Eigen  3.4.0 (git rev e3e74001f7c4bf95f0dde572e8a08c5b2918a3ab)
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 // Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved.
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 #ifndef EIGEN_MATHFUNCTIONS_H
12 #define EIGEN_MATHFUNCTIONS_H
13 
14 // TODO this should better be moved to NumTraits
15 // Source: WolframAlpha
16 #define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L
17 #define EIGEN_LOG2E 1.442695040888963407359924681001892137426645954152985934135449406931109219L
18 #define EIGEN_LN2 0.693147180559945309417232121458176568075500134360255254120680009493393621L
19 
20 namespace Eigen {
21 
22 // On WINCE, std::abs is defined for int only, so let's defined our own overloads:
23 // This issue has been confirmed with MSVC 2008 only, but the issue might exist for more recent versions too.
24 #if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC<=1500
25 long abs(long x) { return (labs(x)); }
26 double abs(double x) { return (fabs(x)); }
27 float abs(float x) { return (fabsf(x)); }
28 long double abs(long double x) { return (fabsl(x)); }
29 #endif
30 
31 namespace internal {
32 
53 template<typename T, typename dummy = void>
54 struct global_math_functions_filtering_base
55 {
56  typedef T type;
57 };
58 
59 template<typename T> struct always_void { typedef void type; };
60 
61 template<typename T>
62 struct global_math_functions_filtering_base
63  <T,
64  typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
65  >
66 {
67  typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
68 };
69 
70 #define EIGEN_MATHFUNC_IMPL(func, scalar) Eigen::internal::func##_impl<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>
71 #define EIGEN_MATHFUNC_RETVAL(func, scalar) typename Eigen::internal::func##_retval<typename Eigen::internal::global_math_functions_filtering_base<scalar>::type>::type
72 
73 /****************************************************************************
74 * Implementation of real *
75 ****************************************************************************/
76 
77 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
78 struct real_default_impl
79 {
80  typedef typename NumTraits<Scalar>::Real RealScalar;
81  EIGEN_DEVICE_FUNC
82  static inline RealScalar run(const Scalar& x)
83  {
84  return x;
85  }
86 };
87 
88 template<typename Scalar>
89 struct real_default_impl<Scalar,true>
90 {
91  typedef typename NumTraits<Scalar>::Real RealScalar;
92  EIGEN_DEVICE_FUNC
93  static inline RealScalar run(const Scalar& x)
94  {
95  using std::real;
96  return real(x);
97  }
98 };
99 
100 template<typename Scalar> struct real_impl : real_default_impl<Scalar> {};
101 
102 #if defined(EIGEN_GPU_COMPILE_PHASE)
103 template<typename T>
104 struct real_impl<std::complex<T> >
105 {
106  typedef T RealScalar;
107  EIGEN_DEVICE_FUNC
108  static inline T run(const std::complex<T>& x)
109  {
110  return x.real();
111  }
112 };
113 #endif
114 
115 template<typename Scalar>
116 struct real_retval
117 {
118  typedef typename NumTraits<Scalar>::Real type;
119 };
120 
121 /****************************************************************************
122 * Implementation of imag *
123 ****************************************************************************/
124 
125 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
126 struct imag_default_impl
127 {
128  typedef typename NumTraits<Scalar>::Real RealScalar;
129  EIGEN_DEVICE_FUNC
130  static inline RealScalar run(const Scalar&)
131  {
132  return RealScalar(0);
133  }
134 };
135 
136 template<typename Scalar>
137 struct imag_default_impl<Scalar,true>
138 {
139  typedef typename NumTraits<Scalar>::Real RealScalar;
140  EIGEN_DEVICE_FUNC
141  static inline RealScalar run(const Scalar& x)
142  {
143  using std::imag;
144  return imag(x);
145  }
146 };
147 
148 template<typename Scalar> struct imag_impl : imag_default_impl<Scalar> {};
149 
150 #if defined(EIGEN_GPU_COMPILE_PHASE)
151 template<typename T>
152 struct imag_impl<std::complex<T> >
153 {
154  typedef T RealScalar;
155  EIGEN_DEVICE_FUNC
156  static inline T run(const std::complex<T>& x)
157  {
158  return x.imag();
159  }
160 };
161 #endif
162 
163 template<typename Scalar>
164 struct imag_retval
165 {
166  typedef typename NumTraits<Scalar>::Real type;
167 };
168 
169 /****************************************************************************
170 * Implementation of real_ref *
171 ****************************************************************************/
172 
173 template<typename Scalar>
174 struct real_ref_impl
175 {
176  typedef typename NumTraits<Scalar>::Real RealScalar;
177  EIGEN_DEVICE_FUNC
178  static inline RealScalar& run(Scalar& x)
179  {
180  return reinterpret_cast<RealScalar*>(&x)[0];
181  }
182  EIGEN_DEVICE_FUNC
183  static inline const RealScalar& run(const Scalar& x)
184  {
185  return reinterpret_cast<const RealScalar*>(&x)[0];
186  }
187 };
188 
189 template<typename Scalar>
190 struct real_ref_retval
191 {
192  typedef typename NumTraits<Scalar>::Real & type;
193 };
194 
195 /****************************************************************************
196 * Implementation of imag_ref *
197 ****************************************************************************/
198 
199 template<typename Scalar, bool IsComplex>
200 struct imag_ref_default_impl
201 {
202  typedef typename NumTraits<Scalar>::Real RealScalar;
203  EIGEN_DEVICE_FUNC
204  static inline RealScalar& run(Scalar& x)
205  {
206  return reinterpret_cast<RealScalar*>(&x)[1];
207  }
208  EIGEN_DEVICE_FUNC
209  static inline const RealScalar& run(const Scalar& x)
210  {
211  return reinterpret_cast<RealScalar*>(&x)[1];
212  }
213 };
214 
215 template<typename Scalar>
216 struct imag_ref_default_impl<Scalar, false>
217 {
218  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
219  static inline Scalar run(Scalar&)
220  {
221  return Scalar(0);
222  }
223  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
224  static inline const Scalar run(const Scalar&)
225  {
226  return Scalar(0);
227  }
228 };
229 
230 template<typename Scalar>
231 struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
232 
233 template<typename Scalar>
234 struct imag_ref_retval
235 {
236  typedef typename NumTraits<Scalar>::Real & type;
237 };
238 
239 /****************************************************************************
240 * Implementation of conj *
241 ****************************************************************************/
242 
243 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
244 struct conj_default_impl
245 {
246  EIGEN_DEVICE_FUNC
247  static inline Scalar run(const Scalar& x)
248  {
249  return x;
250  }
251 };
252 
253 template<typename Scalar>
254 struct conj_default_impl<Scalar,true>
255 {
256  EIGEN_DEVICE_FUNC
257  static inline Scalar run(const Scalar& x)
258  {
259  using std::conj;
260  return conj(x);
261  }
262 };
263 
264 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
265 struct conj_impl : conj_default_impl<Scalar, IsComplex> {};
266 
267 template<typename Scalar>
268 struct conj_retval
269 {
270  typedef Scalar type;
271 };
272 
273 /****************************************************************************
274 * Implementation of abs2 *
275 ****************************************************************************/
276 
277 template<typename Scalar,bool IsComplex>
278 struct abs2_impl_default
279 {
280  typedef typename NumTraits<Scalar>::Real RealScalar;
281  EIGEN_DEVICE_FUNC
282  static inline RealScalar run(const Scalar& x)
283  {
284  return x*x;
285  }
286 };
287 
288 template<typename Scalar>
289 struct abs2_impl_default<Scalar, true> // IsComplex
290 {
291  typedef typename NumTraits<Scalar>::Real RealScalar;
292  EIGEN_DEVICE_FUNC
293  static inline RealScalar run(const Scalar& x)
294  {
295  return x.real()*x.real() + x.imag()*x.imag();
296  }
297 };
298 
299 template<typename Scalar>
300 struct abs2_impl
301 {
302  typedef typename NumTraits<Scalar>::Real RealScalar;
303  EIGEN_DEVICE_FUNC
304  static inline RealScalar run(const Scalar& x)
305  {
306  return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);
307  }
308 };
309 
310 template<typename Scalar>
311 struct abs2_retval
312 {
313  typedef typename NumTraits<Scalar>::Real type;
314 };
315 
316 /****************************************************************************
317 * Implementation of sqrt/rsqrt *
318 ****************************************************************************/
319 
320 template<typename Scalar>
321 struct sqrt_impl
322 {
323  EIGEN_DEVICE_FUNC
324  static EIGEN_ALWAYS_INLINE Scalar run(const Scalar& x)
325  {
326  EIGEN_USING_STD(sqrt);
327  return sqrt(x);
328  }
329 };
330 
331 // Complex sqrt defined in MathFunctionsImpl.h.
332 template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_sqrt(const std::complex<T>& a_x);
333 
334 // Custom implementation is faster than `std::sqrt`, works on
335 // GPU, and correctly handles special cases (unlike MSVC).
336 template<typename T>
337 struct sqrt_impl<std::complex<T> >
338 {
339  EIGEN_DEVICE_FUNC
340  static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x)
341  {
342  return complex_sqrt<T>(x);
343  }
344 };
345 
346 template<typename Scalar>
347 struct sqrt_retval
348 {
349  typedef Scalar type;
350 };
351 
352 // Default implementation relies on numext::sqrt, at bottom of file.
353 template<typename T>
354 struct rsqrt_impl;
355 
356 // Complex rsqrt defined in MathFunctionsImpl.h.
357 template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_rsqrt(const std::complex<T>& a_x);
358 
359 template<typename T>
360 struct rsqrt_impl<std::complex<T> >
361 {
362  EIGEN_DEVICE_FUNC
363  static EIGEN_ALWAYS_INLINE std::complex<T> run(const std::complex<T>& x)
364  {
365  return complex_rsqrt<T>(x);
366  }
367 };
368 
369 template<typename Scalar>
370 struct rsqrt_retval
371 {
372  typedef Scalar type;
373 };
374 
375 /****************************************************************************
376 * Implementation of norm1 *
377 ****************************************************************************/
378 
379 template<typename Scalar, bool IsComplex>
380 struct norm1_default_impl;
381 
382 template<typename Scalar>
383 struct norm1_default_impl<Scalar,true>
384 {
385  typedef typename NumTraits<Scalar>::Real RealScalar;
386  EIGEN_DEVICE_FUNC
387  static inline RealScalar run(const Scalar& x)
388  {
389  EIGEN_USING_STD(abs);
390  return abs(x.real()) + abs(x.imag());
391  }
392 };
393 
394 template<typename Scalar>
395 struct norm1_default_impl<Scalar, false>
396 {
397  EIGEN_DEVICE_FUNC
398  static inline Scalar run(const Scalar& x)
399  {
400  EIGEN_USING_STD(abs);
401  return abs(x);
402  }
403 };
404 
405 template<typename Scalar>
406 struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
407 
408 template<typename Scalar>
409 struct norm1_retval
410 {
411  typedef typename NumTraits<Scalar>::Real type;
412 };
413 
414 /****************************************************************************
415 * Implementation of hypot *
416 ****************************************************************************/
417 
418 template<typename Scalar> struct hypot_impl;
419 
420 template<typename Scalar>
421 struct hypot_retval
422 {
423  typedef typename NumTraits<Scalar>::Real type;
424 };
425 
426 /****************************************************************************
427 * Implementation of cast *
428 ****************************************************************************/
429 
430 template<typename OldType, typename NewType, typename EnableIf = void>
431 struct cast_impl
432 {
433  EIGEN_DEVICE_FUNC
434  static inline NewType run(const OldType& x)
435  {
436  return static_cast<NewType>(x);
437  }
438 };
439 
440 // Casting from S -> Complex<T> leads to an implicit conversion from S to T,
441 // generating warnings on clang. Here we explicitly cast the real component.
442 template<typename OldType, typename NewType>
443 struct cast_impl<OldType, NewType,
444  typename internal::enable_if<
445  !NumTraits<OldType>::IsComplex && NumTraits<NewType>::IsComplex
446  >::type>
447 {
448  EIGEN_DEVICE_FUNC
449  static inline NewType run(const OldType& x)
450  {
451  typedef typename NumTraits<NewType>::Real NewReal;
452  return static_cast<NewType>(static_cast<NewReal>(x));
453  }
454 };
455 
456 // here, for once, we're plainly returning NewType: we don't want cast to do weird things.
457 
458 template<typename OldType, typename NewType>
459 EIGEN_DEVICE_FUNC
460 inline NewType cast(const OldType& x)
461 {
462  return cast_impl<OldType, NewType>::run(x);
463 }
464 
465 /****************************************************************************
466 * Implementation of round *
467 ****************************************************************************/
468 
469 template<typename Scalar>
470 struct round_impl
471 {
472  EIGEN_DEVICE_FUNC
473  static inline Scalar run(const Scalar& x)
474  {
475  EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
476 #if EIGEN_HAS_CXX11_MATH
477  EIGEN_USING_STD(round);
478 #endif
479  return Scalar(round(x));
480  }
481 };
482 
483 #if !EIGEN_HAS_CXX11_MATH
484 #if EIGEN_HAS_C99_MATH
485 // Use ::roundf for float.
486 template<>
487 struct round_impl<float> {
488  EIGEN_DEVICE_FUNC
489  static inline float run(const float& x)
490  {
491  return ::roundf(x);
492  }
493 };
494 #else
495 template<typename Scalar>
496 struct round_using_floor_ceil_impl
497 {
498  EIGEN_DEVICE_FUNC
499  static inline Scalar run(const Scalar& x)
500  {
501  EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
502  // Without C99 round/roundf, resort to floor/ceil.
503  EIGEN_USING_STD(floor);
504  EIGEN_USING_STD(ceil);
505  // If not enough precision to resolve a decimal at all, return the input.
506  // Otherwise, adding 0.5 can trigger an increment by 1.
507  const Scalar limit = Scalar(1ull << (NumTraits<Scalar>::digits() - 1));
508  if (x >= limit || x <= -limit) {
509  return x;
510  }
511  return (x > Scalar(0)) ? Scalar(floor(x + Scalar(0.5))) : Scalar(ceil(x - Scalar(0.5)));
512  }
513 };
514 
515 template<>
516 struct round_impl<float> : round_using_floor_ceil_impl<float> {};
517 
518 template<>
519 struct round_impl<double> : round_using_floor_ceil_impl<double> {};
520 #endif // EIGEN_HAS_C99_MATH
521 #endif // !EIGEN_HAS_CXX11_MATH
522 
523 template<typename Scalar>
524 struct round_retval
525 {
526  typedef Scalar type;
527 };
528 
529 /****************************************************************************
530 * Implementation of rint *
531 ****************************************************************************/
532 
533 template<typename Scalar>
534 struct rint_impl {
535  EIGEN_DEVICE_FUNC
536  static inline Scalar run(const Scalar& x)
537  {
538  EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
539 #if EIGEN_HAS_CXX11_MATH
540  EIGEN_USING_STD(rint);
541 #endif
542  return rint(x);
543  }
544 };
545 
546 #if !EIGEN_HAS_CXX11_MATH
547 template<>
548 struct rint_impl<double> {
549  EIGEN_DEVICE_FUNC
550  static inline double run(const double& x)
551  {
552  return ::rint(x);
553  }
554 };
555 template<>
556 struct rint_impl<float> {
557  EIGEN_DEVICE_FUNC
558  static inline float run(const float& x)
559  {
560  return ::rintf(x);
561  }
562 };
563 #endif
564 
565 template<typename Scalar>
566 struct rint_retval
567 {
568  typedef Scalar type;
569 };
570 
571 /****************************************************************************
572 * Implementation of arg *
573 ****************************************************************************/
574 
575 // Visual Studio 2017 has a bug where arg(float) returns 0 for negative inputs.
576 // This seems to be fixed in VS 2019.
577 #if EIGEN_HAS_CXX11_MATH && (!EIGEN_COMP_MSVC || EIGEN_COMP_MSVC >= 1920)
578 // std::arg is only defined for types of std::complex, or integer types or float/double/long double
579 template<typename Scalar,
580  bool HasStdImpl = NumTraits<Scalar>::IsComplex || is_integral<Scalar>::value
581  || is_same<Scalar, float>::value || is_same<Scalar, double>::value
582  || is_same<Scalar, long double>::value >
583 struct arg_default_impl;
584 
585 template<typename Scalar>
586 struct arg_default_impl<Scalar, true> {
587  typedef typename NumTraits<Scalar>::Real RealScalar;
588  EIGEN_DEVICE_FUNC
589  static inline RealScalar run(const Scalar& x)
590  {
591  #if defined(EIGEN_HIP_DEVICE_COMPILE)
592  // HIP does not seem to have a native device side implementation for the math routine "arg"
593  using std::arg;
594  #else
595  EIGEN_USING_STD(arg);
596  #endif
597  return static_cast<RealScalar>(arg(x));
598  }
599 };
600 
601 // Must be non-complex floating-point type (e.g. half/bfloat16).
602 template<typename Scalar>
603 struct arg_default_impl<Scalar, false> {
604  typedef typename NumTraits<Scalar>::Real RealScalar;
605  EIGEN_DEVICE_FUNC
606  static inline RealScalar run(const Scalar& x)
607  {
608  return (x < Scalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0);
609  }
610 };
611 #else
612 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
613 struct arg_default_impl
614 {
615  typedef typename NumTraits<Scalar>::Real RealScalar;
616  EIGEN_DEVICE_FUNC
617  static inline RealScalar run(const Scalar& x)
618  {
619  return (x < RealScalar(0)) ? RealScalar(EIGEN_PI) : RealScalar(0);
620  }
621 };
622 
623 template<typename Scalar>
624 struct arg_default_impl<Scalar,true>
625 {
626  typedef typename NumTraits<Scalar>::Real RealScalar;
627  EIGEN_DEVICE_FUNC
628  static inline RealScalar run(const Scalar& x)
629  {
630  EIGEN_USING_STD(arg);
631  return arg(x);
632  }
633 };
634 #endif
635 template<typename Scalar> struct arg_impl : arg_default_impl<Scalar> {};
636 
637 template<typename Scalar>
638 struct arg_retval
639 {
640  typedef typename NumTraits<Scalar>::Real type;
641 };
642 
643 /****************************************************************************
644 * Implementation of expm1 *
645 ****************************************************************************/
646 
647 // This implementation is based on GSL Math's expm1.
648 namespace std_fallback {
649  // fallback expm1 implementation in case there is no expm1(Scalar) function in namespace of Scalar,
650  // or that there is no suitable std::expm1 function available. Implementation
651  // attributed to Kahan. See: http://www.plunk.org/~hatch/rightway.php.
652  template<typename Scalar>
653  EIGEN_DEVICE_FUNC inline Scalar expm1(const Scalar& x) {
654  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
655  typedef typename NumTraits<Scalar>::Real RealScalar;
656 
657  EIGEN_USING_STD(exp);
658  Scalar u = exp(x);
659  if (numext::equal_strict(u, Scalar(1))) {
660  return x;
661  }
662  Scalar um1 = u - RealScalar(1);
663  if (numext::equal_strict(um1, Scalar(-1))) {
664  return RealScalar(-1);
665  }
666 
667  EIGEN_USING_STD(log);
668  Scalar logu = log(u);
669  return numext::equal_strict(u, logu) ? u : (u - RealScalar(1)) * x / logu;
670  }
671 }
672 
673 template<typename Scalar>
674 struct expm1_impl {
675  EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
676  {
677  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
678  #if EIGEN_HAS_CXX11_MATH
679  using std::expm1;
680  #else
681  using std_fallback::expm1;
682  #endif
683  return expm1(x);
684  }
685 };
686 
687 template<typename Scalar>
688 struct expm1_retval
689 {
690  typedef Scalar type;
691 };
692 
693 /****************************************************************************
694 * Implementation of log *
695 ****************************************************************************/
696 
697 // Complex log defined in MathFunctionsImpl.h.
698 template<typename T> EIGEN_DEVICE_FUNC std::complex<T> complex_log(const std::complex<T>& z);
699 
700 template<typename Scalar>
701 struct log_impl {
702  EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
703  {
704  EIGEN_USING_STD(log);
705  return static_cast<Scalar>(log(x));
706  }
707 };
708 
709 template<typename Scalar>
710 struct log_impl<std::complex<Scalar> > {
711  EIGEN_DEVICE_FUNC static inline std::complex<Scalar> run(const std::complex<Scalar>& z)
712  {
713  return complex_log(z);
714  }
715 };
716 
717 /****************************************************************************
718 * Implementation of log1p *
719 ****************************************************************************/
720 
721 namespace std_fallback {
722  // fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar,
723  // or that there is no suitable std::log1p function available
724  template<typename Scalar>
725  EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
726  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
727  typedef typename NumTraits<Scalar>::Real RealScalar;
728  EIGEN_USING_STD(log);
729  Scalar x1p = RealScalar(1) + x;
730  Scalar log_1p = log_impl<Scalar>::run(x1p);
731  const bool is_small = numext::equal_strict(x1p, Scalar(1));
732  const bool is_inf = numext::equal_strict(x1p, log_1p);
733  return (is_small || is_inf) ? x : x * (log_1p / (x1p - RealScalar(1)));
734  }
735 }
736 
737 template<typename Scalar>
738 struct log1p_impl {
739  EIGEN_DEVICE_FUNC static inline Scalar run(const Scalar& x)
740  {
741  EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
742  #if EIGEN_HAS_CXX11_MATH
743  using std::log1p;
744  #else
745  using std_fallback::log1p;
746  #endif
747  return log1p(x);
748  }
749 };
750 
751 // Specialization for complex types that are not supported by std::log1p.
752 template <typename RealScalar>
753 struct log1p_impl<std::complex<RealScalar> > {
754  EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(
755  const std::complex<RealScalar>& x) {
756  EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
757  return std_fallback::log1p(x);
758  }
759 };
760 
761 template<typename Scalar>
762 struct log1p_retval
763 {
764  typedef Scalar type;
765 };
766 
767 /****************************************************************************
768 * Implementation of pow *
769 ****************************************************************************/
770 
771 template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>
772 struct pow_impl
773 {
774  //typedef Scalar retval;
775  typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
776  static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)
777  {
778  EIGEN_USING_STD(pow);
779  return pow(x, y);
780  }
781 };
782 
783 template<typename ScalarX,typename ScalarY>
784 struct pow_impl<ScalarX,ScalarY, true>
785 {
786  typedef ScalarX result_type;
787  static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y)
788  {
789  ScalarX res(1);
790  eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
791  if(y & 1) res *= x;
792  y >>= 1;
793  while(y)
794  {
795  x *= x;
796  if(y&1) res *= x;
797  y >>= 1;
798  }
799  return res;
800  }
801 };
802 
803 /****************************************************************************
804 * Implementation of random *
805 ****************************************************************************/
806 
807 template<typename Scalar,
808  bool IsComplex,
809  bool IsInteger>
810 struct random_default_impl {};
811 
812 template<typename Scalar>
813 struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
814 
815 template<typename Scalar>
816 struct random_retval
817 {
818  typedef Scalar type;
819 };
820 
821 template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
822 template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
823 
824 template<typename Scalar>
825 struct random_default_impl<Scalar, false, false>
826 {
827  static inline Scalar run(const Scalar& x, const Scalar& y)
828  {
829  return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
830  }
831  static inline Scalar run()
832  {
833  return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
834  }
835 };
836 
837 enum {
838  meta_floor_log2_terminate,
839  meta_floor_log2_move_up,
840  meta_floor_log2_move_down,
841  meta_floor_log2_bogus
842 };
843 
844 template<unsigned int n, int lower, int upper> struct meta_floor_log2_selector
845 {
846  enum { middle = (lower + upper) / 2,
847  value = (upper <= lower + 1) ? int(meta_floor_log2_terminate)
848  : (n < (1 << middle)) ? int(meta_floor_log2_move_down)
849  : (n==0) ? int(meta_floor_log2_bogus)
850  : int(meta_floor_log2_move_up)
851  };
852 };
853 
854 template<unsigned int n,
855  int lower = 0,
856  int upper = sizeof(unsigned int) * CHAR_BIT - 1,
857  int selector = meta_floor_log2_selector<n, lower, upper>::value>
858 struct meta_floor_log2 {};
859 
860 template<unsigned int n, int lower, int upper>
861 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down>
862 {
863  enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value };
864 };
865 
866 template<unsigned int n, int lower, int upper>
867 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up>
868 {
869  enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value };
870 };
871 
872 template<unsigned int n, int lower, int upper>
873 struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate>
874 {
875  enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
876 };
877 
878 template<unsigned int n, int lower, int upper>
879 struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>
880 {
881  // no value, error at compile time
882 };
883 
884 template<typename Scalar>
885 struct random_default_impl<Scalar, false, true>
886 {
887  static inline Scalar run(const Scalar& x, const Scalar& y)
888  {
889  if (y <= x)
890  return x;
891  // ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself.
892  typedef typename make_unsigned<Scalar>::type ScalarU;
893  // ScalarX is the widest of ScalarU and unsigned int.
894  // We'll deal only with ScalarX and unsigned int below thus avoiding signed
895  // types and arithmetic and signed overflows (which are undefined behavior).
896  typedef typename conditional<(ScalarU(-1) > unsigned(-1)), ScalarU, unsigned>::type ScalarX;
897  // The following difference doesn't overflow, provided our integer types are two's
898  // complement and have the same number of padding bits in signed and unsigned variants.
899  // This is the case in most modern implementations of C++.
900  ScalarX range = ScalarX(y) - ScalarX(x);
901  ScalarX offset = 0;
902  ScalarX divisor = 1;
903  ScalarX multiplier = 1;
904  const unsigned rand_max = RAND_MAX;
905  if (range <= rand_max) divisor = (rand_max + 1) / (range + 1);
906  else multiplier = 1 + range / (rand_max + 1);
907  // Rejection sampling.
908  do {
909  offset = (unsigned(std::rand()) * multiplier) / divisor;
910  } while (offset > range);
911  return Scalar(ScalarX(x) + offset);
912  }
913 
914  static inline Scalar run()
915  {
916 #ifdef EIGEN_MAKING_DOCS
917  return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
918 #else
919  enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value,
920  scalar_bits = sizeof(Scalar) * CHAR_BIT,
921  shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
922  offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
923  };
924  return Scalar((std::rand() >> shift) - offset);
925 #endif
926  }
927 };
928 
929 template<typename Scalar>
930 struct random_default_impl<Scalar, true, false>
931 {
932  static inline Scalar run(const Scalar& x, const Scalar& y)
933  {
934  return Scalar(random(x.real(), y.real()),
935  random(x.imag(), y.imag()));
936  }
937  static inline Scalar run()
938  {
939  typedef typename NumTraits<Scalar>::Real RealScalar;
940  return Scalar(random<RealScalar>(), random<RealScalar>());
941  }
942 };
943 
944 template<typename Scalar>
945 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
946 {
947  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
948 }
949 
950 template<typename Scalar>
951 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
952 {
953  return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
954 }
955 
956 // Implementation of is* functions
957 
958 // std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang.
959 #if (EIGEN_HAS_CXX11_MATH && !(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC>=1800) || (EIGEN_COMP_CLANG)
960 #define EIGEN_USE_STD_FPCLASSIFY 1
961 #else
962 #define EIGEN_USE_STD_FPCLASSIFY 0
963 #endif
964 
965 template<typename T>
966 EIGEN_DEVICE_FUNC
967 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
968 isnan_impl(const T&) { return false; }
969 
970 template<typename T>
971 EIGEN_DEVICE_FUNC
972 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
973 isinf_impl(const T&) { return false; }
974 
975 template<typename T>
976 EIGEN_DEVICE_FUNC
977 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
978 isfinite_impl(const T&) { return true; }
979 
980 template<typename T>
981 EIGEN_DEVICE_FUNC
982 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
983 isfinite_impl(const T& x)
984 {
985  #if defined(EIGEN_GPU_COMPILE_PHASE)
986  return (::isfinite)(x);
987  #elif EIGEN_USE_STD_FPCLASSIFY
988  using std::isfinite;
989  return isfinite EIGEN_NOT_A_MACRO (x);
990  #else
991  return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
992  #endif
993 }
994 
995 template<typename T>
996 EIGEN_DEVICE_FUNC
997 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
998 isinf_impl(const T& x)
999 {
1000  #if defined(EIGEN_GPU_COMPILE_PHASE)
1001  return (::isinf)(x);
1002  #elif EIGEN_USE_STD_FPCLASSIFY
1003  using std::isinf;
1004  return isinf EIGEN_NOT_A_MACRO (x);
1005  #else
1006  return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
1007  #endif
1008 }
1009 
1010 template<typename T>
1011 EIGEN_DEVICE_FUNC
1012 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
1013 isnan_impl(const T& x)
1014 {
1015  #if defined(EIGEN_GPU_COMPILE_PHASE)
1016  return (::isnan)(x);
1017  #elif EIGEN_USE_STD_FPCLASSIFY
1018  using std::isnan;
1019  return isnan EIGEN_NOT_A_MACRO (x);
1020  #else
1021  return x != x;
1022  #endif
1023 }
1024 
1025 #if (!EIGEN_USE_STD_FPCLASSIFY)
1026 
1027 #if EIGEN_COMP_MSVC
1028 
1029 template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
1030 {
1031  return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;
1032 }
1033 
1034 //MSVC defines a _isnan builtin function, but for double only
1035 EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
1036 EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) { return _isnan(x)!=0; }
1037 EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) { return _isnan(x)!=0; }
1038 
1039 EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
1040 EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) { return isinf_msvc_helper(x); }
1041 EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) { return isinf_msvc_helper(x); }
1042 
1043 #elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)
1044 
1045 #if EIGEN_GNUC_AT_LEAST(5,0)
1046  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only")))
1047 #else
1048  // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol),
1049  // while the second prevent too aggressive optimizations in fast-math mode:
1050  #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only")))
1051 #endif
1052 
1053 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }
1054 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) { return __builtin_isnan(x); }
1055 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) { return __builtin_isnan(x); }
1056 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) { return __builtin_isinf(x); }
1057 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) { return __builtin_isinf(x); }
1058 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }
1059 
1060 #undef EIGEN_TMP_NOOPT_ATTRIB
1061 
1062 #endif
1063 
1064 #endif
1065 
1066 // The following overload are defined at the end of this file
1067 template<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
1068 template<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
1069 template<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
1070 
1071 template<typename T> T generic_fast_tanh_float(const T& a_x);
1072 } // end namespace internal
1073 
1074 /****************************************************************************
1075 * Generic math functions *
1076 ****************************************************************************/
1077 
1078 namespace numext {
1079 
1080 #if (!defined(EIGEN_GPUCC) || defined(EIGEN_CONSTEXPR_ARE_DEVICE_FUNC))
1081 template<typename T>
1082 EIGEN_DEVICE_FUNC
1083 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
1084 {
1085  EIGEN_USING_STD(min)
1086  return min EIGEN_NOT_A_MACRO (x,y);
1087 }
1088 
1089 template<typename T>
1090 EIGEN_DEVICE_FUNC
1091 EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
1092 {
1093  EIGEN_USING_STD(max)
1094  return max EIGEN_NOT_A_MACRO (x,y);
1095 }
1096 #else
1097 template<typename T>
1098 EIGEN_DEVICE_FUNC
1099 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
1100 {
1101  return y < x ? y : x;
1102 }
1103 template<>
1104 EIGEN_DEVICE_FUNC
1105 EIGEN_ALWAYS_INLINE float mini(const float& x, const float& y)
1106 {
1107  return fminf(x, y);
1108 }
1109 template<>
1110 EIGEN_DEVICE_FUNC
1111 EIGEN_ALWAYS_INLINE double mini(const double& x, const double& y)
1112 {
1113  return fmin(x, y);
1114 }
1115 template<>
1116 EIGEN_DEVICE_FUNC
1117 EIGEN_ALWAYS_INLINE long double mini(const long double& x, const long double& y)
1118 {
1119 #if defined(EIGEN_HIPCC)
1120  // no "fminl" on HIP yet
1121  return (x < y) ? x : y;
1122 #else
1123  return fminl(x, y);
1124 #endif
1125 }
1126 
1127 template<typename T>
1128 EIGEN_DEVICE_FUNC
1129 EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
1130 {
1131  return x < y ? y : x;
1132 }
1133 template<>
1134 EIGEN_DEVICE_FUNC
1135 EIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y)
1136 {
1137  return fmaxf(x, y);
1138 }
1139 template<>
1140 EIGEN_DEVICE_FUNC
1141 EIGEN_ALWAYS_INLINE double maxi(const double& x, const double& y)
1142 {
1143  return fmax(x, y);
1144 }
1145 template<>
1146 EIGEN_DEVICE_FUNC
1147 EIGEN_ALWAYS_INLINE long double maxi(const long double& x, const long double& y)
1148 {
1149 #if defined(EIGEN_HIPCC)
1150  // no "fmaxl" on HIP yet
1151  return (x > y) ? x : y;
1152 #else
1153  return fmaxl(x, y);
1154 #endif
1155 }
1156 #endif
1157 
1158 #if defined(SYCL_DEVICE_ONLY)
1159 
1160 
1161 #define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
1162  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \
1163  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \
1164  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \
1165  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_long)
1166 #define SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
1167  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_char) \
1168  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_short) \
1169  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_int) \
1170  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_long)
1171 #define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
1172  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \
1173  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \
1174  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \
1175  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong)
1176 #define SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
1177  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uchar) \
1178  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ushort) \
1179  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_uint) \
1180  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_ulong)
1181 #define SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(NAME, FUNC) \
1182  SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY(NAME, FUNC) \
1183  SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY(NAME, FUNC)
1184 #define SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(NAME, FUNC) \
1185  SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY(NAME, FUNC) \
1186  SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY(NAME, FUNC)
1187 #define SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(NAME, FUNC) \
1188  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \
1189  SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC,cl::sycl::cl_double)
1190 #define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(NAME, FUNC) \
1191  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, cl::sycl::cl_float) \
1192  SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC,cl::sycl::cl_double)
1193 #define SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(NAME, FUNC, RET_TYPE) \
1194  SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_float) \
1195  SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, cl::sycl::cl_double)
1196 
1197 #define SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \
1198 template<> \
1199  EIGEN_DEVICE_FUNC \
1200  EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE& x) { \
1201  return cl::sycl::FUNC(x); \
1202  }
1203 
1204 #define SYCL_SPECIALIZE_UNARY_FUNC(NAME, FUNC, TYPE) \
1205  SYCL_SPECIALIZE_GEN_UNARY_FUNC(NAME, FUNC, TYPE, TYPE)
1206 
1207 #define SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE1, ARG_TYPE2) \
1208  template<> \
1209  EIGEN_DEVICE_FUNC \
1210  EIGEN_ALWAYS_INLINE RET_TYPE NAME(const ARG_TYPE1& x, const ARG_TYPE2& y) { \
1211  return cl::sycl::FUNC(x, y); \
1212  }
1213 
1214 #define SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE) \
1215  SYCL_SPECIALIZE_GEN1_BINARY_FUNC(NAME, FUNC, RET_TYPE, ARG_TYPE, ARG_TYPE)
1216 
1217 #define SYCL_SPECIALIZE_BINARY_FUNC(NAME, FUNC, TYPE) \
1218  SYCL_SPECIALIZE_GEN2_BINARY_FUNC(NAME, FUNC, TYPE, TYPE)
1219 
1220 SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(mini, min)
1221 SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(mini, fmin)
1222 SYCL_SPECIALIZE_INTEGER_TYPES_BINARY(maxi, max)
1223 SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(maxi, fmax)
1224 
1225 #endif
1226 
1227 
1228 template<typename Scalar>
1229 EIGEN_DEVICE_FUNC
1230 inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
1231 {
1232  return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
1233 }
1234 
1235 template<typename Scalar>
1236 EIGEN_DEVICE_FUNC
1237 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
1238 {
1239  return internal::real_ref_impl<Scalar>::run(x);
1240 }
1241 
1242 template<typename Scalar>
1243 EIGEN_DEVICE_FUNC
1244 inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
1245 {
1246  return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
1247 }
1248 
1249 template<typename Scalar>
1250 EIGEN_DEVICE_FUNC
1251 inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
1252 {
1253  return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
1254 }
1255 
1256 template<typename Scalar>
1257 EIGEN_DEVICE_FUNC
1258 inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x)
1259 {
1260  return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
1261 }
1262 
1263 template<typename Scalar>
1264 EIGEN_DEVICE_FUNC
1265 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
1266 {
1267  return internal::imag_ref_impl<Scalar>::run(x);
1268 }
1269 
1270 template<typename Scalar>
1271 EIGEN_DEVICE_FUNC
1272 inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
1273 {
1274  return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
1275 }
1276 
1277 template<typename Scalar>
1278 EIGEN_DEVICE_FUNC
1279 inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
1280 {
1281  return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
1282 }
1283 
1284 template<typename Scalar>
1285 EIGEN_DEVICE_FUNC
1286 inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
1287 {
1288  return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
1289 }
1290 
1291 EIGEN_DEVICE_FUNC
1292 inline bool abs2(bool x) { return x; }
1293 
1294 template<typename T>
1295 EIGEN_DEVICE_FUNC
1296 EIGEN_ALWAYS_INLINE T absdiff(const T& x, const T& y)
1297 {
1298  return x > y ? x - y : y - x;
1299 }
1300 template<>
1301 EIGEN_DEVICE_FUNC
1302 EIGEN_ALWAYS_INLINE float absdiff(const float& x, const float& y)
1303 {
1304  return fabsf(x - y);
1305 }
1306 template<>
1307 EIGEN_DEVICE_FUNC
1308 EIGEN_ALWAYS_INLINE double absdiff(const double& x, const double& y)
1309 {
1310  return fabs(x - y);
1311 }
1312 
1313 #if !defined(EIGEN_GPUCC)
1314 // HIP and CUDA do not support long double.
1315 template<>
1316 EIGEN_DEVICE_FUNC
1317 EIGEN_ALWAYS_INLINE long double absdiff(const long double& x, const long double& y) {
1318  return fabsl(x - y);
1319 }
1320 #endif
1321 
1322 template<typename Scalar>
1323 EIGEN_DEVICE_FUNC
1324 inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
1325 {
1326  return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
1327 }
1328 
1329 template<typename Scalar>
1330 EIGEN_DEVICE_FUNC
1331 inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
1332 {
1333  return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
1334 }
1335 
1336 #if defined(SYCL_DEVICE_ONLY)
1337  SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(hypot, hypot)
1338 #endif
1339 
1340 template<typename Scalar>
1341 EIGEN_DEVICE_FUNC
1342 inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)
1343 {
1344  return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
1345 }
1346 
1347 #if defined(SYCL_DEVICE_ONLY)
1348 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log1p, log1p)
1349 #endif
1350 
1351 #if defined(EIGEN_GPUCC)
1352 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1353 float log1p(const float &x) { return ::log1pf(x); }
1354 
1355 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1356 double log1p(const double &x) { return ::log1p(x); }
1357 #endif
1358 
1359 template<typename ScalarX,typename ScalarY>
1360 EIGEN_DEVICE_FUNC
1361 inline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(const ScalarX& x, const ScalarY& y)
1362 {
1363  return internal::pow_impl<ScalarX,ScalarY>::run(x, y);
1364 }
1365 
1366 #if defined(SYCL_DEVICE_ONLY)
1367 SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(pow, pow)
1368 #endif
1369 
1370 template<typename T> EIGEN_DEVICE_FUNC bool (isnan) (const T &x) { return internal::isnan_impl(x); }
1371 template<typename T> EIGEN_DEVICE_FUNC bool (isinf) (const T &x) { return internal::isinf_impl(x); }
1372 template<typename T> EIGEN_DEVICE_FUNC bool (isfinite)(const T &x) { return internal::isfinite_impl(x); }
1373 
1374 #if defined(SYCL_DEVICE_ONLY)
1375 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isnan, isnan, bool)
1376 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isinf, isinf, bool)
1377 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE(isfinite, isfinite, bool)
1378 #endif
1379 
1380 template<typename Scalar>
1381 EIGEN_DEVICE_FUNC
1382 inline EIGEN_MATHFUNC_RETVAL(rint, Scalar) rint(const Scalar& x)
1383 {
1384  return EIGEN_MATHFUNC_IMPL(rint, Scalar)::run(x);
1385 }
1386 
1387 template<typename Scalar>
1388 EIGEN_DEVICE_FUNC
1389 inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x)
1390 {
1391  return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x);
1392 }
1393 
1394 #if defined(SYCL_DEVICE_ONLY)
1395 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(round, round)
1396 #endif
1397 
1398 template<typename T>
1399 EIGEN_DEVICE_FUNC
1400 T (floor)(const T& x)
1401 {
1402  EIGEN_USING_STD(floor)
1403  return floor(x);
1404 }
1405 
1406 #if defined(SYCL_DEVICE_ONLY)
1407 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(floor, floor)
1408 #endif
1409 
1410 #if defined(EIGEN_GPUCC)
1411 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1412 float floor(const float &x) { return ::floorf(x); }
1413 
1414 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1415 double floor(const double &x) { return ::floor(x); }
1416 #endif
1417 
1418 template<typename T>
1419 EIGEN_DEVICE_FUNC
1420 T (ceil)(const T& x)
1421 {
1422  EIGEN_USING_STD(ceil);
1423  return ceil(x);
1424 }
1425 
1426 #if defined(SYCL_DEVICE_ONLY)
1427 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(ceil, ceil)
1428 #endif
1429 
1430 #if defined(EIGEN_GPUCC)
1431 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1432 float ceil(const float &x) { return ::ceilf(x); }
1433 
1434 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1435 double ceil(const double &x) { return ::ceil(x); }
1436 #endif
1437 
1438 
1441 inline int log2(int x)
1442 {
1443  eigen_assert(x>=0);
1444  unsigned int v(x);
1445  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 };
1446  v |= v >> 1;
1447  v |= v >> 2;
1448  v |= v >> 4;
1449  v |= v >> 8;
1450  v |= v >> 16;
1451  return table[(v * 0x07C4ACDDU) >> 27];
1452 }
1453 
1463 template<typename Scalar>
1464 EIGEN_DEVICE_FUNC
1465 EIGEN_ALWAYS_INLINE EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x)
1466 {
1467  return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
1468 }
1469 
1470 // Boolean specialization, avoids implicit float to bool conversion (-Wimplicit-conversion-floating-point-to-bool).
1471 template<>
1472 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_DEVICE_FUNC
1473 bool sqrt<bool>(const bool &x) { return x; }
1474 
1475 #if defined(SYCL_DEVICE_ONLY)
1476 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sqrt, sqrt)
1477 #endif
1478 
1480 template<typename T>
1481 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1482 T rsqrt(const T& x)
1483 {
1484  return internal::rsqrt_impl<T>::run(x);
1485 }
1486 
1487 template<typename T>
1488 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1489 T log(const T &x) {
1490  return internal::log_impl<T>::run(x);
1491 }
1492 
1493 #if defined(SYCL_DEVICE_ONLY)
1494 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(log, log)
1495 #endif
1496 
1497 
1498 #if defined(EIGEN_GPUCC)
1499 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1500 float log(const float &x) { return ::logf(x); }
1501 
1502 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1503 double log(const double &x) { return ::log(x); }
1504 #endif
1505 
1506 template<typename T>
1507 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1508 typename internal::enable_if<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex,typename NumTraits<T>::Real>::type
1509 abs(const T &x) {
1510  EIGEN_USING_STD(abs);
1511  return abs(x);
1512 }
1513 
1514 template<typename T>
1515 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1516 typename internal::enable_if<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex),typename NumTraits<T>::Real>::type
1517 abs(const T &x) {
1518  return x;
1519 }
1520 
1521 #if defined(SYCL_DEVICE_ONLY)
1522 SYCL_SPECIALIZE_INTEGER_TYPES_UNARY(abs, abs)
1523 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(abs, fabs)
1524 #endif
1525 
1526 #if defined(EIGEN_GPUCC)
1527 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1528 float abs(const float &x) { return ::fabsf(x); }
1529 
1530 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1531 double abs(const double &x) { return ::fabs(x); }
1532 
1533 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1534 float abs(const std::complex<float>& x) {
1535  return ::hypotf(x.real(), x.imag());
1536 }
1537 
1538 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1539 double abs(const std::complex<double>& x) {
1540  return ::hypot(x.real(), x.imag());
1541 }
1542 #endif
1543 
1544 template<typename T>
1545 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1546 T exp(const T &x) {
1547  EIGEN_USING_STD(exp);
1548  return exp(x);
1549 }
1550 
1551 #if defined(SYCL_DEVICE_ONLY)
1552 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(exp, exp)
1553 #endif
1554 
1555 #if defined(EIGEN_GPUCC)
1556 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1557 float exp(const float &x) { return ::expf(x); }
1558 
1559 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1560 double exp(const double &x) { return ::exp(x); }
1561 
1562 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1563 std::complex<float> exp(const std::complex<float>& x) {
1564  float com = ::expf(x.real());
1565  float res_real = com * ::cosf(x.imag());
1566  float res_imag = com * ::sinf(x.imag());
1567  return std::complex<float>(res_real, res_imag);
1568 }
1569 
1570 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1571 std::complex<double> exp(const std::complex<double>& x) {
1572  double com = ::exp(x.real());
1573  double res_real = com * ::cos(x.imag());
1574  double res_imag = com * ::sin(x.imag());
1575  return std::complex<double>(res_real, res_imag);
1576 }
1577 #endif
1578 
1579 template<typename Scalar>
1580 EIGEN_DEVICE_FUNC
1581 inline EIGEN_MATHFUNC_RETVAL(expm1, Scalar) expm1(const Scalar& x)
1582 {
1583  return EIGEN_MATHFUNC_IMPL(expm1, Scalar)::run(x);
1584 }
1585 
1586 #if defined(SYCL_DEVICE_ONLY)
1587 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(expm1, expm1)
1588 #endif
1589 
1590 #if defined(EIGEN_GPUCC)
1591 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1592 float expm1(const float &x) { return ::expm1f(x); }
1593 
1594 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1595 double expm1(const double &x) { return ::expm1(x); }
1596 #endif
1597 
1598 template<typename T>
1599 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1600 T cos(const T &x) {
1601  EIGEN_USING_STD(cos);
1602  return cos(x);
1603 }
1604 
1605 #if defined(SYCL_DEVICE_ONLY)
1606 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cos,cos)
1607 #endif
1608 
1609 #if defined(EIGEN_GPUCC)
1610 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1611 float cos(const float &x) { return ::cosf(x); }
1612 
1613 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1614 double cos(const double &x) { return ::cos(x); }
1615 #endif
1616 
1617 template<typename T>
1618 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1619 T sin(const T &x) {
1620  EIGEN_USING_STD(sin);
1621  return sin(x);
1622 }
1623 
1624 #if defined(SYCL_DEVICE_ONLY)
1625 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sin, sin)
1626 #endif
1627 
1628 #if defined(EIGEN_GPUCC)
1629 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1630 float sin(const float &x) { return ::sinf(x); }
1631 
1632 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1633 double sin(const double &x) { return ::sin(x); }
1634 #endif
1635 
1636 template<typename T>
1637 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1638 T tan(const T &x) {
1639  EIGEN_USING_STD(tan);
1640  return tan(x);
1641 }
1642 
1643 #if defined(SYCL_DEVICE_ONLY)
1644 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tan, tan)
1645 #endif
1646 
1647 #if defined(EIGEN_GPUCC)
1648 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1649 float tan(const float &x) { return ::tanf(x); }
1650 
1651 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1652 double tan(const double &x) { return ::tan(x); }
1653 #endif
1654 
1655 template<typename T>
1656 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1657 T acos(const T &x) {
1658  EIGEN_USING_STD(acos);
1659  return acos(x);
1660 }
1661 
1662 #if EIGEN_HAS_CXX11_MATH
1663 template<typename T>
1664 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1665 T acosh(const T &x) {
1666  EIGEN_USING_STD(acosh);
1667  return static_cast<T>(acosh(x));
1668 }
1669 #endif
1670 
1671 #if defined(SYCL_DEVICE_ONLY)
1672 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acos, acos)
1673 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(acosh, acosh)
1674 #endif
1675 
1676 #if defined(EIGEN_GPUCC)
1677 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1678 float acos(const float &x) { return ::acosf(x); }
1679 
1680 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1681 double acos(const double &x) { return ::acos(x); }
1682 #endif
1683 
1684 template<typename T>
1685 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1686 T asin(const T &x) {
1687  EIGEN_USING_STD(asin);
1688  return asin(x);
1689 }
1690 
1691 #if EIGEN_HAS_CXX11_MATH
1692 template<typename T>
1693 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1694 T asinh(const T &x) {
1695  EIGEN_USING_STD(asinh);
1696  return static_cast<T>(asinh(x));
1697 }
1698 #endif
1699 
1700 #if defined(SYCL_DEVICE_ONLY)
1701 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asin, asin)
1702 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(asinh, asinh)
1703 #endif
1704 
1705 #if defined(EIGEN_GPUCC)
1706 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1707 float asin(const float &x) { return ::asinf(x); }
1708 
1709 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1710 double asin(const double &x) { return ::asin(x); }
1711 #endif
1712 
1713 template<typename T>
1714 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1715 T atan(const T &x) {
1716  EIGEN_USING_STD(atan);
1717  return static_cast<T>(atan(x));
1718 }
1719 
1720 #if EIGEN_HAS_CXX11_MATH
1721 template<typename T>
1722 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1723 T atanh(const T &x) {
1724  EIGEN_USING_STD(atanh);
1725  return static_cast<T>(atanh(x));
1726 }
1727 #endif
1728 
1729 #if defined(SYCL_DEVICE_ONLY)
1730 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atan, atan)
1731 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(atanh, atanh)
1732 #endif
1733 
1734 #if defined(EIGEN_GPUCC)
1735 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1736 float atan(const float &x) { return ::atanf(x); }
1737 
1738 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1739 double atan(const double &x) { return ::atan(x); }
1740 #endif
1741 
1742 
1743 template<typename T>
1744 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1745 T cosh(const T &x) {
1746  EIGEN_USING_STD(cosh);
1747  return static_cast<T>(cosh(x));
1748 }
1749 
1750 #if defined(SYCL_DEVICE_ONLY)
1751 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(cosh, cosh)
1752 #endif
1753 
1754 #if defined(EIGEN_GPUCC)
1755 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1756 float cosh(const float &x) { return ::coshf(x); }
1757 
1758 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1759 double cosh(const double &x) { return ::cosh(x); }
1760 #endif
1761 
1762 template<typename T>
1763 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1764 T sinh(const T &x) {
1765  EIGEN_USING_STD(sinh);
1766  return static_cast<T>(sinh(x));
1767 }
1768 
1769 #if defined(SYCL_DEVICE_ONLY)
1770 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(sinh, sinh)
1771 #endif
1772 
1773 #if defined(EIGEN_GPUCC)
1774 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1775 float sinh(const float &x) { return ::sinhf(x); }
1776 
1777 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1778 double sinh(const double &x) { return ::sinh(x); }
1779 #endif
1780 
1781 template<typename T>
1782 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1783 T tanh(const T &x) {
1784  EIGEN_USING_STD(tanh);
1785  return tanh(x);
1786 }
1787 
1788 #if (!defined(EIGEN_GPUCC)) && EIGEN_FAST_MATH && !defined(SYCL_DEVICE_ONLY)
1789 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1790 float tanh(float x) { return internal::generic_fast_tanh_float(x); }
1791 #endif
1792 
1793 #if defined(SYCL_DEVICE_ONLY)
1794 SYCL_SPECIALIZE_FLOATING_TYPES_UNARY(tanh, tanh)
1795 #endif
1796 
1797 #if defined(EIGEN_GPUCC)
1798 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1799 float tanh(const float &x) { return ::tanhf(x); }
1800 
1801 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1802 double tanh(const double &x) { return ::tanh(x); }
1803 #endif
1804 
1805 template <typename T>
1806 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1807 T fmod(const T& a, const T& b) {
1808  EIGEN_USING_STD(fmod);
1809  return fmod(a, b);
1810 }
1811 
1812 #if defined(SYCL_DEVICE_ONLY)
1813 SYCL_SPECIALIZE_FLOATING_TYPES_BINARY(fmod, fmod)
1814 #endif
1815 
1816 #if defined(EIGEN_GPUCC)
1817 template <>
1818 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1819 float fmod(const float& a, const float& b) {
1820  return ::fmodf(a, b);
1821 }
1822 
1823 template <>
1824 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1825 double fmod(const double& a, const double& b) {
1826  return ::fmod(a, b);
1827 }
1828 #endif
1829 
1830 #if defined(SYCL_DEVICE_ONLY)
1831 #undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_BINARY
1832 #undef SYCL_SPECIALIZE_SIGNED_INTEGER_TYPES_UNARY
1833 #undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_BINARY
1834 #undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY
1835 #undef SYCL_SPECIALIZE_INTEGER_TYPES_BINARY
1836 #undef SYCL_SPECIALIZE_UNSIGNED_INTEGER_TYPES_UNARY
1837 #undef SYCL_SPECIALIZE_FLOATING_TYPES_BINARY
1838 #undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY
1839 #undef SYCL_SPECIALIZE_FLOATING_TYPES_UNARY_FUNC_RET_TYPE
1840 #undef SYCL_SPECIALIZE_GEN_UNARY_FUNC
1841 #undef SYCL_SPECIALIZE_UNARY_FUNC
1842 #undef SYCL_SPECIALIZE_GEN1_BINARY_FUNC
1843 #undef SYCL_SPECIALIZE_GEN2_BINARY_FUNC
1844 #undef SYCL_SPECIALIZE_BINARY_FUNC
1845 #endif
1846 
1847 } // end namespace numext
1848 
1849 namespace internal {
1850 
1851 template<typename T>
1852 EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x)
1853 {
1854  return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
1855 }
1856 
1857 template<typename T>
1858 EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x)
1859 {
1860  return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
1861 }
1862 
1863 template<typename T>
1864 EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x)
1865 {
1866  return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
1867 }
1868 
1869 /****************************************************************************
1870 * Implementation of fuzzy comparisons *
1871 ****************************************************************************/
1872 
1873 template<typename Scalar,
1874  bool IsComplex,
1875  bool IsInteger>
1876 struct scalar_fuzzy_default_impl {};
1877 
1878 template<typename Scalar>
1879 struct scalar_fuzzy_default_impl<Scalar, false, false>
1880 {
1881  typedef typename NumTraits<Scalar>::Real RealScalar;
1882  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1883  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
1884  {
1885  return numext::abs(x) <= numext::abs(y) * prec;
1886  }
1887  EIGEN_DEVICE_FUNC
1888  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
1889  {
1890  return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
1891  }
1892  EIGEN_DEVICE_FUNC
1893  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
1894  {
1895  return x <= y || isApprox(x, y, prec);
1896  }
1897 };
1898 
1899 template<typename Scalar>
1900 struct scalar_fuzzy_default_impl<Scalar, false, true>
1901 {
1902  typedef typename NumTraits<Scalar>::Real RealScalar;
1903  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1904  static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
1905  {
1906  return x == Scalar(0);
1907  }
1908  EIGEN_DEVICE_FUNC
1909  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
1910  {
1911  return x == y;
1912  }
1913  EIGEN_DEVICE_FUNC
1914  static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
1915  {
1916  return x <= y;
1917  }
1918 };
1919 
1920 template<typename Scalar>
1921 struct scalar_fuzzy_default_impl<Scalar, true, false>
1922 {
1923  typedef typename NumTraits<Scalar>::Real RealScalar;
1924  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1925  static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
1926  {
1927  return numext::abs2(x) <= numext::abs2(y) * prec * prec;
1928  }
1929  EIGEN_DEVICE_FUNC
1930  static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
1931  {
1932  return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;
1933  }
1934 };
1935 
1936 template<typename Scalar>
1937 struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
1938 
1939 template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC
1940 inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
1941  const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1942 {
1943  return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
1944 }
1945 
1946 template<typename Scalar> EIGEN_DEVICE_FUNC
1947 inline bool isApprox(const Scalar& x, const Scalar& y,
1948  const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1949 {
1950  return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
1951 }
1952 
1953 template<typename Scalar> EIGEN_DEVICE_FUNC
1954 inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
1955  const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1956 {
1957  return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
1958 }
1959 
1960 /******************************************
1961 *** The special case of the bool type ***
1962 ******************************************/
1963 
1964 template<> struct random_impl<bool>
1965 {
1966  static inline bool run()
1967  {
1968  return random<int>(0,1)==0 ? false : true;
1969  }
1970 
1971  static inline bool run(const bool& a, const bool& b)
1972  {
1973  return random<int>(a, b)==0 ? false : true;
1974  }
1975 };
1976 
1977 template<> struct scalar_fuzzy_impl<bool>
1978 {
1979  typedef bool RealScalar;
1980 
1981  template<typename OtherScalar> EIGEN_DEVICE_FUNC
1982  static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
1983  {
1984  return !x;
1985  }
1986 
1987  EIGEN_DEVICE_FUNC
1988  static inline bool isApprox(bool x, bool y, bool)
1989  {
1990  return x == y;
1991  }
1992 
1993  EIGEN_DEVICE_FUNC
1994  static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
1995  {
1996  return (!x) || y;
1997  }
1998 
1999 };
2000 
2001 } // end namespace internal
2002 
2003 // Default implementations that rely on other numext implementations
2004 namespace internal {
2005 
2006 // Specialization for complex types that are not supported by std::expm1.
2007 template <typename RealScalar>
2008 struct expm1_impl<std::complex<RealScalar> > {
2009  EIGEN_DEVICE_FUNC static inline std::complex<RealScalar> run(
2010  const std::complex<RealScalar>& x) {
2011  EIGEN_STATIC_ASSERT_NON_INTEGER(RealScalar)
2012  RealScalar xr = x.real();
2013  RealScalar xi = x.imag();
2014  // expm1(z) = exp(z) - 1
2015  // = exp(x + i * y) - 1
2016  // = exp(x) * (cos(y) + i * sin(y)) - 1
2017  // = exp(x) * cos(y) - 1 + i * exp(x) * sin(y)
2018  // Imag(expm1(z)) = exp(x) * sin(y)
2019  // Real(expm1(z)) = exp(x) * cos(y) - 1
2020  // = exp(x) * cos(y) - 1.
2021  // = expm1(x) + exp(x) * (cos(y) - 1)
2022  // = expm1(x) + exp(x) * (2 * sin(y / 2) ** 2)
2023  RealScalar erm1 = numext::expm1<RealScalar>(xr);
2024  RealScalar er = erm1 + RealScalar(1.);
2025  RealScalar sin2 = numext::sin(xi / RealScalar(2.));
2026  sin2 = sin2 * sin2;
2027  RealScalar s = numext::sin(xi);
2028  RealScalar real_part = erm1 - RealScalar(2.) * er * sin2;
2029  return std::complex<RealScalar>(real_part, er * s);
2030  }
2031 };
2032 
2033 template<typename T>
2034 struct rsqrt_impl {
2035  EIGEN_DEVICE_FUNC
2036  static EIGEN_ALWAYS_INLINE T run(const T& x) {
2037  return T(1)/numext::sqrt(x);
2038  }
2039 };
2040 
2041 #if defined(EIGEN_GPU_COMPILE_PHASE)
2042 template<typename T>
2043 struct conj_impl<std::complex<T>, true>
2044 {
2045  EIGEN_DEVICE_FUNC
2046  static inline std::complex<T> run(const std::complex<T>& x)
2047  {
2048  return std::complex<T>(numext::real(x), -numext::imag(x));
2049  }
2050 };
2051 #endif
2052 
2053 } // end namespace internal
2054 
2055 } // end namespace Eigen
2056 
2057 #endif // EIGEN_MATHFUNCTIONS_H
Namespace containing all symbols from the Eigen library.
Definition: Core:141
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tanh_op< typename Derived::Scalar >, const Derived > tanh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_rint_op< typename Derived::Scalar >, const Derived > rint(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_imag_op< typename Derived::Scalar >, const Derived > imag(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_isinf_op< typename Derived::Scalar >, const Derived > isinf(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_atan_op< typename Derived::Scalar >, const Derived > atan(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cosh_op< typename Derived::Scalar >, const Derived > cosh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tan_op< typename Derived::Scalar >, const Derived > tan(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_atanh_op< typename Derived::Scalar >, const Derived > atanh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs2_op< typename Derived::Scalar >, const Derived > abs2(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_rsqrt_op< typename Derived::Scalar >, const Derived > rsqrt(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_asin_op< typename Derived::Scalar >, const Derived > asin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_asinh_op< typename Derived::Scalar >, const Derived > asinh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acosh_op< typename Derived::Scalar >, const Derived > acosh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_isnan_op< typename Derived::Scalar >, const Derived > isnan(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_arg_op< typename Derived::Scalar >, const Derived > arg(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_ceil_op< typename Derived::Scalar >, const Derived > ceil(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_conjugate_op< typename Derived::Scalar >, const Derived > conj(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_isfinite_op< typename Derived::Scalar >, const Derived > isfinite(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_floor_op< typename Derived::Scalar >, const Derived > floor(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log1p_op< typename Derived::Scalar >, const Derived > log1p(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_real_op< typename Derived::Scalar >, const Derived > real(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log2_op< typename Derived::Scalar >, const Derived > log2(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_round_op< typename Derived::Scalar >, const Derived > round(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp_op< typename Derived::Scalar >, const Derived > exp(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_expm1_op< typename Derived::Scalar >, const Derived > expm1(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log_op< typename Derived::Scalar >, const Derived > log(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sinh_op< typename Derived::Scalar >, const Derived > sinh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)