test_expint.cpp

Boost provides free peer-reviewed portable C++ source libraries. We emphasize libraries that work

//  (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)

#include <boost/math/concepts/real_concept.hpp>
#include <boost/math/special_functions/expint.hpp>
#include <boost/math/special_functions/trunc.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/tools/stats.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/type_traits/is_floating_point.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
#include "test_expint_hooks.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the expint functions. There are two sets of tests:
// 1) Sanity checks: comparison to test values created with the
// online calculator at functions.wolfram.com
// 2) 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";
   }
   else
   {
      largest_type = "long double";
   }
#else
   largest_type = "(long\\s+)?double";
#endif

   //
   // On MacOS X erfc has much higher error levels than
   // expected: given that the implementation is basically
   // just a rational function 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
      "float|double|long double",    // test type(s)
      ".*E1.*",                      // test data group
      ".*", 30, 10);                   // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                      // platform
      "float|double|long double",    // test type(s)
      ".*Ei.*",                      // test data group
      ".*", 300, 200);                   // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                      // platform
      ".*",                          // test type(s)
      ".*",                          // test data group
      ".*", 40, 15);                   // test function

   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "float|double|long double",    // test type(s)
      ".*E1.*",                      // test data group
      ".*", 2, 1);                   // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "float|double|long double",    // test type(s)
      ".*Ei.*",                      // test data group
      ".*", 6, 3);                   // test function
   if(std::numeric_limits<long double>::digits > 100)
   {
      add_expected_result(
         ".*",                          // compiler
         ".*",                          // stdlib
         ".*",                          // platform
         "real_concept",                // test type(s)
         ".*Ei.*",                      // test data group
         ".*", 150, 50);                // test function
   }
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                // test type(s)
      ".*Ei.*",                      // test data group
      ".*", 50, 20);                 // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      ".*",                          // test type(s)
      ".*",                          // test data group
      ".*", 25, 5);                   // test function

   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
}

template <class T>
T expint_wrapper(T n, T z)
{
   return boost::math::expint(
      boost::math::itrunc(n), z);
}

#ifdef TEST_OTHER
template <class T>
T other_expint_wrapper(T n, T z)
{
   return other::expint(
      boost::math::itrunc(n), z);
}
#endif
template <class T>
void do_test_expint(const T& data, const char* type_name, const char* test_name)
{
   //
   // test En(T) against data:
   //
   using namespace std;
   typedef typename T::value_type row_type;
   typedef typename row_type::value_type value_type;

   std::cout << test_name << " with type " << type_name << std::endl;

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

   boost::math::tools::test_result<value_type> result;
   //
   // test expint 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::expint", test_name);
#ifdef TEST_OTHER
   if(boost::is_floating_point<value_type>::value && other::expint(2u, 2.0))
   {
      funcp = other_expint_wrapper;
      //