test_bessel_k.cpp

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//  Copyright John Maddock 2006, 2007
//  Copyright Paul A. Bristow 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)

#ifdef _MSC_VER
#  pragma warning(disable : 4756) // overflow in constant arithmetic
// Constants are too big for float case, but this doesn't matter for test.
#endif

#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/concepts/real_concept.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/bessel.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
#include "test_bessel_hooks.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the bessel K function.  There are two sets of tests, spot
// tests which compare our results with selected values computed
// using the online special function calculator at 
// functions.wolfram.com, while the bulk of the accuracy tests
// use values generated with NTL::RR at 1000-bit precision
// and our generic versions of these functions.
//
// Note that when this file is first run on a new platform many of
// these tests will fail: the default accuracy is 1 epsilon which
// is too tight for most platforms.  In this situation you will 
// need to cast a human eye over the error rates reported and make
// a judgement as to whether they are acceptable.  Either way please
// report the results to the Boost mailing list.  Acceptable rates of
// error are marked up below as a series of regular expressions that
// identify the compiler/stdlib/platform/data-type/test-data/test-function
// along with the maximum expected peek and RMS mean errors for that
// test.
//

void expected_results()
{
   //
   // Define the max and mean errors expected for
   // various compilers and platforms.
   //
   const char* largest_type;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
   {
      largest_type = "(long\\s+)?double|real_concept";
   }
   else
   {
      largest_type = "long double|real_concept";
   }
#else
   largest_type = "(long\\s+)?double|real_concept";
#endif
   //
   // On MacOS X cyl_bessel_k has much higher error levels than
   // expected: given that the implementation is basically
   // just a continued fraction evaluation combined with
   // exponentiation, we conclude that exp and pow are less
   // accurate on this platform, especially when the result 
   // is outside the range of a double.
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                      // platform
      largest_type,                  // test type(s)
      ".*",                          // test data group
      ".*", 4000, 1300);             // test function

   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*",                          // test data group
      ".*", 35, 15);                 // test function
   //
   // Finish off by printing out the compiler/stdlib/platform names,
   // we do this to make it easier to mark up expected error rates.
   //
   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}

template <class T>
T cyl_bessel_k_int_wrapper(T v, T x)
{
   return static_cast<T>(
      boost::math::cyl_bessel_k(
      boost::math::itrunc(v), x));
}

template <class T>
void do_test_cyl_bessel_k(const T& data, const char* type_name, const char* test_name)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   typedef value_type (*pg)(value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg funcp = boost::math::cyl_bessel_k<value_type, value_type>;
#else
   pg funcp = boost::math::cyl_bessel_k;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test cyl_bessel_k against data:
   //
   result = boost::math::tools::test(
      data, 
      bind_func(funcp, 0, 1), 
      extract_result(2));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_bessel_k", test_name);
   std::cout << std::endl;

#ifdef TEST_OTHER
   if(boost::is_floating_point<value_type>::value)
   {
      funcp = other::cyl_bessel_k;

      //
      // test other::cyl_bessel_k against data:
      //
      result = boost::math::tools::test(
         data, 
         bind_func(funcp, 0, 1), 
         extract_result(2));
      print_test_result(result, data[result.worst()], result.worst(), type_name, "other::cyl_bessel_k");
      std::cout << std::endl;
   }
#endif
}

template <class T>
void do_test_cyl_bessel_k_int(const T& data, const char* type_name, const char* test_name)
{
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   typedef value_type (*pg)(value_type, value_type);
#if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg funcp = cyl_bessel_k_int_wrapper<value_type>;
#else
   pg funcp = cyl_bessel_k_int_wrapper;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test cyl_bessel_k against data:
   //
   result = boost::math::tools::test(
      data, 
      bind_func(funcp, 0, 1), 
      extract_result(2));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::cyl_bessel_k", test_name);
   std::cout << std::endl;
}

template <class T>
void test_bessel(T, const char* name)
{
    // function values calculated on http://functions.wolfram.com/
    #define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
    static const boost::array<boost::array<T, 3>, 9> k0_data = {{
        SC_(0), SC_(1), SC_(0.421024438240708333335627379212609036136219748226660472298970),
        SC_(0), SC_(2), SC_(0.113893872749533435652719574932481832998326624388808882892530),
        SC_(0), SC_(4), SC_(0.0111596760858530242697451959798334892250090238884743405382553),
        SC_(0), SC_(8), SC_(0.000146470705222815387096584408698677921967305368833759024089154),
        SC_(0), T(std::ldexp(1.0, -15)), SC_(10.5131392267382037062459525561594822400447325776672021972753),
        SC_(0), T(std::ldexp(1.0, -30)), SC_(20.9103469324567717360787328239372191382743831365906131108531),
        SC_(0), T(std::ldexp(1.0, -60)), SC_(41.7047623492551310138446473188663682295952219631968830346918),
        SC_(0), SC_(50), SC_(3.41016774978949551392067551235295223184502537762334808993276e-23),
        SC_(0), SC_(100), SC_(4.65662822917590201893900528948388635580753948544211387402671e-45),
    }};
    static const boost::array<boost::array<T, 3>, 9> k1_data = {
        SC_(1), SC_(1), SC_(0.601907230197234574737540001535617339261586889968106456017768),
        SC_(1), SC_(2), SC_(0.139865881816522427284598807035411023887234584841515530384442),
        SC_(1), SC_(4), SC_(0.0124834988872684314703841799808060684838415849886258457917076),
        SC_(1), SC_(8), SC_(0.000155369211805001133916862450622474621117065122872616157079566),
        SC_(1), T(std::ldexp(1.0, -15)), SC_(32767.9998319528316432647441316539139725104728341577594326513),
        SC_(1), T(std::ldexp(1.0, -30)), SC_(1.07374182399999999003003028572687332810353799544215073362305e9),
        SC_(1), T(std::ldexp(1.0, -60)), SC_(1.15292150460684697599999999999999998169660198868126604634036e18),
        SC_(1), SC_(50), SC_(3.44410222671755561259185303591267155099677251348256880221927e-23),
        SC_(1), SC_(100), SC_(4.67985373563690928656254424202433530797494354694335352937465e-45),
    };
    static const boost::array<boost::array<T, 3>, 9> kn_data = {
        SC_(2), T(std::ldexp(1.0, -30)), SC_(2.30584300921369395150000000000000000234841952009593636868109e18),
        SC_(5), SC_(10), SC_(0.0000575418499853122792763740236992723196597629124356739596921536),
        SC_(-5), SC_(100), SC_(5.27325611329294989461777188449044716451716555009882448801072e-45),
        SC_(10), SC_(10), SC_(0.00161425530039067002345725193091329085443750382929208307802221),
        SC_(10), T(std::ldexp(1.0, -30)), SC_(3.78470202927236255215249281534478864916684072926050665209083e98),
        SC_(-10), SC_(1), SC_(1.80713289901029454691597861302340015908245782948536080022119e8),
        SC_(100), SC_(5), SC_(7.03986019306167654653386616796116726248616158936088056952477e115),
        SC_(100), SC_(80), SC_(8.39287107246490782848985384895907681748152272748337807033319e-12),
        SC_(-1000), SC_(700), SC_(6.51561979144735818903553852606383312984409361984128221539405e-31),
    };
    static const boost::array<boost::array<T, 3>, 11> kv_data = {
        SC_(0.5), SC_(0.875), SC_(0.558532231646608646115729767013630967055657943463362504577189),
        SC_(0.5), SC_(1.125), SC_(0.383621010650189547146769320487006220295290256657827220786527),
        SC_(2.25), T(std::ldexp(1.0, -30)), SC_(5.62397392719283271332307799146649700147907612095185712015604e20),
        SC_(5.5), SC_(3217)/1024, SC_(1.30623288775012596319554857587765179889689223531159532808379),
        SC_(-5.5), SC_(10), SC_(0.0000733045300798502164644836879577484533096239574909573072142667),
        SC_(-5.5), SC_(100), SC_(5.41274555306792267322084448693957747924412508020839543293369e-45),
        SC_(10240)/1024, SC_(1)/1024, SC_(2.35522579263922076203415803966825431039900000000993410734978e38),
        SC_(10240)/1024, SC_(10), SC_(0.00161425530039067002345725193091329085443750382929208307802221),
        SC_(144793)/1024, SC_(100), SC_(1.39565245860302528069481472855619216759142225046370312329416e-6),
        SC_(144793)/1024, SC_(200), SC_(9.11950412043225432171915100042647230802198254567007382956336e-68),
        SC_(-144793)/1024, SC_(50), SC_(1.30185229717525025165362673848737761549946548375142378172956e42),
    };
    #undef SC_

    do_test_cyl_bessel_k(k0_data, name, "Bessel K0: Mathworld Data");
    do_test_cyl_bessel_k(k1_data, name, "Bessel K1: Mathworld Data");
    do_test_cyl_bessel_k(kn_data, name, "Bessel Kn: Mathworld Data");

    do_test_cyl_bessel_k_int(k0_data, name, "Bessel K0: Mathworld Data (Integer Version)");
    do_test_cyl_bessel_k_int(k1_data, name, "Bessel K1: Mathworld Data (Integer Version)");
    do_test_cyl_bessel_k_int(kn_data, name, "Bessel Kn: Mathworld Data (Integer Version)");

    do_test_cyl_bessel_k(kv_data, name, "Bessel Kv: Mathworld Data");

#include "bessel_k_int_data.ipp"
    do_test_cyl_bessel_k(bessel_k_int_data, name, "Bessel Kn: Random Data");
#include "bessel_k_data.ipp"
    do_test_cyl_bessel_k(bessel_k_data, name, "Bessel Kv: Random Data");
}

int test_main(int, char* [])
{
#ifdef TEST_GSL
   gsl_set_error_handler_off();
#endif
   expected_results();
   BOOST_MATH_CONTROL_FP;

#ifndef BOOST_MATH_BUGGY_LARGE_FLOAT_CONSTANTS
   test_bessel(0.1F, "float");
#endif
   test_bessel(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   test_bessel(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
   test_bessel(boost::math::concepts::real_concept(0.1), "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::cout;
#endif
   return 0;
}