10 #ifndef EIGEN_MATHFUNCTIONS_H 11 #define EIGEN_MATHFUNCTIONS_H 15 #define EIGEN_PI 3.141592653589793238462643383279502884197169399375105820974944592307816406L 22 #if EIGEN_OS_WINCE && EIGEN_COMP_MSVC && EIGEN_COMP_MSVC<=1500 23 long abs(
long x) {
return (labs(x)); }
24 double abs(
double x) {
return (fabs(x)); }
25 float abs(
float x) {
return (fabsf(x)); }
26 long double abs(
long double x) {
return (fabsl(x)); }
51 template<
typename T,
typename dummy =
void>
52 struct global_math_functions_filtering_base
57 template<
typename T>
struct always_void {
typedef void type; };
60 struct global_math_functions_filtering_base
62 typename always_void<typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl>::type
65 typedef typename T::Eigen_BaseClassForSpecializationOfGlobalMathFuncImpl type;
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 75 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
76 struct real_default_impl
78 typedef typename NumTraits<Scalar>::Real RealScalar;
80 static inline RealScalar run(
const Scalar& x)
86 template<
typename Scalar>
87 struct real_default_impl<Scalar,true>
89 typedef typename NumTraits<Scalar>::Real RealScalar;
91 static inline RealScalar run(
const Scalar& x)
98 template<
typename Scalar>
struct real_impl : real_default_impl<Scalar> {};
102 struct real_impl<
std::complex<T> >
104 typedef T RealScalar;
106 static inline T run(
const std::complex<T>& x)
113 template<
typename Scalar>
116 typedef typename NumTraits<Scalar>::Real type;
123 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
124 struct imag_default_impl
126 typedef typename NumTraits<Scalar>::Real RealScalar;
128 static inline RealScalar run(
const Scalar&)
130 return RealScalar(0);
134 template<
typename Scalar>
135 struct imag_default_impl<Scalar,true>
137 typedef typename NumTraits<Scalar>::Real RealScalar;
139 static inline RealScalar run(
const Scalar& x)
146 template<
typename Scalar>
struct imag_impl : imag_default_impl<Scalar> {};
150 struct imag_impl<
std::complex<T> >
152 typedef T RealScalar;
154 static inline T run(
const std::complex<T>& x)
161 template<
typename Scalar>
164 typedef typename NumTraits<Scalar>::Real type;
171 template<
typename Scalar>
174 typedef typename NumTraits<Scalar>::Real RealScalar;
176 static inline RealScalar& run(Scalar& x)
178 return reinterpret_cast<RealScalar*
>(&x)[0];
181 static inline const RealScalar& run(
const Scalar& x)
183 return reinterpret_cast<const RealScalar*
>(&x)[0];
187 template<
typename Scalar>
188 struct real_ref_retval
190 typedef typename NumTraits<Scalar>::Real & type;
197 template<
typename Scalar,
bool IsComplex>
198 struct imag_ref_default_impl
200 typedef typename NumTraits<Scalar>::Real RealScalar;
202 static inline RealScalar& run(Scalar& x)
204 return reinterpret_cast<RealScalar*
>(&x)[1];
207 static inline const RealScalar& run(
const Scalar& x)
209 return reinterpret_cast<RealScalar*
>(&x)[1];
213 template<
typename Scalar>
214 struct imag_ref_default_impl<Scalar, false>
217 static inline Scalar run(Scalar&)
222 static inline const Scalar run(
const Scalar&)
228 template<
typename Scalar>
229 struct imag_ref_impl : imag_ref_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
231 template<
typename Scalar>
232 struct imag_ref_retval
234 typedef typename NumTraits<Scalar>::Real & type;
241 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
245 static inline Scalar run(
const Scalar& x)
251 template<
typename Scalar>
252 struct conj_impl<Scalar,true>
255 static inline Scalar run(
const Scalar& x)
262 template<
typename Scalar>
272 template<
typename Scalar,
bool IsComplex>
273 struct abs2_impl_default
275 typedef typename NumTraits<Scalar>::Real RealScalar;
277 static inline RealScalar run(
const Scalar& x)
283 template<
typename Scalar>
284 struct abs2_impl_default<Scalar, true>
286 typedef typename NumTraits<Scalar>::Real RealScalar;
288 static inline RealScalar run(
const Scalar& x)
294 template<
typename Scalar>
297 typedef typename NumTraits<Scalar>::Real RealScalar;
299 static inline RealScalar run(
const Scalar& x)
301 return abs2_impl_default<Scalar,NumTraits<Scalar>::IsComplex>::run(x);
305 template<
typename Scalar>
308 typedef typename NumTraits<Scalar>::Real type;
315 template<
typename Scalar,
bool IsComplex>
316 struct norm1_default_impl
318 typedef typename NumTraits<Scalar>::Real RealScalar;
320 static inline RealScalar run(
const Scalar& x)
322 EIGEN_USING_STD_MATH(
abs);
327 template<
typename Scalar>
328 struct norm1_default_impl<Scalar, false>
331 static inline Scalar run(
const Scalar& x)
333 EIGEN_USING_STD_MATH(
abs);
338 template<
typename Scalar>
339 struct norm1_impl : norm1_default_impl<Scalar, NumTraits<Scalar>::IsComplex> {};
341 template<
typename Scalar>
344 typedef typename NumTraits<Scalar>::Real type;
351 template<
typename Scalar>
struct hypot_impl;
353 template<
typename Scalar>
356 typedef typename NumTraits<Scalar>::Real type;
363 template<
typename OldType,
typename NewType>
367 static inline NewType run(
const OldType& x)
369 return static_cast<NewType
>(x);
375 template<
typename OldType,
typename NewType>
377 inline NewType cast(
const OldType& x)
379 return cast_impl<OldType, NewType>::run(x);
386 #if EIGEN_HAS_CXX11_MATH 387 template<
typename Scalar>
389 static inline Scalar run(
const Scalar& x)
391 EIGEN_STATIC_ASSERT((!NumTraits<Scalar>::IsComplex), NUMERIC_TYPE_MUST_BE_REAL)
397 template<
typename Scalar>
400 static inline Scalar run(
const Scalar& x)
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));
410 template<
typename Scalar>
420 #if EIGEN_HAS_CXX11_MATH 421 template<
typename Scalar>
423 static inline Scalar run(
const Scalar& x)
425 EIGEN_USING_STD_MATH(
arg);
430 template<typename Scalar, bool IsComplex = NumTraits<Scalar>::IsComplex>
431 struct arg_default_impl
433 typedef typename NumTraits<Scalar>::Real RealScalar;
435 static inline RealScalar run(
const Scalar& x)
437 return (x < Scalar(0)) ? Scalar(EIGEN_PI) : Scalar(0); }
440 template<
typename Scalar>
441 struct arg_default_impl<Scalar,true>
443 typedef typename NumTraits<Scalar>::Real RealScalar;
445 static inline RealScalar run(
const Scalar& x)
447 EIGEN_USING_STD_MATH(
arg);
452 template<
typename Scalar>
struct arg_impl : arg_default_impl<Scalar> {};
455 template<
typename Scalar>
458 typedef typename NumTraits<Scalar>::Real type;
465 namespace std_fallback {
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)) );
478 template<
typename Scalar>
480 static inline Scalar run(
const Scalar& x)
482 EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
483 #if EIGEN_HAS_CXX11_MATH 486 using std_fallback::log1p;
492 template<
typename Scalar>
502 template<typename ScalarX,typename ScalarY, bool IsInteger = NumTraits<ScalarX>::IsInteger&&NumTraits<ScalarY>::IsInteger>
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)
509 EIGEN_USING_STD_MATH(pow);
514 template<
typename ScalarX,
typename ScalarY>
515 struct pow_impl<ScalarX,ScalarY, true>
517 typedef ScalarX result_type;
518 static EIGEN_DEVICE_FUNC
inline ScalarX run(ScalarX x, ScalarY y)
521 eigen_assert(!NumTraits<ScalarY>::IsSigned || y >= 0);
538 template<
typename Scalar,
541 struct random_default_impl {};
543 template<
typename Scalar>
544 struct random_impl : random_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
546 template<
typename Scalar>
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();
555 template<
typename Scalar>
556 struct random_default_impl<Scalar, false, false>
558 static inline Scalar run(
const Scalar& x,
const Scalar& y)
560 return x + (y-x) * Scalar(std::rand()) / Scalar(RAND_MAX);
562 static inline Scalar run()
564 return run(Scalar(NumTraits<Scalar>::IsSigned ? -1 : 0), Scalar(1));
569 meta_floor_log2_terminate,
570 meta_floor_log2_move_up,
571 meta_floor_log2_move_down,
572 meta_floor_log2_bogus
575 template<
unsigned int n,
int lower,
int upper>
struct meta_floor_log2_selector
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)
585 template<
unsigned int n,
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 {};
591 template<
unsigned int n,
int lower,
int upper>
592 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_down>
594 enum { value = meta_floor_log2<n, lower, meta_floor_log2_selector<n, lower, upper>::middle>::value };
597 template<
unsigned int n,
int lower,
int upper>
598 struct meta_floor_log2<n, lower, upper, meta_floor_log2_move_up>
600 enum { value = meta_floor_log2<n, meta_floor_log2_selector<n, lower, upper>::middle, upper>::value };
603 template<
unsigned int n,
int lower,
int upper>
604 struct meta_floor_log2<n, lower, upper, meta_floor_log2_terminate>
606 enum { value = (n >= ((
unsigned int)(1) << (lower+1))) ? lower+1 : lower };
609 template<
unsigned int n,
int lower,
int upper>
610 struct meta_floor_log2<n, lower, upper, meta_floor_log2_bogus>
615 template<
typename Scalar>
616 struct random_default_impl<Scalar, false, true>
618 static inline Scalar run(
const Scalar& x,
const Scalar& y)
623 typedef typename make_unsigned<Scalar>::type ScalarU;
627 typedef typename conditional<(ScalarU(-1) > unsigned(-1)), ScalarU,
unsigned>::type ScalarX;
631 ScalarX range = ScalarX(y) - ScalarX(x);
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);
640 offset = (unsigned(std::rand()) * multiplier) / divisor;
641 }
while (offset > range);
642 return Scalar(ScalarX(x) + offset);
645 static inline Scalar run()
647 #ifdef EIGEN_MAKING_DOCS 648 return run(Scalar(NumTraits<Scalar>::IsSigned ? -10 : 0), Scalar(10));
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
655 return Scalar((std::rand() >> shift) - offset);
660 template<
typename Scalar>
661 struct random_default_impl<Scalar, true, false>
663 static inline Scalar run(
const Scalar& x,
const Scalar& y)
665 return Scalar(random(
real(x),
real(y)),
668 static inline Scalar run()
670 typedef typename NumTraits<Scalar>::Real RealScalar;
671 return Scalar(random<RealScalar>(), random<RealScalar>());
675 template<
typename Scalar>
676 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random(
const Scalar& x,
const Scalar& y)
678 return EIGEN_MATHFUNC_IMPL(random, Scalar)::run(x, y);
681 template<
typename Scalar>
682 inline EIGEN_MATHFUNC_RETVAL(random, Scalar) random()
684 return EIGEN_MATHFUNC_IMPL(random, Scalar)::run();
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 1 693 #define EIGEN_USE_STD_FPCLASSIFY 0 698 typename internal::enable_if<internal::is_integral<T>::value,
bool>::type
699 isnan_impl(
const T&) {
return false; }
703 typename internal::enable_if<internal::is_integral<T>::value,
bool>::type
704 isinf_impl(
const T&) {
return false; }
708 typename internal::enable_if<internal::is_integral<T>::value,
bool>::type
709 isfinite_impl(
const T&) {
return true; }
713 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),
bool>::type
714 isfinite_impl(
const T& x)
718 #elif EIGEN_USE_STD_FPCLASSIFY 720 return isfinite EIGEN_NOT_A_MACRO (x);
722 return x<=NumTraits<T>::highest() && x>=NumTraits<T>::lowest();
728 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),
bool>::type
729 isinf_impl(
const T& x)
733 #elif EIGEN_USE_STD_FPCLASSIFY 735 return isinf EIGEN_NOT_A_MACRO (x);
737 return x>NumTraits<T>::highest() || x<NumTraits<T>::lowest();
743 typename internal::enable_if<(!internal::is_integral<T>::value)&&(!NumTraits<T>::IsComplex),
bool>::type
744 isnan_impl(
const T& x)
748 #elif EIGEN_USE_STD_FPCLASSIFY 750 return isnan EIGEN_NOT_A_MACRO (x);
756 #if (!EIGEN_USE_STD_FPCLASSIFY) 760 template<
typename T> EIGEN_DEVICE_FUNC
bool isinf_msvc_helper(T x)
762 return _fpclass(x)==_FPCLASS_NINF || _fpclass(x)==_FPCLASS_PINF;
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; }
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); }
774 #elif (defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ && EIGEN_COMP_GNUC) 776 #if EIGEN_GNUC_AT_LEAST(5,0) 777 #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((optimize("no-finite-math-only"))) 781 #define EIGEN_TMP_NOOPT_ATTRIB EIGEN_DEVICE_FUNC inline __attribute__((noinline,optimize("no-finite-math-only"))) 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); }
791 #undef EIGEN_TMP_NOOPT_ATTRIB 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);
802 template<
typename T> T generic_fast_tanh_float(
const T& a_x);
812 #ifndef __CUDA_ARCH__ 815 EIGEN_ALWAYS_INLINE T mini(
const T& x,
const T& y)
817 EIGEN_USING_STD_MATH(min);
818 return min EIGEN_NOT_A_MACRO (x,y);
823 EIGEN_ALWAYS_INLINE T maxi(
const T& x,
const T& y)
825 EIGEN_USING_STD_MATH(max);
826 return max EIGEN_NOT_A_MACRO (x,y);
831 EIGEN_ALWAYS_INLINE T mini(
const T& x,
const T& y)
833 return y < x ? y : x;
837 EIGEN_ALWAYS_INLINE
float mini(
const float& x,
const float& y)
843 EIGEN_ALWAYS_INLINE T maxi(
const T& x,
const T& y)
845 return x < y ? y : x;
849 EIGEN_ALWAYS_INLINE
float maxi(
const float& x,
const float& y)
856 template<
typename Scalar>
858 inline EIGEN_MATHFUNC_RETVAL(
real, Scalar)
real(
const Scalar& x)
860 return EIGEN_MATHFUNC_IMPL(
real, Scalar)::run(x);
863 template<
typename Scalar>
865 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) >::type real_ref(
const Scalar& x)
867 return internal::real_ref_impl<Scalar>::run(x);
870 template<
typename Scalar>
872 inline EIGEN_MATHFUNC_RETVAL(real_ref, Scalar) real_ref(Scalar& x)
874 return EIGEN_MATHFUNC_IMPL(real_ref, Scalar)::run(x);
877 template<
typename Scalar>
879 inline EIGEN_MATHFUNC_RETVAL(
imag, Scalar)
imag(
const Scalar& x)
881 return EIGEN_MATHFUNC_IMPL(
imag, Scalar)::run(x);
884 template<
typename Scalar>
886 inline EIGEN_MATHFUNC_RETVAL(
arg, Scalar)
arg(
const Scalar& x)
888 return EIGEN_MATHFUNC_IMPL(
arg, Scalar)::run(x);
891 template<
typename Scalar>
893 inline typename internal::add_const_on_value_type< EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) >::type imag_ref(
const Scalar& x)
895 return internal::imag_ref_impl<Scalar>::run(x);
898 template<
typename Scalar>
900 inline EIGEN_MATHFUNC_RETVAL(imag_ref, Scalar) imag_ref(Scalar& x)
902 return EIGEN_MATHFUNC_IMPL(imag_ref, Scalar)::run(x);
905 template<
typename Scalar>
907 inline EIGEN_MATHFUNC_RETVAL(
conj, Scalar)
conj(
const Scalar& x)
909 return EIGEN_MATHFUNC_IMPL(
conj, Scalar)::run(x);
912 template<
typename Scalar>
914 inline EIGEN_MATHFUNC_RETVAL(
abs2, Scalar)
abs2(
const Scalar& x)
916 return EIGEN_MATHFUNC_IMPL(
abs2, Scalar)::run(x);
919 template<
typename Scalar>
921 inline EIGEN_MATHFUNC_RETVAL(norm1, Scalar) norm1(
const Scalar& x)
923 return EIGEN_MATHFUNC_IMPL(norm1, Scalar)::run(x);
926 template<
typename Scalar>
928 inline EIGEN_MATHFUNC_RETVAL(hypot, Scalar) hypot(
const Scalar& x,
const Scalar& y)
930 return EIGEN_MATHFUNC_IMPL(hypot, Scalar)::run(x, y);
933 template<
typename Scalar>
935 inline EIGEN_MATHFUNC_RETVAL(
log1p, Scalar)
log1p(
const Scalar& x)
937 return EIGEN_MATHFUNC_IMPL(
log1p, Scalar)::run(x);
941 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
942 float log1p(
const float &x) { return ::log1pf(x); }
944 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
945 double log1p(
const double &x) { return ::log1p(x); }
948 template<
typename ScalarX,
typename ScalarY>
950 inline typename internal::pow_impl<ScalarX,ScalarY>::result_type pow(
const ScalarX& x,
const ScalarY& y)
952 return internal::pow_impl<ScalarX,ScalarY>::run(x, y);
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); }
959 template<
typename Scalar>
961 inline EIGEN_MATHFUNC_RETVAL(
round, Scalar)
round(
const Scalar& x)
963 return EIGEN_MATHFUNC_IMPL(
round, Scalar)::run(x);
968 T (
floor)(
const T& x)
970 EIGEN_USING_STD_MATH(
floor);
975 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
976 float floor(
const float &x) { return ::floorf(x); }
978 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
979 double floor(
const double &x) { return ::floor(x); }
986 EIGEN_USING_STD_MATH(
ceil);
991 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
992 float ceil(
const float &x) { return ::ceilf(x); }
994 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
995 double ceil(
const double &x) { return ::ceil(x); }
1001 inline int log2(
int 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 };
1011 return table[(v * 0x07C4ACDDU) >> 27];
1023 template<
typename T>
1024 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1027 EIGEN_USING_STD_MATH(
sqrt);
1031 template<
typename T>
1032 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1034 EIGEN_USING_STD_MATH(
log);
1039 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1040 float log(
const float &x) { return ::logf(x); }
1042 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1043 double log(
const double &x) { return ::log(x); }
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
1050 EIGEN_USING_STD_MATH(
abs);
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
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__) 1067 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1068 float abs(
const float &x) { return ::fabsf(x); }
1070 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1071 double abs(
const double &x) { return ::fabs(x); }
1073 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1074 float abs(
const std::complex<float>& x) {
1075 return ::hypotf(x.real(), x.imag());
1078 template <> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1079 double abs(
const std::complex<double>& x) {
1080 return ::hypot(x.real(), x.imag());
1084 template<
typename T>
1085 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1087 EIGEN_USING_STD_MATH(
exp);
1092 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1093 float exp(
const float &x) { return ::expf(x); }
1095 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1096 double exp(
const double &x) { return ::exp(x); }
1099 template<
typename T>
1100 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1102 EIGEN_USING_STD_MATH(
cos);
1107 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1108 float cos(
const float &x) { return ::cosf(x); }
1110 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1111 double cos(
const double &x) { return ::cos(x); }
1114 template<
typename T>
1115 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1117 EIGEN_USING_STD_MATH(
sin);
1122 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1123 float sin(
const float &x) { return ::sinf(x); }
1125 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1126 double sin(
const double &x) { return ::sin(x); }
1129 template<
typename T>
1130 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1132 EIGEN_USING_STD_MATH(
tan);
1137 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1138 float tan(
const float &x) { return ::tanf(x); }
1140 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1141 double tan(
const double &x) { return ::tan(x); }
1144 template<
typename T>
1145 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1146 T
acos(
const T &x) {
1147 EIGEN_USING_STD_MATH(
acos);
1152 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1153 float acos(
const float &x) { return ::acosf(x); }
1155 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1156 double acos(
const double &x) { return ::acos(x); }
1159 template<
typename T>
1160 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1161 T
asin(
const T &x) {
1162 EIGEN_USING_STD_MATH(
asin);
1167 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1168 float asin(
const float &x) { return ::asinf(x); }
1170 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1171 double asin(
const double &x) { return ::asin(x); }
1174 template<
typename T>
1175 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1176 T
atan(
const T &x) {
1177 EIGEN_USING_STD_MATH(
atan);
1182 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1183 float atan(
const float &x) { return ::atanf(x); }
1185 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1186 double atan(
const double &x) { return ::atan(x); }
1190 template<
typename T>
1191 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1192 T
cosh(
const T &x) {
1193 EIGEN_USING_STD_MATH(
cosh);
1198 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1199 float cosh(
const float &x) { return ::coshf(x); }
1201 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1202 double cosh(
const double &x) { return ::cosh(x); }
1205 template<
typename T>
1206 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1207 T
sinh(
const T &x) {
1208 EIGEN_USING_STD_MATH(
sinh);
1213 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1214 float sinh(
const float &x) { return ::sinhf(x); }
1216 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1217 double sinh(
const double &x) { return ::sinh(x); }
1220 template<
typename T>
1221 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1222 T
tanh(
const T &x) {
1223 EIGEN_USING_STD_MATH(
tanh);
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); }
1233 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1234 float tanh(
const float &x) { return ::tanhf(x); }
1236 template<> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1237 double tanh(
const double &x) { return ::tanh(x); }
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);
1249 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1250 float fmod(
const float& a,
const float& b) {
1251 return ::fmodf(a, b);
1255 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
1256 double fmod(
const double& a,
const double& b) {
1257 return ::fmod(a, b);
1265 template<
typename T>
1266 EIGEN_DEVICE_FUNC
bool isfinite_impl(
const std::complex<T>& x)
1268 return (numext::isfinite)(numext::real(x)) && (numext::isfinite)(numext::imag(x));
1271 template<
typename T>
1272 EIGEN_DEVICE_FUNC
bool isnan_impl(
const std::complex<T>& x)
1274 return (numext::isnan)(numext::real(x)) || (numext::isnan)(numext::imag(x));
1277 template<
typename T>
1278 EIGEN_DEVICE_FUNC
bool isinf_impl(
const std::complex<T>& x)
1280 return ((numext::isinf)(numext::real(x)) || (numext::isinf)(numext::imag(x))) && (!(numext::isnan)(x));
1287 template<
typename Scalar,
1290 struct scalar_fuzzy_default_impl {};
1292 template<
typename Scalar>
1293 struct scalar_fuzzy_default_impl<Scalar, false, false>
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)
1299 return numext::abs(x) <= numext::abs(y) * prec;
1302 static inline bool isApprox(
const Scalar& x,
const Scalar& y,
const RealScalar& prec)
1304 return numext::abs(x - y) <= numext::mini(numext::abs(x), numext::abs(y)) * prec;
1307 static inline bool isApproxOrLessThan(
const Scalar& x,
const Scalar& y,
const RealScalar& prec)
1309 return x <= y || isApprox(x, y, prec);
1313 template<
typename Scalar>
1314 struct scalar_fuzzy_default_impl<Scalar, false, true>
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&)
1320 return x == Scalar(0);
1323 static inline bool isApprox(
const Scalar& x,
const Scalar& y,
const RealScalar&)
1328 static inline bool isApproxOrLessThan(
const Scalar& x,
const Scalar& y,
const RealScalar&)
1334 template<
typename Scalar>
1335 struct scalar_fuzzy_default_impl<Scalar, true, false>
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)
1341 return numext::abs2(x) <= numext::abs2(y) * prec * prec;
1344 static inline bool isApprox(
const Scalar& x,
const Scalar& y,
const RealScalar& prec)
1346 return numext::abs2(x - y) <= numext::mini(numext::abs2(x), numext::abs2(y)) * prec * prec;
1350 template<
typename Scalar>
1351 struct scalar_fuzzy_impl : scalar_fuzzy_default_impl<Scalar, NumTraits<Scalar>::IsComplex, NumTraits<Scalar>::IsInteger> {};
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())
1357 return scalar_fuzzy_impl<Scalar>::template isMuchSmallerThan<OtherScalar>(x, y, precision);
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())
1364 return scalar_fuzzy_impl<Scalar>::isApprox(x, y, precision);
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())
1371 return scalar_fuzzy_impl<Scalar>::isApproxOrLessThan(x, y, precision);
1378 template<>
struct random_impl<bool>
1380 static inline bool run()
1382 return random<int>(0,1)==0 ?
false :
true;
1386 template<>
struct scalar_fuzzy_impl<bool>
1388 typedef bool RealScalar;
1390 template<
typename OtherScalar> EIGEN_DEVICE_FUNC
1391 static inline bool isMuchSmallerThan(
const bool& x,
const bool&,
const bool&)
1397 static inline bool isApprox(
bool x,
bool y,
bool)
1403 static inline bool isApproxOrLessThan(
const bool& x,
const bool& y,
const bool&)
1415 #endif // EIGEN_MATHFUNCTIONS_H 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_sinh_op< typename Derived::Scalar >, const Derived > sinh(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_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(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_arg_op< typename Derived::Scalar >, const Derived > arg(const Eigen::ArrayBase< Derived > &x)
Namespace containing all symbols from the Eigen library.
Definition: Core:306
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_asin_op< typename Derived::Scalar >, const Derived > asin(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_acos_op< typename Derived::Scalar >, const Derived > acos(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_cos_op< typename Derived::Scalar >, const Derived > cos(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_round_op< typename Derived::Scalar >, const Derived > round(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_isinf_op< typename Derived::Scalar >, const Derived > isinf(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_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cosh_op< typename Derived::Scalar >, const Derived > cosh(const Eigen::ArrayBase< Derived > &x)
Definition: Eigen_Colamd.h:50
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_tan_op< typename Derived::Scalar >, const Derived > tan(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_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp_op< typename Derived::Scalar >, const Derived > exp(const Eigen::ArrayBase< Derived > &x)