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
abs(long x)23 long abs(long x) { return (labs(x)); }
abs(double x)24 double abs(double x) { return (fabs(x)); }
abs(float x)25 float abs(float x) { return (fabsf(x)); }
abs(long double x)26 long double abs(long double x) { return (fabsl(x)); }
27 #endif
28
29 namespace internal {
30
31 /** \internal \class global_math_functions_filtering_base
32 *
33 * What it does:
34 * Defines a typedef 'type' as follows:
35 * - if type T has a member typedef Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl, then
36 * global_math_functions_filtering_base<T>::type is a typedef for it.
37 * - otherwise, global_math_functions_filtering_base<T>::type is a typedef for T.
38 *
39 * How it's used:
40 * To allow to defined the global math functions (like sin...) in certain cases, like the Array expressions.
41 * When you do sin(array1+array2), the object array1+array2 has a complicated expression type, all what you want to know
42 * is that it inherits ArrayBase. So we implement a partial specialization of sin_impl for ArrayBase<Derived>.
43 * So we must make sure to use sin_impl<ArrayBase<Derived> > and not sin_impl<Derived>, otherwise our partial specialization
44 * won't be used. How does sin know that? That's exactly what global_math_functions_filtering_base tells it.
45 *
46 * How it's implemented:
47 * SFINAE in the style of enable_if. Highly susceptible of breaking compilers. With GCC, it sure does work, but if you replace
48 * the typename dummy by an integer template parameter, it doesn't work anymore!
49 */
50
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> struct hypot_impl;
352
353 template<typename Scalar>
354 struct hypot_retval
355 {
356 typedef typename NumTraits<Scalar>::Real type;
357 };
358
359 /****************************************************************************
360 * Implementation of cast *
361 ****************************************************************************/
362
363 template<typename OldType, typename NewType>
364 struct cast_impl
365 {
366 EIGEN_DEVICE_FUNC
367 static inline NewType run(const OldType& x)
368 {
369 return static_cast<NewType>(x);
370 }
371 };
372
373 // here, for once, we're plainly returning NewType: we don't want cast to do weird things.
374
375 template<typename OldType, typename NewType>
376 EIGEN_DEVICE_FUNC
377 inline NewType cast(const OldType& x)
378 {
379 return cast_impl<OldType, NewType>::run(x);
380 }
381
382 /****************************************************************************
383 * Implementation of round *
384 ****************************************************************************/
385
386 #if EIGEN_HAS_CXX11_MATH
387 template<typename Scalar>
388 struct round_impl {
389 static inline Scalar run(const Scalar& x)
390 {
391 EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
392 using std::round;
393 return round(x);
394 }
395 };
396 #else
397 template<typename Scalar>
398 struct round_impl
399 {
400 static inline Scalar run(const Scalar& x)
401 {
402 EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
403 EIGEN_USING_STD_MATH(floor);
404 EIGEN_USING_STD_MATH(ceil);
405 return (x > Scalar(0)) ? floor(x + Scalar(0.5)) : ceil(x - Scalar(0.5));
406 }
407 };
408 #endif
409
410 template<typename Scalar>
411 struct round_retval
412 {
413 typedef Scalar type;
414 };
415
416 /****************************************************************************
417 * Implementation of arg *
418 ****************************************************************************/
419
420 #if EIGEN_HAS_CXX11_MATH
421 template<typename Scalar>
422 struct arg_impl {
423 static inline Scalar run(const Scalar& x)
424 {
425 EIGEN_USING_STD_MATH(arg);
426 return arg(x);
427 }
428 };
429 #else
430 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
431 struct arg_default_impl
432 {
433 typedef typename NumTraits<Scalar>::Real RealScalar;
434 EIGEN_DEVICE_FUNC
435 static inline RealScalar run(const Scalar& x)
436 {
437 return (x < Scalar(0)) ? Scalar(EIGEN_PI) : Scalar(0); }
438 };
439
440 template<typename Scalar>
441 struct arg_default_impl<Scalar,true>
442 {
443 typedef typename NumTraits<Scalar>::Real RealScalar;
444 EIGEN_DEVICE_FUNC
445 static inline RealScalar run(const Scalar& x)
446 {
447 EIGEN_USING_STD_MATH(arg);
448 return arg(x);
449 }
450 };
451
452 template<typename Scalar> struct arg_impl : arg_default_impl<Scalar> {};
453 #endif
454
455 template<typename Scalar>
456 struct arg_retval
457 {
458 typedef typename NumTraits<Scalar>::Real type;
459 };
460
461 /****************************************************************************
462 * Implementation of log1p *
463 ****************************************************************************/
464
465 namespace std_fallback {
466 // fallback log1p implementation in case there is no log1p(Scalar) function in namespace of Scalar,
467 // or that there is no suitable std::log1p function available
468 template<typename Scalar>
469 EIGEN_DEVICE_FUNC inline Scalar log1p(const Scalar& x) {
470 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
471 typedef typename NumTraits<Scalar>::Real RealScalar;
472 EIGEN_USING_STD_MATH(log);
473 Scalar x1p = RealScalar(1) + x;
474 return numext::equal_strict(x1p, Scalar(1)) ? x : x * ( log(x1p) / (x1p - RealScalar(1)) );
475 }
476 }
477
478 template<typename Scalar>
479 struct log1p_impl {
480 static inline Scalar run(const Scalar& x)
481 {
482 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
483 #if EIGEN_HAS_CXX11_MATH
484 using std::log1p;
485 #endif
486 using std_fallback::log1p;
487 return log1p(x);
488 }
489 };
490
491
492 template<typename Scalar>
493 struct log1p_retval
494 {
495 typedef Scalar type;
496 };
497
498 /****************************************************************************
499 * Implementation of pow *
500 ****************************************************************************/
501
502 template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>
503 struct pow_impl
504 {
505 //typedef Scalar retval;
506 typedef typename ScalarBinaryOpTraits<ScalarX,ScalarY,internal::scalar_pow_op<ScalarX,ScalarY> >::ReturnType result_type;
507 static EIGEN_DEVICE_FUNC inline result_type run(const ScalarX& x, const ScalarY& y)
508 {
509 EIGEN_USING_STD_MATH(pow);
510 return pow(x, y);
511 }
512 };
513
514 template<typename ScalarX,typename ScalarY>
515 struct pow_impl<ScalarX,ScalarY, true>
516 {
517 typedef ScalarX result_type;
518 static EIGEN_DEVICE_FUNC inline ScalarX run(ScalarX x, ScalarY y)
519 {
520 ScalarX res(1);
521 eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
522 if(y & 1) res *= x;
523 y >>= 1;
524 while(y)
525 {
526 x *= x;
527 if(y&1) res *= x;
528 y >>= 1;
529 }
530 return res;
531 }
532 };
533
534 /****************************************************************************
535 * Implementation of random *
536 ****************************************************************************/
537
538 template<typename Scalar,
539 bool IsComplex,
540 bool IsInteger>
541 struct random_default_impl {};
542
543 template<typename Scalar>
544 struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
545
546 template<typename Scalar>
547 struct random_retval
548 {
549 typedef Scalar type;
550 };
551
552 template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y);
553 template<typename Scalar> inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random();
554
555 template<typename Scalar>
556 struct random_default_impl<Scalar, false, false>
557 {
558 static inline Scalar run(const Scalar& x, const Scalar& y)
559 {
560 return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
561 }
562 static inline Scalar run()
563 {
564 return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
565 }
566 };
567
568 enum {
569 meta_floor_log2_terminate,
570 meta_floor_log2_move_up,
571 meta_floor_log2_move_down,
572 meta_floor_log2_bogus
573 };
574
575 template<unsigned int n, int lower, int upper> struct meta_floor_log2_selector
576 {
577 enum { middle = (lower + upper) / 2,
578 value = (upper <= lower + 1) ? int(meta_floor_log2_terminate)
579 : (n < (1 << middle)) ? int(meta_floor_log2_move_down)
580 : (n==0) ? int(meta_floor_log2_bogus)
581 : int(meta_floor_log2_move_up)
582 };
583 };
584
585 template<unsigned int n,
586 int lower = 0,
587 int upper = sizeof(unsigned int) * CHAR_BIT - 1,
588 int selector = meta_floor_log2_selector<n, lower, upper>::value>
589 struct meta_floor_log2 {};
590
591 template<unsigned int n, int lower, int upper>
592 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down>
593 {
594 enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value };
595 };
596
597 template<unsigned int n, int lower, int upper>
598 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up>
599 {
600 enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value };
601 };
602
603 template<unsigned int n, int lower, int upper>
604 struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate>
605 {
606 enum { value = (n >= ((unsigned int)(1) << (lower+1))) ? lower+1 : lower };
607 };
608
609 template<unsigned int n, int lower, int upper>
610 struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>
611 {
612 // no value, error at compile time
613 };
614
615 template<typename Scalar>
616 struct random_default_impl<Scalar, false, true>
617 {
618 static inline Scalar run(const Scalar& x, const Scalar& y)
619 {
620 if (y <= x)
621 return x;
622 // ScalarU is the unsigned counterpart of Scalar, possibly Scalar itself.
623 typedef typename make_unsigned<Scalar>::type ScalarU;
624 // ScalarX is the widest of ScalarU and unsigned int.
625 // We'll deal only with ScalarX and unsigned int below thus avoiding signed
626 // types and arithmetic and signed overflows (which are undefined behavior).
627 typedef typename conditional<(ScalarU(-1) > unsigned(-1)), ScalarU, unsigned>::type ScalarX;
628 // The following difference doesn't overflow, provided our integer types are two's
629 // complement and have the same number of padding bits in signed and unsigned variants.
630 // This is the case in most modern implementations of C++.
631 ScalarX range = ScalarX(y) - ScalarX(x);
632 ScalarX offset = 0;
633 ScalarX divisor = 1;
634 ScalarX multiplier = 1;
635 const unsigned rand_max = RAND_MAX;
636 if (range <= rand_max) divisor = (rand_max + 1) / (range + 1);
637 else multiplier = 1 + range / (rand_max + 1);
638 // Rejection sampling.
639 do {
640 offset = (unsigned(std::rand()) * multiplier) / divisor;
641 } while (offset > range);
642 return Scalar(ScalarX(x) + offset);
643 }
644
645 static inline Scalar run()
646 {
647 #ifdef EIGEN_MAKING_DOCS
648 return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
649 #else
650 enum { rand_bits = meta_floor_log2<(unsigned int)(RAND_MAX)+1>::value,
651 scalar_bits = sizeof(Scalar) * CHAR_BIT,
652 shift = EIGEN_PLAIN_ENUM_MAX(0, int(rand_bits) - int(scalar_bits)),
653 offset = NumTraits<Scalar>::IsSigned ? (1 << (EIGEN_PLAIN_ENUM_MIN(rand_bits,scalar_bits)-1)) : 0
654 };
655 return Scalar((std::rand() >> shift) - offset);
656 #endif
657 }
658 };
659
660 template<typename Scalar>
661 struct random_default_impl<Scalar, true, false>
662 {
663 static inline Scalar run(const Scalar& x, const Scalar& y)
664 {
665 return Scalar(random(real(x), real(y)),
666 random(imag(x), imag(y)));
667 }
668 static inline Scalar run()
669 {
670 typedef typename NumTraits<Scalar>::Real RealScalar;
671 return Scalar(random<RealScalar>(), random<RealScalar>());
672 }
673 };
674
675 template<typename Scalar>
676 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(const Scalar& x, const Scalar& y)
677 {
678 return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
679 }
680
681 template<typename Scalar>
682 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
683 {
684 return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
685 }
686
687 // Implementatin of is* functions
688
689 // std::is* do not work with fast-math and gcc, std::is* are available on MSVC 2013 and newer, as well as in clang.
690 #if (EIGEN_HAS_CXX11_MATH && !(EIGEN_COMP_GNUC_STRICT && __FINITE_MATH_ONLY__)) || (EIGEN_COMP_MSVC>=1800) || (EIGEN_COMP_CLANG)
691 #define EIGEN_USE_STD_FPCLASSIFY 1
692 #else
693 #define EIGEN_USE_STD_FPCLASSIFY 0
694 #endif
695
696 template<typename T>
697 EIGEN_DEVICE_FUNC
698 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
699 isnan_impl(const T&) { return false; }
700
701 template<typename T>
702 EIGEN_DEVICE_FUNC
703 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
704 isinf_impl(const T&) { return false; }
705
706 template<typename T>
707 EIGEN_DEVICE_FUNC
708 typename internal::enable_if<internal::is_integral<T>::value,bool>::type
709 isfinite_impl(const T&) { return true; }
710
711 template<typename T>
712 EIGEN_DEVICE_FUNC
713 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
714 isfinite_impl(const T& x)
715 {
716 #ifdef __CUDA_ARCH__
717 return (::isfinite)(x);
718 #elif EIGEN_USE_STD_FPCLASSIFY
719 using std::isfinite;
720 return isfinite EIGEN_NOT_A_MACRO (x);
721 #else
722 return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
723 #endif
724 }
725
726 template<typename T>
727 EIGEN_DEVICE_FUNC
728 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
729 isinf_impl(const T& x)
730 {
731 #ifdef __CUDA_ARCH__
732 return (::isinf)(x);
733 #elif EIGEN_USE_STD_FPCLASSIFY
734 using std::isinf;
735 return isinf EIGEN_NOT_A_MACRO (x);
736 #else
737 return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
738 #endif
739 }
740
741 template<typename T>
742 EIGEN_DEVICE_FUNC
743 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),bool>::type
744 isnan_impl(const T& x)
745 {
746 #ifdef __CUDA_ARCH__
747 return (::isnan)(x);
748 #elif EIGEN_USE_STD_FPCLASSIFY
749 using std::isnan;
750 return isnan EIGEN_NOT_A_MACRO (x);
751 #else
752 return x != x;
753 #endif
754 }
755
756 #if (!EIGEN_USE_STD_FPCLASSIFY)
757
758 #if EIGEN_COMP_MSVC
759
760 template<typename T> EIGEN_DEVICE_FUNC bool isinf_msvc_helper(T x)
761 {
762 return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;
763 }
764
765 //MSVC defines a _isnan builtin function, but for double only
766 EIGEN_DEVICE_FUNC inline bool isnan_impl(const long double& x) { return _isnan(x)!=0; }
767 EIGEN_DEVICE_FUNC inline bool isnan_impl(const double& x) { return _isnan(x)!=0; }
768 EIGEN_DEVICE_FUNC inline bool isnan_impl(const float& x) { return _isnan(x)!=0; }
769
770 EIGEN_DEVICE_FUNC inline bool isinf_impl(const long double& x) { return isinf_msvc_helper(x); }
771 EIGEN_DEVICE_FUNC inline bool isinf_impl(const double& x) { return isinf_msvc_helper(x); }
772 EIGEN_DEVICE_FUNC inline bool isinf_impl(const float& x) { return isinf_msvc_helper(x); }
773
774 #elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC)
775
776 #if EIGEN_GNUC_AT_LEAST(5,0)
777 #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only")))
778 #else
779 // NOTE the inline qualifier and noinline attribute are both needed: the former is to avoid linking issue (duplicate symbol),
780 // while the second prevent too aggressive optimizations in fast-math mode:
781 #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only")))
782 #endif
783
784 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const long double& x) { return __builtin_isnan(x); }
785 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const double& x) { return __builtin_isnan(x); }
786 template<> EIGEN_TMP_NOOPT_ATTRIB bool isnan_impl(const float& x) { return __builtin_isnan(x); }
787 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const double& x) { return __builtin_isinf(x); }
788 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const float& x) { return __builtin_isinf(x); }
789 template<> EIGEN_TMP_NOOPT_ATTRIB bool isinf_impl(const long double& x) { return __builtin_isinf(x); }
790
791 #undef EIGEN_TMP_NOOPT_ATTRIB
792
793 #endif
794
795 #endif
796
797 // The following overload are defined at the end of this file
798 template<typename T> EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x);
799 template<typename T> EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x);
800 template<typename T> EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x);
801
802 template<typename T> T generic_fast_tanh_float(const T& a_x);
803
804 } // end namespace internal
805
806 /****************************************************************************
807 * Generic math functions *
808 ****************************************************************************/
809
810 namespace numext {
811
812 #ifndef __CUDA_ARCH__
813 template<typename T>
814 EIGEN_DEVICE_FUNC
815 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
816 {
817 EIGEN_USING_STD_MATH(min);
818 return min EIGEN_NOT_A_MACRO (x,y);
819 }
820
821 template<typename T>
822 EIGEN_DEVICE_FUNC
823 EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
824 {
825 EIGEN_USING_STD_MATH(max);
826 return max EIGEN_NOT_A_MACRO (x,y);
827 }
828 #else
829 template<typename T>
830 EIGEN_DEVICE_FUNC
831 EIGEN_ALWAYS_INLINE T mini(const T& x, const T& y)
832 {
833 return y < x ? y : x;
834 }
835 template<>
836 EIGEN_DEVICE_FUNC
837 EIGEN_ALWAYS_INLINE float mini(const float& x, const float& y)
838 {
839 return fminf(x, y);
840 }
841 template<typename T>
842 EIGEN_DEVICE_FUNC
843 EIGEN_ALWAYS_INLINE T maxi(const T& x, const T& y)
844 {
845 return x < y ? y : x;
846 }
847 template<>
848 EIGEN_DEVICE_FUNC
849 EIGEN_ALWAYS_INLINE float maxi(const float& x, const float& y)
850 {
851 return fmaxf(x, y);
852 }
853 #endif
854
855
856 template<typename Scalar>
857 EIGEN_DEVICE_FUNC
858 inline EIGEN_MATHFUNC_RETVAL(real, Scalar) real(const Scalar& x)
859 {
860 return EIGEN_MATHFUNC_IMPL(real, Scalar)::run(x);
861 }
862
863 template<typename Scalar>
864 EIGEN_DEVICE_FUNC
865 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(const Scalar& x)
866 {
867 return internal::real_ref_impl<Scalar>::run(x);
868 }
869
870 template<typename Scalar>
871 EIGEN_DEVICE_FUNC
872 inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
873 {
874 return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
875 }
876
877 template<typename Scalar>
878 EIGEN_DEVICE_FUNC
879 inline EIGEN_MATHFUNC_RETVAL(imag, Scalar) imag(const Scalar& x)
880 {
881 return EIGEN_MATHFUNC_IMPL(imag, Scalar)::run(x);
882 }
883
884 template<typename Scalar>
885 EIGEN_DEVICE_FUNC
886 inline EIGEN_MATHFUNC_RETVAL(arg, Scalar) arg(const Scalar& x)
887 {
888 return EIGEN_MATHFUNC_IMPL(arg, Scalar)::run(x);
889 }
890
891 template<typename Scalar>
892 EIGEN_DEVICE_FUNC
893 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(const Scalar& x)
894 {
895 return internal::imag_ref_impl<Scalar>::run(x);
896 }
897
898 template<typename Scalar>
899 EIGEN_DEVICE_FUNC
900 inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
901 {
902 return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
903 }
904
905 template<typename Scalar>
906 EIGEN_DEVICE_FUNC
907 inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
908 {
909 return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
910 }
911
912 template<typename Scalar>
913 EIGEN_DEVICE_FUNC
914 inline EIGEN_MATHFUNC_RETVAL(abs2, Scalar) abs2(const Scalar& x)
915 {
916 return EIGEN_MATHFUNC_IMPL(abs2, Scalar)::run(x);
917 }
918
919 template<typename Scalar>
920 EIGEN_DEVICE_FUNC
921 inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(const Scalar& x)
922 {
923 return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
924 }
925
926 template<typename Scalar>
927 EIGEN_DEVICE_FUNC
928 inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(const Scalar& x, const Scalar& y)
929 {
930 return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
931 }
932
933 template<typename Scalar>
934 EIGEN_DEVICE_FUNC
935 inline EIGEN_MATHFUNC_RETVAL(log1p, Scalar) log1p(const Scalar& x)
936 {
937 return EIGEN_MATHFUNC_IMPL(log1p, Scalar)::run(x);
938 }
939
940 #ifdef __CUDACC__
941 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
942 float log1p(const float &x) { return ::log1pf(x); }
943
944 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
945 double log1p(const double &x) { return ::log1p(x); }
946 #endif
947
948 template<typename ScalarX,typename ScalarY>
949 EIGEN_DEVICE_FUNC
950 inline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(const ScalarX& x, const ScalarY& y)
951 {
952 return internal::pow_impl<ScalarX,ScalarY>::run(x, y);
953 }
954
955 template<typename T> EIGEN_DEVICE_FUNC bool (isnan) (const T &x) { return internal::isnan_impl(x); }
956 template<typename T> EIGEN_DEVICE_FUNC bool (isinf) (const T &x) { return internal::isinf_impl(x); }
957 template<typename T> EIGEN_DEVICE_FUNC bool (isfinite)(const T &x) { return internal::isfinite_impl(x); }
958
959 template<typename Scalar>
960 EIGEN_DEVICE_FUNC
961 inline EIGEN_MATHFUNC_RETVAL(round, Scalar) round(const Scalar& x)
962 {
963 return EIGEN_MATHFUNC_IMPL(round, Scalar)::run(x);
964 }
965
966 template<typename T>
967 EIGEN_DEVICE_FUNC
968 T (floor)(const T& x)
969 {
970 EIGEN_USING_STD_MATH(floor);
971 return floor(x);
972 }
973
974 #ifdef __CUDACC__
975 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
976 float floor(const float &x) { return ::floorf(x); }
977
978 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
979 double floor(const double &x) { return ::floor(x); }
980 #endif
981
982 template<typename T>
983 EIGEN_DEVICE_FUNC
984 T (ceil)(const T& x)
985 {
986 EIGEN_USING_STD_MATH(ceil);
987 return ceil(x);
988 }
989
990 #ifdef __CUDACC__
991 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
992 float ceil(const float &x) { return ::ceilf(x); }
993
994 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
995 double ceil(const double &x) { return ::ceil(x); }
996 #endif
997
998
999 /** Log base 2 for 32 bits positive integers.
1000 * Conveniently returns 0 for x==0. */
1001 inline int log2(int x)
1002 {
1003 eigen_assert(x>=0);
1004 unsigned int v(x);
1005 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 };
1006 v |= v >> 1;
1007 v |= v >> 2;
1008 v |= v >> 4;
1009 v |= v >> 8;
1010 v |= v >> 16;
1011 return table[(v * 0x07C4ACDDU) >> 27];
1012 }
1013
1014 /** \returns the square root of \a x.
1015 *
1016 * It is essentially equivalent to
1017 * \code using std::sqrt; return sqrt(x); \endcode
1018 * but slightly faster for float/double and some compilers (e.g., gcc), thanks to
1019 * specializations when SSE is enabled.
1020 *
1021 * It's usage is justified in performance critical functions, like norm/normalize.
1022 */
1023 template<typename T>
1024 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1025 T sqrt(const T &x)
1026 {
1027 EIGEN_USING_STD_MATH(sqrt);
1028 return sqrt(x);
1029 }
1030
1031 template<typename T>
1032 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1033 T log(const T &x) {
1034 EIGEN_USING_STD_MATH(log);
1035 return log(x);
1036 }
1037
1038 #ifdef __CUDACC__
1039 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1040 float log(const float &x) { return ::logf(x); }
1041
1042 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1043 double log(const double &x) { return ::log(x); }
1044 #endif
1045
1046 template<typename T>
1047 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1048 typename internal::enable_if<NumTraits<T>::IsSigned || NumTraits<T>::IsComplex,typename NumTraits<T>::Real>::type
1049 abs(const T &x) {
1050 EIGEN_USING_STD_MATH(abs);
1051 return abs(x);
1052 }
1053
1054 template<typename T>
1055 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1056 typename internal::enable_if<!(NumTraits<T>::IsSigned || NumTraits<T>::IsComplex),typename NumTraits<T>::Real>::type
1057 abs(const T &x) {
1058 return x;
1059 }
1060
1061 #if defined(__SYCL_DEVICE_ONLY__)
1062 EIGEN_ALWAYS_INLINE float abs(float x) { return cl::sycl::fabs(x); }
1063 EIGEN_ALWAYS_INLINE double abs(double x) { return cl::sycl::fabs(x); }
1064 #endif // defined(__SYCL_DEVICE_ONLY__)
1065
1066 #ifdef __CUDACC__
1067 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1068 float abs(const float &x) { return ::fabsf(x); }
1069
1070 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1071 double abs(const double &x) { return ::fabs(x); }
1072
1073 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1074 float abs(const std::complex<float>& x) {
1075 return ::hypotf(x.real(), x.imag());
1076 }
1077
1078 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1079 double abs(const std::complex<double>& x) {
1080 return ::hypot(x.real(), x.imag());
1081 }
1082 #endif
1083
1084 template<typename T>
1085 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1086 T exp(const T &x) {
1087 EIGEN_USING_STD_MATH(exp);
1088 return exp(x);
1089 }
1090
1091 #ifdef __CUDACC__
1092 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1093 float exp(const float &x) { return ::expf(x); }
1094
1095 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1096 double exp(const double &x) { return ::exp(x); }
1097 #endif
1098
1099 template<typename T>
1100 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1101 T cos(const T &x) {
1102 EIGEN_USING_STD_MATH(cos);
1103 return cos(x);
1104 }
1105
1106 #ifdef __CUDACC__
1107 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1108 float cos(const float &x) { return ::cosf(x); }
1109
1110 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1111 double cos(const double &x) { return ::cos(x); }
1112 #endif
1113
1114 template<typename T>
1115 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1116 T sin(const T &x) {
1117 EIGEN_USING_STD_MATH(sin);
1118 return sin(x);
1119 }
1120
1121 #ifdef __CUDACC__
1122 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1123 float sin(const float &x) { return ::sinf(x); }
1124
1125 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1126 double sin(const double &x) { return ::sin(x); }
1127 #endif
1128
1129 template<typename T>
1130 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1131 T tan(const T &x) {
1132 EIGEN_USING_STD_MATH(tan);
1133 return tan(x);
1134 }
1135
1136 #ifdef __CUDACC__
1137 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1138 float tan(const float &x) { return ::tanf(x); }
1139
1140 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1141 double tan(const double &x) { return ::tan(x); }
1142 #endif
1143
1144 template<typename T>
1145 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1146 T acos(const T &x) {
1147 EIGEN_USING_STD_MATH(acos);
1148 return acos(x);
1149 }
1150
1151 #ifdef __CUDACC__
1152 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1153 float acos(const float &x) { return ::acosf(x); }
1154
1155 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1156 double acos(const double &x) { return ::acos(x); }
1157 #endif
1158
1159 template<typename T>
1160 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1161 T asin(const T &x) {
1162 EIGEN_USING_STD_MATH(asin);
1163 return asin(x);
1164 }
1165
1166 #ifdef __CUDACC__
1167 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1168 float asin(const float &x) { return ::asinf(x); }
1169
1170 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1171 double asin(const double &x) { return ::asin(x); }
1172 #endif
1173
1174 template<typename T>
1175 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1176 T atan(const T &x) {
1177 EIGEN_USING_STD_MATH(atan);
1178 return atan(x);
1179 }
1180
1181 #ifdef __CUDACC__
1182 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1183 float atan(const float &x) { return ::atanf(x); }
1184
1185 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1186 double atan(const double &x) { return ::atan(x); }
1187 #endif
1188
1189
1190 template<typename T>
1191 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1192 T cosh(const T &x) {
1193 EIGEN_USING_STD_MATH(cosh);
1194 return cosh(x);
1195 }
1196
1197 #ifdef __CUDACC__
1198 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1199 float cosh(const float &x) { return ::coshf(x); }
1200
1201 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1202 double cosh(const double &x) { return ::cosh(x); }
1203 #endif
1204
1205 template<typename T>
1206 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1207 T sinh(const T &x) {
1208 EIGEN_USING_STD_MATH(sinh);
1209 return sinh(x);
1210 }
1211
1212 #ifdef __CUDACC__
1213 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1214 float sinh(const float &x) { return ::sinhf(x); }
1215
1216 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1217 double sinh(const double &x) { return ::sinh(x); }
1218 #endif
1219
1220 template<typename T>
1221 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1222 T tanh(const T &x) {
1223 EIGEN_USING_STD_MATH(tanh);
1224 return tanh(x);
1225 }
1226
1227 #if (!defined(__CUDACC__)) && EIGEN_FAST_MATH
1228 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1229 float tanh(float x) { return internal::generic_fast_tanh_float(x); }
1230 #endif
1231
1232 #ifdef __CUDACC__
1233 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1234 float tanh(const float &x) { return ::tanhf(x); }
1235
1236 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1237 double tanh(const double &x) { return ::tanh(x); }
1238 #endif
1239
1240 template <typename T>
1241 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1242 T fmod(const T& a, const T& b) {
1243 EIGEN_USING_STD_MATH(fmod);
1244 return fmod(a, b);
1245 }
1246
1247 #ifdef __CUDACC__
1248 template <>
1249 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1250 float fmod(const float& a, const float& b) {
1251 return ::fmodf(a, b);
1252 }
1253
1254 template <>
1255 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1256 double fmod(const double& a, const double& b) {
1257 return ::fmod(a, b);
1258 }
1259 #endif
1260
1261 } // end namespace numext
1262
1263 namespace internal {
1264
1265 template<typename T>
1266 EIGEN_DEVICE_FUNC bool isfinite_impl(const std::complex<T>& x)
1267 {
1268 return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
1269 }
1270
1271 template<typename T>
1272 EIGEN_DEVICE_FUNC bool isnan_impl(const std::complex<T>& x)
1273 {
1274 return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
1275 }
1276
1277 template<typename T>
1278 EIGEN_DEVICE_FUNC bool isinf_impl(const std::complex<T>& x)
1279 {
1280 return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
1281 }
1282
1283 /****************************************************************************
1284 * Implementation of fuzzy comparisons *
1285 ****************************************************************************/
1286
1287 template<typename Scalar,
1288 bool IsComplex,
1289 bool IsInteger>
1290 struct scalar_fuzzy_default_impl {};
1291
1292 template<typename Scalar>
1293 struct scalar_fuzzy_default_impl<Scalar, false, false>
1294 {
1295 typedef typename NumTraits<Scalar>::Real RealScalar;
1296 template<typename OtherScalar> EIGEN_DEVICE_FUNC
1297 static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
1298 {
1299 return numext::abs(x) <= numext::abs(y) * prec;
1300 }
1301 EIGEN_DEVICE_FUNC
1302 static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
1303 {
1304 return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
1305 }
1306 EIGEN_DEVICE_FUNC
1307 static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)
1308 {
1309 return x <= y || isApprox(x, y, prec);
1310 }
1311 };
1312
1313 template<typename Scalar>
1314 struct scalar_fuzzy_default_impl<Scalar, false, true>
1315 {
1316 typedef typename NumTraits<Scalar>::Real RealScalar;
1317 template<typename OtherScalar> EIGEN_DEVICE_FUNC
1318 static inline bool isMuchSmallerThan(const Scalar& x, const Scalar&, const RealScalar&)
1319 {
1320 return x == Scalar(0);
1321 }
1322 EIGEN_DEVICE_FUNC
1323 static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar&)
1324 {
1325 return x == y;
1326 }
1327 EIGEN_DEVICE_FUNC
1328 static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar&)
1329 {
1330 return x <= y;
1331 }
1332 };
1333
1334 template<typename Scalar>
1335 struct scalar_fuzzy_default_impl<Scalar, true, false>
1336 {
1337 typedef typename NumTraits<Scalar>::Real RealScalar;
1338 template<typename OtherScalar> EIGEN_DEVICE_FUNC
1339 static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
1340 {
1341 return numext::abs2(x) <= numext::abs2(y) * prec * prec;
1342 }
1343 EIGEN_DEVICE_FUNC
1344 static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
1345 {
1346 return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;
1347 }
1348 };
1349
1350 template<typename Scalar>
1351 struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
1352
1353 template<typename Scalar, typename OtherScalar> EIGEN_DEVICE_FUNC
1354 inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y,
1355 const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1356 {
1357 return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
1358 }
1359
1360 template<typename Scalar> EIGEN_DEVICE_FUNC
1361 inline bool isApprox(const Scalar& x, const Scalar& y,
1362 const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1363 {
1364 return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
1365 }
1366
1367 template<typename Scalar> EIGEN_DEVICE_FUNC
1368 inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y,
1369 const typename NumTraits<Scalar>::Real &precision = NumTraits<Scalar>::dummy_precision())
1370 {
1371 return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
1372 }
1373
1374 /******************************************
1375 *** The special case of the bool type ***
1376 ******************************************/
1377
1378 template<> struct random_impl<bool>
1379 {
1380 static inline bool run()
1381 {
1382 return random<int>(0,1)==0 ? false : true;
1383 }
1384 };
1385
1386 template<> struct scalar_fuzzy_impl<bool>
1387 {
1388 typedef bool RealScalar;
1389
1390 template<typename OtherScalar> EIGEN_DEVICE_FUNC
1391 static inline bool isMuchSmallerThan(const bool& x, const bool&, const bool&)
1392 {
1393 return !x;
1394 }
1395
1396 EIGEN_DEVICE_FUNC
1397 static inline bool isApprox(bool x, bool y, bool)
1398 {
1399 return x == y;
1400 }
1401
1402 EIGEN_DEVICE_FUNC
1403 static inline bool isApproxOrLessThan(const bool& x, const bool& y, const bool&)
1404 {
1405 return (!x) || y;
1406 }
1407
1408 };
1409
1410
1411 } // end namespace internal
1412
1413 } // end namespace Eigen
1414
1415 #endif // EIGEN_MATHFUNCTIONS_H
1416