test_bessel_y.cpp

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//  (C) Copyright John Maddock 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)

#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 Y 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";
#endif

   //
   // HP-UX and Solaris rates are very slightly higher:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "HP-UX|Sun Solaris",                          // platform
      largest_type,                // test type(s)
      ".*(Y[nv]|y).*Random.*",           // test data group
      ".*", 30000, 30000);             // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "HP-UX|Sun Solaris",                          // platform
      largest_type,                  // test type(s)
      ".*Y[01Nv].*",           // test data group
      ".*", 1300, 500);               // test function
   //
   // Tru64:
   //
   add_expected_result(
      ".*Tru64.*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                // test type(s)
      ".*(Y[nv]|y).*Random.*",           // test data group
      ".*", 30000, 30000);             // test function
   add_expected_result(
      ".*Tru64.*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                      // test type(s)
      ".*Y[01Nv].*",           // test data group
      ".*", 400, 200);               // test function

   //
   // Mac OS X rates are very slightly higher:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      largest_type,                // test type(s)
      ".*(Y[nv1]).*",           // test data group
      ".*", 600000, 100000);             // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                          // platform
      "long double|real_concept",        // test type(s)
      ".*Y[0].*",           // test data group
      ".*", 1200, 1000);               // test function

   //
   // Linux:
   //
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         "linux",                          // platform
         largest_type,                  // test type(s)
         ".*Yv.*Random.*",              // test data group
         ".*", 200000, 200000);         // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         "linux",                          // platform
         largest_type,                  // test type(s)
         ".*Y[01v].*",              // test data group
         ".*", 2000, 1000);         // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         "linux",                          // platform
         largest_type,                  // test type(s)
         ".*Yn.*",              // test data group
         ".*", 30000, 30000);         // test function
   //
   // MinGW:
   //
      add_expected_result(
         ".*mingw.*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         ".*Yv.*Random.*",              // test data group
         ".*", 200000, 200000);         // test function
      add_expected_result(
         ".*mingw.*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         ".*Y[01v].*",              // test data group
         ".*", 2000, 1000);         // test function
      add_expected_result(
         ".*mingw.*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         largest_type,                  // test type(s)
         ".*Yn.*",              // test data group
         ".*", 30000, 30000);         // test function
   //
   // Solaris version of long double has it's own error rates,
   // again just a touch higher than msvc's 64-bit double:
   //
   add_expected_result(
      "GNU.*",                          // compiler
      ".*",                          // stdlib
      "Sun.*",                          // platform
      largest_type,                  // test type(s)
      "Y[0N].*Mathworld.*",              // test data group
      ".*", 2000, 2000);         // test function

#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   if((std::numeric_limits<double>::digits != std::numeric_limits<long double>::digits)
      && (std::numeric_limits<long double>::digits < 90))
   {
      // some errors spill over into type double as well:
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*Y[Nn].*",              // test data group
         ".*", 20, 20);         // test function
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "double",                      // test type(s)
         ".*Yv.*",              // test data group
         ".*", 80, 70);         // test function
   }
#endif
   //
   // defaults are based on MSVC-8 on Win32:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*Y0.*Random.*",           // test data group
      ".*", 600, 400);               // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                // test type(s)
      ".*(Y[nv]|y).*Random.*",           // test data group
      ".*", 2000, 2000);             // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      largest_type,                  // test type(s)
      ".*(Y[nv]|y).*Random.*",           // test data group
      ".*", 1500, 1000);               // test function
   //
   // Fallback for sun has to go after the general cases above:
   //
   add_expected_result(
      "GNU.*",                          // compiler
      ".*",                          // stdlib
      "Sun.*",                          // platform
      largest_type,                  // test type(s)
      "Y[0N].*",              // test data group
      ".*", 200, 200);         // test function
   //
   // General fallback:
   //
   add_expected_result(