compbio
MathFunctions.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_MATHFUNCTIONS_H
11 #define EIGEN_MATHFUNCTIONS_H
12 
13 // source: http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html
14 // TODO this should better be moved to NumTraits
15 #define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L
16 
17 
18 namespace Eigen {
19 
20 // On WINCE, std::abs is defined for int only, so let's defined our own overloads:
21 // This issue has been confirmed with MSVC 2008 only, but the issue might exist for more recent versions too.
22 #if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC<=1500
23 long abs(long x) { return (labs(x)); }
24 double abs(double x) { return (fabs(x)); }
25 float abs(float x) { return (fabsf(x)); }
26 long double abs(long double x) { return (fabsl(x)); }
27 #endif
28 
29 namespace internal {
30 
51 template<typename T, typename dummy = void>
52 struct global_math_functions_filtering_base
53 {
54  typedef T type;
55 };
56 
57 template<typename T> struct always_void { typedef void type; };
58 
59 template<typename T>
60 struct global_math_functions_filtering_base
61  <T,
62  typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
63  >
64 {
65  typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
66 };
67 
68 #define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
69 #define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
70 
71 /****************************************************************************
72 * Implementation of real *
73 ****************************************************************************/
74 
75 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
76 struct real_default_impl
77 {
78  typedef typename NumTraits<Scalar>::Real RealScalar;
79  EIGEN_DEVICE_FUNC
80  static inline RealScalar run(const Scalar& x)
81  {
82  return x;
83  }
84 };
85 
86 template<typename Scalar>
87 struct real_default_impl<Scalar,true>
88 {
89  typedef typename NumTraits<Scalar>::Real RealScalar;
90  EIGEN_DEVICE_FUNC
91  static inline RealScalar run(const Scalar& x)
92  {
93  using std::real;
94  return real(x);
95  }
96 };
97 
98 template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
99 
100 #ifdef __CUDA_ARCH__
101 template<typename T>
102 struct real_impl<std::complex<T> >
103 {
104  typedef T RealScalar;
105  EIGEN_DEVICE_FUNC
106  static inline T run(const std::complex<T>& x)
107  {
108  return x.real();
109  }
110 };
111 #endif
112 
113 template<typename Scalar>
114 struct real_retval
115 {
116  typedef typename NumTraits<Scalar>::Real type;
117 };
118 
119 /****************************************************************************
120 * Implementation of imag *
121 ****************************************************************************/
122 
123 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
124 struct imag_default_impl
125 {
126  typedef typename NumTraits<Scalar>::Real RealScalar;
127  EIGEN_DEVICE_FUNC
128  static inline RealScalar run(const Scalar&)
129  {
130  return RealScalar(0);
131  }
132 };
133 
134 template<typename Scalar>
135 struct imag_default_impl<Scalar,true>
136 {
137  typedef typename NumTraits<Scalar>::Real RealScalar;
138  EIGEN_DEVICE_FUNC
139  static inline RealScalar run(const Scalar& x)
140  {
141  using std::imag;
142  return imag(x);
143  }
144 };
145 
146 template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
147 
148 #ifdef __CUDA_ARCH__
149 template<typename T>
150 struct imag_impl<std::complex<T> >
151 {
152  typedef T RealScalar;
153  EIGEN_DEVICE_FUNC
154  static inline T run(const std::complex<T>& x)
155  {
156  return x.imag();
157  }
158 };
159 #endif
160 
161 template<typename Scalar>
162 struct imag_retval
163 {
164  typedef typename NumTraits<Scalar>::Real type;
165 };
166 
167 /****************************************************************************
168 * Implementation of real_ref *
169 ****************************************************************************/
170 
171 template<typename Scalar>
172 struct real_ref_impl
173 {
174  typedef typename NumTraits<Scalar>::Real RealScalar;
175  EIGEN_DEVICE_FUNC
176  static inline RealScalar& run(Scalar& x)
177  {
178  return reinterpret_cast<RealScalar*>(&x)[0];
179  }
180  EIGEN_DEVICE_FUNC
181  static inline const RealScalar& run(const Scalar& x)
182  {
183  return reinterpret_cast<const RealScalar*>(&x)[0];
184  }
185 };
186 
187 template<typename Scalar>
188 struct real_ref_retval
189 {
190  typedef typename NumTraits<Scalar>::Real & type;
191 };
192 
193 /****************************************************************************
194 * Implementation of imag_ref *
195 ****************************************************************************/
196 
197 template<typename Scalar, bool IsComplex>
198 struct imag_ref_default_impl
199 {
200  typedef typename NumTraits<Scalar>::Real RealScalar;
201  EIGEN_DEVICE_FUNC
202  static inline RealScalar& run(Scalar& x)
203  {
204  return reinterpret_cast<RealScalar*>(&x)[1];
205  }
206  EIGEN_DEVICE_FUNC
207  static inline const RealScalar& run(const Scalar& x)
208  {
209  return reinterpret_cast<RealScalar*>(&x)[1];
210  }
211 };
212 
213 template<typename Scalar>
214 struct imag_ref_default_impl<Scalar, false>
215 {
216  EIGEN_DEVICE_FUNC
217  static inline Scalar run(Scalar&)
218  {
219  return Scalar(0);
220  }
221  EIGEN_DEVICE_FUNC
222  static inline const Scalar run(const Scalar&)
223  {
224  return Scalar(0);
225  }
226 };
227 
228 template<typename Scalar>
229 struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
230 
231 template<typename Scalar>
232 struct imag_ref_retval
233 {
234  typedef typename NumTraits<Scalar>::Real & type;
235 };
236 
237 /****************************************************************************
238 * Implementation of conj *
239 ****************************************************************************/
240 
241 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
242 struct conj_impl
243 {
244  EIGEN_DEVICE_FUNC
245  static inline Scalar run(const Scalar& x)
246  {
247  return x;
248  }
249 };
250 
251 template<typename Scalar>
252 struct conj_impl<Scalar,true>
253 {
254  EIGEN_DEVICE_FUNC
255  static inline Scalar run(const Scalar& x)
256  {
257  using std::conj;
258  return conj(x);
259  }
260 };
261 
262 template<typename Scalar>
263 struct conj_retval
264 {
265  typedef Scalar type;
266 };
267 
268 /****************************************************************************
269 * Implementation of abs2 *
270 ****************************************************************************/
271 
272 template<typename Scalar,bool IsComplex>
273 struct abs2_impl_default
274 {
275  typedef typename NumTraits<Scalar>::Real RealScalar;
276  EIGEN_DEVICE_FUNC
277  static inline RealScalar run(const Scalar& x)
278  {
279  return x*x;
280  }
281 };
282 
283 template<typename Scalar>
284 struct abs2_impl_default<Scalar, true> // IsComplex
285 {
286  typedef typename NumTraits<Scalar>::Real RealScalar;
287  EIGEN_DEVICE_FUNC
288  static inline RealScalar run(const Scalar& x)
289  {
290  return real(x)*real(x) + imag(x)*imag(x);
291  }
292 };
293 
294 template<typename Scalar>
295 struct abs2_impl
296 {
297  typedef typename NumTraits<Scalar>::Real RealScalar;
298  EIGEN_DEVICE_FUNC
299  static inline RealScalar run(const Scalar& x)
300  {
301  return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);
302  }
303 };
304 
305 template<typename Scalar>
306 struct abs2_retval
307 {
308  typedef typename NumTraits<Scalar>::Real type;
309 };
310 
311 /****************************************************************************
312 * Implementation of norm1 *
313 ****************************************************************************/
314 
315 template<typename Scalar, bool IsComplex>
316 struct norm1_default_impl
317 {
318  typedef typename NumTraits<Scalar>::Real RealScalar;
319  EIGEN_DEVICE_FUNC
320  static inline RealScalar run(const Scalar& x)
321  {
322  EIGEN_USING_STD_MATH(abs);
323  return abs(real(x)) + abs(imag(x));
324  }
325 };
326 
327 template<typename Scalar>
328 struct norm1_default_impl<Scalar, false>
329 {
330  EIGEN_DEVICE_FUNC
331  static inline Scalar run(const Scalar& x)
332  {
333  EIGEN_USING_STD_MATH(abs);
334  return abs(x);
335  }
336 };
337 
338 template<typename Scalar>
339 struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
340 
341 template<typename Scalar>
342 struct norm1_retval
343 {
344  typedef typename NumTraits<Scalar>::Real type;
345 };
346 
347 /****************************************************************************
348 * Implementation of hypot *
349 ****************************************************************************/
350 
351 template<typename Scalar>
352 struct hypot_impl
353 {
354  typedef typename NumTraits<Scalar>::Real RealScalar;
355  static inline RealScalar run(const Scalar& x, const Scalar& y)
356  {
357  EIGEN_USING_STD_MATH(abs);
358  EIGEN_USING_STD_MATH(sqrt);
359  RealScalar _x = abs(x);
360  RealScalar _y = abs(y);
361  Scalar p, qp;
362  if(_x>_y)
363  {
364  p = _x;
365  qp = _y / p;
366  }
367  else
368  {
369  p = _y;
370  qp = _x / p;
371  }
372  if(p==RealScalar(0)) return RealScalar(0);
373  return p * sqrt(RealScalar(1) + qp*qp);
374  }
375 };
376 
377 template<typename Scalar>
378 struct hypot_retval
379 {
380  typedef typename NumTraits<Scalar>::Real type;
381 };
382 
383 /****************************************************************************
384 * Implementation of cast *
385 ****************************************************************************/
386 
387 template<typename OldType, typename NewType>
388 struct cast_impl
389 {
390  EIGEN_DEVICE_FUNC
391  static inline NewType run(const OldType& x)
392  {
393  return static_cast<NewType>(x);
394  }
395 };
396 
397 // here, for once, we're plainly returning NewType: we don't want cast to do weird things.
398 
399 template<typename OldType, typename NewType>
400 EIGEN_DEVICE_FUNC
401 inline NewType cast(const OldType& x)
402 {
403  return cast_impl<OldType, NewType>::run(x);
404 }
405 
406 /****************************************************************************
407 * Implementation of round *
408 ****************************************************************************/
409 
410 #if EIGEN_HAS_CXX11_MATH
411  template<typename Scalar>
412  struct round_impl {
413  static inline Scalar run(const Scalar& x)
414  {
415  EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
416  using std::round;
417  return round(x);
418  }
419  };
420 #else
421  template<typename Scalar>
422  struct round_impl
423  {
424  static inline Scalar run(const Scalar& x)
425  {
426  EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
427  EIGEN_USING_STD_MATH(floor);
428  EIGEN_USING_STD_MATH(ceil);
429  return (x > Scalar(0)) ? floor(x + Scalar(0.5)) : ceil(x - Scalar(0.5));
430  }
431  };
432 #endif
433 
434 template<typename Scalar>
435 struct round_retval
436 {
437  typedef Scalar type;
438 };
439 
440 /****************************************************************************
441 * Implementation of arg *
442 ****************************************************************************/
443 
444 #if EIGEN_HAS_CXX11_MATH
445  template<typename Scalar>
446  struct arg_impl {
447  static inline Scalar run(const Scalar& x)
448  {
449  EIGEN_USING_STD_MATH(arg);
450  return arg(x);
451  }
452  };
453 #else
454  template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
455  struct arg_default_impl
456  {
457  typedef typename NumTraits<Scalar>::Real RealScalar;
458  EIGEN_DEVICE_FUNC
459  static inline RealScalar run(const Scalar& x)
460  {
461  return (x < Scalar(0)) ? Scalar(EIGEN_PI) : Scalar(0); }
462  };
463 
464  template<typename Scalar>
465  struct arg_default_impl<Scalar,true>
466  {
467  typedef typename NumTraits<Scalar>::Real RealScalar;
468  EIGEN_DEVICE_FUNC
469  static inline RealScalar run(const Scalar& x)
470  {
471  EIGEN_USING_STD_MATH(arg);
472  return arg(x);
473  }
474  };
475 
476  template<typename Scalar> struct arg_impl : arg_default_impl<Scalar> {};
477 #endif
478 
479 template<typename Scalar>
480 struct arg_retval
481 {
482  typedef typename NumTraits<Scalar>::Real type;
483 };
484 
485 /****************************************************************************
486 * Implementation of log1p *
487 ****************************************************************************/
488 
489 namespace std_fallback {
490  // fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar,
491  // or that there is no suitable std::log1p function available
492  template<typename Scalar>
493  EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
494  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
495  typedef typename NumTraits<Scalar>::Real RealScalar;
496  EIGEN_USING_STD_MATH(log);
497  Scalar x1p = RealScalar(1) + x;
498  return ( x1p == Scalar(1) ) ? x : x * ( log(x1p) / (x1p - RealScalar(1)) );
499  }
500 }
501 
502 template<typename Scalar>
503 struct log1p_impl {
504  static inline Scalar run(const Scalar& x)
505  {
506  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
507  #if EIGEN_HAS_CXX11_MATH
508  using std::log1p;
509  #endif
510  using std_fallback::log1p;
511  return log1p(x);
512  }
513 };
514 
515 
516 template<typename Scalar>
517 struct log1p_retval
518 {
519  typedef Scalar type;
520 };
521 
522 /****************************************************************************
523 * Implementation of pow *
524 ****************************************************************************/
525 
526 template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>
527 struct pow_impl
528 {
529  //typedef Scalar retval;
530  typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
531  static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)
532  {
533  EIGEN_USING_STD_MATH(pow);
534  return pow(x, y);
535  }
536 };
537 
538 template<typename ScalarX,typename ScalarY>
539 struct pow_impl<ScalarX,ScalarY, true>
540 {
541  typedef ScalarX result_type;
542  static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y)
543  {
544  ScalarX res(1);
545  eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
546  if(y & 1) res *= x;
547  y >>= 1;
548  while(y)
549  {
550  x *= x;
551  if(y&1) res *= x;
552  y >>= 1;
553  }
554  return res;
555  }
556 };
557 
558 /****************************************************************************
559 * Implementation of random *
560 ****************************************************************************/
561 
562 template<typename Scalar,
563  bool IsComplex,
564  bool IsInteger>
565 struct random_default_impl {};
566 
567 template<typename Scalar>
568 struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
569 
570 template<typename Scalar>
571 struct random_retval
572 {
573  typedef Scalar type;
574 };
575 
576 template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
577 template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
578 
579 template<typename Scalar>
580 struct random_default_impl<Scalar, false, false>
581 {
582  static inline Scalar run(const Scalar& x, const Scalar& y)
583  {
584  return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
585  }
586  static inline Scalar run()
587  {
588  return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
589  }
590 };
591 
592 enum {
593  meta_floor_log2_terminate,
594  meta_floor_log2_move_up,
595  meta_floor_log2_move_down,
596  meta_floor_log2_bogus
597 };
598 
599 template<unsigned int n, int lower, int upper> struct meta_floor_log2_selector
600 {
601  enum { middle = (lower + upper) / 2,
602  value = (upper <= lower + 1) ? int(meta_floor_log2_terminate)
603  : (n < (1 << middle)) ? int(meta_floor_log2_move_down)
604  : (n==0) ? int(meta_floor_log2_bogus)
605  : int(meta_floor_log2_move_up)
606  };
607 };
608 
609 template<unsigned int n,
610  int lower = 0,
611  int upper = sizeof(unsigned int) * CHAR_BIT - 1,
612  int selector = meta_floor_log2_selector<n, lower, upper>::value>
613 struct meta_floor_log2 {};
614 
615 template<unsigned int n, int lower, int upper>
616 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down>
617 {
618  enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value };
619 };
620 
621 template<unsigned int n, int lower, int upper>
622 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up>
623 {
624  enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value };
625 };
626 
627 template<unsigned int n, int lower, int upper>
628 struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate>
629 {
630  enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
631 };
632 
633 template<unsigned int n, int lower, int upper>
634 struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>
635 {
636  // no value, error at compile time
637 };
638 
639 template<typename Scalar>
640 struct random_default_impl<Scalar, false, true>
641 {
642  static inline Scalar run(const Scalar& x, const Scalar& y)
643  {
644  typedef typename conditional<NumTraits<Scalar>::IsSigned,std::ptrdiff_t,std::size_t>::type ScalarX;
645  if(y<x)
646  return x;
647  // the following difference might overflow on a 32 bits system,
648  // but since y>=x the result converted to an unsigned long is still correct.
649  std::size_t range = ScalarX(y)-ScalarX(x);
650  std::size_t offset = 0;
651  // rejection sampling
652  std::size_t divisor = 1;
653  std::size_t multiplier = 1;
654  if(range<RAND_MAX) divisor = (std::size_t(RAND_MAX)+1)/(range+1);
655  else multiplier = 1 + range/(std::size_t(RAND_MAX)+1);
656  do {
657  offset = (std::size_t(std::rand()) * multiplier) / divisor;
658  } while (offset > range);
659  return Scalar(ScalarX(x) + offset);
660  }
661 
662  static inline Scalar run()
663  {
664 #ifdef EIGEN_MAKING_DOCS
665  return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
666 #else
667  enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value,
668  scalar_bits = sizeof(Scalar) * CHAR_BIT,
669  shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
670  offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
671  };
672  return Scalar((std::rand() >> shift) - offset);
673 #endif
674  }
675 };
676 
677 template<typename Scalar>
678 struct random_default_impl<Scalar, true, false>
679 {
680  static inline Scalar run(const Scalar& x, const Scalar& y)
681  {
682  return Scalar(random(real(x), real(y)),
683  random(imag(x), imag(y)));
684  }
685  static inline Scalar run()
686  {
687  typedef typename NumTraits<Scalar>::Real RealScalar;
688  return Scalar(random<RealScalar>(), random<RealScalar>());
689  }
690 };
691 
692 template<typename Scalar>
693 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
694 {
695  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
696 }
697 
698 template<typename Scalar>
699 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
700 {
701  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
702 }
703 
704 // Implementatin of is* functions
705 
706 // std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang.
707 #if (EIGEN_HAS_CXX11_MATH && !(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC>=1800) || (EIGEN_COMP_CLANG)
708 #define EIGEN_USE_STD_FPCLASSIFY 1
709 #else
710 #define EIGEN_USE_STD_FPCLASSIFY 0
711 #endif
712 
713 template<typename T>
714 EIGEN_DEVICE_FUNC
715 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
716 isnan_impl(const T&) { return false; }
717 
718 template<typename T>
719 EIGEN_DEVICE_FUNC
720 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
721 isinf_impl(const T&) { return false; }
722 
723 template<typename T>
724 EIGEN_DEVICE_FUNC
725 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
726 isfinite_impl(const T&) { return true; }
727 
728 template<typename T>
729 EIGEN_DEVICE_FUNC
730 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
731 isfinite_impl(const T& x)
732 {
733  #ifdef __CUDA_ARCH__
734  return (::isfinite)(x);
735  #elif EIGEN_USE_STD_FPCLASSIFY
736  using std::isfinite;
737  return isfinite EIGEN_NOT_A_MACRO (x);
738  #else
739  return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
740  #endif
741 }
742 
743 template<typename T>
744 EIGEN_DEVICE_FUNC
745 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
746 isinf_impl(const T& x)
747 {
748  #ifdef __CUDA_ARCH__
749  return (::isinf)(x);
750  #elif EIGEN_USE_STD_FPCLASSIFY
751  using std::isinf;
752  return isinf EIGEN_NOT_A_MACRO (x);
753  #else
754  return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
755  #endif
756 }
757 
758 template<typename T>
759 EIGEN_DEVICE_FUNC
760 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
761 isnan_impl(const T& x)
762 {
763  #ifdef __CUDA_ARCH__
764  return (::isnan)(x);
765  #elif EIGEN_USE_STD_FPCLASSIFY
766  using std::isnan;
767  return isnan EIGEN_NOT_A_MACRO (x);
768  #else
769  return x != x;
770  #endif
771 }
772 
773 #if (!EIGEN_USE_STD_FPCLASSIFY)
774 
775 #if EIGEN_COMP_MSVC
776 
777 template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
778 {
779  return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;
780 }
781 
782 //MSVC defines a _isnan builtin function, but for double only
783 EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
784 EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) { return _isnan(x)!=0; }
785 EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) { return _isnan(x)!=0; }
786 
787 EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
788 EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) { return isinf_msvc_helper(x); }
789 EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) { return isinf_msvc_helper(x); }
790 
791 #elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)
792 
793 #if EIGEN_GNUC_AT_LEAST(5,0)
794  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only")))
795 #else
796  // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol),
797  // while the second prevent too aggressive optimizations in fast-math mode:
798  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only")))
799 #endif
800 
801 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }
802 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) { return __builtin_isnan(x); }
803 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) { return __builtin_isnan(x); }
804 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) { return __builtin_isinf(x); }
805 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) { return __builtin_isinf(x); }
806 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }
807 
808 #undef EIGEN_TMP_NOOPT_ATTRIB
809 
810 #endif
811 
812 #endif
813 
814 // The following overload are defined at the end of this file
815 template<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
816 template<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
817 template<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
818 
819 template<typename T> T generic_fast_tanh_float(const T& a_x);
820 
821 } // end namespace internal
822 
823 /****************************************************************************
824 * Generic math functions *
825 ****************************************************************************/
826 
827 namespace numext {
828 
829 #ifndef __CUDA_ARCH__
830 template<typename T>
831 EIGEN_DEVICE_FUNC
832 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
833 {
834  EIGEN_USING_STD_MATH(min);
835  return min EIGEN_NOT_A_MACRO (x,y);
836 }
837 
838 template<typename T>
839 EIGEN_DEVICE_FUNC
840 EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
841 {
842  EIGEN_USING_STD_MATH(max);
843  return max EIGEN_NOT_A_MACRO (x,y);
844 }
845 #else
846 template<typename T>
847 EIGEN_DEVICE_FUNC
848 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
849 {
850  return y < x ? y : x;
851 }
852 template<>
853 EIGEN_DEVICE_FUNC
854 EIGEN_ALWAYS_INLINE float mini(const float& x, const float& y)
855 {
856  return fminf(x, y);
857 }
858 template<typename T>
859 EIGEN_DEVICE_FUNC
860 EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
861 {
862  return x < y ? y : x;
863 }
864 template<>
865 EIGEN_DEVICE_FUNC
866 EIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y)
867 {
868  return fmaxf(x, y);
869 }
870 #endif
871 
872 
873 template<typename Scalar>
874 EIGEN_DEVICE_FUNC
875 inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
876 {
877  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
878 }
879 
880 template<typename Scalar>
881 EIGEN_DEVICE_FUNC
882 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
883 {
884  return internal::real_ref_impl<Scalar>::run(x);
885 }
886 
887 template<typename Scalar>
888 EIGEN_DEVICE_FUNC
889 inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
890 {
891  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
892 }
893 
894 template<typename Scalar>
895 EIGEN_DEVICE_FUNC
896 inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
897 {
898  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
899 }
900 
901 template<typename Scalar>
902 EIGEN_DEVICE_FUNC
903 inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x)
904 {
905  return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
906 }
907 
908 template<typename Scalar>
909 EIGEN_DEVICE_FUNC
910 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
911 {
912  return internal::imag_ref_impl<Scalar>::run(x);
913 }
914 
915 template<typename Scalar>
916 EIGEN_DEVICE_FUNC
917 inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
918 {
919  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
920 }
921 
922 template<typename Scalar>
923 EIGEN_DEVICE_FUNC
924 inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
925 {
926  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
927 }
928 
929 template<typename Scalar>
930 EIGEN_DEVICE_FUNC
931 inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
932 {
933  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
934 }
935 
936 template<typename Scalar>
937 EIGEN_DEVICE_FUNC
938 inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
939 {
940  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
941 }
942 
943 template<typename Scalar>
944 EIGEN_DEVICE_FUNC
945 inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
946 {
947  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
948 }
949 
950 template<typename Scalar>
951 EIGEN_DEVICE_FUNC
952 inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)
953 {
954  return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
955 }
956 
957 #ifdef __CUDACC__
958 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
959 float log1p(const float &x) { return ::log1pf(x); }
960 
961 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
962 double log1p(const double &x) { return ::log1p(x); }
963 #endif
964 
965 template<typename ScalarX,typename ScalarY>
966 EIGEN_DEVICE_FUNC
967 inline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(const ScalarX& x, const ScalarY& y)
968 {
969  return internal::pow_impl<ScalarX,ScalarY>::run(x, y);
970 }
971 
972 template<typename T> EIGEN_DEVICE_FUNC bool (isnan) (const T &x) { return internal::isnan_impl(x); }
973 template<typename T> EIGEN_DEVICE_FUNC bool (isinf) (const T &x) { return internal::isinf_impl(x); }
974 template<typename T> EIGEN_DEVICE_FUNC bool (isfinite)(const T &x) { return internal::isfinite_impl(x); }
975 
976 template<typename Scalar>
977 EIGEN_DEVICE_FUNC
978 inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x)
979 {
980  return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x);
981 }
982 
983 template<typename T>
984 EIGEN_DEVICE_FUNC
985 T (floor)(const T& x)
986 {
987  EIGEN_USING_STD_MATH(floor);
988  return floor(x);
989 }
990 
991 #ifdef __CUDACC__
992 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
993 float floor(const float &x) { return ::floorf(x); }
994 
995 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
996 double floor(const double &x) { return ::floor(x); }
997 #endif
998 
999 template<typename T>
1000 EIGEN_DEVICE_FUNC
1001 T (ceil)(const T& x)
1002 {
1003  EIGEN_USING_STD_MATH(ceil);
1004  return ceil(x);
1005 }
1006 
1007 #ifdef __CUDACC__
1008 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1009 float ceil(const float &x) { return ::ceilf(x); }
1010 
1011 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1012 double ceil(const double &x) { return ::ceil(x); }
1013 #endif
1014 
1015 
1018 inline int log2(int x)
1019 {
1020  eigen_assert(x>=0);
1021  unsigned int v(x);
1022  static const int table[32] = { 0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30, 8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31 };
1023  v |= v >> 1;
1024  v |= v >> 2;
1025  v |= v >> 4;
1026  v |= v >> 8;
1027  v |= v >> 16;
1028  return table[(v * 0x07C4ACDDU) >> 27];
1029 }
1030 
1039 template<typename T>
1040 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1041 T sqrt(const T &x)
1042 {
1043  EIGEN_USING_STD_MATH(sqrt);
1044  return sqrt(x);
1045 }
1046 
1047 template<typename T>
1048 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1049 T log(const T &x) {
1050  EIGEN_USING_STD_MATH(log);
1051  return log(x);
1052 }
1053 
1054 #ifdef __CUDACC__
1055 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1056 float log(const float &x) { return ::logf(x); }
1057 
1058 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1059 double log(const double &x) { return ::log(x); }
1060 #endif
1061 
1062 template<typename T>
1063 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1064 typename NumTraits<T>::Real abs(const T &x) {
1065  EIGEN_USING_STD_MATH(abs);
1066  return abs(x);
1067 }
1068 
1069 #ifdef __CUDACC__
1070 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1071 float abs(const float &x) { return ::fabsf(x); }
1072 
1073 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1074 double abs(const double &x) { return ::fabs(x); }
1075 
1076 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1077 float abs(const std::complex<float>& x) {
1078  return ::hypotf(x.real(), x.imag());
1079 }
1080 
1081 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1082 double abs(const std::complex<double>& x) {
1083  return ::hypot(x.real(), x.imag());
1084 }
1085 #endif
1086 
1087 template<typename T>
1088 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1089 T exp(const T &x) {
1090  EIGEN_USING_STD_MATH(exp);
1091  return exp(x);
1092 }
1093 
1094 #ifdef __CUDACC__
1095 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1096 float exp(const float &x) { return ::expf(x); }
1097 
1098 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1099 double exp(const double &x) { return ::exp(x); }
1100 #endif
1101 
1102 template<typename T>
1103 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1104 T cos(const T &x) {
1105  EIGEN_USING_STD_MATH(cos);
1106  return cos(x);
1107 }
1108 
1109 #ifdef __CUDACC__
1110 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1111 float cos(const float &x) { return ::cosf(x); }
1112 
1113 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1114 double cos(const double &x) { return ::cos(x); }
1115 #endif
1116 
1117 template<typename T>
1118 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1119 T sin(const T &x) {
1120  EIGEN_USING_STD_MATH(sin);
1121  return sin(x);
1122 }
1123 
1124 #ifdef __CUDACC__
1125 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1126 float sin(const float &x) { return ::sinf(x); }
1127 
1128 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1129 double sin(const double &x) { return ::sin(x); }
1130 #endif
1131 
1132 template<typename T>
1133 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1134 T tan(const T &x) {
1135  EIGEN_USING_STD_MATH(tan);
1136  return tan(x);
1137 }
1138 
1139 #ifdef __CUDACC__
1140 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1141 float tan(const float &x) { return ::tanf(x); }
1142 
1143 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1144 double tan(const double &x) { return ::tan(x); }
1145 #endif
1146 
1147 template<typename T>
1148 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1149 T acos(const T &x) {
1150  EIGEN_USING_STD_MATH(acos);
1151  return acos(x);
1152 }
1153 
1154 #ifdef __CUDACC__
1155 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1156 float acos(const float &x) { return ::acosf(x); }
1157 
1158 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1159 double acos(const double &x) { return ::acos(x); }
1160 #endif
1161 
1162 template<typename T>
1163 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1164 T asin(const T &x) {
1165  EIGEN_USING_STD_MATH(asin);
1166  return asin(x);
1167 }
1168 
1169 #ifdef __CUDACC__
1170 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1171 float asin(const float &x) { return ::asinf(x); }
1172 
1173 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1174 double asin(const double &x) { return ::asin(x); }
1175 #endif
1176 
1177 template<typename T>
1178 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1179 T atan(const T &x) {
1180  EIGEN_USING_STD_MATH(atan);
1181  return atan(x);
1182 }
1183 
1184 #ifdef __CUDACC__
1185 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1186 float atan(const float &x) { return ::atanf(x); }
1187 
1188 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1189 double atan(const double &x) { return ::atan(x); }
1190 #endif
1191 
1192 
1193 template<typename T>
1194 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1195 T cosh(const T &x) {
1196  EIGEN_USING_STD_MATH(cosh);
1197  return cosh(x);
1198 }
1199 
1200 #ifdef __CUDACC__
1201 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1202 float cosh(const float &x) { return ::coshf(x); }
1203 
1204 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1205 double cosh(const double &x) { return ::cosh(x); }
1206 #endif
1207 
1208 template<typename T>
1209 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1210 T sinh(const T &x) {
1211  EIGEN_USING_STD_MATH(sinh);
1212  return sinh(x);
1213 }
1214 
1215 #ifdef __CUDACC__
1216 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1217 float sinh(const float &x) { return ::sinhf(x); }
1218 
1219 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1220 double sinh(const double &x) { return ::sinh(x); }
1221 #endif
1222 
1223 template<typename T>
1224 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1225 T tanh(const T &x) {
1226  EIGEN_USING_STD_MATH(tanh);
1227  return tanh(x);
1228 }
1229 
1230 #if (!defined(__CUDACC__)) && EIGEN_FAST_MATH
1231 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1232 float tanh(float x) { return internal::generic_fast_tanh_float(x); }
1233 #endif
1234 
1235 #ifdef __CUDACC__
1236 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1237 float tanh(const float &x) { return ::tanhf(x); }
1238 
1239 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1240 double tanh(const double &x) { return ::tanh(x); }
1241 #endif
1242 
1243 template <typename T>
1244 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1245 T fmod(const T& a, const T& b) {
1246  EIGEN_USING_STD_MATH(fmod);
1247  return fmod(a, b);
1248 }
1249 
1250 #ifdef __CUDACC__
1251 template <>
1252 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1253 float fmod(const float& a, const float& b) {
1254  return ::fmodf(a, b);
1255 }
1256 
1257 template <>
1258 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1259 double fmod(const double& a, const double& b) {
1260  return ::fmod(a, b);
1261 }
1262 #endif
1263 
1264 } // end namespace numext
1265 
1266 namespace internal {
1267 
1268 template<typename T>
1269 EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x)
1270 {
1271  return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
1272 }
1273 
1274 template<typename T>
1275 EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x)
1276 {
1277  return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
1278 }
1279 
1280 template<typename T>
1281 EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x)
1282 {
1283  return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
1284 }
1285 
1286 /****************************************************************************
1287 * Implementation of fuzzy comparisons *
1288 ****************************************************************************/
1289 
1290 template<typename Scalar,
1291  bool IsComplex,
1292  bool IsInteger>
1293 struct scalar_fuzzy_default_impl {};
1294 
1295 template<typename Scalar>
1296 struct scalar_fuzzy_default_impl<Scalar, false, false>
1297 {
1298  typedef typename NumTraits<Scalar>::Real RealScalar;
1299  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1300  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
1301  {
1302  return numext::abs(x) <= numext::abs(y) * prec;
1303  }
1304  EIGEN_DEVICE_FUNC
1305  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
1306  {
1307  return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
1308  }
1309  EIGEN_DEVICE_FUNC
1310  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
1311  {
1312  return x <= y || isApprox(x, y, prec);
1313  }
1314 };
1315 
1316 template<typename Scalar>
1317 struct scalar_fuzzy_default_impl<Scalar, false, true>
1318 {
1319  typedef typename NumTraits<Scalar>::Real RealScalar;
1320  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1321  static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
1322  {
1323  return x == Scalar(0);
1324  }
1325  EIGEN_DEVICE_FUNC
1326  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
1327  {
1328  return x == y;
1329  }
1330  EIGEN_DEVICE_FUNC
1331  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
1332  {
1333  return x <= y;
1334  }
1335 };
1336 
1337 template<typename Scalar>
1338 struct scalar_fuzzy_default_impl<Scalar, true, false>
1339 {
1340  typedef typename NumTraits<Scalar>::Real RealScalar;
1341  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1342  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
1343  {
1344  return numext::abs2(x) <= numext::abs2(y) * prec * prec;
1345  }
1346  EIGEN_DEVICE_FUNC
1347  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
1348  {
1349  return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;
1350  }
1351 };
1352 
1353 template<typename Scalar>
1354 struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
1355 
1356 template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC
1357 inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
1358  const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1359 {
1360  return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
1361 }
1362 
1363 template<typename Scalar> EIGEN_DEVICE_FUNC
1364 inline bool isApprox(const Scalar& x, const Scalar& y,
1365  const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1366 {
1367  return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
1368 }
1369 
1370 template<typename Scalar> EIGEN_DEVICE_FUNC
1371 inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
1372  const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1373 {
1374  return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
1375 }
1376 
1377 /******************************************
1378 *** The special case of the bool type ***
1379 ******************************************/
1380 
1381 template<> struct random_impl<bool>
1382 {
1383  static inline bool run()
1384  {
1385  return random<int>(0,1)==0 ? false : true;
1386  }
1387 };
1388 
1389 template<> struct scalar_fuzzy_impl<bool>
1390 {
1391  typedef bool RealScalar;
1392 
1393  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1394  static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
1395  {
1396  return !x;
1397  }
1398 
1399  EIGEN_DEVICE_FUNC
1400  static inline bool isApprox(bool x, bool y, bool)
1401  {
1402  return x == y;
1403  }
1404 
1405  EIGEN_DEVICE_FUNC
1406  static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
1407  {
1408  return (!x) || y;
1409  }
1410 
1411 };
1412 
1413 
1414 } // end namespace internal
1415 
1416 } // end namespace Eigen
1417 
1418 #endif // EIGEN_MATHFUNCTIONS_H
Eigen
Namespace containing all symbols from the Eigen library.
Definition: bench_norm.cpp:85
std
Definition: Half.h:529
internal
Definition: BandTriangularSolver.h:13
complex
Definition: datatypes.h:12
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