10 #ifndef EIGEN_BESSEL_FUNCTIONS_H 11 #define EIGEN_BESSEL_FUNCTIONS_H 44 template <
typename Scalar>
45 struct bessel_i0e_retval {
49 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
52 static EIGEN_STRONG_INLINE T run(
const T&) {
53 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
54 THIS_TYPE_IS_NOT_SUPPORTED);
60 struct generic_i0e<T, float> {
62 static EIGEN_STRONG_INLINE T run(
const T& x) {
96 const float A[] = {-1.30002500998624804212E-8f, 6.04699502254191894932E-8f,
97 -2.67079385394061173391E-7f, 1.11738753912010371815E-6f,
98 -4.41673835845875056359E-6f, 1.64484480707288970893E-5f,
99 -5.75419501008210370398E-5f, 1.88502885095841655729E-4f,
100 -5.76375574538582365885E-4f, 1.63947561694133579842E-3f,
101 -4.32430999505057594430E-3f, 1.05464603945949983183E-2f,
102 -2.37374148058994688156E-2f, 4.93052842396707084878E-2f,
103 -9.49010970480476444210E-2f, 1.71620901522208775349E-1f,
104 -3.04682672343198398683E-1f, 6.76795274409476084995E-1f};
106 const float B[] = {3.39623202570838634515E-9f, 2.26666899049817806459E-8f,
107 2.04891858946906374183E-7f, 2.89137052083475648297E-6f,
108 6.88975834691682398426E-5f, 3.36911647825569408990E-3f,
109 8.04490411014108831608E-1f};
111 T y_le_eight = internal::pchebevl<T, 18>::run(
112 pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A);
114 internal::pchebevl<T, 7>::run(
115 psub(pdiv(pset1<T>(32.0f), y), pset1<T>(2.0f)), B),
120 return pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight);
124 template <
typename T>
125 struct generic_i0e<T, double> {
127 static EIGEN_STRONG_INLINE T run(
const T& x) {
161 const double A[] = {-4.41534164647933937950E-18, 3.33079451882223809783E-17,
162 -2.43127984654795469359E-16, 1.71539128555513303061E-15,
163 -1.16853328779934516808E-14, 7.67618549860493561688E-14,
164 -4.85644678311192946090E-13, 2.95505266312963983461E-12,
165 -1.72682629144155570723E-11, 9.67580903537323691224E-11,
166 -5.18979560163526290666E-10, 2.65982372468238665035E-9,
167 -1.30002500998624804212E-8, 6.04699502254191894932E-8,
168 -2.67079385394061173391E-7, 1.11738753912010371815E-6,
169 -4.41673835845875056359E-6, 1.64484480707288970893E-5,
170 -5.75419501008210370398E-5, 1.88502885095841655729E-4,
171 -5.76375574538582365885E-4, 1.63947561694133579842E-3,
172 -4.32430999505057594430E-3, 1.05464603945949983183E-2,
173 -2.37374148058994688156E-2, 4.93052842396707084878E-2,
174 -9.49010970480476444210E-2, 1.71620901522208775349E-1,
175 -3.04682672343198398683E-1, 6.76795274409476084995E-1};
177 -7.23318048787475395456E-18, -4.83050448594418207126E-18,
178 4.46562142029675999901E-17, 3.46122286769746109310E-17,
179 -2.82762398051658348494E-16, -3.42548561967721913462E-16,
180 1.77256013305652638360E-15, 3.81168066935262242075E-15,
181 -9.55484669882830764870E-15, -4.15056934728722208663E-14,
182 1.54008621752140982691E-14, 3.85277838274214270114E-13,
183 7.18012445138366623367E-13, -1.79417853150680611778E-12,
184 -1.32158118404477131188E-11, -3.14991652796324136454E-11,
185 1.18891471078464383424E-11, 4.94060238822496958910E-10,
186 3.39623202570838634515E-9, 2.26666899049817806459E-8,
187 2.04891858946906374183E-7, 2.89137052083475648297E-6,
188 6.88975834691682398426E-5, 3.36911647825569408990E-3,
189 8.04490411014108831608E-1};
191 T y_le_eight = internal::pchebevl<T, 30>::run(
192 pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A);
194 internal::pchebevl<T, 25>::run(
195 psub(pdiv(pset1<T>(32.0), y), pset1<T>(2.0)), B),
200 return pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight);
204 template <
typename T>
205 struct bessel_i0e_impl {
207 static EIGEN_STRONG_INLINE T run(
const T x) {
208 return generic_i0e<T>::run(x);
212 template <
typename Scalar>
213 struct bessel_i0_retval {
217 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
220 static EIGEN_STRONG_INLINE T run(
const T& x) {
223 generic_i0e<T, ScalarType>::run(x));
227 template <
typename T>
228 struct bessel_i0_impl {
230 static EIGEN_STRONG_INLINE T run(
const T x) {
231 return generic_i0<T>::run(x);
235 template <
typename Scalar>
236 struct bessel_i1e_retval {
240 template <typename T, typename ScalarType = typename unpacket_traits<T>::type >
243 static EIGEN_STRONG_INLINE T run(
const T&) {
244 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
245 THIS_TYPE_IS_NOT_SUPPORTED);
246 return ScalarType(0);
250 template <
typename T>
251 struct generic_i1e<T, float> {
253 static EIGEN_STRONG_INLINE T run(
const T& x) {
286 const float A[] = {9.38153738649577178388E-9f, -4.44505912879632808065E-8f,
287 2.00329475355213526229E-7f, -8.56872026469545474066E-7f,
288 3.47025130813767847674E-6f, -1.32731636560394358279E-5f,
289 4.78156510755005422638E-5f, -1.61760815825896745588E-4f,
290 5.12285956168575772895E-4f, -1.51357245063125314899E-3f,
291 4.15642294431288815669E-3f, -1.05640848946261981558E-2f,
292 2.47264490306265168283E-2f, -5.29459812080949914269E-2f,
293 1.02643658689847095384E-1f, -1.76416518357834055153E-1f,
294 2.52587186443633654823E-1f};
296 const float B[] = {-3.83538038596423702205E-9f, -2.63146884688951950684E-8f,
297 -2.51223623787020892529E-7f, -3.88256480887769039346E-6f,
298 -1.10588938762623716291E-4f, -9.76109749136146840777E-3f,
299 7.78576235018280120474E-1f};
303 T y_le_eight = pmul(y, internal::pchebevl<T, 17>::run(
304 pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A));
306 internal::pchebevl<T, 7>::run(
307 psub(pdiv(pset1<T>(32.0f), y),
313 y = pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight);
314 return pselect(pcmp_lt(x, pset1<T>(0.0f)), pnegate(y), y);
318 template <
typename T>
319 struct generic_i1e<T, double> {
321 static EIGEN_STRONG_INLINE T run(
const T& x) {
354 const double A[] = {2.77791411276104639959E-18, -2.11142121435816608115E-17,
355 1.55363195773620046921E-16, -1.10559694773538630805E-15,
356 7.60068429473540693410E-15, -5.04218550472791168711E-14,
357 3.22379336594557470981E-13, -1.98397439776494371520E-12,
358 1.17361862988909016308E-11, -6.66348972350202774223E-11,
359 3.62559028155211703701E-10, -1.88724975172282928790E-9,
360 9.38153738649577178388E-9, -4.44505912879632808065E-8,
361 2.00329475355213526229E-7, -8.56872026469545474066E-7,
362 3.47025130813767847674E-6, -1.32731636560394358279E-5,
363 4.78156510755005422638E-5, -1.61760815825896745588E-4,
364 5.12285956168575772895E-4, -1.51357245063125314899E-3,
365 4.15642294431288815669E-3, -1.05640848946261981558E-2,
366 2.47264490306265168283E-2, -5.29459812080949914269E-2,
367 1.02643658689847095384E-1, -1.76416518357834055153E-1,
368 2.52587186443633654823E-1};
370 7.51729631084210481353E-18, 4.41434832307170791151E-18,
371 -4.65030536848935832153E-17, -3.20952592199342395980E-17,
372 2.96262899764595013876E-16, 3.30820231092092828324E-16,
373 -1.88035477551078244854E-15, -3.81440307243700780478E-15,
374 1.04202769841288027642E-14, 4.27244001671195135429E-14,
375 -2.10154184277266431302E-14, -4.08355111109219731823E-13,
376 -7.19855177624590851209E-13, 2.03562854414708950722E-12,
377 1.41258074366137813316E-11, 3.25260358301548823856E-11,
378 -1.89749581235054123450E-11, -5.58974346219658380687E-10,
379 -3.83538038596423702205E-9, -2.63146884688951950684E-8,
380 -2.51223623787020892529E-7, -3.88256480887769039346E-6,
381 -1.10588938762623716291E-4, -9.76109749136146840777E-3,
382 7.78576235018280120474E-1};
384 T y_le_eight = pmul(y, internal::pchebevl<T, 29>::run(
385 pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A));
387 internal::pchebevl<T, 25>::run(
388 psub(pdiv(pset1<T>(32.0), y),
394 y = pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight);
395 return pselect(pcmp_lt(x, pset1<T>(0.0)), pnegate(y), y);
399 template <
typename T>
400 struct bessel_i1e_impl {
402 static EIGEN_STRONG_INLINE T run(
const T x) {
403 return generic_i1e<T>::run(x);
407 template <
typename T>
408 struct bessel_i1_retval {
412 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
415 static EIGEN_STRONG_INLINE T run(
const T& x) {
418 generic_i1e<T, ScalarType>::run(x));
422 template <
typename T>
423 struct bessel_i1_impl {
425 static EIGEN_STRONG_INLINE T run(
const T x) {
426 return generic_i1<T>::run(x);
430 template <
typename T>
431 struct bessel_k0e_retval {
435 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
438 static EIGEN_STRONG_INLINE T run(
const T&) {
439 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
440 THIS_TYPE_IS_NOT_SUPPORTED);
441 return ScalarType(0);
445 template <
typename T>
446 struct generic_k0e<T, float> {
448 static EIGEN_STRONG_INLINE T run(
const T& x) {
479 const float A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,
480 2.28621210311945178607E-5f, 1.26461541144692592338E-3f,
481 3.59799365153615016266E-2f, 3.44289899924628486886E-1f,
482 -5.35327393233902768720E-1f};
484 const float B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,
485 -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,
486 -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,
487 -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,
488 -3.14481013119645005427E-2f, 2.44030308206595545468E0f};
489 const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
490 const T two = pset1<T>(2.0);
491 T x_le_two = internal::pchebevl<T, 7>::run(
492 pmadd(x, x, pset1<T>(-2.0)), A);
494 generic_i0<T, float>::run(x), pnegate(
495 plog(pmul(pset1<T>(0.5), x))), x_le_two);
496 x_le_two = pmul(pexp(x), x_le_two);
498 internal::pchebevl<T, 10>::run(
499 psub(pdiv(pset1<T>(8.0), x), two), B),
502 pcmp_le(x, pset1<T>(0.0)),
504 pselect(pcmp_le(x, two), x_le_two, x_gt_two));
508 template <
typename T>
509 struct generic_k0e<T, double> {
511 static EIGEN_STRONG_INLINE T run(
const T& x) {
543 1.37446543561352307156E-16,
544 4.25981614279661018399E-14,
545 1.03496952576338420167E-11,
546 1.90451637722020886025E-9,
547 2.53479107902614945675E-7,
548 2.28621210311945178607E-5,
549 1.26461541144692592338E-3,
550 3.59799365153615016266E-2,
551 3.44289899924628486886E-1,
552 -5.35327393233902768720E-1};
554 5.30043377268626276149E-18, -1.64758043015242134646E-17,
555 5.21039150503902756861E-17, -1.67823109680541210385E-16,
556 5.51205597852431940784E-16, -1.84859337734377901440E-15,
557 6.34007647740507060557E-15, -2.22751332699166985548E-14,
558 8.03289077536357521100E-14, -2.98009692317273043925E-13,
559 1.14034058820847496303E-12, -4.51459788337394416547E-12,
560 1.85594911495471785253E-11, -7.95748924447710747776E-11,
561 3.57739728140030116597E-10, -1.69753450938905987466E-9,
562 8.57403401741422608519E-9, -4.66048989768794782956E-8,
563 2.76681363944501510342E-7, -1.83175552271911948767E-6,
564 1.39498137188764993662E-5, -1.28495495816278026384E-4,
565 1.56988388573005337491E-3, -3.14481013119645005427E-2,
566 2.44030308206595545468E0
568 const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
569 const T two = pset1<T>(2.0);
570 T x_le_two = internal::pchebevl<T, 10>::run(
571 pmadd(x, x, pset1<T>(-2.0)), A);
573 generic_i0<T, double>::run(x), pmul(
574 pset1<T>(-1.0), plog(pmul(pset1<T>(0.5), x))), x_le_two);
575 x_le_two = pmul(pexp(x), x_le_two);
576 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
578 internal::pchebevl<T, 25>::run(
579 psub(pdiv(pset1<T>(8.0), x), two), B),
581 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
585 template <
typename T>
586 struct bessel_k0e_impl {
588 static EIGEN_STRONG_INLINE T run(
const T x) {
589 return generic_k0e<T>::run(x);
593 template <
typename T>
594 struct bessel_k0_retval {
598 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
601 static EIGEN_STRONG_INLINE T run(
const T&) {
602 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
603 THIS_TYPE_IS_NOT_SUPPORTED);
604 return ScalarType(0);
608 template <
typename T>
609 struct generic_k0<T, float> {
611 static EIGEN_STRONG_INLINE T run(
const T& x) {
651 const float A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,
652 2.28621210311945178607E-5f, 1.26461541144692592338E-3f,
653 3.59799365153615016266E-2f, 3.44289899924628486886E-1f,
654 -5.35327393233902768720E-1f};
656 const float B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,
657 -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,
658 -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,
659 -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,
660 -3.14481013119645005427E-2f, 2.44030308206595545468E0f};
661 const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
662 const T two = pset1<T>(2.0);
663 T x_le_two = internal::pchebevl<T, 7>::run(
664 pmadd(x, x, pset1<T>(-2.0)), A);
666 generic_i0<T, float>::run(x), pnegate(
667 plog(pmul(pset1<T>(0.5), x))), x_le_two);
668 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
672 internal::pchebevl<T, 10>::run(
673 psub(pdiv(pset1<T>(8.0), x), two), B)),
675 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
679 template <
typename T>
680 struct generic_k0<T, double> {
682 static EIGEN_STRONG_INLINE T run(
const T& x) {
714 1.37446543561352307156E-16,
715 4.25981614279661018399E-14,
716 1.03496952576338420167E-11,
717 1.90451637722020886025E-9,
718 2.53479107902614945675E-7,
719 2.28621210311945178607E-5,
720 1.26461541144692592338E-3,
721 3.59799365153615016266E-2,
722 3.44289899924628486886E-1,
723 -5.35327393233902768720E-1};
725 5.30043377268626276149E-18, -1.64758043015242134646E-17,
726 5.21039150503902756861E-17, -1.67823109680541210385E-16,
727 5.51205597852431940784E-16, -1.84859337734377901440E-15,
728 6.34007647740507060557E-15, -2.22751332699166985548E-14,
729 8.03289077536357521100E-14, -2.98009692317273043925E-13,
730 1.14034058820847496303E-12, -4.51459788337394416547E-12,
731 1.85594911495471785253E-11, -7.95748924447710747776E-11,
732 3.57739728140030116597E-10, -1.69753450938905987466E-9,
733 8.57403401741422608519E-9, -4.66048989768794782956E-8,
734 2.76681363944501510342E-7, -1.83175552271911948767E-6,
735 1.39498137188764993662E-5, -1.28495495816278026384E-4,
736 1.56988388573005337491E-3, -3.14481013119645005427E-2,
737 2.44030308206595545468E0
739 const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
740 const T two = pset1<T>(2.0);
741 T x_le_two = internal::pchebevl<T, 10>::run(
742 pmadd(x, x, pset1<T>(-2.0)), A);
744 generic_i0<T, double>::run(x), pnegate(
745 plog(pmul(pset1<T>(0.5), x))), x_le_two);
746 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
750 internal::pchebevl<T, 25>::run(
751 psub(pdiv(pset1<T>(8.0), x), two), B)),
753 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
757 template <
typename T>
758 struct bessel_k0_impl {
760 static EIGEN_STRONG_INLINE T run(
const T x) {
761 return generic_k0<T>::run(x);
765 template <
typename T>
766 struct bessel_k1e_retval {
770 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
773 static EIGEN_STRONG_INLINE T run(
const T&) {
774 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
775 THIS_TYPE_IS_NOT_SUPPORTED);
776 return ScalarType(0);
780 template <
typename T>
781 struct generic_k1e<T, float> {
783 static EIGEN_STRONG_INLINE T run(
const T& x) {
817 const float A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,
818 -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,
819 -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,
820 1.52530022733894777053E0f};
821 const float B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,
822 5.74108412545004946722E-8f, -3.50196060308781257119E-7f,
823 2.40648494783721712015E-6f, -1.93619797416608296024E-5f,
824 1.95215518471351631108E-4f, -2.85781685962277938680E-3f,
825 1.03923736576817238437E-1f, 2.72062619048444266945E0f};
826 const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
827 const T two = pset1<T>(2.0);
828 T x_le_two = pdiv(internal::pchebevl<T, 7>::run(
829 pmadd(x, x, pset1<T>(-2.0)), A), x);
831 generic_i1<T, float>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
832 x_le_two = pmul(x_le_two, pexp(x));
833 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
835 internal::pchebevl<T, 10>::run(
836 psub(pdiv(pset1<T>(8.0), x), two), B),
838 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
842 template <
typename T>
843 struct generic_k1e<T, double> {
845 static EIGEN_STRONG_INLINE T run(
const T& x) {
878 const double A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,
879 -6.66690169419932900609E-13, -1.41148839263352776110E-10,
880 -2.21338763073472585583E-8, -2.43340614156596823496E-6,
881 -1.73028895751305206302E-4, -6.97572385963986435018E-3,
882 -1.22611180822657148235E-1, -3.53155960776544875667E-1,
883 1.52530022733894777053E0};
884 const double B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,
885 -5.68946255844285935196E-17, 1.83809354436663880070E-16,
886 -6.05704724837331885336E-16, 2.03870316562433424052E-15,
887 -7.01983709041831346144E-15, 2.47715442448130437068E-14,
888 -8.97670518232499435011E-14, 3.34841966607842919884E-13,
889 -1.28917396095102890680E-12, 5.13963967348173025100E-12,
890 -2.12996783842756842877E-11, 9.21831518760500529508E-11,
891 -4.19035475934189648750E-10, 2.01504975519703286596E-9,
892 -1.03457624656780970260E-8, 5.74108412545004946722E-8,
893 -3.50196060308781257119E-7, 2.40648494783721712015E-6,
894 -1.93619797416608296024E-5, 1.95215518471351631108E-4,
895 -2.85781685962277938680E-3, 1.03923736576817238437E-1,
896 2.72062619048444266945E0};
897 const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
898 const T two = pset1<T>(2.0);
899 T x_le_two = pdiv(internal::pchebevl<T, 11>::run(
900 pmadd(x, x, pset1<T>(-2.0)), A), x);
902 generic_i1<T, double>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
903 x_le_two = pmul(x_le_two, pexp(x));
904 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
906 internal::pchebevl<T, 25>::run(
907 psub(pdiv(pset1<T>(8.0), x), two), B),
909 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
913 template <
typename T>
914 struct bessel_k1e_impl {
916 static EIGEN_STRONG_INLINE T run(
const T x) {
917 return generic_k1e<T>::run(x);
921 template <
typename T>
922 struct bessel_k1_retval {
926 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
929 static EIGEN_STRONG_INLINE T run(
const T&) {
930 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
931 THIS_TYPE_IS_NOT_SUPPORTED);
932 return ScalarType(0);
936 template <
typename T>
937 struct generic_k1<T, float> {
939 static EIGEN_STRONG_INLINE T run(
const T& x) {
977 const float A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,
978 -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,
979 -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,
980 1.52530022733894777053E0f};
981 const float B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,
982 5.74108412545004946722E-8f, -3.50196060308781257119E-7f,
983 2.40648494783721712015E-6f, -1.93619797416608296024E-5f,
984 1.95215518471351631108E-4f, -2.85781685962277938680E-3f,
985 1.03923736576817238437E-1f, 2.72062619048444266945E0f};
986 const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
987 const T two = pset1<T>(2.0);
988 T x_le_two = pdiv(internal::pchebevl<T, 7>::run(
989 pmadd(x, x, pset1<T>(-2.0)), A), x);
991 generic_i1<T, float>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
992 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
996 internal::pchebevl<T, 10>::run(
997 psub(pdiv(pset1<T>(8.0), x), two), B),
999 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
1003 template <
typename T>
1004 struct generic_k1<T, double> {
1006 static EIGEN_STRONG_INLINE T run(
const T& x) {
1043 const double A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,
1044 -6.66690169419932900609E-13, -1.41148839263352776110E-10,
1045 -2.21338763073472585583E-8, -2.43340614156596823496E-6,
1046 -1.73028895751305206302E-4, -6.97572385963986435018E-3,
1047 -1.22611180822657148235E-1, -3.53155960776544875667E-1,
1048 1.52530022733894777053E0};
1049 const double B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,
1050 -5.68946255844285935196E-17, 1.83809354436663880070E-16,
1051 -6.05704724837331885336E-16, 2.03870316562433424052E-15,
1052 -7.01983709041831346144E-15, 2.47715442448130437068E-14,
1053 -8.97670518232499435011E-14, 3.34841966607842919884E-13,
1054 -1.28917396095102890680E-12, 5.13963967348173025100E-12,
1055 -2.12996783842756842877E-11, 9.21831518760500529508E-11,
1056 -4.19035475934189648750E-10, 2.01504975519703286596E-9,
1057 -1.03457624656780970260E-8, 5.74108412545004946722E-8,
1058 -3.50196060308781257119E-7, 2.40648494783721712015E-6,
1059 -1.93619797416608296024E-5, 1.95215518471351631108E-4,
1060 -2.85781685962277938680E-3, 1.03923736576817238437E-1,
1061 2.72062619048444266945E0};
1062 const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
1063 const T two = pset1<T>(2.0);
1064 T x_le_two = pdiv(internal::pchebevl<T, 11>::run(
1065 pmadd(x, x, pset1<T>(-2.0)), A), x);
1067 generic_i1<T, double>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
1068 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
1072 internal::pchebevl<T, 25>::run(
1073 psub(pdiv(pset1<T>(8.0), x), two), B),
1075 return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
1079 template <
typename T>
1080 struct bessel_k1_impl {
1082 static EIGEN_STRONG_INLINE T run(
const T x) {
1083 return generic_k1<T>::run(x);
1087 template <
typename T>
1088 struct bessel_j0_retval {
1092 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
1095 static EIGEN_STRONG_INLINE T run(
const T&) {
1096 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
1097 THIS_TYPE_IS_NOT_SUPPORTED);
1098 return ScalarType(0);
1102 template <
typename T>
1103 struct generic_j0<T, float> {
1105 static EIGEN_STRONG_INLINE T run(
const T& x) {
1152 const float JP[] = {-6.068350350393235E-008f, 6.388945720783375E-006f,
1153 -3.969646342510940E-004f, 1.332913422519003E-002f,
1154 -1.729150680240724E-001f};
1155 const float MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,
1156 -2.145007480346739E-001f, 1.197549369473540E-001f,
1157 -3.560281861530129E-003f, -4.969382655296620E-002f,
1158 -3.355424622293709E-006f, 7.978845717621440E-001f};
1159 const float PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,
1160 1.756221482109099E+001f, -4.974978466280903E+000f,
1161 1.001973420681837E+000f, -1.939906941791308E-001f,
1162 6.490598792654666E-002f, -1.249992184872738E-001f};
1163 const T DR1 = pset1<T>(5.78318596294678452118f);
1164 const T NEG_PIO4F = pset1<T>(-0.7853981633974483096f);
1167 T y_le_two = pselect(
1168 pcmp_lt(y, pset1<T>(1.0e-3f)),
1169 pmadd(z, pset1<T>(-0.25f), pset1<T>(1.0f)),
1170 pmul(psub(z, DR1), internal::ppolevl<T, 4>::run(z, JP)));
1171 T q = pdiv(pset1<T>(1.0f), y);
1173 T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO));
1175 T yn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH), NEG_PIO4F);
1176 T y_gt_two = pmul(p, pcos(padd(yn, y)));
1177 return pselect(pcmp_le(y, pset1<T>(2.0)), y_le_two, y_gt_two);
1181 template <
typename T>
1182 struct generic_j0<T, double> {
1184 static EIGEN_STRONG_INLINE T run(
const T& x) {
1228 const double PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,
1229 1.23953371646414299388E0, 5.44725003058768775090E0,
1230 8.74716500199817011941E0, 5.30324038235394892183E0,
1231 9.99999999999999997821E-1};
1232 const double PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,
1233 1.25352743901058953537E0, 5.47097740330417105182E0,
1234 8.76190883237069594232E0, 5.30605288235394617618E0,
1235 1.00000000000000000218E0};
1236 const double QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,
1237 -1.95539544257735972385E1, -9.32060152123768231369E1,
1238 -1.77681167980488050595E2, -1.47077505154951170175E2,
1239 -5.14105326766599330220E1, -6.05014350600728481186E0};
1240 const double QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,
1241 8.56430025976980587198E2, 3.88240183605401609683E3,
1242 7.24046774195652478189E3, 5.93072701187316984827E3,
1243 2.06209331660327847417E3, 2.42005740240291393179E2};
1244 const double RP[] = {-4.79443220978201773821E9, 1.95617491946556577543E12,
1245 -2.49248344360967716204E14, 9.70862251047306323952E15};
1246 const double RQ[] = {1.00000000000000000000E0, 4.99563147152651017219E2,
1247 1.73785401676374683123E5, 4.84409658339962045305E7,
1248 1.11855537045356834862E10, 2.11277520115489217587E12,
1249 3.10518229857422583814E14, 3.18121955943204943306E16,
1250 1.71086294081043136091E18};
1251 const T DR1 = pset1<T>(5.78318596294678452118E0);
1252 const T DR2 = pset1<T>(3.04712623436620863991E1);
1253 const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1);
1254 const T NEG_PIO4 = pset1<T>(-0.7853981633974483096);
1258 T y_le_five = pselect(
1259 pcmp_lt(y, pset1<T>(1.0e-5)),
1260 pmadd(z, pset1<T>(-0.25), pset1<T>(1.0)),
1261 pmul(pmul(psub(z, DR1), psub(z, DR2)),
1262 pdiv(internal::ppolevl<T, 3>::run(z, RP),
1263 internal::ppolevl<T, 8>::run(z, RQ))));
1264 T s = pdiv(pset1<T>(25.0), z);
1266 internal::ppolevl<T, 6>::run(s, PP),
1267 internal::ppolevl<T, 6>::run(s, PQ));
1269 internal::ppolevl<T, 7>::run(s, QP),
1270 internal::ppolevl<T, 7>::run(s, QQ));
1271 T yn = padd(y, NEG_PIO4);
1272 T w = pdiv(pset1<T>(-5.0), y);
1273 p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));
1274 T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));
1275 return pselect(pcmp_le(y, pset1<T>(5.0)), y_le_five, y_gt_five);
1279 template <
typename T>
1280 struct bessel_j0_impl {
1282 static EIGEN_STRONG_INLINE T run(
const T x) {
1283 return generic_j0<T>::run(x);
1287 template <
typename T>
1288 struct bessel_y0_retval {
1292 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
1295 static EIGEN_STRONG_INLINE T run(
const T&) {
1296 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
1297 THIS_TYPE_IS_NOT_SUPPORTED);
1298 return ScalarType(0);
1302 template <
typename T>
1303 struct generic_y0<T, float> {
1305 static EIGEN_STRONG_INLINE T run(
const T& x) {
1354 const float YP[] = {9.454583683980369E-008f, -9.413212653797057E-006f,
1355 5.344486707214273E-004f, -1.584289289821316E-002f,
1356 1.707584643733568E-001f};
1357 const float MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,
1358 -2.145007480346739E-001f, 1.197549369473540E-001f,
1359 -3.560281861530129E-003f, -4.969382655296620E-002f,
1360 -3.355424622293709E-006f, 7.978845717621440E-001f};
1361 const float PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,
1362 1.756221482109099E+001f, -4.974978466280903E+000f,
1363 1.001973420681837E+000f, -1.939906941791308E-001f,
1364 6.490598792654666E-002f, -1.249992184872738E-001f};
1365 const T YZ1 = pset1<T>(0.43221455686510834878f);
1366 const T TWOOPI = pset1<T>(0.636619772367581343075535f);
1367 const T NEG_PIO4F = pset1<T>(-0.7853981633974483096f);
1368 const T NEG_MAXNUM = pset1<T>(-NumTraits<float>::infinity());
1370 T x_le_two = pmul(TWOOPI, pmul(plog(x), generic_j0<T, float>::run(x)));
1372 psub(z, YZ1), internal::ppolevl<T, 4>::run(z, YP), x_le_two);
1373 x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_two);
1374 T q = pdiv(pset1<T>(1.0), x);
1376 T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO));
1378 T xn = pmadd(q, internal::ppolevl<T, 7>::run(u, PH), NEG_PIO4F);
1379 T x_gt_two = pmul(p, psin(padd(xn, x)));
1380 return pselect(pcmp_le(x, pset1<T>(2.0)), x_le_two, x_gt_two);
1384 template <
typename T>
1385 struct generic_y0<T, double> {
1387 static EIGEN_STRONG_INLINE T run(
const T& x) {
1427 const double PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,
1428 1.23953371646414299388E0, 5.44725003058768775090E0,
1429 8.74716500199817011941E0, 5.30324038235394892183E0,
1430 9.99999999999999997821E-1};
1431 const double PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,
1432 1.25352743901058953537E0, 5.47097740330417105182E0,
1433 8.76190883237069594232E0, 5.30605288235394617618E0,
1434 1.00000000000000000218E0};
1435 const double QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,
1436 -1.95539544257735972385E1, -9.32060152123768231369E1,
1437 -1.77681167980488050595E2, -1.47077505154951170175E2,
1438 -5.14105326766599330220E1, -6.05014350600728481186E0};
1439 const double QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,
1440 8.56430025976980587198E2, 3.88240183605401609683E3,
1441 7.24046774195652478189E3, 5.93072701187316984827E3,
1442 2.06209331660327847417E3, 2.42005740240291393179E2};
1443 const double YP[] = {1.55924367855235737965E4, -1.46639295903971606143E7,
1444 5.43526477051876500413E9, -9.82136065717911466409E11,
1445 8.75906394395366999549E13, -3.46628303384729719441E15,
1446 4.42733268572569800351E16, -1.84950800436986690637E16};
1447 const double YQ[] = {1.00000000000000000000E0, 1.04128353664259848412E3,
1448 6.26107330137134956842E5, 2.68919633393814121987E8,
1449 8.64002487103935000337E10, 2.02979612750105546709E13,
1450 3.17157752842975028269E15, 2.50596256172653059228E17};
1451 const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1);
1452 const T TWOOPI = pset1<T>(0.636619772367581343075535);
1453 const T NEG_PIO4 = pset1<T>(-0.7853981633974483096);
1454 const T NEG_MAXNUM = pset1<T>(-NumTraits<double>::infinity());
1457 T x_le_five = pdiv(internal::ppolevl<T, 7>::run(z, YP),
1458 internal::ppolevl<T, 7>::run(z, YQ));
1460 pmul(TWOOPI, plog(x)), generic_j0<T, double>::run(x), x_le_five);
1461 x_le_five = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_five);
1462 T s = pdiv(pset1<T>(25.0), z);
1464 internal::ppolevl<T, 6>::run(s, PP),
1465 internal::ppolevl<T, 6>::run(s, PQ));
1467 internal::ppolevl<T, 7>::run(s, QP),
1468 internal::ppolevl<T, 7>::run(s, QQ));
1469 T xn = padd(x, NEG_PIO4);
1470 T w = pdiv(pset1<T>(5.0), x);
1471 p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));
1472 T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));
1473 return pselect(pcmp_le(x, pset1<T>(5.0)), x_le_five, x_gt_five);
1477 template <
typename T>
1478 struct bessel_y0_impl {
1480 static EIGEN_STRONG_INLINE T run(
const T x) {
1481 return generic_y0<T>::run(x);
1485 template <
typename T>
1486 struct bessel_j1_retval {
1490 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
1493 static EIGEN_STRONG_INLINE T run(
const T&) {
1494 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
1495 THIS_TYPE_IS_NOT_SUPPORTED);
1496 return ScalarType(0);
1500 template <
typename T>
1501 struct generic_j1<T, float> {
1503 static EIGEN_STRONG_INLINE T run(
const T& x) {
1547 const float JP[] = {-4.878788132172128E-009f, 6.009061827883699E-007f,
1548 -4.541343896997497E-005f, 1.937383947804541E-003f,
1549 -3.405537384615824E-002f};
1550 const float MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,
1551 3.138238455499697E-001f, -2.102302420403875E-001f,
1552 5.435364690523026E-003f, 1.493389585089498E-001f,
1553 4.976029650847191E-006f, 7.978845453073848E-001f};
1554 const float PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,
1555 -2.485774108720340E+001f, 7.222973196770240E+000f,
1556 -1.544842782180211E+000f, 3.503787691653334E-001f,
1557 -1.637986776941202E-001f, 3.749989509080821E-001f};
1558 const T Z1 = pset1<T>(1.46819706421238932572E1f);
1559 const T NEG_THPIO4F = pset1<T>(-2.35619449019234492885f);
1565 pmul(x, internal::ppolevl<T, 4>::run(z, JP)));
1566 T q = pdiv(pset1<T>(1.0f), y);
1568 T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO1));
1570 T yn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH1), NEG_THPIO4F);
1571 T y_gt_two = pmul(p, pcos(padd(yn, y)));
1575 pcmp_lt(x, pset1<T>(0.0f)), pnegate(y_gt_two), y_gt_two);
1576 return pselect(pcmp_le(y, pset1<T>(2.0f)), y_le_two, y_gt_two);
1580 template <
typename T>
1581 struct generic_j1<T, double> {
1583 static EIGEN_STRONG_INLINE T run(
const T& x) {
1617 const double PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,
1618 1.12719608129684925192E0, 5.11207951146807644818E0,
1619 8.42404590141772420927E0, 5.21451598682361504063E0,
1620 1.00000000000000000254E0};
1621 const double PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,
1622 1.10514232634061696926E0, 5.07386386128601488557E0,
1623 8.39985554327604159757E0, 5.20982848682361821619E0,
1624 9.99999999999999997461E-1};
1625 const double QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,
1626 7.58238284132545283818E1, 3.66779609360150777800E2,
1627 7.10856304998926107277E2, 5.97489612400613639965E2,
1628 2.11688757100572135698E2, 2.52070205858023719784E1};
1629 const double QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,
1630 1.05644886038262816351E3, 4.98641058337653607651E3,
1631 9.56231892404756170795E3, 7.99704160447350683650E3,
1632 2.82619278517639096600E3, 3.36093607810698293419E2};
1633 const double RP[] = {-8.99971225705559398224E8, 4.52228297998194034323E11,
1634 -7.27494245221818276015E13, 3.68295732863852883286E15};
1635 const double RQ[] = {1.00000000000000000000E0, 6.20836478118054335476E2,
1636 2.56987256757748830383E5, 8.35146791431949253037E7,
1637 2.21511595479792499675E10, 4.74914122079991414898E12,
1638 7.84369607876235854894E14, 8.95222336184627338078E16,
1639 5.32278620332680085395E18};
1640 const T Z1 = pset1<T>(1.46819706421238932572E1);
1641 const T Z2 = pset1<T>(4.92184563216946036703E1);
1642 const T NEG_THPIO4 = pset1<T>(-2.35619449019234492885);
1643 const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1);
1646 T y_le_five = pdiv(internal::ppolevl<T, 3>::run(z, RP),
1647 internal::ppolevl<T, 8>::run(z, RQ));
1648 y_le_five = pmul(pmul(pmul(y_le_five, x), psub(z, Z1)), psub(z, Z2));
1649 T s = pdiv(pset1<T>(25.0), z);
1651 internal::ppolevl<T, 6>::run(s, PP),
1652 internal::ppolevl<T, 6>::run(s, PQ));
1654 internal::ppolevl<T, 7>::run(s, QP),
1655 internal::ppolevl<T, 7>::run(s, QQ));
1656 T yn = padd(y, NEG_THPIO4);
1657 T w = pdiv(pset1<T>(-5.0), y);
1658 p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));
1659 T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));
1662 y_gt_five = pselect(
1663 pcmp_lt(x, pset1<T>(0.0)), pnegate(y_gt_five), y_gt_five);
1664 return pselect(pcmp_le(y, pset1<T>(5.0)), y_le_five, y_gt_five);
1668 template <
typename T>
1669 struct bessel_j1_impl {
1671 static EIGEN_STRONG_INLINE T run(
const T x) {
1672 return generic_j1<T>::run(x);
1676 template <
typename T>
1677 struct bessel_y1_retval {
1681 template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
1684 static EIGEN_STRONG_INLINE T run(
const T&) {
1685 EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value ==
false),
1686 THIS_TYPE_IS_NOT_SUPPORTED);
1687 return ScalarType(0);
1691 template <
typename T>
1692 struct generic_y1<T, float> {
1694 static EIGEN_STRONG_INLINE T run(
const T& x) {
1743 const float YP[] = {8.061978323326852E-009f, -9.496460629917016E-007f,
1744 6.719543806674249E-005f, -2.641785726447862E-003f,
1745 4.202369946500099E-002f};
1746 const float MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,
1747 3.138238455499697E-001f, -2.102302420403875E-001f,
1748 5.435364690523026E-003f, 1.493389585089498E-001f,
1749 4.976029650847191E-006f, 7.978845453073848E-001f};
1750 const float PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,
1751 -2.485774108720340E+001f, 7.222973196770240E+000f,
1752 -1.544842782180211E+000f, 3.503787691653334E-001f,
1753 -1.637986776941202E-001f, 3.749989509080821E-001f};
1754 const T YO1 = pset1<T>(4.66539330185668857532f);
1755 const T NEG_THPIO4F = pset1<T>(-2.35619449019234492885f);
1756 const T TWOOPI = pset1<T>(0.636619772367581343075535f);
1757 const T NEG_MAXNUM = pset1<T>(-NumTraits<float>::infinity());
1760 T x_le_two = pmul(psub(z, YO1), internal::ppolevl<T, 4>::run(z, YP));
1764 generic_j1<T, float>::run(x), plog(x),
1765 pdiv(pset1<T>(-1.0f), x))));
1766 x_le_two = pselect(pcmp_lt(x, pset1<T>(0.0f)), NEG_MAXNUM, x_le_two);
1768 T q = pdiv(pset1<T>(1.0), x);
1770 T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO1));
1772 T xn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH1), NEG_THPIO4F);
1773 T x_gt_two = pmul(p, psin(padd(xn, x)));
1774 return pselect(pcmp_le(x, pset1<T>(2.0)), x_le_two, x_gt_two);
1778 template <
typename T>
1779 struct generic_y1<T, double> {
1781 static EIGEN_STRONG_INLINE T run(
const T& x) {
1818 const double PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,
1819 1.12719608129684925192E0, 5.11207951146807644818E0,
1820 8.42404590141772420927E0, 5.21451598682361504063E0,
1821 1.00000000000000000254E0};
1822 const double PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,
1823 1.10514232634061696926E0, 5.07386386128601488557E0,
1824 8.39985554327604159757E0, 5.20982848682361821619E0,
1825 9.99999999999999997461E-1};
1826 const double QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,
1827 7.58238284132545283818E1, 3.66779609360150777800E2,
1828 7.10856304998926107277E2, 5.97489612400613639965E2,
1829 2.11688757100572135698E2, 2.52070205858023719784E1};
1830 const double QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,
1831 1.05644886038262816351E3, 4.98641058337653607651E3,
1832 9.56231892404756170795E3, 7.99704160447350683650E3,
1833 2.82619278517639096600E3, 3.36093607810698293419E2};
1834 const double YP[] = {1.26320474790178026440E9, -6.47355876379160291031E11,
1835 1.14509511541823727583E14, -8.12770255501325109621E15,
1836 2.02439475713594898196E17, -7.78877196265950026825E17};
1837 const double YQ[] = {1.00000000000000000000E0, 5.94301592346128195359E2,
1838 2.35564092943068577943E5, 7.34811944459721705660E7,
1839 1.87601316108706159478E10, 3.88231277496238566008E12,
1840 6.20557727146953693363E14, 6.87141087355300489866E16,
1841 3.97270608116560655612E18};
1842 const T SQ2OPI = pset1<T>(.79788456080286535588);
1843 const T NEG_THPIO4 = pset1<T>(-2.35619449019234492885);
1844 const T TWOOPI = pset1<T>(0.636619772367581343075535);
1845 const T NEG_MAXNUM = pset1<T>(-NumTraits<double>::infinity());
1848 T x_le_five = pdiv(internal::ppolevl<T, 5>::run(z, YP),
1849 internal::ppolevl<T, 8>::run(z, YQ));
1852 TWOOPI, pmadd(generic_j1<T, double>::run(x), plog(x),
1853 pdiv(pset1<T>(-1.0), x))));
1855 x_le_five = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_five);
1856 T s = pdiv(pset1<T>(25.0), z);
1858 internal::ppolevl<T, 6>::run(s, PP),
1859 internal::ppolevl<T, 6>::run(s, PQ));
1861 internal::ppolevl<T, 7>::run(s, QP),
1862 internal::ppolevl<T, 7>::run(s, QQ));
1863 T xn = padd(x, NEG_THPIO4);
1864 T w = pdiv(pset1<T>(5.0), x);
1865 p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));
1866 T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));
1867 return pselect(pcmp_le(x, pset1<T>(5.0)), x_le_five, x_gt_five);
1871 template <
typename T>
1872 struct bessel_y1_impl {
1874 static EIGEN_STRONG_INLINE T run(
const T x) {
1875 return generic_y1<T>::run(x);
1883 template <
typename Scalar>
1884 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_i0, Scalar)
1886 return EIGEN_MATHFUNC_IMPL(
bessel_i0, Scalar)::run(x);
1889 template <
typename Scalar>
1890 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_i0e, Scalar)
1892 return EIGEN_MATHFUNC_IMPL(
bessel_i0e, Scalar)::run(x);
1895 template <
typename Scalar>
1896 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_i1, Scalar)
1898 return EIGEN_MATHFUNC_IMPL(
bessel_i1, Scalar)::run(x);
1901 template <
typename Scalar>
1902 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_i1e, Scalar)
1904 return EIGEN_MATHFUNC_IMPL(
bessel_i1e, Scalar)::run(x);
1907 template <
typename Scalar>
1908 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_k0, Scalar)
1910 return EIGEN_MATHFUNC_IMPL(
bessel_k0, Scalar)::run(x);
1913 template <
typename Scalar>
1914 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_k0e, Scalar)
1916 return EIGEN_MATHFUNC_IMPL(
bessel_k0e, Scalar)::run(x);
1919 template <
typename Scalar>
1920 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_k1, Scalar)
1922 return EIGEN_MATHFUNC_IMPL(
bessel_k1, Scalar)::run(x);
1925 template <
typename Scalar>
1926 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_k1e, Scalar)
1928 return EIGEN_MATHFUNC_IMPL(
bessel_k1e, Scalar)::run(x);
1931 template <
typename Scalar>
1932 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_j0, Scalar)
1934 return EIGEN_MATHFUNC_IMPL(
bessel_j0, Scalar)::run(x);
1937 template <
typename Scalar>
1938 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_y0, Scalar)
1940 return EIGEN_MATHFUNC_IMPL(
bessel_y0, Scalar)::run(x);
1943 template <
typename Scalar>
1944 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_j1, Scalar)
1946 return EIGEN_MATHFUNC_IMPL(
bessel_j1, Scalar)::run(x);
1949 template <
typename Scalar>
1950 EIGEN_DEVICE_FUNC
inline EIGEN_MATHFUNC_RETVAL(
bessel_y1, Scalar)
1952 return EIGEN_MATHFUNC_IMPL(
bessel_y1, Scalar)::run(x);
1959 #endif // EIGEN_BESSEL_FUNCTIONS_H const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_y1_op< typename Derived::Scalar >, const Derived > bessel_y1(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:278
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_j0_op< typename Derived::Scalar >, const Derived > bessel_j0(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:212
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_j1_op< typename Derived::Scalar >, const Derived > bessel_j1(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:256
Namespace containing all symbols from the Eigen library.
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i0_op< typename Derived::Scalar >, const Derived > bessel_i0(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:32
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i0e_op< typename Derived::Scalar >, const Derived > bessel_i0e(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:55
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1e_op< typename Derived::Scalar >, const Derived > bessel_k1e(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:190
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_y0_op< typename Derived::Scalar >, const Derived > bessel_y0(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:234
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k1_op< typename Derived::Scalar >, const Derived > bessel_k1(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:167
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1e_op< typename Derived::Scalar >, const Derived > bessel_i1e(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:100
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k0_op< typename Derived::Scalar >, const Derived > bessel_k0(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:122
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_i1_op< typename Derived::Scalar >, const Derived > bessel_i1(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:77
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_bessel_k0e_op< typename Derived::Scalar >, const Derived > bessel_k0e(const Eigen::ArrayBase< Derived > &x)
Definition: BesselFunctionsArrayAPI.h:145