Boost_1_39_0/libs/math/test/test_erf.cpp

   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 <boost/math/concepts/real_concept.hpp>
   8 #include <boost/test/included/test_exec_monitor.hpp>
   9 #include <boost/test/floating_point_comparison.hpp>
  10 #include <boost/math/special_functions/erf.hpp>
  11 #include <boost/math/constants/constants.hpp>
  12 #include <boost/type_traits/is_floating_point.hpp>
  13 #include <boost/array.hpp>
  14 #include "functor.hpp"
  15
  16 #include "test_erf_hooks.hpp"
  17 #include "handle_test_result.hpp"
  18
  19 //
  20 // DESCRIPTION:
  21 // ~~~~~~~~~~~~
  22 //
  23 // This file tests the functions erf, erfc, and the inverses
  24 // erf_inv and erfc_inv.  There are two sets of tests, spot
  25 // tests which compare our results with selected values computed
  26 // using the online special function calculator at
  27 // functions.wolfram.com, while the bulk of the accuracy tests
  28 // use values generated with NTL::RR at 1000-bit precision
  29 // and our generic versions of these functions.
  30 //
  31 // Note that when this file is first run on a new platform many of
  32 // these tests will fail: the default accuracy is 1 epsilon which
  33 // is too tight for most platforms.  In this situation you will
  34 // need to cast a human eye over the error rates reported and make
  35 // a judgement as to whether they are acceptable.  Either way please
  36 // report the results to the Boost mailing list.  Acceptable rates of
  37 // error are marked up below as a series of regular expressions that
  38 // identify the compiler/stdlib/platform/data-type/test-data/test-function
  39 // along with the maximum expected peek and RMS mean errors for that
  40 // test.
  41 //
  42
  43 void expected_results()
  44 {
  45    //
  46    // Define the max and mean errors expected for
  47    // various compilers and platforms.
  48    //
  49    const char* largest_type;
  50 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  51    if(boost::math::policies::digits<double, boost::math::policies::policy<> >() == boost::math::policies::digits<long double, boost::math::policies::policy<> >())
  52    {
  53       largest_type = "(long\\s+)?double|real_concept";
  54    }
  55    else
  56    {
  57       largest_type = "long double|real_concept";
  58    }
  59 #else
  60    largest_type = "(long\\s+)?double";
  61 #endif
  62    //
  63    // On MacOS X erfc has much higher error levels than
  64    // expected: given that the implementation is basically
  65    // just a rational function evaluation combined with
  66    // exponentiation, we conclude that exp and pow are less
  67    // accurate on this platform, especially when the result
  68    // is outside the range of a double.
  69    //
  70    add_expected_result(
  71       ".*",                          // compiler
  72       ".*",                          // stdlib
  73       "Mac OS",                      // platform
  74       largest_type,                  // test type(s)
  75       "Erf Function:.*Large.*",      // test data group
  76       "boost::math::erfc", 4300, 1300);  // test function
  77    add_expected_result(
  78       ".*",                          // compiler
  79       ".*",                          // stdlib
  80       "Mac OS",                      // platform
  81       largest_type,                  // test type(s)
  82       "Erf Function:.*",             // test data group
  83       "boost::math::erfc", 40, 10);  // test function
  84
  85    add_expected_result(
  86       ".*",                          // compiler
  87       ".*",                          // stdlib
  88       ".*",                          // platform
  89       "real_concept",                // test type(s)
  90       "Erf Function:.*",             // test data group
  91       "boost::math::erfc?", 20, 6);   // test function
  92    add_expected_result(
  93       ".*",                           // compiler
  94       ".*",                           // stdlib
  95       ".*",                           // platform
  96       "real_concept",                 // test type(s)
  97       "Inverse Erfc.*",               // test data group
  98       "boost::math::erfc_inv", 80, 10);  // test function
  99
 100
 101    //
 102    // Catch all cases come last:
 103    //
 104    add_expected_result(
 105       ".*",                          // compiler
 106       ".*",                          // stdlib
 107       ".*",                          // platform
 108       ".*",                          // test type(s)
 109       "Erf Function:.*",             // test data group
 110       "boost::math::erfc?", 2, 2);   // test function
 111    add_expected_result(
 112       ".*aCC.*",                     // compiler
 113       ".*",                          // stdlib
 114       ".*",                          // platform
 115       ".*",                          // test type(s)
 116       "Inverse Erfc.*",               // test data group
 117       "boost::math::erfc_inv", 80, 10);  // test function
 118    add_expected_result(
 119       ".*",                          // compiler
 120       ".*",                          // stdlib
 121       ".*",                          // platform
 122       ".*",                          // test type(s)
 123       "Inverse Erf.*",               // test data group
 124       "boost::math::erfc?_inv", 18, 4);  // test function
 125
 126    //
 127    // Finish off by printing out the compiler/stdlib/platform names,
 128    // we do this to make it easier to mark up expected error rates.
 129    //
 130    std::cout << "Tests run with " << BOOST_COMPILER << ", "
 131       << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
 132 }
 133
 134 template <class T>
 135 void do_test_erf(const T& data, const char* type_name, const char* test_name)
 136 {
 137    typedef typename T::value_type row_type;
 138    typedef typename row_type::value_type value_type;
 139
 140    typedef value_type (*pg)(value_type);
 141 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 142    pg funcp = boost::math::erf<value_type>;
 143 #else
 144    pg funcp = boost::math::erf;
 145 #endif
 146
 147    boost::math::tools::test_result<value_type> result;
 148
 149    std::cout << "Testing " << test_name << " with type " << type_name
 150       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
 151
 152    //
 153    // test erf against data:
 154    //
 155    result = boost::math::tools::test(
 156       data,
 157       bind_func(funcp, 0),
 158       extract_result(1));
 159    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::erf", test_name);
 160 #ifdef TEST_OTHER
 161    if(::boost::is_floating_point<value_type>::value){
 162       funcp = other::erf;
 163       result = boost::math::tools::test(
 164          data,
 165          bind_func(funcp, 0),
 166          extract_result(1));
 167       print_test_result(result, data[result.worst()], result.worst(), type_name, "other::erf");
 168    }
 169 #endif
 170    //
 171    // test erfc against data:
 172    //
 173 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 174    funcp = boost::math::erfc<value_type>;
 175 #else
 176    funcp = boost::math::erfc;
 177 #endif
 178    result = boost::math::tools::test(
 179       data,
 180       bind_func(funcp, 0),
 181       extract_result(2));
 182    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::erfc", test_name);
 183 #ifdef TEST_OTHER
 184    if(::boost::is_floating_point<value_type>::value){
 185       funcp = other::erfc;
 186       result = boost::math::tools::test(
 187          data,
 188          bind(funcp, 0),
 189          extract_result(2));
 190       print_test_result(result, data[result.worst()], result.worst(), type_name, "other::erfc");
 191    }
 192 #endif
 193    std::cout << std::endl;
 194 }
 195
 196 template <class T>
 197 void do_test_erf_inv(const T& data, const char* type_name, const char* test_name)
 198 {
 199    typedef typename T::value_type row_type;
 200    typedef typename row_type::value_type value_type;
 201
 202    typedef value_type (*pg)(value_type);
 203
 204    boost::math::tools::test_result<value_type> result;
 205    std::cout << "Testing " << test_name << " with type " << type_name
 206       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
 207    //
 208    // test erf_inv against data:
 209    //
 210 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 211    pg funcp = boost::math::erf_inv<value_type>;
 212 #else
 213    pg funcp = boost::math::erf_inv;
 214 #endif
 215    result = boost::math::tools::test(
 216       data,
 217       bind_func(funcp, 0),
 218       extract_result(1));
 219    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::erf_inv", test_name);
 220    std::cout << std::endl;
 221 }
 222
 223 template <class T>
 224 void do_test_erfc_inv(const T& data, const char* type_name, const char* test_name)
 225 {
 226    typedef typename T::value_type row_type;
 227    typedef typename row_type::value_type value_type;
 228
 229    typedef value_type (*pg)(value_type);
 230 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 231    pg funcp = boost::math::erf<value_type>;
 232 #else
 233    pg funcp = boost::math::erf;
 234 #endif
 235
 236    boost::math::tools::test_result<value_type> result;
 237    std::cout << "Testing " << test_name << " with type " << type_name
 238       << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
 239    //
 240    // test erfc_inv against data:
 241    //
 242 #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
 243    funcp = boost::math::erfc_inv<value_type>;
 244 #else
 245    funcp = boost::math::erfc_inv;
 246 #endif
 247    result = boost::math::tools::test(
 248       data,
 249       bind_func(funcp, 0),
 250       extract_result(1));
 251    handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::erfc_inv", test_name);
 252    std::cout << std::endl;
 253 }
 254
 255 template <class T>
 256 void test_erf(T, const char* name)
 257 {
 258    //
 259    // The actual test data is rather verbose, so it's in a separate file
 260    //
 261    // The contents are as follows, each row of data contains
 262    // three items, input value a, input value b and erf(a, b):
 263    //
 264 #  include "erf_small_data.ipp"
 265
 266    do_test_erf(erf_small_data, name, "Erf Function: Small Values");
 267
 268 #  include "erf_data.ipp"
 269
 270    do_test_erf(erf_data, name, "Erf Function: Medium Values");
 271
 272 #  include "erf_large_data.ipp"
 273
 274    do_test_erf(erf_large_data, name, "Erf Function: Large Values");
 275
 276 #  include "erf_inv_data.ipp"
 277
 278    do_test_erf_inv(erf_inv_data, name, "Inverse Erf Function");
 279
 280 #  include "erfc_inv_data.ipp"
 281
 282    do_test_erfc_inv(erfc_inv_data, name, "Inverse Erfc Function");
 283
 284 #  include "erfc_inv_big_data.ipp"
 285
 286    if(std::numeric_limits<T>::min_exponent <= -4500)
 287    {
 288       do_test_erfc_inv(erfc_inv_big_data, name, "Inverse Erfc Function: extreme values");
 289    }
 290 }
 291
 292 template <class T>
 293 void test_spots(T, const char* t)
 294 {
 295    std::cout << "Testing basic sanity checks for type " << t << std::endl;
 296    //
 297    // basic sanity checks, tolerance is 10 epsilon expressed as a percentage:
 298    //
 299    T tolerance = boost::math::tools::epsilon<T>() * 1000;
 300    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.125)), static_cast<T>(0.85968379519866618260697055347837660181302041685015L), tolerance);
 301    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0.5)), static_cast<T>(0.47950012218695346231725334610803547126354842424204L), tolerance);
 302    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(1)), static_cast<T>(0.15729920705028513065877936491739074070393300203370L), tolerance);
 303    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(5)), static_cast<T>(1.5374597944280348501883434853833788901180503147234e-12L), tolerance);
 304    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.125)), static_cast<T>(1.1403162048013338173930294465216233981869795831498L), tolerance);
 305    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(-0.5)), static_cast<T>(1.5204998778130465376827466538919645287364515757580L), tolerance);
 306    BOOST_CHECK_CLOSE(::boost::math::erfc(static_cast<T>(0)), static_cast<T>(1), tolerance);
 307
 308    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.125)), static_cast<T>(0.14031620480133381739302944652162339818697958314985L), tolerance);
 309    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0.5)), static_cast<T>(0.52049987781304653768274665389196452873645157575796L), tolerance);
 310    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(1)), static_cast<T>(0.84270079294971486934122063508260925929606699796630L), tolerance);
 311    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(5)), static_cast<T>(0.9999999999984625402055719651498116565146166211099L), tolerance);
 312    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.125)), static_cast<T>(-0.14031620480133381739302944652162339818697958314985L), tolerance);
 313    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(-0.5)), static_cast<T>(-0.52049987781304653768274665389196452873645157575796L), tolerance);
 314    BOOST_CHECK_CLOSE(::boost::math::erf(static_cast<T>(0)), static_cast<T>(0), tolerance);
 315
 316    tolerance = boost::math::tools::epsilon<T>() * 100 * 200; // 200 eps %.
 317 #if defined(__CYGWIN__)
 318    // some platforms long double is only reliably accurate to double precision:
 319    if(sizeof(T) == sizeof(long double))
 320       tolerance = boost::math::tools::epsilon<double>() * 100 * 200; // 200 eps %.
 321 #endif
 322
 323    for(T i = -0.95f; i < 1; i += 0.125f)
 324    {
 325       T inv = boost::math::erf_inv(i);
 326       T b = boost::math::erf(inv);
 327       BOOST_CHECK_CLOSE(b, i, tolerance);
 328    }
 329    for(T j = 0.125f; j < 2; j += 0.125f)
 330    {
 331       T inv = boost::math::erfc_inv(j);
 332       T b = boost::math::erfc(inv);
 333       BOOST_CHECK_CLOSE(b, j, tolerance);
 334    }
 335 }
 336
 337 int test_main(int, char* [])
 338 {
 339    BOOST_MATH_CONTROL_FP;
 340    test_spots(0.0F, "float");
 341    test_spots(0.0, "double");
 342 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 343    test_spots(0.0L, "long double");
 344 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 345    test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
 346 #endif
 347 #endif
 348
 349    expected_results();
 350
 351    test_erf(0.1F, "float");
 352    test_erf(0.1, "double");
 353 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 354    test_erf(0.1L, "long double");
 355 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
 356 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 357    test_erf(boost::math::concepts::real_concept(0.1), "real_concept");
 358 #endif
 359 #endif
 360 #else
 361    std::cout << "<note>The long double tests have been disabled on this platform "
 362       "either because the long double overloads of the usual math functions are "
 363       "not available at all, or because they are too inaccurate for these tests "
 364       "to pass.</note>" << std::cout;
 365 #endif
 366    return 0;
 367 }
 368
 369 /*
 370
 371 Output:
 372
 373 test_erf.cpp
 374 Compiling manifest to resources...
 375 Linking...
 376 Embedding manifest...
 377 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_erf.exe"
 378 Running 1 test case...
 379 Testing basic sanity checks for type float
 380 Testing basic sanity checks for type double
 381 Testing basic sanity checks for type long double
 382 Testing basic sanity checks for type real_concept
 383 Tests run with Microsoft Visual C++ version 8.0, Dinkumware standard library version 405, Win32
 384 Testing Erf Function: Small Values with type float
 385 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 386 boost::math::erf<float> Max = 0 RMS Mean=0
 387 boost::math::erfc<float> Max = 0 RMS Mean=0
 388 Testing Erf Function: Medium Values with type float
 389 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 390 boost::math::erf<float> Max = 0 RMS Mean=0
 391 boost::math::erfc<float> Max = 0 RMS Mean=0
 392 Testing Erf Function: Large Values with type float
 393 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 394 boost::math::erf<float> Max = 0 RMS Mean=0
 395 boost::math::erfc<float> Max = 0 RMS Mean=0
 396 Testing Inverse Erf Function with type float
 397 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 398 boost::math::erf_inv<float> Max = 0 RMS Mean=0
 399 Testing Inverse Erfc Function with type float
 400 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 401 boost::math::erfc_inv<float> Max = 0 RMS Mean=0
 402 Testing Erf Function: Small Values with type double
 403 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 404 boost::math::erf<double> Max = 0 RMS Mean=0
 405 boost::math::erfc<double> Max = 0.7857 RMS Mean=0.06415
 406     worst case at row: 149
 407     { 0.3343, 0.3636, 0.6364 }
 408 Testing Erf Function: Medium Values with type double
 409 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 410 boost::math::erf<double> Max = 0.9219 RMS Mean=0.1016
 411     worst case at row: 273
 412     { 0.5252, 0.5424, 0.4576 }
 413 boost::math::erfc<double> Max = 1.08 RMS Mean=0.3224
 414     worst case at row: 287
 415     { 0.8461, 0.7685, 0.2315 }
 416 Testing Erf Function: Large Values with type double
 417 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 418 boost::math::erf<double> Max = 0 RMS Mean=0
 419 boost::math::erfc<double> Max = 1.048 RMS Mean=0.2032
 420     worst case at row: 50
 421     { 20.96, 1, 4.182e-193 }
 422 Testing Inverse Erf Function with type double
 423 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 424 boost::math::erf_inv<double> Max = 1.124 RMS Mean=0.5082
 425     worst case at row: 98
 426     { 0.9881, 1.779 }
 427 Testing Inverse Erfc Function with type double
 428 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 429 boost::math::erfc_inv<double> Max = 1.124 RMS Mean=0.5006
 430     worst case at row: 98
 431     { 1.988, -1.779 }
 432 Testing Erf Function: Small Values with type long double
 433 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 434 boost::math::erf<long double> Max = 0 RMS Mean=0
 435 boost::math::erfc<long double> Max = 0.7857 RMS Mean=0.06415
 436     worst case at row: 149
 437     { 0.3343, 0.3636, 0.6364 }
 438 Testing Erf Function: Medium Values with type long double
 439 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 440 boost::math::erf<long double> Max = 0.9219 RMS Mean=0.1016
 441     worst case at row: 273
 442     { 0.5252, 0.5424, 0.4576 }
 443 boost::math::erfc<long double> Max = 1.08 RMS Mean=0.3224
 444     worst case at row: 287
 445     { 0.8461, 0.7685, 0.2315 }
 446 Testing Erf Function: Large Values with type long double
 447 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 448 boost::math::erf<long double> Max = 0 RMS Mean=0
 449 boost::math::erfc<long double> Max = 1.048 RMS Mean=0.2032
 450     worst case at row: 50
 451     { 20.96, 1, 4.182e-193 }
 452 Testing Inverse Erf Function with type long double
 453 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 454 boost::math::erf_inv<long double> Max = 1.124 RMS Mean=0.5082
 455     worst case at row: 98
 456     { 0.9881, 1.779 }
 457 Testing Inverse Erfc Function with type long double
 458 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 459 boost::math::erfc_inv<long double> Max = 1.124 RMS Mean=0.5006
 460     worst case at row: 98
 461     { 1.988, -1.779 }
 462 Testing Erf Function: Small Values with type real_concept
 463 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 464 boost::math::erf<real_concept> Max = 1.271 RMS Mean=0.5381
 465     worst case at row: 144
 466     { 0.0109, 0.0123, 0.9877 }
 467 boost::math::erfc<real_concept> Max = 0.7857 RMS Mean=0.07777
 468     worst case at row: 149
 469     { 0.3343, 0.3636, 0.6364 }
 470 Testing Erf Function: Medium Values with type real_concept
 471 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 472 boost::math::erf<real_concept> Max = 22.5 RMS Mean=4.224
 473     worst case at row: 233
 474     { -0.7852, -0.7332, 1.733 }
 475 Peak error greater than expected value of 20
 476 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
 477 boost::math::erfc<real_concept> Max = 97.77 RMS Mean=8.373
 478     worst case at row: 289
 479     { 0.9849, 0.8363, 0.1637 }
 480 Peak error greater than expected value of 20
 481 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
 482 Mean error greater than expected value of 6
 483 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
 484 Testing Erf Function: Large Values with type real_concept
 485 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 486 boost::math::erf<real_concept> Max = 0 RMS Mean=0
 487 boost::math::erfc<real_concept> Max = 1.395 RMS Mean=0.2908
 488     worst case at row: 11
 489     { 10.99, 1, 1.87e-054 }
 490 Testing Inverse Erf Function with type real_concept
 491 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 492 boost::math::erf_inv<real_concept> Max = 1.124 RMS Mean=0.5082
 493     worst case at row: 98
 494     { 0.9881, 1.779 }
 495 Testing Inverse Erfc Function with type real_concept
 496 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 497 boost::math::erfc_inv<real_concept> Max = 1.124 RMS Mean=0.5006
 498     worst case at row: 98
 499     { 1.988, -1.779 }
 500 Test suite "Test Program" failed with:
 501   181 assertions out of 184 passed
 502   3 assertions out of 184 failed
 503   1 test case out of 1 failed
 504   Test case "test_main_caller( argc, argv )" failed with:
 505     181 assertions out of 184 passed
 506     3 assertions out of 184 failed
 507 Build Time 0:15
 508
 509 */