that are errors.
 449
 450     // Construction with 'bad' parameters.
 451     BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(+1, -1), std::domain_error); // max < min.
 452     BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(+1, 0), std::domain_error);  // max < min.
 453
 454     arcsine_distribution<> dist;
 455     BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
 456     BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
 457     BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
 458     BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
 459     BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
 460     BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
 461     BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
 462
 463     // Various combinations of bad contructor and member function parameters.
 464     BOOST_MATH_CHECK_THROW(pdf(boost::math::arcsine_distribution<RealType>(0, 1), -1), std::domain_error);
 465     BOOST_MATH_CHECK_THROW(pdf(boost::math::arcsine_distribution<RealType>(-1, 1), +2), std::domain_error);
 466     BOOST_MATH_CHECK_THROW(quantile(boost::math::arcsine_distribution<RealType>(1, 1), -1), std::domain_error);
 467     BOOST_MATH_CHECK_THROW(quantile(boost::math::arcsine_distribution<RealType>(1, 1), 2), std::domain_error);
 468
 469     // No longer allow any parameter to be NaN or inf, so all these tests should throw.
 470     if (std::numeric_limits<RealType>::has_quiet_NaN)
 471     {
 472       // Attempt to construct from non-finite parameters should throw.
 473       RealType nan = std::numeric_limits<RealType>::quiet_NaN();
 474 #ifndef BOOST_NO_EXCEPTIONS
 475       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(nan), std::domain_error);
 476       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, nan), std::domain_error);
 477       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(nan, 1), std::domain_error);
 478 #else
 479       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(nan), std::domain_error);
 480       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, nan), std::domain_error);
 481       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(nan, 1), std::domain_error);
 482 #endif
 483
 484       arcsine_distribution<RealType> w(RealType(-1), RealType(+1));
 485       // NaN parameters to member functions should throw.
 486       BOOST_MATH_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN
 487       BOOST_MATH_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN
 488       BOOST_MATH_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan
 489       BOOST_MATH_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan
 490       BOOST_MATH_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan
 491     } // has_quiet_NaN
 492
 493     if (std::numeric_limits<RealType>::has_infinity)
 494     {
 495       // Attempt to construct from non-finite should throw.
 496       RealType inf = std::numeric_limits<RealType>::infinity();
 497 #ifndef BOOST_NO_EXCEPTIONS
 498       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(inf), std::domain_error);
 499       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, inf), std::domain_error);
 500 #else
 501       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(inf), std::domain_error);
 502       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, inf), std::domain_error);
 503 #endif
 504       // Infinite parameters to member functions should throw.
 505       arcsine_distribution<RealType> w(RealType(0), RealType(1));
 506 #ifndef BOOST_NO_EXCEPTIONS
 507       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(inf), std::domain_error);
 508       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType> w(1, inf), std::domain_error);
 509 #else
 510       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(inf), std::domain_error);
 511       BOOST_MATH_CHECK_THROW(arcsine_distribution<RealType>(1, inf), std::domain_error);
 512 #endif
 513       BOOST_MATH_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf
 514       BOOST_MATH_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf
 515       BOOST_MATH_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf
 516       BOOST_MATH_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf
 517       BOOST_MATH_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf
 518     } // has_infinity
 519
 520     // Error handling checks:
 521     check_out_of_range<boost::math::arcsine_distribution<RealType> >(-1, +1); // (All) valid constructor parameter values.
 522     // and range and non-finite.
 523
 524     test_ignore_policy(static_cast<RealType>(0));
 525
 526   } // template <class RealType>void test_spots(RealType)
 527
 528   BOOST_AUTO_TEST_CASE(test_main)
 529   {
 530     BOOST_MATH_CONTROL_FP;
 531
 532     // Check that can generate arcsine distribution using convenience method:
 533     using boost::math::arcsine;
 534
 535     arcsine_distribution<> arcsine_01; // Using default RealType double.
 536     // Note: NOT arcsine01() - or compiler will assume a function.
 537
 538     arcsine as; // Using typedef for default standard arcsine.
 539
 540     //
 541     BOOST_CHECK_EQUAL(as.x_min(), 0); //
 542     BOOST_CHECK_EQUAL(as.x_max(), 1);
 543     BOOST_CHECK_EQUAL(mean(as), 0.5); // 1 / (1 + 1) = 1/2 exactly.
 544     BOOST_CHECK_EQUAL(median(as), 0.5); // 1 / (1 + 1) = 1/2 exactly.
 545     BOOST_CHECK_EQUAL(variance(as), 0.125); //0.125
 546     BOOST_CHECK_CLOSE_FRACTION(standard_deviation(as), one_div_root_two<double>() / 2, std::numeric_limits<double>::epsilon()); // 0.353553
 547     BOOST_CHECK_EQUAL(skewness(as), 0); //
 548     BOOST_CHECK_EQUAL(kurtosis_excess(as), -1.5); // 3/2
 549     BOOST_CHECK_EQUAL(support(as).first, 0); //
 550     BOOST_CHECK_EQUAL(range(as).first, 0); //
 551     BOOST_MATH_CHECK_THROW(mode(as), std::domain_error); //  Two modes at x_min and x_max, so throw instead.
 552
 553     // (Parameter value, arbitrarily zero, only communicates the floating point type).
 554     test_spots(0.0F); // Test float.
 555     test_spots(0.0); // Test double.
 556     #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 557       test_spots(0.0L); // Test long double.
 558       #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 559         test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 560       #endif
 561     #endif
 562   /*    */
 563   } // BOOST_AUTO_TEST_CASE( test_main )
 564
 565   /*
 566
 567
 568 Microsoft Visual Studio Professional 2013
 569 Version 12.0.30110.00 Update 1
 570
 571   1>  Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe"
 572   1>  Running 1 test case...
 573   1>  Platform: Win32
 574   1>  Compiler: Microsoft Visual C++ version 12.0  ???? MSVC says 2013
 575   1>  STL     : Dinkumware standard library version 610
 576   1>  Boost   : 1.56.0
 577
 578   Sample Output is:
 579
 580   1>  Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_arcsine.exe"
 581   1>  Running 1 test case...
 582   1>  Platform: Win32
 583   1>  Compiler: Microsoft Visual C++ version 12.0
 584   1>  STL     : Dinkumware standard library version 610
 585   1>  Boost   : 1.56.0
 586   1>  tolerance = 2.38419e-007
 587   1>  tolerance = 4.44089e-016
 588   1>  tolerance = 4.44089e-016
 589   1>  tolerance = 4.44089e-016
 590   1>
 591   1>  *** No errors detected
 592
 593   GCC 4.9.1
 594
 595   Running 1 test case...
 596   tolerance = 2.38419e-007
 597   tolerance = 4.44089e-016
 598   tolerance = 4.44089e-016
 599   tolerance = 4.44089e-016
 600
 601   *** No errors detected
 602
 603   RUN SUCCESSFUL (total time: 141ms)
 604
 605   */