Adding upstream version 14.2.21.upstream/14.2.21upstream

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

1 files changed, 650 insertions, 0 deletions

diff --git a/src/boost/libs/math/test/test_poisson.cpp b/src/boost/libs/math/test/test_poisson.cpp
new file mode 100644
index 00000000..3d54e5a9
--- /dev/null
+++ b/src/boost/libs/math/test/test_poisson.cpp
@@ -0,0 +1,650 @@
+// test_poisson.cpp
+
+// Copyright Paul A. Bristow 2007.
+// Copyright John Maddock 2006.
+
+// 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)
+
+// Basic sanity test for Poisson Cumulative Distribution Function.
+
+#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
+
+#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
+#  define TEST_FLOAT
+#  define TEST_DOUBLE
+#  define TEST_LDOUBLE
+#  define TEST_REAL_CONCEPT
+#endif
+
+#ifdef _MSC_VER
+#  pragma warning(disable: 4127) // conditional expression is constant.
+#endif
+
+#define BOOST_TEST_MAIN
+#include <boost/test/unit_test.hpp> // Boost.Test
+#include <boost/test/tools/floating_point_comparison.hpp>
+
+#include <boost/math/concepts/real_concept.hpp> // for real_concept
+#include <boost/math/distributions/poisson.hpp>
+    using boost::math::poisson_distribution;
+#include <boost/math/tools/test.hpp> // for real_concept
+
+#include <boost/math/special_functions/gamma.hpp> // for (incomplete) gamma.
+//   using boost::math::qamma_Q;
+#include "table_type.hpp"
+#include "test_out_of_range.hpp"
+
+#include <iostream>
+   using std::cout;
+   using std::endl;
+   using std::setprecision;
+   using std::showpoint;
+   using std::ios;
+#include <limits>
+  using std::numeric_limits;
+
+template <class RealType> // Any floating-point type RealType.
+void test_spots(RealType)
+{
+  // Basic sanity checks, tolerance is about numeric_limits<RealType>::digits10 decimal places,
+   // guaranteed for type RealType, eg 6 for float, 15 for double,
+   // expressed as a percentage (so -2) for BOOST_CHECK_CLOSE,
+
+   int decdigits = numeric_limits<RealType>::digits10;
+  // May eb >15 for 80 and 128-bit FP typtes.
+  if (decdigits <= 0)
+  { // decdigits is not defined, for example real concept,
+    // so assume precision of most test data is double (for example, MathCAD).
+     decdigits = numeric_limits<double>::digits10; // == 15 for 64-bit
+  }
+  if (decdigits > 15 ) // numeric_limits<double>::digits10)
+  { // 15 is the accuracy of the MathCAD test data.
+    decdigits = 15; // numeric_limits<double>::digits10;
+  }
+
+   decdigits -= 1; // Perhaps allow some decimal digit(s) margin of numerical error.
+   RealType tolerance = static_cast<RealType>(std::pow(10., static_cast<double>(2-decdigits))); // 1e-6 (-2 so as %)
+   tolerance *= 2; // Allow some bit(s) small margin (2 means + or - 1 bit) of numerical error.
+   // Typically 2e-13% = 2e-15 as fraction for double.
+
+   // Sources of spot test values:
+
+  // Many be some combinations for which the result is 'exact',
+  // or at least is good to 40 decimal digits.
+   // 40 decimal digits includes 128-bit significand User Defined Floating-Point types,
+   
+   // Best source of accurate values is:
+   // Mathworld online calculator (40 decimal digits precision, suitable for up to 128-bit significands)
+   // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=GammaRegularized
+   // GammaRegularized is same as gamma incomplete, gamma or gamma_q(a, x) or Q(a, z).
+
+  // http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/PoissonDistribution.html
+
+  // MathCAD defines ppois(k, lambda== mean) as k integer, k >=0.
+  // ppois(0, 5) =  6.73794699908547e-3
+  // ppois(1, 5) = 0.040427681994513;
+  // ppois(10, 10) = 5.830397501929850E-001
+  // ppois(10, 1) = 9.999999899522340E-001
+  // ppois(5,5) = 0.615960654833065
+
+  // qpois returns inverse Poission distribution, that is the smallest (floor) k so that ppois(k, lambda) >= p
+  // p is real number, real mean lambda > 0
+  // k is approximately the integer for which probability(X <= k) = p
+  // when random variable X has the Poisson distribution with parameters lambda.
+  // Uses discrete bisection.
+  // qpois(6.73794699908547e-3, 5) = 1
+  // qpois(0.040427681994513, 5) = 
+
+  // Test Poisson with spot values from MathCAD 'known good'.
+
+  using boost::math::poisson_distribution;
+  using  ::boost::math::poisson;
+  using  ::boost::math::cdf;
+  using  ::boost::math::pdf;
+
+   // Check that bad arguments throw.
+   BOOST_MATH_CHECK_THROW(
+   cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
+      static_cast<RealType>(0)),  // even for a good k.
+      std::domain_error); // Expected error to be thrown.
+
+    BOOST_MATH_CHECK_THROW(
+   cdf(poisson_distribution<RealType>(static_cast<RealType>(-1)), // mean negative is bad.
+      static_cast<RealType>(0)),
+      std::domain_error);
+
+   BOOST_MATH_CHECK_THROW(
+   cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unit OK,
+      static_cast<RealType>(-1)),  // but negative events is bad.
+      std::domain_error);
+
+  BOOST_MATH_CHECK_THROW(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
+      static_cast<RealType>(99999)),  // for any k events. 
+      std::domain_error);
+  
+  BOOST_MATH_CHECK_THROW(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero is bad.
+      static_cast<RealType>(99999)),  // for any k events. 
+      std::domain_error);
+
+  BOOST_MATH_CHECK_THROW(
+     quantile(poisson_distribution<RealType>(static_cast<RealType>(0)), // mean zero.
+      static_cast<RealType>(0.5)),  // probability OK. 
+      std::domain_error);
+
+  BOOST_MATH_CHECK_THROW(
+     quantile(poisson_distribution<RealType>(static_cast<RealType>(-1)), 
+      static_cast<RealType>(-1)),  // bad probability. 
+      std::domain_error);
+
+  BOOST_MATH_CHECK_THROW(
+     quantile(poisson_distribution<RealType>(static_cast<RealType>(1)), 
+      static_cast<RealType>(-1)),  // bad probability. 
+      std::domain_error);
+
+  BOOST_MATH_CHECK_THROW(
+     quantile(poisson_distribution<RealType>(static_cast<RealType>(1)), 
+      static_cast<RealType>(1)),  // bad probability. 
+      std::overflow_error);
+
+  BOOST_MATH_CHECK_THROW(
+     quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)), 
+      static_cast<RealType>(0))),  // bad probability. 
+      std::overflow_error);
+
+  BOOST_CHECK_EQUAL(
+     quantile(poisson_distribution<RealType>(static_cast<RealType>(1)), 
+      static_cast<RealType>(0)),  // bad probability. 
+      0);
+
+  BOOST_CHECK_EQUAL(
+     quantile(complement(poisson_distribution<RealType>(static_cast<RealType>(1)), 
+      static_cast<RealType>(1))),  // bad probability. 
+      0);
+
+  // Check some test values.
+
+  BOOST_CHECK_CLOSE( // mode
+     mode(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
+      static_cast<RealType>(4), // mode.
+         tolerance);
+
+  //BOOST_CHECK_CLOSE( // mode
+  //   median(poisson_distribution<RealType>(static_cast<RealType>(4))), // mode = mean = 4.
+  //    static_cast<RealType>(4), // mode.
+      //   tolerance);
+  poisson_distribution<RealType> dist4(static_cast<RealType>(40));
+
+  BOOST_CHECK_CLOSE( // median
+     median(dist4), // mode = mean = 4. median = 40.328333333333333 
+      quantile(dist4, static_cast<RealType>(0.5)), // 39.332839138842637
+         tolerance);
+
+  // PDF
+  BOOST_CHECK_CLOSE(
+     pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
+      static_cast<RealType>(0)),   
+      static_cast<RealType>(1.831563888873410E-002), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
+      static_cast<RealType>(2)),   
+      static_cast<RealType>(1.465251111098740E-001), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     pdf(poisson_distribution<RealType>(static_cast<RealType>(20)), // mean big.
+      static_cast<RealType>(1)),   //  k small
+      static_cast<RealType>(4.122307244877130E-008), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     pdf(poisson_distribution<RealType>(static_cast<RealType>(4)), // mean 4.
+      static_cast<RealType>(20)),   //  K>> mean 
+      static_cast<RealType>(8.277463646553730E-009), // probability.
+         tolerance);
+  
+  // CDF
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(0)),  // zero k events. 
+      static_cast<RealType>(3.678794411714420E-1), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(1)),  // one k event. 
+      static_cast<RealType>(7.357588823428830E-1), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(2)),  // two k events. 
+      static_cast<RealType>(9.196986029286060E-1), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(10)),  // two k events. 
+      static_cast<RealType>(9.999999899522340E-1), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(15)),  // two k events. 
+      static_cast<RealType>(9.999999999999810E-1), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(16)),  // two k events. 
+      static_cast<RealType>(9.999999999999990E-1), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(17)),  // two k events. 
+      static_cast<RealType>(1.), // probability unity for double.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(33)),  // k events at limit for float unchecked_factorial table. 
+      static_cast<RealType>(1.), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(100)), // mean 100.
+      static_cast<RealType>(33)),  // k events at limit for float unchecked_factorial table. 
+      static_cast<RealType>(6.328271240363390E-15), // probability is tiny.
+         tolerance * static_cast<RealType>(2e11)); // 6.3495253382825722e-015 MathCAD
+      // Note that there two tiny probability are much more different.
+
+   BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(100)), // mean 100.
+      static_cast<RealType>(34)),  // k events at limit for float unchecked_factorial table. 
+      static_cast<RealType>(1.898481372109020E-14), // probability is tiny.
+         tolerance*static_cast<RealType>(2e11)); //         1.8984813721090199e-014 MathCAD
+
+
+ BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(33)), // mean = k
+      static_cast<RealType>(33)),  // k events above limit for float unchecked_factorial table. 
+      static_cast<RealType>(5.461191812386560E-1), // probability.
+         tolerance);
+
+ BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(33)), // mean = k-1
+      static_cast<RealType>(34)),  // k events above limit for float unchecked_factorial table. 
+      static_cast<RealType>(6.133535681502950E-1), // probability.
+         tolerance);
+
+ BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1)), // mean unity.
+      static_cast<RealType>(34)),  // k events above limit for float unchecked_factorial table. 
+      static_cast<RealType>(1.), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
+      static_cast<RealType>(5)),  // k events. 
+      static_cast<RealType>(0.615960654833065), // probability.
+         tolerance);
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
+      static_cast<RealType>(1)),  // k events. 
+      static_cast<RealType>(0.040427681994512805), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(5.)), // mean
+      static_cast<RealType>(0)),  // k events (uses special case formula, not gamma). 
+      static_cast<RealType>(0.006737946999085467), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(1.)), // mean
+      static_cast<RealType>(0)),  // k events (uses special case formula, not gamma). 
+      static_cast<RealType>(0.36787944117144233), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
+      static_cast<RealType>(10)),  // k events. 
+      static_cast<RealType>(0.5830397501929856), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
+      static_cast<RealType>(5)),  // k events. 
+      static_cast<RealType>(0.785130387030406), // probability.
+         tolerance);
+
+  // complement CDF
+  BOOST_CHECK_CLOSE( // Complement CDF
+     cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
+      static_cast<RealType>(5))),  // k events. 
+      static_cast<RealType>(1 - 0.785130387030406), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE( // Complement CDF
+     cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
+      static_cast<RealType>(0))),  // Zero k events (uses special case formula, not gamma).
+      static_cast<RealType>(0.98168436111126578), // probability.
+         tolerance);
+  BOOST_CHECK_CLOSE( // Complement CDF
+     cdf(complement(poisson_distribution<RealType>(static_cast<RealType>(1.)), // mean
+      static_cast<RealType>(0))),  // Zero k events (uses special case formula, not gamma).
+      static_cast<RealType>(0.63212055882855767), // probability.
+         tolerance);
+
+  // Example where k is bigger than max_factorial (>34 for float)
+  // (therefore using log gamma so perhaps less accurate).
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(40.)), // mean
+      static_cast<RealType>(40)),  // k events. 
+      static_cast<RealType>(0.5419181783625430), // probability.
+         tolerance);
+
+   // Quantile & complement.
+  BOOST_CHECK_CLOSE(
+    boost::math::quantile(
+         poisson_distribution<RealType>(5),  // mean.
+         static_cast<RealType>(0.615960654833065)),  //  probability.
+         static_cast<RealType>(5.), // Expect k = 5
+         tolerance/5); // 
+
+  // EQUAL is too optimistic - fails [5.0000000000000124 != 5]
+  // BOOST_CHECK_EQUAL(boost::math::quantile( // 
+  //       poisson_distribution<RealType>(5.),  // mean.
+  //       static_cast<RealType>(0.615960654833065)),  //  probability.
+  //       static_cast<RealType>(5.)); // Expect k = 5 events.
+ 
+  BOOST_CHECK_CLOSE(boost::math::quantile(
+         poisson_distribution<RealType>(4),  // mean.
+         static_cast<RealType>(0.785130387030406)),  //  probability.
+         static_cast<RealType>(5.), // Expect k = 5 events.
+         tolerance/5); 
+
+  // Check on quantile of other examples of inverse of cdf.
+  BOOST_CHECK_CLOSE( 
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(10.)), // mean
+      static_cast<RealType>(10)),  // k events. 
+      static_cast<RealType>(0.5830397501929856), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
+         poisson_distribution<RealType>(10.),  // mean.
+         static_cast<RealType>(0.5830397501929856)),  //  probability.
+         static_cast<RealType>(10.), // Expect k = 10 events.
+         tolerance/5); 
+
+
+  BOOST_CHECK_CLOSE(
+     cdf(poisson_distribution<RealType>(static_cast<RealType>(4.)), // mean
+      static_cast<RealType>(5)),  // k events. 
+      static_cast<RealType>(0.785130387030406), // probability.
+         tolerance);
+
+  BOOST_CHECK_CLOSE(boost::math::quantile( // inverse of cdf above.
+         poisson_distribution<RealType>(4.),  // mean.
+         static_cast<RealType>(0.785130387030406)),  //  probability.
+         static_cast<RealType>(5.), // Expect k = 10 events.
+         tolerance/5); 
+
+
+
+  //BOOST_CHECK_CLOSE(boost::math::quantile(
+  //       poisson_distribution<RealType>(5),  // mean.
+  //       static_cast<RealType>(0.785130387030406)),  //  probability.
+  //        // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
+  //       static_cast<RealType>(6.), // Expect k = 6 events. 
+  //       tolerance/5); 
+
+  //BOOST_CHECK_CLOSE(boost::math::quantile(
+  //       poisson_distribution<RealType>(5),  // mean.
+  //       static_cast<RealType>(0.77)),  //  probability.
+  //        // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
+  //       static_cast<RealType>(7.), // Expect k = 6 events. 
+  //       tolerance/5); 
+
+  //BOOST_CHECK_CLOSE(boost::math::quantile(
+  //       poisson_distribution<RealType>(5),  // mean.
+  //       static_cast<RealType>(0.75)),  //  probability.
+  //        // 6.1882832344329559 result but MathCAD givest smallest integer ppois(k, mean) >= prob
+  //       static_cast<RealType>(6.), // Expect k = 6 events. 
+  //       tolerance/5); 
+
+  BOOST_CHECK_CLOSE(
+    boost::math::quantile(
+         complement(
+           poisson_distribution<RealType>(4),
+           static_cast<RealType>(1 - 0.785130387030406))),  // complement.
+           static_cast<RealType>(5), // Expect k = 5 events.
+         tolerance/5);
+
+  BOOST_CHECK_EQUAL(boost::math::quantile( // Check case when probability < cdf(0) (== pdf(0))
+         poisson_distribution<RealType>(1),  // mean is small, so cdf and pdf(0) are about 0.35.
+         static_cast<RealType>(0.0001)),  //  probability < cdf(0).
+         static_cast<RealType>(0)); // Expect k = 0 events exactly.
+          
+  BOOST_CHECK_EQUAL(
+    boost::math::quantile(
+         complement(
+           poisson_distribution<RealType>(1),
+           static_cast<RealType>(0.9999))),  // complement, so 1-probability < cdf(0)
+           static_cast<RealType>(0)); // Expect k = 0 events exactly.
+
+  //
+  // Test quantile policies against test data:
+  //
+#define T RealType
+#include "poisson_quantile.ipp"
+
+  for(unsigned i = 0; i < poisson_quantile_data.size(); ++i)
+  {
+     using namespace boost::math::policies;
+     typedef policy<discrete_quantile<boost::math::policies::real> > P1;
+     typedef policy<discrete_quantile<integer_round_down> > P2;
+     typedef policy<discrete_quantile<integer_round_up> > P3;
+     typedef policy<discrete_quantile<integer_round_outwards> > P4;
+     typedef policy<discrete_quantile<integer_round_inwards> > P5;
+     typedef policy<discrete_quantile<integer_round_nearest> > P6;
+     RealType tol = boost::math::tools::epsilon<RealType>() * 20;
+     if(!boost::is_floating_point<RealType>::value)
+        tol *= 7;
+     //
+     // Check full real value first:
+     //
+     poisson_distribution<RealType, P1> p1(poisson_quantile_data[i][0]);
+     RealType x = quantile(p1, poisson_quantile_data[i][1]);
+     BOOST_CHECK_CLOSE_FRACTION(x, poisson_quantile_data[i][2], tol);
+     x = quantile(complement(p1, poisson_quantile_data[i][1]));
+     BOOST_CHECK_CLOSE_FRACTION(x, poisson_quantile_data[i][3], tol * 3);
+     //
+     // Now with round down to integer:
+     //
+     poisson_distribution<RealType, P2> p2(poisson_quantile_data[i][0]);
+     x = quantile(p2, poisson_quantile_data[i][1]);
+     BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][2]));
+     x = quantile(complement(p2, poisson_quantile_data[i][1]));
+     BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][3]));
+     //
+     // Now with round up to integer:
+     //
+     poisson_distribution<RealType, P3> p3(poisson_quantile_data[i][0]);
+     x = quantile(p3, poisson_quantile_data[i][1]);
+     BOOST_CHECK_EQUAL(x, ceil(poisson_quantile_data[i][2]));
+     x = quantile(complement(p3, poisson_quantile_data[i][1]));
+     BOOST_CHECK_EQUAL(x, ceil(poisson_quantile_data[i][3]));
+     //
+     // Now with round to integer "outside":
+     //
+     poisson_distribution<RealType, P4> p4(poisson_quantile_data[i][0]);
+     x = quantile(p4, poisson_quantile_data[i][1]);
+     BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? floor(poisson_quantile_data[i][2]) : ceil(poisson_quantile_data[i][2]));
+     x = quantile(complement(p4, poisson_quantile_data[i][1]));
+     BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? ceil(poisson_quantile_data[i][3]) : floor(poisson_quantile_data[i][3]));
+     //
+     // Now with round to integer "inside":
+     //
+     poisson_distribution<RealType, P5> p5(poisson_quantile_data[i][0]);
+     x = quantile(p5, poisson_quantile_data[i][1]);
+     BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? ceil(poisson_quantile_data[i][2]) : floor(poisson_quantile_data[i][2]));
+     x = quantile(complement(p5, poisson_quantile_data[i][1]));
+     BOOST_CHECK_EQUAL(x, poisson_quantile_data[i][1] < 0.5f ? floor(poisson_quantile_data[i][3]) : ceil(poisson_quantile_data[i][3]));
+     //
+     // Now with round to nearest integer:
+     //
+     poisson_distribution<RealType, P6> p6(poisson_quantile_data[i][0]);
+     x = quantile(p6, poisson_quantile_data[i][1]);
+     BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][2] + 0.5f));
+     x = quantile(complement(p6, poisson_quantile_data[i][1]));
+     BOOST_CHECK_EQUAL(x, floor(poisson_quantile_data[i][3] + 0.5f));
+  }
+   check_out_of_range<poisson_distribution<RealType> >(1);
+} // template <class RealType>void test_spots(RealType)
+
+//
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+  // Check that can construct normal distribution using the two convenience methods:
+  using namespace boost::math;
+  poisson myp1(2); // Using typedef
+   poisson_distribution<> myp2(2); // Using default RealType double.
+
+   // Basic sanity-check spot values.
+
+  // Some plain double examples & tests:
+  cout.precision(17); // double max_digits10
+  cout.setf(ios::showpoint);
+  
+  poisson mypoisson(4.); // // mean = 4, default FP type is double.
+  cout << "mean(mypoisson, 4.) == " << mean(mypoisson) << endl;
+  cout << "mean(mypoisson, 0.) == " << mean(mypoisson) << endl;
+  cout << "cdf(mypoisson, 2.) == " << cdf(mypoisson, 2.) << endl;
+  cout << "pdf(mypoisson, 2.) == " << pdf(mypoisson, 2.) << endl;
+  
+  // poisson mydudpoisson(0.);
+  // throws (if BOOST_MATH_DOMAIN_ERROR_POLICY == throw_on_error).
+
+#ifndef BOOST_NO_EXCEPTIONS
+  BOOST_MATH_CHECK_THROW(poisson mydudpoisson(-1), std::domain_error);// Mean must be > 0.
+  BOOST_MATH_CHECK_THROW(poisson mydudpoisson(-1), std::logic_error);// Mean must be > 0.
+#else
+  BOOST_MATH_CHECK_THROW(poisson(-1), std::domain_error);// Mean must be > 0.
+  BOOST_MATH_CHECK_THROW(poisson(-1), std::logic_error);// Mean must be > 0.
+#endif
+  // Passes the check because logic_error is a parent????
+  // BOOST_MATH_CHECK_THROW(poisson mydudpoisson(-1), std::overflow_error); // fails the check
+  // because overflow_error is unrelated - except from std::exception
+  BOOST_MATH_CHECK_THROW(cdf(mypoisson, -1), std::domain_error); // k must be >= 0
+
+  BOOST_CHECK_EQUAL(mean(mypoisson), 4.);
+  BOOST_CHECK_CLOSE(
+  pdf(mypoisson, 2.),  // k events = 2. 
+    1.465251111098740E-001, // probability.
+      5e-13);
+
+  BOOST_CHECK_CLOSE(
+  cdf(mypoisson, 2.),  // k events = 2. 
+    0.238103305553545, // probability.
+      5e-13);
+
+
+#if 0
+  // Compare cdf from finite sum of pdf and gamma_q.
+  using boost::math::cdf;
+  using boost::math::pdf;
+
+  double mean = 4.;
+  cout.precision(17); // double max_digits10
+  cout.setf(ios::showpoint);
+  cout << showpoint << endl;  // Ensure trailing zeros are shown.
+  // This also helps show the expected precision max_digits10
+  //cout.unsetf(ios::showpoint); // No trailing zeros are shown.
+
+  cout << "k          pdf                     sum                  cdf                   diff" << endl;
+  double sum = 0.;
+  for (int i = 0; i <= 50; i++)
+  {
+   cout << i << ' ' ;
+   double p =  pdf(poisson_distribution<double>(mean), static_cast<double>(i));
+   sum += p;
+
+   cout << p << ' ' << sum << ' ' 
+   << cdf(poisson_distribution<double>(mean), static_cast<double>(i)) << ' ';
+     {
+       cout << boost::math::gamma_q<double>(i+1, mean); // cdf
+       double diff = boost::math::gamma_q<double>(i+1, mean) - sum; // cdf -sum
+       cout << setprecision (2) << ' ' << diff; // 0 0 to 4, 1 eps 5 to 9, 10 to 20 2 eps, 21 upwards 3 eps
+      
+     }
+    BOOST_CHECK_CLOSE(
+    cdf(mypoisson, static_cast<double>(i)),
+      sum, // of pdfs.
+      4e-14); // Fails at 2e-14
+   // This call puts the precision etc back to default 6 !!!
+   cout << setprecision(17) << showpoint;
+
+
+     cout << endl;
+  }
+
+   cout << cdf(poisson_distribution<double>(5), static_cast<double>(0)) << ' ' << endl; // 0.006737946999085467
+   cout << cdf(poisson_distribution<double>(5), static_cast<double>(1)) << ' ' << endl; // 0.040427681994512805
+   cout << cdf(poisson_distribution<double>(2), static_cast<double>(3)) << ' ' << endl; // 0.85712346049854715 
+
+   { // Compare approximate formula in Wikipedia with quantile(half)
+     for (int i = 1; i < 100; i++)
+     {
+       poisson_distribution<double> distn(static_cast<double>(i));
+       cout << i << ' ' << median(distn) << ' ' << quantile(distn, 0.5) << ' ' 
+         << median(distn) - quantile(distn, 0.5) << endl; // formula appears to be out-by-one??
+     }  // so quantile(half) used via derived accressors.
+   }
+#endif
+
+   // (Parameter value, arbitrarily zero, only communicates the floating-point type).
+#ifdef TEST_POISSON
+  test_spots(0.0F); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+  test_spots(0.0); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+  if (numeric_limits<long double>::digits10 > numeric_limits<double>::digits10)
+  { // long double is better than double (so not MSVC where they are same).
+#ifdef TEST_LDOUBLE
+     test_spots(0.0L); // Test long double.
+#endif
+  }
+
+#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
+#ifdef TEST_REAL_CONCEPT
+  test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#endif
+#endif
+   
+} // BOOST_AUTO_TEST_CASE( test_main )
+
+/*
+
+Output:
+
+Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_poisson.exe"
+Running 1 test case...
+mean(mypoisson, 4.) == 4.0000000000000000
+mean(mypoisson, 0.) == 4.0000000000000000
+cdf(mypoisson, 2.) == 0.23810330555354431
+pdf(mypoisson, 2.) == 0.14652511110987343
+*** No errors detected
+
+*/