Adding upstream version 14.2.21.upstream/14.2.21upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 761 insertions, 0 deletions

diff --git a/src/boost/libs/math/test/test_triangular.cpp b/src/boost/libs/math/test/test_triangular.cpp
new file mode 100644
index 00000000..b0620a6a
--- /dev/null
+++ b/src/boost/libs/math/test/test_triangular.cpp
@@ -0,0 +1,761 @@
+// Copyright Paul Bristow 2006, 2007.
+// Copyright John Maddock 2006, 2007.
+
+// 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)
+
+// test_triangular.cpp
+
+#include <pch.hpp>
+
+#ifdef _MSC_VER
+#  pragma warning(disable: 4127) // conditional expression is constant.
+#  pragma warning(disable: 4305) // truncation from 'long double' to 'float'
+#endif
+
+#include <boost/math/concepts/real_concept.hpp> // for real_concept
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp> // Boost.Test
+#include <boost/test/tools/floating_point_comparison.hpp>
+
+#include <boost/math/distributions/triangular.hpp>
+using boost::math::triangular_distribution;
+#include <boost/math/tools/test.hpp>
+#include <boost/math/special_functions/fpclassify.hpp>
+#include "test_out_of_range.hpp"
+
+#include <iostream>
+#include <iomanip>
+using std::cout;
+using std::endl;
+using std::scientific;
+using std::fixed;
+using std::left;
+using std::right;
+using std::setw;
+using std::setprecision;
+using std::showpos;
+#include <limits>
+using std::numeric_limits;
+
+template <class RealType>
+void check_triangular(RealType lower, RealType mode, RealType upper, RealType x, RealType p, RealType q, RealType tol)
+{
+  BOOST_CHECK_CLOSE_FRACTION(
+    ::boost::math::cdf(
+    triangular_distribution<RealType>(lower, mode, upper),   // distribution.
+    x),  // random variable.
+    p,    // probability.
+    tol);   // tolerance.
+  BOOST_CHECK_CLOSE_FRACTION(
+    ::boost::math::cdf(
+    complement(
+    triangular_distribution<RealType>(lower, mode, upper), // distribution.
+    x)),    // random variable.
+    q,    // probability complement.
+    tol);  // tolerance.
+  BOOST_CHECK_CLOSE_FRACTION(
+    ::boost::math::quantile(
+    triangular_distribution<RealType>(lower,mode, upper),  // distribution.
+    p),   // probability.
+    x,  // random variable.
+    tol);  // tolerance.
+  BOOST_CHECK_CLOSE_FRACTION(
+    ::boost::math::quantile(
+    complement(
+    triangular_distribution<RealType>(lower, mode, upper),  // distribution.
+    q)),     // probability complement.
+    x,                                             // random variable.
+    tol);  // tolerance.
+} // void check_triangular
+
+template <class RealType>
+void test_spots(RealType)
+{
+  // Basic sanity checks:
+  //
+  // Some test values were generated for the triangular distribution
+  // using the online calculator at
+  // http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
+  //
+  // Tolerance is just over 5 epsilon expressed as a fraction:
+  RealType tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction.
+  RealType tol5eps = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction.
+
+  cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << "." << endl;
+
+  using namespace std; // for ADL of std::exp;
+
+  // Tests on construction
+  // Default should be 0, 0, 1
+  BOOST_CHECK_EQUAL(triangular_distribution<RealType>().lower(), -1);
+  BOOST_CHECK_EQUAL(triangular_distribution<RealType>().mode(), 0);
+  BOOST_CHECK_EQUAL(triangular_distribution<RealType>().upper(), 1);
+  BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).first, triangular_distribution<RealType>().lower());
+  BOOST_CHECK_EQUAL(support(triangular_distribution<RealType>()).second, triangular_distribution<RealType>().upper());
+
+  if (std::numeric_limits<RealType>::has_quiet_NaN == true)
+  {
+  BOOST_MATH_CHECK_THROW( // duff parameter lower.
+    triangular_distribution<RealType>(static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0, 0),
+    std::domain_error);
+
+  BOOST_MATH_CHECK_THROW( // duff parameter mode.
+    triangular_distribution<RealType>(0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN()), 0),
+    std::domain_error);
+
+  BOOST_MATH_CHECK_THROW( // duff parameter upper.
+    triangular_distribution<RealType>(0, 0, static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
+    std::domain_error);
+  } // quiet_NaN tests.
+
+  BOOST_MATH_CHECK_THROW( // duff parameters upper < lower.
+    triangular_distribution<RealType>(1, 0, -1),
+    std::domain_error);
+
+  BOOST_MATH_CHECK_THROW( // duff parameters upper == lower.
+    triangular_distribution<RealType>(0, 0, 0),
+    std::domain_error);
+  BOOST_MATH_CHECK_THROW( // duff parameters mode < lower.
+    triangular_distribution<RealType>(0, -1, 1),
+    std::domain_error);
+
+  BOOST_MATH_CHECK_THROW( // duff parameters mode > upper.
+    triangular_distribution<RealType>(0, 2, 1),
+    std::domain_error);
+
+  // Tests for PDF
+  // // triangular_distribution<RealType>() default is (0, 0, 1), mode == lower.
+  BOOST_CHECK_CLOSE_FRACTION( // x == lower == mode
+    pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0)),
+    static_cast<RealType>(2),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x == upper
+    pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x > upper
+    pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1)),
+    static_cast<RealType>(0),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION( // x < lower
+    pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x < lower
+    pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  // triangular_distribution<RealType>() (0, 1, 1) mode == upper
+  BOOST_CHECK_CLOSE_FRACTION( // x == lower
+    pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x == upper
+    pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)),
+    static_cast<RealType>(2),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x > upper
+    pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)),
+    static_cast<RealType>(0),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION( // x < lower
+    pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case pdf = 2 * x
+    pdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)),
+    static_cast<RealType>(0.5),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x < middle so Wiki says special case cdf = x * x
+    cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.25)),
+    static_cast<RealType>(0.25 * 0.25),
+    tolerance);
+
+  // triangular_distribution<RealType>() (0, 0.5, 1) mode == middle.
+  BOOST_CHECK_CLOSE_FRACTION( // x == lower
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x == upper
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(1)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x > upper
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(-1)),
+    static_cast<RealType>(0),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION( // x < lower
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(2)),
+    static_cast<RealType>(0),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x == mode
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.5)),
+    static_cast<RealType>(2),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x == half mode
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.25)),
+    static_cast<RealType>(1),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION( // x == half mode
+    pdf(triangular_distribution<RealType>(0, 0.5, 1), static_cast<RealType>(0.75)),
+    static_cast<RealType>(1),
+    tolerance);
+
+  if(std::numeric_limits<RealType>::has_infinity)
+  { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
+    // Note that infinity is not implemented for real_concept, so these tests
+    // are only done for types, like built-in float, double.. that have infinity.
+    // Note that these assume that  BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
+    // #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
+    // #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
+    // of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
+
+    BOOST_MATH_CHECK_THROW( // x == infinity NOT OK.
+      pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(std::numeric_limits<RealType>::infinity())),
+      std::domain_error);
+
+    BOOST_MATH_CHECK_THROW( // x == minus infinity not OK too.
+      pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::infinity())),
+      std::domain_error);
+  }
+  if(std::numeric_limits<RealType>::has_quiet_NaN)
+  { // BOOST_CHECK tests for NaN using std::numeric_limits<>::has_quiet_NaN() - should throw.
+    BOOST_MATH_CHECK_THROW(
+      pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(std::numeric_limits<RealType>::quiet_NaN())),
+      std::domain_error);
+    BOOST_MATH_CHECK_THROW(
+      pdf(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-std::numeric_limits<RealType>::quiet_NaN())),
+      std::domain_error);
+  } // test for x = NaN using std::numeric_limits<>::quiet_NaN()
+
+  // cdf
+  BOOST_CHECK_EQUAL( // x < lower
+    cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(-1)),
+    static_cast<RealType>(0) );
+  BOOST_CHECK_CLOSE_FRACTION( // x == lower
+    cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0)),
+    static_cast<RealType>(0),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION( // x == upper
+    cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1)),
+    static_cast<RealType>(1),
+    tolerance);
+   BOOST_CHECK_EQUAL( // x > upper
+    cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(2)),
+    static_cast<RealType>(1));
+
+  BOOST_CHECK_CLOSE_FRACTION( // x == mode
+    cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)),
+    //static_cast<RealType>((mode - lower) / (upper - lower)),
+    static_cast<RealType>(0.5),    // (0 --1) / (1 -- 1) = 0.5
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(
+    cdf(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(0.9L)),
+    static_cast<RealType>(0.81L),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION(
+    cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-1)),
+    static_cast<RealType>(0),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(
+    cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5L)),
+    static_cast<RealType>(0.125L),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(
+    cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0)),
+    static_cast<RealType>(0.5),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(
+    cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(+0.5L)),
+    static_cast<RealType>(0.875L),
+    tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(
+    cdf(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(1)),
+    static_cast<RealType>(1),
+    tolerance);
+
+   // cdf complement
+  BOOST_CHECK_EQUAL( // x < lower
+    cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(-1))),
+    static_cast<RealType>(1));
+  BOOST_CHECK_EQUAL( // x == lower
+    cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))),
+    static_cast<RealType>(1));
+
+  BOOST_CHECK_EQUAL( // x == mode
+    cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0))),
+    static_cast<RealType>(0.5));
+
+  BOOST_CHECK_EQUAL( // x == mode
+    cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(0))),
+    static_cast<RealType>(1));
+  BOOST_CHECK_EQUAL( // x == mode
+    cdf(complement(triangular_distribution<RealType>(0, 1, 1), static_cast<RealType>(1))),
+    static_cast<RealType>(0));
+
+  BOOST_CHECK_EQUAL( // x > upper
+    cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(2))),
+    static_cast<RealType>(0));
+  BOOST_CHECK_EQUAL( // x == upper
+    cdf(complement(triangular_distribution<RealType>(0, 0, 1), static_cast<RealType>(1))),
+    static_cast<RealType>(0));
+
+  BOOST_CHECK_CLOSE_FRACTION( // x = -0.5
+    cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(-0.5))),
+    static_cast<RealType>(0.875L),
+    tolerance);
+
+  BOOST_CHECK_CLOSE_FRACTION( // x = +0.5
+    cdf(complement(triangular_distribution<RealType>(-1, 0, 1), static_cast<RealType>(0.5))),
+    static_cast<RealType>(0.125),
+    tolerance);
+
+  triangular_distribution<RealType> triang; // Using typedef == triangular_distribution<double> tristd;
+  triangular_distribution<RealType> tristd(0, 0.5, 1); // 'Standard' triangular distribution.
+
+  BOOST_CHECK_CLOSE_FRACTION( // median of Standard triangular is sqrt(mode/2) if c > 1/2 else 1 - sqrt((1-c)/2)
+    median(tristd),
+    static_cast<RealType>(0.5),
+    tolerance);
+  triangular_distribution<RealType> tri011(0, 1, 1); // Using default RealType double.
+  triangular_distribution<RealType> tri0q1(0, 0.25, 1); // mode is near bottom.
+  triangular_distribution<RealType> tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle.
+  triangular_distribution<RealType> trim12(-1, -0.5, 2); // mode is negative.
+
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02L), static_cast<RealType>(0.0016L), tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5L), static_cast<RealType>(0.66666666666666666666666666666666666666666666667L), tolerance);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98L), static_cast<RealType>(0.9994666666666666666666666666666666666666666666L), tolerance);
+
+  // quantile
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.0016L)), static_cast<RealType>(0.02L), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.66666666666666666666666666666666666666666666667L)), static_cast<RealType>(0.5), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(0.3333333333333333333333333333333333333333333333333L))), static_cast<RealType>(0.5), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, static_cast<RealType>(0.999466666666666666666666666666666666666666666666666L)), static_cast<RealType>(98) / 100, 10 * tol5eps);
+
+  BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), static_cast<RealType>(0.533333333333333333333333333333333333333333333L), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), static_cast<RealType>(0.466666666666666666666666666666666666666666667L), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), static_cast<RealType>(1 - 0.466666666666666666666666666666666666666666667L), tol5eps);
+
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, static_cast<RealType>(1 - 0.999466666666666666666666666666666666666666666666L))), static_cast<RealType>(0.98L), 10 * tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1))), static_cast<RealType>(0), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(0.5))), static_cast<RealType>(0.5), tol5eps); // OK
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1 - 0.02L))), static_cast<RealType>(0.1L), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, static_cast<RealType>(1 - 0.98L))), static_cast<RealType>(0.9L), tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0)), static_cast<RealType>(1), tol5eps);
+
+  RealType xs [] = {0, 0.01L, 0.02L, 0.05L, 0.1L, 0.2L, 0.3L, 0.4L, 0.5L, 0.6L, 0.7L, 0.8L, 0.9L, 0.95L, 0.98L, 0.99L, 1};
+
+  const triangular_distribution<RealType>& distr = triang;
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(distr, 1.)), static_cast<RealType>(-1), tol5eps);
+  const triangular_distribution<RealType>* distp = &triang;
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*distp, 1.)), static_cast<RealType>(-1), tol5eps);
+
+  const triangular_distribution<RealType>* dists [] = {&tristd, &tri011, &tri0q1, &tri0h1, &trim12};
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*dists[1], 1.)), static_cast<RealType>(0), tol5eps);
+
+   for (int i = 0; i < 5; i++)
+  {
+    const triangular_distribution<RealType>* const dist = dists[i];
+    // cout << "Distribution " << i << endl;
+    BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5L), quantile(complement(*dist, 0.5L)),  tol5eps);
+    BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98L), quantile(complement(*dist, 1.L - 0.98L)),tol5eps);
+    BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98L), quantile(complement(*dist, 1.L - 0.98L)),tol5eps);
+  } // for i
+
+   // quantile complement
+  for (int i = 0; i < 5; i++)
+  {
+    const triangular_distribution<RealType>* const dist = dists[i];
+    //cout << "Distribution " << i << endl;
+    BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
+    for (unsigned j = 0; j < sizeof(xs) /sizeof(RealType); j++)
+    {
+      RealType x = xs[j];
+      BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], x), quantile(complement(*dist, 1 - x)),  tol5eps);
+    } // for j
+  } // for i
+
+
+  check_triangular(
+    static_cast<RealType>(0),       // lower
+    static_cast<RealType>(0.5),     // mode
+    static_cast<RealType>(1),       // upper
+    static_cast<RealType>(0.5),     // x
+    static_cast<RealType>(0.5),     // p
+    static_cast<RealType>(1 - 0.5), // q
+    tolerance);
+
+  // Some Not-standard triangular tests.
+  check_triangular(
+    static_cast<RealType>(-1),    // lower
+    static_cast<RealType>(0),     // mode
+    static_cast<RealType>(1),     // upper
+    static_cast<RealType>(0),     // x
+    static_cast<RealType>(0.5),   // p
+    static_cast<RealType>(1 - 0.5), // q = 1 - p
+    tolerance);
+
+  check_triangular(
+    static_cast<RealType>(1),       // lower
+    static_cast<RealType>(1),       // mode
+    static_cast<RealType>(3),       // upper
+    static_cast<RealType>(2),    // x
+    static_cast<RealType>(0.75),     // p
+    static_cast<RealType>(1 - 0.75), // q = 1 - p
+    tolerance);
+
+  check_triangular(
+    static_cast<RealType>(-1),    // lower
+    static_cast<RealType>(1),       // mode
+    static_cast<RealType>(2),     // upper
+    static_cast<RealType>(1),     // x
+    static_cast<RealType>(0.66666666666666666666666666666666666666666667L),   // p
+    static_cast<RealType>(0.33333333333333333333333333333333333333333333L), // q = 1 - p
+    tolerance);
+  tolerance = (std::max)(
+    boost::math::tools::epsilon<RealType>(),
+    static_cast<RealType>(boost::math::tools::epsilon<double>())) * 10; // 10 eps as a fraction.
+  cout << "Tolerance (as fraction) for type " << typeid(RealType).name()  << " is " << tolerance << "." << endl;
+  
+    triangular_distribution<RealType> tridef; // (-1, 0, 1) // Default distribution.
+    RealType x = static_cast<RealType>(0.5);
+    using namespace std; // ADL of std names.
+    // mean:
+    BOOST_CHECK_CLOSE_FRACTION(
+      mean(tridef), static_cast<RealType>(0), tolerance);
+    // variance:
+    BOOST_CHECK_CLOSE_FRACTION(
+      variance(tridef), static_cast<RealType>(0.16666666666666666666666666666666666666666667L), tolerance);
+    // was 0.0833333333333333333333333333333333333333333L
+
+    // std deviation:
+    BOOST_CHECK_CLOSE_FRACTION(
+      standard_deviation(tridef), sqrt(variance(tridef)), tolerance);
+    // hazard:
+    BOOST_CHECK_CLOSE_FRACTION(
+      hazard(tridef, x), pdf(tridef, x) / cdf(complement(tridef, x)), tolerance);
+    // cumulative hazard:
+    BOOST_CHECK_CLOSE_FRACTION(
+      chf(tridef, x), -log(cdf(complement(tridef, x))), tolerance);
+    // coefficient_of_variation:
+    if (mean(tridef) != 0)
+    {
+      BOOST_CHECK_CLOSE_FRACTION(
+        coefficient_of_variation(tridef), standard_deviation(tridef) / mean(tridef), tolerance);
+    }
+    // mode:
+    BOOST_CHECK_CLOSE_FRACTION(
+      mode(tridef), static_cast<RealType>(0), tolerance);
+    // skewness:
+    BOOST_CHECK_CLOSE_FRACTION(
+      median(tridef), static_cast<RealType>(0), tolerance);
+    // https://reference.wolfram.com/language/ref/Skewness.html  skewness{-1, 0, +1} = 0
+    // skewness[triangulardistribution{-1, 0, +1}] does not compute a result.
+    // skewness[triangulardistribution{0, +1}] result == 0
+    // skewness[normaldistribution{0,1}] result == 0
+
+    BOOST_CHECK_EQUAL(
+      skewness(tridef), static_cast<RealType>(0));
+    // kurtosis:
+    BOOST_CHECK_CLOSE_FRACTION(
+      kurtosis_excess(tridef), kurtosis(tridef) - static_cast<RealType>(3L), tolerance);
+    // kurtosis excess = kurtosis - 3;
+    BOOST_CHECK_CLOSE_FRACTION(
+      kurtosis_excess(tridef), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
+
+  {
+    triangular_distribution<RealType> tri01(0, 1, 1); //  Asymmetric 0, 1, 1 distribution.
+    RealType x = static_cast<RealType>(0.5);
+    using namespace std; // ADL of std names.
+                         // mean:
+    BOOST_CHECK_CLOSE_FRACTION(
+      mean(tri01), static_cast<RealType>(0.66666666666666666666666666666666666666666666666667L), tolerance);
+    // variance: N[variance[triangulardistribution{0, 1}, 1], 50]
+    BOOST_CHECK_CLOSE_FRACTION(
+      variance(tri01), static_cast<RealType>(0.055555555555555555555555555555555555555555555555556L), tolerance);
+    // std deviation:
+    BOOST_CHECK_CLOSE_FRACTION(
+      standard_deviation(tri01), sqrt(variance(tri01)), tolerance);
+    // hazard:
+    BOOST_CHECK_CLOSE_FRACTION(
+      hazard(tri01, x), pdf(tri01, x) / cdf(complement(tri01, x)), tolerance);
+    // cumulative hazard:
+    BOOST_CHECK_CLOSE_FRACTION(
+      chf(tri01, x), -log(cdf(complement(tri01, x))), tolerance);
+    // coefficient_of_variation:
+    if (mean(tri01) != 0)
+    {
+      BOOST_CHECK_CLOSE_FRACTION(
+        coefficient_of_variation(tri01), standard_deviation(tri01) / mean(tri01), tolerance);
+    }
+    // mode:
+    BOOST_CHECK_CLOSE_FRACTION(
+      mode(tri01), static_cast<RealType>(1), tolerance);
+    // skewness:
+    BOOST_CHECK_CLOSE_FRACTION(
+      median(tri01), static_cast<RealType>(0.70710678118654752440084436210484903928483593768847L), tolerance);
+
+    // https://reference.wolfram.com/language/ref/Skewness.html
+    // N[skewness[triangulardistribution{0, 1}, 1], 50]
+    BOOST_CHECK_CLOSE_FRACTION(
+      skewness(tri01), static_cast<RealType>(-0.56568542494923801952067548968387923142786875015078L), tolerance);
+    // kurtosis:
+    BOOST_CHECK_CLOSE_FRACTION(
+      kurtosis_excess(tri01), kurtosis(tri01) - static_cast<RealType>(3L), tolerance);
+    // kurtosis excess = kurtosis - 3;
+    BOOST_CHECK_CLOSE_FRACTION(
+      kurtosis_excess(tri01), static_cast<RealType>(-0.6), tolerance); // Constant value of -3/5 for all distributions.
+  } // tri01 tests
+
+  if(std::numeric_limits<RealType>::has_infinity)
+  { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
+    // Note that infinity is not implemented for real_concept, so these tests
+    // are only done for types, like built-in float, double.. that have infinity.
+    // Note that these assume that BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
+    // #define BOOST_MATH_OVERFLOW_ERROR_POLICY == throw_on_error would give a throw here.
+    // #define BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error IS defined, so the throw path
+    // of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
+
+    using boost::math::policies::policy;
+    using boost::math::policies::domain_error;
+    using boost::math::policies::ignore_error;
+
+    // Define a (bad?) policy to ignore domain errors ('bad' arguments):
+    typedef policy<domain_error<ignore_error> > inf_policy; // domain error returns infinity.
+    triangular_distribution<RealType, inf_policy> tridef_inf(-1, 0., 1);
+    // But can't use BOOST_CHECK_EQUAL(?, quiet_NaN)
+    using boost::math::isnan;
+    BOOST_CHECK((isnan)(pdf(tridef_inf, std::numeric_limits<RealType>::infinity())));
+  } // test for infinity using std::numeric_limits<>::infinity()
+  else
+  { // real_concept case, does has_infinfity == false, so can't check it throws.
+    // cout << std::numeric_limits<RealType>::infinity() << ' '
+    // << (boost::math::fpclassify)(std::numeric_limits<RealType>::infinity()) << endl;
+    // value of std::numeric_limits<RealType>::infinity() is zero, so FPclassify is zero,
+    // so (boost::math::isfinite)(std::numeric_limits<RealType>::infinity()) does not detect infinity.
+    // so these tests would never throw.
+    //BOOST_MATH_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::infinity()),  std::domain_error);
+    //BOOST_MATH_CHECK_THROW(pdf(tridef, std::numeric_limits<RealType>::quiet_NaN()),  std::domain_error);
+    // BOOST_MATH_CHECK_THROW(pdf(tridef, boost::math::tools::max_value<RealType>() * 2),  std::domain_error); // Doesn't throw.
+    BOOST_CHECK_EQUAL(pdf(tridef, boost::math::tools::max_value<RealType>()), 0);
+  }
+  // Special cases:
+  BOOST_CHECK(pdf(tridef, -1) == 0);
+  BOOST_CHECK(pdf(tridef, 1) == 0);
+  BOOST_CHECK(cdf(tridef, 0) == 0.5);
+  BOOST_CHECK(pdf(tridef, 1) == 0);
+  BOOST_CHECK(cdf(tridef, 1) == 1);
+  BOOST_CHECK(cdf(complement(tridef, -1)) == 1);
+  BOOST_CHECK(cdf(complement(tridef, 1)) == 0);
+  BOOST_CHECK(quantile(tridef, 1) == 1);
+  BOOST_CHECK(quantile(complement(tridef, 1)) == -1);
+
+  BOOST_CHECK_EQUAL(support(trim12).first, trim12.lower());
+  BOOST_CHECK_EQUAL(support(trim12).second, trim12.upper());
+
+  // Error checks:
+  if(std::numeric_limits<RealType>::has_quiet_NaN)
+  { // BOOST_CHECK tests for quiet_NaN (not for real_concept, for example - see notes above).
+    BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(0, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
+    BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(0, -std::numeric_limits<RealType>::quiet_NaN()), std::domain_error);
+  }
+  BOOST_MATH_CHECK_THROW(triangular_distribution<RealType>(1, 0), std::domain_error); // lower > upper!
+
+  check_out_of_range<triangular_distribution<RealType> >(-1, 0, 1);
+} // template <class RealType>void test_spots(RealType)
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+  //  double toleps = std::numeric_limits<double>::epsilon(); // 5 eps as a fraction.
+  double tol5eps = std::numeric_limits<double>::epsilon() * 5; // 5 eps as a fraction.
+  // double tol50eps = std::numeric_limits<double>::epsilon() * 50; // 50 eps as a fraction.
+  double tol500eps = std::numeric_limits<double>::epsilon() * 500; // 500 eps as a fraction.
+
+  // Check that can construct triangular distribution using the two convenience methods:
+  using namespace boost::math;
+  triangular triang; // Using typedef
+  // == triangular_distribution<double> triang;
+
+  BOOST_CHECK_EQUAL(triang.lower(), -1); // Check default.
+  BOOST_CHECK_EQUAL(triang.mode(), 0);
+  BOOST_CHECK_EQUAL(triang.upper(), 1);
+
+  triangular tristd (0, 0.5, 1); // Using typedef
+
+  BOOST_CHECK_EQUAL(tristd.lower(), 0);
+  BOOST_CHECK_EQUAL(tristd.mode(), 0.5);
+  BOOST_CHECK_EQUAL(tristd.upper(), 1);
+
+  //cout << "X range from " << range(tristd).first << " to " << range(tristd).second << endl;
+  //cout << "Supported from "<< support(tristd).first << ' ' << support(tristd).second << endl;
+
+  BOOST_CHECK_EQUAL(support(tristd).first, tristd.lower());
+  BOOST_CHECK_EQUAL(support(tristd).second, tristd.upper());
+
+  triangular_distribution<> tri011(0, 1, 1); // Using default RealType double.
+  // mode is upper
+  BOOST_CHECK_EQUAL(tri011.lower(), 0); // Check defaults again.
+  BOOST_CHECK_EQUAL(tri011.mode(), 1); // Check defaults again.
+  BOOST_CHECK_EQUAL(tri011.upper(), 1);
+  BOOST_CHECK_EQUAL(mode(tri011), 1);
+
+  BOOST_CHECK_EQUAL(pdf(tri011, 0), 0);
+  BOOST_CHECK_EQUAL(pdf(tri011, 0.1), 0.2);
+  BOOST_CHECK_EQUAL(pdf(tri011, 0.5), 1);
+  BOOST_CHECK_EQUAL(pdf(tri011, 0.9), 1.8);
+  BOOST_CHECK_EQUAL(pdf(tri011, 1), 2);
+
+  BOOST_CHECK_EQUAL(cdf(tri011, 0), 0);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri011, 0.1), 0.01, tol5eps);
+  BOOST_CHECK_EQUAL(cdf(tri011, 0.5), 0.25);
+  BOOST_CHECK_EQUAL(cdf(tri011, 0.9), 0.81);
+  BOOST_CHECK_EQUAL(cdf(tri011, 1), 1);
+  BOOST_CHECK_EQUAL(cdf(tri011, 9), 1);
+  BOOST_CHECK_EQUAL(mean(tri011), 0.666666666666666666666666666666666666666666666666667);
+  BOOST_CHECK_EQUAL(variance(tri011), 1./18.);
+
+  triangular tri0h1(0, 0.5, 1); // Equilateral triangle - mode is the middle.
+  BOOST_CHECK_EQUAL(tri0h1.lower(), 0);
+  BOOST_CHECK_EQUAL(tri0h1.mode(), 0.5);
+  BOOST_CHECK_EQUAL(tri0h1.upper(), 1);
+  BOOST_CHECK_EQUAL(mean(tri0h1), 0.5);
+  BOOST_CHECK_EQUAL(mode(tri0h1), 0.5);
+  BOOST_CHECK_EQUAL(pdf(tri0h1, -1), 0);
+  BOOST_CHECK_EQUAL(cdf(tri0h1, -1), 0);
+  BOOST_CHECK_EQUAL(pdf(tri0h1, 1), 0);
+  BOOST_CHECK_EQUAL(pdf(tri0h1, 999), 0);
+  BOOST_CHECK_EQUAL(cdf(tri0h1, 999), 1);
+  BOOST_CHECK_EQUAL(cdf(tri0h1, 1), 1);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0h1, 0.1), 0.02, tol5eps);
+  BOOST_CHECK_EQUAL(cdf(tri0h1, 0.5), 0.5);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0h1, 0.9), 0.98, tol5eps);
+
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.), 0., tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.02), 0.1, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.5), 0.5, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 0.98), 0.9, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0h1, 1.), 1., tol5eps);
+
+  triangular tri0q1(0, 0.25, 1); // mode is near bottom.
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.02), 0.0016, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.5), 0.66666666666666666666666666666666666666666666667, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(tri0q1, 0.98), 0.99946666666666661, tol5eps);
+
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.0016), 0.02, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.66666666666666666666666666666666666666666666667), 0.5, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, 0.3333333333333333333333333333333333333333333333333)), 0.5, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(tri0q1, 0.99946666666666661), 0.98, 10 * tol5eps);
+
+  triangular trim12(-1, -0.5, 2); // mode is negative.
+  BOOST_CHECK_CLOSE_FRACTION(pdf(trim12, 0), 0.533333333333333333333333333333333333333333333, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(trim12, 0), 0.466666666666666666666666666666666666666666667, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(cdf(complement(trim12, 0)), 1 - 0.466666666666666666666666666666666666666666667, tol5eps);
+
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0q1, 1 - 0.99946666666666661)), 0.98, 10 * tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1.)), 0., tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0.5)), 0.5, tol5eps); // OK
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1. - 0.02)), 0.1, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 1. - 0.98)), 0.9, tol5eps);
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(tri0h1, 0)), 1., tol5eps);
+
+  double xs [] = {0., 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.98, 0.99, 1.};
+
+  const triangular_distribution<double>& distr = tristd;
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(distr, 1.)), 0., tol5eps);
+  const triangular_distribution<double>* distp = &tristd;
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*distp, 1.)), 0., tol5eps);
+
+  const triangular_distribution<double>* dists [] = {&tristd, &tri011, &tri0q1, &tri0h1, &trim12};
+  BOOST_CHECK_CLOSE_FRACTION(quantile(complement(*dists[1], 1.)), 0., tol5eps);
+
+  for (int i = 0; i < 5; i++)
+  {
+    const triangular_distribution<double>* const dist = dists[i];
+    cout << "Distribution " << i << endl;
+    BOOST_CHECK_EQUAL(quantile(complement(*dists[i], 1.)), quantile(*dists[i], 0.));
+    BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.5), quantile(complement(*dist, 0.5)),  tol5eps); // OK
+    BOOST_CHECK_CLOSE_FRACTION(quantile(*dists[i], 0.98), quantile(complement(*dist, 1. - 0.98)),tol5eps);
+    // cout << setprecision(17) <<  median(*dist) << endl;
+  }
+
+  cout << showpos << setprecision(2) << endl;
+
+  //triangular_distribution<double>& dist = trim12;
+  for (unsigned i = 0; i < sizeof(xs) /sizeof(double); i++)
+  {
+    double x = xs[i] * (trim12.upper() - trim12.lower()) + trim12.lower();
+    double dx = cdf(trim12, x);
+    double cx = cdf(complement(trim12, x));
+    //cout << fixed << showpos << setprecision(3)
+    //  << xs[i] << ", " << x << ",  " << pdf(trim12, x) << ",  " << dx << ",  " << cx << ",, " ;
+
+    BOOST_CHECK_CLOSE_FRACTION(cx, 1 - dx, tol500eps); // cx == 1 - dx
+
+    // << setprecision(2) << scientific << cr - x << ", " // difference x - quan(cdf)
+    // << setprecision(3) << fixed
+    // << quantile(trim12, dx) << ", "
+    // << quantile(complement(trim12, 1 - dx)) << ", "
+    // << quantile(complement(trim12, cx)) << ", "
+    // << endl;
+    BOOST_CHECK_CLOSE_FRACTION(quantile(trim12, dx), quantile(complement(trim12, 1 - dx)), tol500eps);
+  }
+  cout << endl;
+  // Basic sanity-check spot values.
+  // (Parameter value, arbitrarily zero, only communicates the floating point type).
+  test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
+  test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
+  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+    test_spots(0.0L); // Test long double.
+  #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
+    test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+  #endif
+  #else
+     std::cout << "<note>The long double tests have been disabled on this platform "
+        "either because the long double overloads of the usual math functions are "
+        "not available at all, or because they are too inaccurate for these tests "
+        "to pass.</note>" << std::endl;
+  #endif
+
+  
+} // BOOST_AUTO_TEST_CASE( test_main )
+
+/*
+
+Output:
+
+Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_triangular.exe"
+Running 1 test case...
+Distribution 0
+Distribution 1
+Distribution 2
+Distribution 3
+Distribution 4
+Tolerance for type float is 5.96046e-007.
+Tolerance for type double is 1.11022e-015.
+Tolerance for type long double is 1.11022e-015.
+Tolerance for type class boost::math::concepts::real_concept is 1.11022e-015.
+*** No errors detected
+
+
+
+*/
+
+
+
+