[ceph.git] / ceph / src / boost / libs / math / test / test_erf.cpp

//  Copyright John Maddock 2006.
//  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)

#include <pch_light.hpp>
#include "test_erf.hpp"

//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the functions erf, erfc, and the inverses
// erf_inv and erfc_inv.  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
   //
   // 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
      largest_type,                  // test type(s)
      "Erf Function:.*Large.*",      // test data group
      "erfc", 4300, 1300);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      "Mac OS",                      // platform
      largest_type,                  // test type(s)
      "Erf Function:.*",             // test data group
      "erfc", 40, 10);  // test function

   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      "real_concept",                // test type(s)
      "Erf Function:.*",             // test data group
      "erfc?", 20, 6);   // test function
   add_expected_result(
      ".*",                           // compiler
      ".*",                           // stdlib
      ".*",                           // platform
      "real_concept",                 // test type(s)
      "Inverse Erfc.*",               // test data group
      "erfc_inv", 80, 10);  // test function


   //
   // Catch all cases come last:
   //
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      ".*",                          // test type(s)
      "Erf Function:.*",             // test data group
      "erfc?", 2, 2);   // test function
   add_expected_result(
      ".*aCC.*",                     // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      ".*",                          // test type(s)
      "Inverse Erfc.*",               // test data group
      "erfc_inv", 80, 10);  // test function
   add_expected_result(
      ".*",                          // compiler
      ".*",                          // stdlib
      ".*",                          // platform
      ".*",                          // test type(s)
      "Inverse Erf.*",               // test data group
      "erfc?_inv", 18, 4);  // 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;
}

BOOST_AUTO_TEST_CASE( test_main )
{
   BOOST_MATH_CONTROL_FP;
   test_spots(0.0F, "float");
   test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   test_spots(0.0L, "long double");
#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x582)) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
   test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#endif

   expected_results();

   test_erf(0.1F, "float");
   test_erf(0.1, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
   test_erf(0.1L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x582))
   test_erf(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#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
}

/*

Output:

test_erf.cpp
Compiling manifest to resources...
Linking...
Embedding manifest...
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_erf.exe"
Running 1 test case...
Testing basic sanity checks for type float
Testing basic sanity checks for type double
Testing basic sanity checks for type long double
Testing basic sanity checks for type real_concept
Tests run with Microsoft Visual C++ version 8.0, Dinkumware standard library version 405, Win32
Testing Erf Function: Small Values with type float
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<float> Max = 0 RMS Mean=0
boost::math::erfc<float> Max = 0 RMS Mean=0
Testing Erf Function: Medium Values with type float
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<float> Max = 0 RMS Mean=0
boost::math::erfc<float> Max = 0 RMS Mean=0
Testing Erf Function: Large Values with type float
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<float> Max = 0 RMS Mean=0
boost::math::erfc<float> Max = 0 RMS Mean=0
Testing Inverse Erf Function with type float
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf_inv<float> Max = 0 RMS Mean=0
Testing Inverse Erfc Function with type float
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erfc_inv<float> Max = 0 RMS Mean=0
Testing Erf Function: Small Values with type double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<double> Max = 0 RMS Mean=0
boost::math::erfc<double> Max = 0.7857 RMS Mean=0.06415
    worst case at row: 149
    { 0.3343, 0.3636, 0.6364 }
Testing Erf Function: Medium Values with type double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<double> Max = 0.9219 RMS Mean=0.1016
    worst case at row: 273
    { 0.5252, 0.5424, 0.4576 }
boost::math::erfc<double> Max = 1.08 RMS Mean=0.3224
    worst case at row: 287
    { 0.8461, 0.7685, 0.2315 }
Testing Erf Function: Large Values with type double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<double> Max = 0 RMS Mean=0
boost::math::erfc<double> Max = 1.048 RMS Mean=0.2032
    worst case at row: 50
    { 20.96, 1, 4.182e-193 }
Testing Inverse Erf Function with type double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf_inv<double> Max = 1.124 RMS Mean=0.5082
    worst case at row: 98
    { 0.9881, 1.779 }
Testing Inverse Erfc Function with type double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erfc_inv<double> Max = 1.124 RMS Mean=0.5006
    worst case at row: 98
    { 1.988, -1.779 }
Testing Erf Function: Small Values with type long double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<long double> Max = 0 RMS Mean=0
boost::math::erfc<long double> Max = 0.7857 RMS Mean=0.06415
    worst case at row: 149
    { 0.3343, 0.3636, 0.6364 }
Testing Erf Function: Medium Values with type long double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<long double> Max = 0.9219 RMS Mean=0.1016
    worst case at row: 273
    { 0.5252, 0.5424, 0.4576 }
boost::math::erfc<long double> Max = 1.08 RMS Mean=0.3224
    worst case at row: 287
    { 0.8461, 0.7685, 0.2315 }
Testing Erf Function: Large Values with type long double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<long double> Max = 0 RMS Mean=0
boost::math::erfc<long double> Max = 1.048 RMS Mean=0.2032
    worst case at row: 50
    { 20.96, 1, 4.182e-193 }
Testing Inverse Erf Function with type long double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf_inv<long double> Max = 1.124 RMS Mean=0.5082
    worst case at row: 98
    { 0.9881, 1.779 }
Testing Inverse Erfc Function with type long double
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erfc_inv<long double> Max = 1.124 RMS Mean=0.5006
    worst case at row: 98
    { 1.988, -1.779 }
Testing Erf Function: Small Values with type real_concept
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<real_concept> Max = 1.271 RMS Mean=0.5381
    worst case at row: 144
    { 0.0109, 0.0123, 0.9877 }
boost::math::erfc<real_concept> Max = 0.7857 RMS Mean=0.07777
    worst case at row: 149
    { 0.3343, 0.3636, 0.6364 }
Testing Erf Function: Medium Values with type real_concept
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<real_concept> Max = 22.5 RMS Mean=4.224
    worst case at row: 233
    { -0.7852, -0.7332, 1.733 }
Peak error greater than expected value of 20
i:/boost-sandbox/math_toolkit/libs/math/test/handle_test_result.hpp(146): error in "test_main_caller( argc, argv )": check bounds.first >= max_error_found failed
boost::math::erfc<real_concept> Max = 97.77 RMS Mean=8.373
    worst case at row: 289
    { 0.9849, 0.8363, 0.1637 }
Peak error greater than expected value of 20
i:/boost-sandbox/math_toolkit/libs/math/test/handle_test_result.hpp(146): error in "test_main_caller( argc, argv )": check bounds.first >= max_error_found failed
Mean error greater than expected value of 6
i:/boost-sandbox/math_toolkit/libs/math/test/handle_test_result.hpp(151): error in "test_main_caller( argc, argv )": check bounds.second >= mean_error_found failed
Testing Erf Function: Large Values with type real_concept
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf<real_concept> Max = 0 RMS Mean=0
boost::math::erfc<real_concept> Max = 1.395 RMS Mean=0.2908
    worst case at row: 11
    { 10.99, 1, 1.87e-054 }
Testing Inverse Erf Function with type real_concept
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erf_inv<real_concept> Max = 1.124 RMS Mean=0.5082
    worst case at row: 98
    { 0.9881, 1.779 }
Testing Inverse Erfc Function with type real_concept
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
boost::math::erfc_inv<real_concept> Max = 1.124 RMS Mean=0.5006
    worst case at row: 98
    { 1.988, -1.779 }
Test suite "Test Program" failed with:
  181 assertions out of 184 passed
  3 assertions out of 184 failed
  1 test case out of 1 failed
  Test case "test_main_caller( argc, argv )" failed with:
    181 assertions out of 184 passed
    3 assertions out of 184 failed
Build Time 0:15

*/
Commit	Line	Data
7c673cae FG	1	// Copyright John Maddock 2006.
	2	// Copyright Paul A. Bristow 2007
	3	// Use, modification and distribution are subject to the
	4	// Boost Software License, Version 1.0. (See accompanying file
	5	// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
	6
	7	#include <pch_light.hpp>
	8	#include "test_erf.hpp"
	9
	10	//
	11	// DESCRIPTION:
	12	// ~~~~~~~~~~~~
	13	//
	14	// This file tests the functions erf, erfc, and the inverses
	15	// erf_inv and erfc_inv. There are two sets of tests, spot
	16	// tests which compare our results with selected values computed
	17	// using the online special function calculator at
	18	// functions.wolfram.com, while the bulk of the accuracy tests
	19	// use values generated with NTL::RR at 1000-bit precision
	20	// and our generic versions of these functions.
	21	//
	22	// Note that when this file is first run on a new platform many of
	23	// these tests will fail: the default accuracy is 1 epsilon which
	24	// is too tight for most platforms. In this situation you will
	25	// need to cast a human eye over the error rates reported and make
	26	// a judgement as to whether they are acceptable. Either way please
	27	// report the results to the Boost mailing list. Acceptable rates of
	28	// error are marked up below as a series of regular expressions that
	29	// identify the compiler/stdlib/platform/data-type/test-data/test-function
	30	// along with the maximum expected peek and RMS mean errors for that
	31	// test.
	32	//
	33
	34	void expected_results()
	35	{
	36	//
	37	// Define the max and mean errors expected for
	38	// various compilers and platforms.
	39	//
	40	const char* largest_type;
	41	#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
	42	if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
	43	{
	44	largest_type = "(long\\s+)?double\|real_concept";
	45	}
	46	else
	47	{
	48	largest_type = "long double\|real_concept";
	49	}
	50	#else
	51	largest_type = "(long\\s+)?double";
	52	#endif
	53	//
	54	// On MacOS X erfc has much higher error levels than
	55	// expected: given that the implementation is basically
	56	// just a rational function evaluation combined with
	57	// exponentiation, we conclude that exp and pow are less
	58	// accurate on this platform, especially when the result
	59	// is outside the range of a double.
	60	//
	61	add_expected_result(
	62	".*", // compiler
	63	".*", // stdlib
	64	"Mac OS", // platform
65	largest_type, // test type(s)
66	"Erf Function:.Large.", // test data group
67	"erfc", 4300, 1300); // test function
68	add_expected_result(
69	".*", // compiler
70	".*", // stdlib
71	"Mac OS", // platform
72	largest_type, // test type(s)
73	"Erf Function:.*", // test data group
74	"erfc", 40, 10); // test function
75
76	add_expected_result(
77	".*", // compiler
78	".*", // stdlib
79	".*", // platform
80	"real_concept", // test type(s)
81	"Erf Function:.*", // test data group
82	"erfc?", 20, 6); // test function
83	add_expected_result(
84	".*", // compiler
85	".*", // stdlib
86	".*", // platform
87	"real_concept", // test type(s)
88	"Inverse Erfc.*", // test data group
89	"erfc_inv", 80, 10); // test function
90
91
92	//
93	// Catch all cases come last:
94	//
95	add_expected_result(
96	".*", // compiler
97	".*", // stdlib
98	".*", // platform
99	".*", // test type(s)
100	"Erf Function:.*", // test data group
101	"erfc?", 2, 2); // test function
102	add_expected_result(
103	".aCC.", // compiler
104	".*", // stdlib
105	".*", // platform
106	".*", // test type(s)
107	"Inverse Erfc.*", // test data group
108	"erfc_inv", 80, 10); // test function
109	add_expected_result(
110	".*", // compiler
111	".*", // stdlib
112	".*", // platform
113	".*", // test type(s)
114	"Inverse Erf.*", // test data group
115	"erfc?_inv", 18, 4); // test function
116
117	//
118	// Finish off by printing out the compiler/stdlib/platform names,
119	// we do this to make it easier to mark up expected error rates.
120	//
121	std::cout << "Tests run with " << BOOST_COMPILER << ", "
122	<< BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
123	}
124
125	BOOST_AUTO_TEST_CASE( test_main )
126	{
127	BOOST_MATH_CONTROL_FP;
128	test_spots(0.0F, "float");
129	test_spots(0.0, "double");
130	#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
131	test_spots(0.0L, "long double");
1e59de90	132	#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x582)) && !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
7c673cae FG	133	test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
	134	#endif
	135	#endif
	136
	137	expected_results();
	138
	139	test_erf(0.1F, "float");
	140	test_erf(0.1, "double");
	141	#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
	142	test_erf(0.1L, "long double");
	143	#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
20effc67	144	#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x582))
7c673cae FG	145	test_erf(boost::math::concepts::real_concept(0.1), "real_concept");
	146	#endif
	147	#endif
	148	#else
	149	std::cout << "<note>The long double tests have been disabled on this platform "
	150	"either because the long double overloads of the usual math functions are "
	151	"not available at all, or because they are too inaccurate for these tests "
	152	"to pass.</note>" << std::endl;
	153	#endif
	154	}
	155
	156	/*
	157
	158	Output:
	159
	160	test_erf.cpp
	161	Compiling manifest to resources...
	162	Linking...
	163	Embedding manifest...
	164	Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_erf.exe"
	165	Running 1 test case...
	166	Testing basic sanity checks for type float
	167	Testing basic sanity checks for type double
	168	Testing basic sanity checks for type long double
	169	Testing basic sanity checks for type real_concept
	170	Tests run with Microsoft Visual C++ version 8.0, Dinkumware standard library version 405, Win32
	171	Testing Erf Function: Small Values with type float
	172	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	173	boost::math::erf<float> Max = 0 RMS Mean=0
	174	boost::math::erfc<float> Max = 0 RMS Mean=0
	175	Testing Erf Function: Medium Values with type float
	176	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	177	boost::math::erf<float> Max = 0 RMS Mean=0
	178	boost::math::erfc<float> Max = 0 RMS Mean=0
	179	Testing Erf Function: Large Values with type float
	180	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	181	boost::math::erf<float> Max = 0 RMS Mean=0
	182	boost::math::erfc<float> Max = 0 RMS Mean=0
	183	Testing Inverse Erf Function with type float
	184	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	185	boost::math::erf_inv<float> Max = 0 RMS Mean=0
	186	Testing Inverse Erfc Function with type float
	187	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	188	boost::math::erfc_inv<float> Max = 0 RMS Mean=0
	189	Testing Erf Function: Small Values with type double
	190	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	191	boost::math::erf<double> Max = 0 RMS Mean=0
	192	boost::math::erfc<double> Max = 0.7857 RMS Mean=0.06415
	193	worst case at row: 149
	194	{ 0.3343, 0.3636, 0.6364 }
	195	Testing Erf Function: Medium Values with type double
	196	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	197	boost::math::erf<double> Max = 0.9219 RMS Mean=0.1016
	198	worst case at row: 273
	199	{ 0.5252, 0.5424, 0.4576 }
	200	boost::math::erfc<double> Max = 1.08 RMS Mean=0.3224
	201	worst case at row: 287
	202	{ 0.8461, 0.7685, 0.2315 }
	203	Testing Erf Function: Large Values with type double
	204	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	205	boost::math::erf<double> Max = 0 RMS Mean=0
	206	boost::math::erfc<double> Max = 1.048 RMS Mean=0.2032
	207	worst case at row: 50
	208	{ 20.96, 1, 4.182e-193 }
209	Testing Inverse Erf Function with type double
210	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
211	boost::math::erf_inv<double> Max = 1.124 RMS Mean=0.5082
212	worst case at row: 98
213	{ 0.9881, 1.779 }
214	Testing Inverse Erfc Function with type double
215	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
216	boost::math::erfc_inv<double> Max = 1.124 RMS Mean=0.5006
217	worst case at row: 98
218	{ 1.988, -1.779 }
219	Testing Erf Function: Small Values with type long double
220	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
221	boost::math::erf<long double> Max = 0 RMS Mean=0
222	boost::math::erfc<long double> Max = 0.7857 RMS Mean=0.06415
223	worst case at row: 149
224	{ 0.3343, 0.3636, 0.6364 }
225	Testing Erf Function: Medium Values with type long double
226	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
227	boost::math::erf<long double> Max = 0.9219 RMS Mean=0.1016
228	worst case at row: 273
229	{ 0.5252, 0.5424, 0.4576 }
230	boost::math::erfc<long double> Max = 1.08 RMS Mean=0.3224
231	worst case at row: 287
232	{ 0.8461, 0.7685, 0.2315 }
233	Testing Erf Function: Large Values with type long double
234	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
235	boost::math::erf<long double> Max = 0 RMS Mean=0
236	boost::math::erfc<long double> Max = 1.048 RMS Mean=0.2032
237	worst case at row: 50
238	{ 20.96, 1, 4.182e-193 }
239	Testing Inverse Erf Function with type long double
240	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
241	boost::math::erf_inv<long double> Max = 1.124 RMS Mean=0.5082
242	worst case at row: 98
243	{ 0.9881, 1.779 }
244	Testing Inverse Erfc Function with type long double
245	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
246	boost::math::erfc_inv<long double> Max = 1.124 RMS Mean=0.5006
247	worst case at row: 98
248	{ 1.988, -1.779 }
249	Testing Erf Function: Small Values with type real_concept
250	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
251	boost::math::erf<real_concept> Max = 1.271 RMS Mean=0.5381
252	worst case at row: 144
253	{ 0.0109, 0.0123, 0.9877 }
254	boost::math::erfc<real_concept> Max = 0.7857 RMS Mean=0.07777
255	worst case at row: 149
256	{ 0.3343, 0.3636, 0.6364 }
257	Testing Erf Function: Medium Values with type real_concept
258	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
259	boost::math::erf<real_concept> Max = 22.5 RMS Mean=4.224
260	worst case at row: 233
261	{ -0.7852, -0.7332, 1.733 }
262	Peak error greater than expected value of 20
263	i:/boost-sandbox/math_toolkit/libs/math/test/handle_test_result.hpp(146): error in "test_main_caller( argc, argv )": check bounds.first >= max_error_found failed
264	boost::math::erfc<real_concept> Max = 97.77 RMS Mean=8.373
265	worst case at row: 289
266	{ 0.9849, 0.8363, 0.1637 }
267	Peak error greater than expected value of 20
268	i:/boost-sandbox/math_toolkit/libs/math/test/handle_test_result.hpp(146): error in "test_main_caller( argc, argv )": check bounds.first >= max_error_found failed
269	Mean error greater than expected value of 6
270	i:/boost-sandbox/math_toolkit/libs/math/test/handle_test_result.hpp(151): error in "test_main_caller( argc, argv )": check bounds.second >= mean_error_found failed
271	Testing Erf Function: Large Values with type real_concept
272	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
273	boost::math::erf<real_concept> Max = 0 RMS Mean=0
274	boost::math::erfc<real_concept> Max = 1.395 RMS Mean=0.2908
275	worst case at row: 11
276	{ 10.99, 1, 1.87e-054 }
277	Testing Inverse Erf Function with type real_concept
278	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
279	boost::math::erf_inv<real_concept> Max = 1.124 RMS Mean=0.5082
280	worst case at row: 98
281	{ 0.9881, 1.779 }
282	Testing Inverse Erfc Function with type real_concept
283	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
284	boost::math::erfc_inv<real_concept> Max = 1.124 RMS Mean=0.5006
285	worst case at row: 98
286	{ 1.988, -1.779 }
287	Test suite "Test Program" failed with:
288	181 assertions out of 184 passed
289	3 assertions out of 184 failed
290	1 test case out of 1 failed
291	Test case "test_main_caller( argc, argv )" failed with:
292	181 assertions out of 184 passed
293	3 assertions out of 184 failed
294	Build Time 0:15
295
296	*/