ground/gcs/src/libs/eigen/test/main.h

   1 // This file is part of Eigen, a lightweight C++ template library
   2 // for linear algebra.
   3 //
   4 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
   5 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
   6 //
   7 // This Source Code Form is subject to the terms of the Mozilla
   8 // Public License v. 2.0. If a copy of the MPL was not distributed
   9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  10
  11 #include <cstdlib>
  12 #include <cerrno>
  13 #include <ctime>
  14 #include <iostream>
  15 #include <fstream>
  16 #include <string>
  17 #include <sstream>
  18 #include <vector>
  19 #include <typeinfo>
  20
  21 // The following includes of STL headers have to be done _before_ the
  22 // definition of macros min() and max().  The reason is that many STL
  23 // implementations will not work properly as the min and max symbols collide
  24 // with the STL functions std:min() and std::max().  The STL headers may check
  25 // for the macro definition of min/max and issue a warning or undefine the
  26 // macros.
  27 //
  28 // Still, Windows defines min() and max() in windef.h as part of the regular
  29 // Windows system interfaces and many other Windows APIs depend on these
  30 // macros being available.  To prevent the macro expansion of min/max and to
  31 // make Eigen compatible with the Windows environment all function calls of
  32 // std::min() and std::max() have to be written with parenthesis around the
  33 // function name.
  34 //
  35 // All STL headers used by Eigen should be included here.  Because main.h is
  36 // included before any Eigen header and because the STL headers are guarded
  37 // against multiple inclusions, no STL header will see our own min/max macro
  38 // definitions.
  39 #include <limits>
  40 #include <algorithm>
  41 #include <complex>
  42 #include <deque>
  43 #include <queue>
  44 #include <list>
  45
  46 // To test that all calls from Eigen code to std::min() and std::max() are
  47 // protected by parenthesis against macro expansion, the min()/max() macros
  48 // are defined here and any not-parenthesized min/max call will cause a
  49 // compiler error.
  50 #define min(A,B) please_protect_your_min_with_parentheses
  51 #define max(A,B) please_protect_your_max_with_parentheses
  52
  53 #define FORBIDDEN_IDENTIFIER (this_identifier_is_forbidden_to_avoid_clashes) this_identifier_is_forbidden_to_avoid_clashes
  54 // B0 is defined in POSIX header termios.h
  55 #define B0 FORBIDDEN_IDENTIFIER
  56
  57
  58 // shuts down ICC's remark #593: variable "XXX" was set but never used
  59 #define TEST_SET_BUT_UNUSED_VARIABLE(X) X = X + 0;
  60
  61 // the following file is automatically generated by cmake
  62 #include "split_test_helper.h"
  63
  64 #ifdef NDEBUG
  65 #undef NDEBUG
  66 #endif
  67
  68 // On windows CE, NDEBUG is automatically defined <assert.h> if NDEBUG is not defined.
  69 #ifndef DEBUG
  70 #define DEBUG
  71 #endif
  72
  73 // bounds integer values for AltiVec
  74 #ifdef __ALTIVEC__
  75 #define EIGEN_MAKING_DOCS
  76 #endif
  77
  78 #ifndef EIGEN_TEST_FUNC
  79 #error EIGEN_TEST_FUNC must be defined
  80 #endif
  81
  82 #define DEFAULT_REPEAT 10
  83
  84 namespace Eigen
  85 {
  86   static std::vector<std::string> g_test_stack;
  87   static int g_repeat;
  88   static unsigned int g_seed;
  89   static bool g_has_set_repeat, g_has_set_seed;
  90 }
  91
  92 #define EI_PP_MAKE_STRING2(S) #S
  93 #define EI_PP_MAKE_STRING(S) EI_PP_MAKE_STRING2(S)
  94
  95 #define EIGEN_DEFAULT_IO_FORMAT IOFormat(4, 0, "  ", "\n", "", "", "", "")
  96
  97 #ifndef EIGEN_NO_ASSERTION_CHECKING
  98
  99   namespace Eigen
 100   {
 101     static const bool should_raise_an_assert = false;
 102
 103     // Used to avoid to raise two exceptions at a time in which
 104     // case the exception is not properly caught.
 105     // This may happen when a second exceptions is triggered in a destructor.
 106     static bool no_more_assert = false;
 107     static bool report_on_cerr_on_assert_failure = true;
 108
 109     struct eigen_assert_exception
 110     {
 111       eigen_assert_exception(void) {}
 112       ~eigen_assert_exception() { Eigen::no_more_assert = false; }
 113     };
 114   }
 115   // If EIGEN_DEBUG_ASSERTS is defined and if no assertion is triggered while
 116   // one should have been, then the list of excecuted assertions is printed out.
 117   //
 118   // EIGEN_DEBUG_ASSERTS is not enabled by default as it
 119   // significantly increases the compilation time
 120   // and might even introduce side effects that would hide
 121   // some memory errors.
 122   #ifdef EIGEN_DEBUG_ASSERTS
 123
 124     namespace Eigen
 125     {
 126       namespace internal
 127       {
 128         static bool push_assert = false;
 129       }
 130       static std::vector<std::string> eigen_assert_list;
 131     }
 132     #define eigen_assert(a)                       \
 133       if( (!(a)) && (!no_more_assert) )     \
 134       { \
 135         if(report_on_cerr_on_assert_failure) \
 136           std::cerr <<  #a << " " __FILE__ << "(" << __LINE__ << ")\n"; \
 137         Eigen::no_more_assert = true;       \
 138         throw Eigen::eigen_assert_exception(); \
 139       }                                     \
 140       else if (Eigen::internal::push_assert)       \
 141       {                                     \
 142         eigen_assert_list.push_back(std::string(EI_PP_MAKE_STRING(__FILE__) " (" EI_PP_MAKE_STRING(__LINE__) ") : " #a) ); \
 143       }
 144
 145     #define VERIFY_RAISES_ASSERT(a)                                                   \
 146       {                                                                               \
 147         Eigen::no_more_assert = false;                                                \
 148         Eigen::eigen_assert_list.clear();                                                \
 149         Eigen::internal::push_assert = true;                                                 \
 150         Eigen::report_on_cerr_on_assert_failure = false;                              \
 151         try {                                                                         \
 152           a;                                                                          \
 153           std::cerr << "One of the following asserts should have been triggered:\n";  \
 154           for (uint ai=0 ; ai<eigen_assert_list.size() ; ++ai)                           \
 155             std::cerr << "  " << eigen_assert_list[ai] << "\n";                          \
 156           VERIFY(Eigen::should_raise_an_assert && # a);                               \
 157         } catch (Eigen::eigen_assert_exception) {                                        \
 158           Eigen::internal::push_assert = false; VERIFY(true);                                \
 159         }                                                                             \
 160         Eigen::report_on_cerr_on_assert_failure = true;                               \
 161         Eigen::internal::push_assert = false;                                                \
 162       }
 163
 164   #else // EIGEN_DEBUG_ASSERTS
 165     // see bug 89. The copy_bool here is working around a bug in gcc <= 4.3
 166     #define eigen_assert(a) \
 167       if( (!Eigen::internal::copy_bool(a)) && (!no_more_assert) )\
 168       {                                       \
 169         Eigen::no_more_assert = true;         \
 170         if(report_on_cerr_on_assert_failure)  \
 171           eigen_plain_assert(a);              \
 172         else                                  \
 173           throw Eigen::eigen_assert_exception(); \
 174       }
 175     #define VERIFY_RAISES_ASSERT(a) {                             \
 176         Eigen::no_more_assert = false;                            \
 177         Eigen::report_on_cerr_on_assert_failure = false;          \
 178         try {                                                     \
 179           a;                                                      \
 180           VERIFY(Eigen::should_raise_an_assert && # a);           \
 181         }                                                         \
 182         catch (Eigen::eigen_assert_exception&) { VERIFY(true); }     \
 183         Eigen::report_on_cerr_on_assert_failure = true;           \
 184       }
 185
 186   #endif // EIGEN_DEBUG_ASSERTS
 187
 188   #define EIGEN_USE_CUSTOM_ASSERT
 189
 190 #else // EIGEN_NO_ASSERTION_CHECKING
 191
 192   #define VERIFY_RAISES_ASSERT(a) {}
 193
 194 #endif // EIGEN_NO_ASSERTION_CHECKING
 195
 196
 197 #define EIGEN_INTERNAL_DEBUGGING
 198 #include <Eigen/QR> // required for createRandomPIMatrixOfRank
 199
 200 inline void verify_impl(bool condition, const char *testname, const char *file, int line, const char *condition_as_string)
 201 {
 202   if (!condition)
 203   {
 204     std::cerr << "Test " << testname << " failed in " << file << " (" << line << ")"
 205       << std::endl << "    " << condition_as_string << std::endl;
 206     std::cerr << "Stack:\n";
 207     const int test_stack_size = static_cast<int>(Eigen::g_test_stack.size());
 208     for(int i=test_stack_size-1; i>=0; --i)
 209       std::cerr << "  - " << Eigen::g_test_stack[i] << "\n";
 210     std::cerr << "\n";
 211     abort();
 212   }
 213 }
 214
 215 #define VERIFY(a) ::verify_impl(a, g_test_stack.back().c_str(), __FILE__, __LINE__, EI_PP_MAKE_STRING(a))
 216
 217 #define VERIFY_IS_EQUAL(a, b) VERIFY(test_is_equal(a, b))
 218 #define VERIFY_IS_APPROX(a, b) VERIFY(test_isApprox(a, b))
 219 #define VERIFY_IS_NOT_APPROX(a, b) VERIFY(!test_isApprox(a, b))
 220 #define VERIFY_IS_MUCH_SMALLER_THAN(a, b) VERIFY(test_isMuchSmallerThan(a, b))
 221 #define VERIFY_IS_NOT_MUCH_SMALLER_THAN(a, b) VERIFY(!test_isMuchSmallerThan(a, b))
 222 #define VERIFY_IS_APPROX_OR_LESS_THAN(a, b) VERIFY(test_isApproxOrLessThan(a, b))
 223 #define VERIFY_IS_NOT_APPROX_OR_LESS_THAN(a, b) VERIFY(!test_isApproxOrLessThan(a, b))
 224
 225 #define VERIFY_IS_UNITARY(a) VERIFY(test_isUnitary(a))
 226
 227 #define CALL_SUBTEST(FUNC) do { \
 228     g_test_stack.push_back(EI_PP_MAKE_STRING(FUNC)); \
 229     FUNC; \
 230     g_test_stack.pop_back(); \
 231   } while (0)
 232
 233
 234 namespace Eigen {
 235
 236 template<typename T> inline typename NumTraits<T>::Real test_precision() { return NumTraits<T>::dummy_precision(); }
 237 template<> inline float test_precision<float>() { return 1e-3f; }
 238 template<> inline double test_precision<double>() { return 1e-6; }
 239 template<> inline float test_precision<std::complex<float> >() { return test_precision<float>(); }
 240 template<> inline double test_precision<std::complex<double> >() { return test_precision<double>(); }
 241 template<> inline long double test_precision<long double>() { return 1e-6; }
 242
 243 inline bool test_isApprox(const int& a, const int& b)
 244 { return internal::isApprox(a, b, test_precision<int>()); }
 245 inline bool test_isMuchSmallerThan(const int& a, const int& b)
 246 { return internal::isMuchSmallerThan(a, b, test_precision<int>()); }
 247 inline bool test_isApproxOrLessThan(const int& a, const int& b)
 248 { return internal::isApproxOrLessThan(a, b, test_precision<int>()); }
 249
 250 inline bool test_isApprox(const float& a, const float& b)
 251 { return internal::isApprox(a, b, test_precision<float>()); }
 252 inline bool test_isMuchSmallerThan(const float& a, const float& b)
 253 { return internal::isMuchSmallerThan(a, b, test_precision<float>()); }
 254 inline bool test_isApproxOrLessThan(const float& a, const float& b)
 255 { return internal::isApproxOrLessThan(a, b, test_precision<float>()); }
 256 inline bool test_isApprox(const double& a, const double& b)
 257 { return internal::isApprox(a, b, test_precision<double>()); }
 258
 259 inline bool test_isMuchSmallerThan(const double& a, const double& b)
 260 { return internal::isMuchSmallerThan(a, b, test_precision<double>()); }
 261 inline bool test_isApproxOrLessThan(const double& a, const double& b)
 262 { return internal::isApproxOrLessThan(a, b, test_precision<double>()); }
 263
 264 inline bool test_isApprox(const std::complex<float>& a, const std::complex<float>& b)
 265 { return internal::isApprox(a, b, test_precision<std::complex<float> >()); }
 266 inline bool test_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b)
 267 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<float> >()); }
 268
 269 inline bool test_isApprox(const std::complex<double>& a, const std::complex<double>& b)
 270 { return internal::isApprox(a, b, test_precision<std::complex<double> >()); }
 271 inline bool test_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b)
 272 { return internal::isMuchSmallerThan(a, b, test_precision<std::complex<double> >()); }
 273
 274 inline bool test_isApprox(const long double& a, const long double& b)
 275 {
 276     bool ret = internal::isApprox(a, b, test_precision<long double>());
 277     if (!ret) std::cerr
 278         << std::endl << "    actual   = " << a
 279         << std::endl << "    expected = " << b << std::endl << std::endl;
 280     return ret;
 281 }
 282
 283 inline bool test_isMuchSmallerThan(const long double& a, const long double& b)
 284 { return internal::isMuchSmallerThan(a, b, test_precision<long double>()); }
 285 inline bool test_isApproxOrLessThan(const long double& a, const long double& b)
 286 { return internal::isApproxOrLessThan(a, b, test_precision<long double>()); }
 287
 288 template<typename Type1, typename Type2>
 289 inline bool test_isApprox(const Type1& a, const Type2& b)
 290 {
 291   return a.isApprox(b, test_precision<typename Type1::Scalar>());
 292 }
 293
 294 // The idea behind this function is to compare the two scalars a and b where
 295 // the scalar ref is a hint about the expected order of magnitude of a and b.
 296 // WARNING: the scalar a and b must be positive
 297 // Therefore, if for some reason a and b are very small compared to ref,
 298 // we won't issue a false negative.
 299 // This test could be: abs(a-b) <= eps * ref
 300 // However, it seems that simply comparing a+ref and b+ref is more sensitive to true error.
 301 template<typename Scalar,typename ScalarRef>
 302 inline bool test_isApproxWithRef(const Scalar& a, const Scalar& b, const ScalarRef& ref)
 303 {
 304   return test_isApprox(a+ref, b+ref);
 305 }
 306
 307 template<typename Derived1, typename Derived2>
 308 inline bool test_isMuchSmallerThan(const MatrixBase<Derived1>& m1,
 309                                    const MatrixBase<Derived2>& m2)
 310 {
 311   return m1.isMuchSmallerThan(m2, test_precision<typename internal::traits<Derived1>::Scalar>());
 312 }
 313
 314 template<typename Derived>
 315 inline bool test_isMuchSmallerThan(const MatrixBase<Derived>& m,
 316                                    const typename NumTraits<typename internal::traits<Derived>::Scalar>::Real& s)
 317 {
 318   return m.isMuchSmallerThan(s, test_precision<typename internal::traits<Derived>::Scalar>());
 319 }
 320
 321 template<typename Derived>
 322 inline bool test_isUnitary(const MatrixBase<Derived>& m)
 323 {
 324   return m.isUnitary(test_precision<typename internal::traits<Derived>::Scalar>());
 325 }
 326
 327 // Forward declaration to avoid ICC warning
 328 template<typename T, typename U>
 329 bool test_is_equal(const T& actual, const U& expected);
 330
 331 template<typename T, typename U>
 332 bool test_is_equal(const T& actual, const U& expected)
 333 {
 334     if (actual==expected)
 335         return true;
 336     // false:
 337     std::cerr
 338         << std::endl << "    actual   = " << actual
 339         << std::endl << "    expected = " << expected << std::endl << std::endl;
 340     return false;
 341 }
 342
 343 /** Creates a random Partial Isometry matrix of given rank.
 344   *
 345   * A partial isometry is a matrix all of whose singular values are either 0 or 1.
 346   * This is very useful to test rank-revealing algorithms.
 347   */
 348 // Forward declaration to avoid ICC warning
 349 template<typename MatrixType>
 350 void createRandomPIMatrixOfRank(typename MatrixType::Index desired_rank, typename MatrixType::Index rows, typename MatrixType::Index cols, MatrixType& m);
 351 template<typename MatrixType>
 352 void createRandomPIMatrixOfRank(typename MatrixType::Index desired_rank, typename MatrixType::Index rows, typename MatrixType::Index cols, MatrixType& m)
 353 {
 354   typedef typename internal::traits<MatrixType>::Index Index;
 355   typedef typename internal::traits<MatrixType>::Scalar Scalar;
 356   enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
 357
 358   typedef Matrix<Scalar, Dynamic, 1> VectorType;
 359   typedef Matrix<Scalar, Rows, Rows> MatrixAType;
 360   typedef Matrix<Scalar, Cols, Cols> MatrixBType;
 361
 362   if(desired_rank == 0)
 363   {
 364     m.setZero(rows,cols);
 365     return;
 366   }
 367
 368   if(desired_rank == 1)
 369   {
 370     // here we normalize the vectors to get a partial isometry
 371     m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
 372     return;
 373   }
 374
 375   MatrixAType a = MatrixAType::Random(rows,rows);
 376   MatrixType d = MatrixType::Identity(rows,cols);
 377   MatrixBType  b = MatrixBType::Random(cols,cols);
 378
 379   // set the diagonal such that only desired_rank non-zero entries reamain
 380   const Index diag_size = (std::min)(d.rows(),d.cols());
 381   if(diag_size != desired_rank)
 382     d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
 383
 384   HouseholderQR<MatrixAType> qra(a);
 385   HouseholderQR<MatrixBType> qrb(b);
 386   m = qra.householderQ() * d * qrb.householderQ();
 387 }
 388
 389 // Forward declaration to avoid ICC warning
 390 template<typename PermutationVectorType>
 391 void randomPermutationVector(PermutationVectorType& v, typename PermutationVectorType::Index size);
 392 template<typename PermutationVectorType>
 393 void randomPermutationVector(PermutationVectorType& v, typename PermutationVectorType::Index size)
 394 {
 395   typedef typename PermutationVectorType::Index Index;
 396   typedef typename PermutationVectorType::Scalar Scalar;
 397   v.resize(size);
 398   for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
 399   if(size == 1) return;
 400   for(Index n = 0; n < 3 * size; ++n)
 401   {
 402     Index i = internal::random<Index>(0, size-1);
 403     Index j;
 404     do j = internal::random<Index>(0, size-1); while(j==i);
 405     std::swap(v(i), v(j));
 406   }
 407 }
 408
 409 template<typename T> bool isNotNaN(const T& x)
 410 {
 411   return x==x;
 412 }
 413
 414 template<typename T> bool isNaN(const T& x)
 415 {
 416   return x!=x;
 417 }
 418
 419 template<typename T> bool isInf(const T& x)
 420 {
 421   return x > NumTraits<T>::highest();
 422 }
 423
 424 template<typename T> bool isMinusInf(const T& x)
 425 {
 426   return x < NumTraits<T>::lowest();
 427 }
 428
 429 } // end namespace Eigen
 430
 431 template<typename T> struct GetDifferentType;
 432
 433 template<> struct GetDifferentType<float> { typedef double type; };
 434 template<> struct GetDifferentType<double> { typedef float type; };
 435 template<typename T> struct GetDifferentType<std::complex<T> >
 436 { typedef std::complex<typename GetDifferentType<T>::type> type; };
 437
 438 // Forward declaration to avoid ICC warning
 439 template<typename T> std::string type_name();
 440 template<typename T> std::string type_name()              { return "other"; }
 441 template<> std::string type_name<float>()                 { return "float"; }
 442 template<> std::string type_name<double>()                { return "double"; }
 443 template<> std::string type_name<int>()                   { return "int"; }
 444 template<> std::string type_name<std::complex<float> >()  { return "complex<float>"; }
 445 template<> std::string type_name<std::complex<double> >() { return "complex<double>"; }
 446 template<> std::string type_name<std::complex<int> >()    { return "complex<int>"; }
 447
 448 // forward declaration of the main test function
 449 void EIGEN_CAT(test_,EIGEN_TEST_FUNC)();
 450
 451 using namespace Eigen;
 452
 453 inline void set_repeat_from_string(const char *str)
 454 {
 455   errno = 0;
 456   g_repeat = int(strtoul(str, 0, 10));
 457   if(errno || g_repeat <= 0)
 458   {
 459     std::cout << "Invalid repeat value " << str << std::endl;
 460     exit(EXIT_FAILURE);
 461   }
 462   g_has_set_repeat = true;
 463 }
 464
 465 inline void set_seed_from_string(const char *str)
 466 {
 467   errno = 0;
 468   g_seed = int(strtoul(str, 0, 10));
 469   if(errno || g_seed == 0)
 470   {
 471     std::cout << "Invalid seed value " << str << std::endl;
 472     exit(EXIT_FAILURE);
 473   }
 474   g_has_set_seed = true;
 475 }
 476
 477 int main(int argc, char *argv[])
 478 {
 479     g_has_set_repeat = false;
 480     g_has_set_seed = false;
 481     bool need_help = false;
 482
 483     for(int i = 1; i < argc; i++)
 484     {
 485       if(argv[i][0] == 'r')
 486       {
 487         if(g_has_set_repeat)
 488         {
 489           std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
 490           return 1;
 491         }
 492         set_repeat_from_string(argv[i]+1);
 493       }
 494       else if(argv[i][0] == 's')
 495       {
 496         if(g_has_set_seed)
 497         {
 498           std::cout << "Argument " << argv[i] << " conflicting with a former argument" << std::endl;
 499           return 1;
 500         }
 501          set_seed_from_string(argv[i]+1);
 502       }
 503       else
 504       {
 505         need_help = true;
 506       }
 507     }
 508
 509     if(need_help)
 510     {
 511       std::cout << "This test application takes the following optional arguments:" << std::endl;
 512       std::cout << "  rN     Repeat each test N times (default: " << DEFAULT_REPEAT << ")" << std::endl;
 513       std::cout << "  sN     Use N as seed for random numbers (default: based on current time)" << std::endl;
 514       std::cout << std::endl;
 515       std::cout << "If defined, the environment variables EIGEN_REPEAT and EIGEN_SEED" << std::endl;
 516       std::cout << "will be used as default values for these parameters." << std::endl;
 517       return 1;
 518     }
 519
 520     char *env_EIGEN_REPEAT = getenv("EIGEN_REPEAT");
 521     if(!g_has_set_repeat && env_EIGEN_REPEAT)
 522       set_repeat_from_string(env_EIGEN_REPEAT);
 523     char *env_EIGEN_SEED = getenv("EIGEN_SEED");
 524     if(!g_has_set_seed && env_EIGEN_SEED)
 525       set_seed_from_string(env_EIGEN_SEED);
 526
 527     if(!g_has_set_seed) g_seed = (unsigned int) time(NULL);
 528     if(!g_has_set_repeat) g_repeat = DEFAULT_REPEAT;
 529
 530     std::cout << "Initializing random number generator with seed " << g_seed << std::endl;
 531     std::stringstream ss;
 532     ss << "Seed: " << g_seed;
 533     g_test_stack.push_back(ss.str());
 534     srand(g_seed);
 535     std::cout << "Repeating each test " << g_repeat << " times" << std::endl;
 536
 537     Eigen::g_test_stack.push_back(std::string(EI_PP_MAKE_STRING(EIGEN_TEST_FUNC)));
 538
 539     EIGEN_CAT(test_,EIGEN_TEST_FUNC)();
 540     return 0;
 541 }
 542
 543 // These warning are disabled here such that they are still ON when parsing Eigen's header files.
 544 #if defined __INTEL_COMPILER
 545   // remark #383: value copied to temporary, reference to temporary used
 546   //  -> this warning is raised even for legal usage as: g_test_stack.push_back("foo"); where g_test_stack is a std::vector<std::string>
 547   // remark #1418: external function definition with no prior declaration
 548   //  -> this warning is raised for all our test functions. Declaring them static would fix the issue.
 549   // warning #279: controlling expression is constant
 550   // remark #1572: floating-point equality and inequality comparisons are unreliable
 551   #pragma warning disable 279 383 1418 1572
 552 #endif