1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_GENERIC_PACKET_MATH_H
12#define EIGEN_GENERIC_PACKET_MATH_H
13
14namespace Eigen {
15
16namespace internal {
17
18/** \internal
19  * \file GenericPacketMath.h
20  *
21  * Default implementation for types not supported by the vectorization.
22  * In practice these functions are provided to make easier the writing
23  * of generic vectorized code.
24  */
25
26#ifndef EIGEN_DEBUG_ALIGNED_LOAD
27#define EIGEN_DEBUG_ALIGNED_LOAD
28#endif
29
30#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
31#define EIGEN_DEBUG_UNALIGNED_LOAD
32#endif
33
34#ifndef EIGEN_DEBUG_ALIGNED_STORE
35#define EIGEN_DEBUG_ALIGNED_STORE
36#endif
37
38#ifndef EIGEN_DEBUG_UNALIGNED_STORE
39#define EIGEN_DEBUG_UNALIGNED_STORE
40#endif
41
42struct default_packet_traits
43{
44  enum {
45    HasHalfPacket = 0,
46
47    HasAdd    = 1,
48    HasSub    = 1,
49    HasMul    = 1,
50    HasNegate = 1,
51    HasAbs    = 1,
52    HasArg    = 0,
53    HasAbs2   = 1,
54    HasMin    = 1,
55    HasMax    = 1,
56    HasConj   = 1,
57    HasSetLinear = 1,
58    HasBlend  = 0,
59
60    HasDiv    = 0,
61    HasSqrt   = 0,
62    HasRsqrt  = 0,
63    HasExp    = 0,
64    HasLog    = 0,
65    HasLog1p  = 0,
66    HasLog10  = 0,
67    HasPow    = 0,
68
69    HasSin    = 0,
70    HasCos    = 0,
71    HasTan    = 0,
72    HasASin   = 0,
73    HasACos   = 0,
74    HasATan   = 0,
75    HasSinh   = 0,
76    HasCosh   = 0,
77    HasTanh   = 0,
78    HasLGamma = 0,
79    HasDiGamma = 0,
80    HasZeta = 0,
81    HasPolygamma = 0,
82    HasErf = 0,
83    HasErfc = 0,
84    HasIGamma = 0,
85    HasIGammac = 0,
86    HasBetaInc = 0,
87
88    HasRound  = 0,
89    HasFloor  = 0,
90    HasCeil   = 0,
91
92    HasSign   = 0
93  };
94};
95
96template<typename T> struct packet_traits : default_packet_traits
97{
98  typedef T type;
99  typedef T half;
100  enum {
101    Vectorizable = 0,
102    size = 1,
103    AlignedOnScalar = 0,
104    HasHalfPacket = 0
105  };
106  enum {
107    HasAdd    = 0,
108    HasSub    = 0,
109    HasMul    = 0,
110    HasNegate = 0,
111    HasAbs    = 0,
112    HasAbs2   = 0,
113    HasMin    = 0,
114    HasMax    = 0,
115    HasConj   = 0,
116    HasSetLinear = 0
117  };
118};
119
120template<typename T> struct packet_traits<const T> : packet_traits<T> { };
121
122template <typename Src, typename Tgt> struct type_casting_traits {
123  enum {
124    VectorizedCast = 0,
125    SrcCoeffRatio = 1,
126    TgtCoeffRatio = 1
127  };
128};
129
130
131/** \internal \returns static_cast<TgtType>(a) (coeff-wise) */
132template <typename SrcPacket, typename TgtPacket>
133EIGEN_DEVICE_FUNC inline TgtPacket
134pcast(const SrcPacket& a) {
135  return static_cast<TgtPacket>(a);
136}
137template <typename SrcPacket, typename TgtPacket>
138EIGEN_DEVICE_FUNC inline TgtPacket
139pcast(const SrcPacket& a, const SrcPacket& /*b*/) {
140  return static_cast<TgtPacket>(a);
141}
142
143template <typename SrcPacket, typename TgtPacket>
144EIGEN_DEVICE_FUNC inline TgtPacket
145pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/) {
146  return static_cast<TgtPacket>(a);
147}
148
149/** \internal \returns a + b (coeff-wise) */
150template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
151padd(const Packet& a,
152        const Packet& b) { return a+b; }
153
154/** \internal \returns a - b (coeff-wise) */
155template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
156psub(const Packet& a,
157        const Packet& b) { return a-b; }
158
159/** \internal \returns -a (coeff-wise) */
160template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
161pnegate(const Packet& a) { return -a; }
162
163/** \internal \returns conj(a) (coeff-wise) */
164
165template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
166pconj(const Packet& a) { return numext::conj(a); }
167
168/** \internal \returns a * b (coeff-wise) */
169template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
170pmul(const Packet& a,
171        const Packet& b) { return a*b; }
172
173/** \internal \returns a / b (coeff-wise) */
174template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
175pdiv(const Packet& a,
176        const Packet& b) { return a/b; }
177
178/** \internal \returns the min of \a a and \a b  (coeff-wise) */
179template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
180pmin(const Packet& a,
181        const Packet& b) { return numext::mini(a, b); }
182
183/** \internal \returns the max of \a a and \a b  (coeff-wise) */
184template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
185pmax(const Packet& a,
186        const Packet& b) { return numext::maxi(a, b); }
187
188/** \internal \returns the absolute value of \a a */
189template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
190pabs(const Packet& a) { using std::abs; return abs(a); }
191
192/** \internal \returns the phase angle of \a a */
193template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
194parg(const Packet& a) { using numext::arg; return arg(a); }
195
196/** \internal \returns the bitwise and of \a a and \a b */
197template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
198pand(const Packet& a, const Packet& b) { return a & b; }
199
200/** \internal \returns the bitwise or of \a a and \a b */
201template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
202por(const Packet& a, const Packet& b) { return a | b; }
203
204/** \internal \returns the bitwise xor of \a a and \a b */
205template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
206pxor(const Packet& a, const Packet& b) { return a ^ b; }
207
208/** \internal \returns the bitwise andnot of \a a and \a b */
209template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
210pandnot(const Packet& a, const Packet& b) { return a & (!b); }
211
212/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
213template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
214pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
215
216/** \internal \returns a packet version of \a *from, (un-aligned load) */
217template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
218ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
219
220/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
221template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
222pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
223
224/** \internal \returns a packet with constant coefficients \a a[0], e.g.: (a[0],a[0],a[0],a[0]) */
225template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
226pload1(const typename unpacket_traits<Packet>::type  *a) { return pset1<Packet>(*a); }
227
228/** \internal \returns a packet with elements of \a *from duplicated.
229  * For instance, for a packet of 8 elements, 4 scalars will be read from \a *from and
230  * duplicated to form: {from[0],from[0],from[1],from[1],from[2],from[2],from[3],from[3]}
231  * Currently, this function is only used for scalar * complex products.
232  */
233template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
234ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
235
236/** \internal \returns a packet with elements of \a *from quadrupled.
237  * For instance, for a packet of 8 elements, 2 scalars will be read from \a *from and
238  * replicated to form: {from[0],from[0],from[0],from[0],from[1],from[1],from[1],from[1]}
239  * Currently, this function is only used in matrix products.
240  * For packet-size smaller or equal to 4, this function is equivalent to pload1
241  */
242template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
243ploadquad(const typename unpacket_traits<Packet>::type* from)
244{ return pload1<Packet>(from); }
245
246/** \internal equivalent to
247  * \code
248  * a0 = pload1(a+0);
249  * a1 = pload1(a+1);
250  * a2 = pload1(a+2);
251  * a3 = pload1(a+3);
252  * \endcode
253  * \sa pset1, pload1, ploaddup, pbroadcast2
254  */
255template<typename Packet> EIGEN_DEVICE_FUNC
256inline void pbroadcast4(const typename unpacket_traits<Packet>::type *a,
257                        Packet& a0, Packet& a1, Packet& a2, Packet& a3)
258{
259  a0 = pload1<Packet>(a+0);
260  a1 = pload1<Packet>(a+1);
261  a2 = pload1<Packet>(a+2);
262  a3 = pload1<Packet>(a+3);
263}
264
265/** \internal equivalent to
266  * \code
267  * a0 = pload1(a+0);
268  * a1 = pload1(a+1);
269  * \endcode
270  * \sa pset1, pload1, ploaddup, pbroadcast4
271  */
272template<typename Packet> EIGEN_DEVICE_FUNC
273inline void pbroadcast2(const typename unpacket_traits<Packet>::type *a,
274                        Packet& a0, Packet& a1)
275{
276  a0 = pload1<Packet>(a+0);
277  a1 = pload1<Packet>(a+1);
278}
279
280/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
281template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
282plset(const typename unpacket_traits<Packet>::type& a) { return a; }
283
284/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
285template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstore(Scalar* to, const Packet& from)
286{ (*to) = from; }
287
288/** \internal copy the packet \a from to \a *to, (un-aligned store) */
289template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pstoreu(Scalar* to, const Packet& from)
290{  (*to) = from; }
291
292 template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather(const Scalar* from, Index /*stride*/)
293 { return ploadu<Packet>(from); }
294
295 template<typename Scalar, typename Packet> EIGEN_DEVICE_FUNC inline void pscatter(Scalar* to, const Packet& from, Index /*stride*/)
296 { pstore(to, from); }
297
298/** \internal tries to do cache prefetching of \a addr */
299template<typename Scalar> EIGEN_DEVICE_FUNC inline void prefetch(const Scalar* addr)
300{
301#ifdef __CUDA_ARCH__
302#if defined(__LP64__)
303  // 64-bit pointer operand constraint for inlined asm
304  asm(" prefetch.L1 [ %1 ];" : "=l"(addr) : "l"(addr));
305#else
306  // 32-bit pointer operand constraint for inlined asm
307  asm(" prefetch.L1 [ %1 ];" : "=r"(addr) : "r"(addr));
308#endif
309#elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC)
310  __builtin_prefetch(addr);
311#endif
312}
313
314/** \internal \returns the first element of a packet */
315template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
316{ return a; }
317
318/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
319template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
320preduxp(const Packet* vecs) { return vecs[0]; }
321
322/** \internal \returns the sum of the elements of \a a*/
323template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux(const Packet& a)
324{ return a; }
325
326/** \internal \returns the sum of the elements of \a a by block of 4 elements.
327  * For a packet {a0, a1, a2, a3, a4, a5, a6, a7}, it returns a half packet {a0+a4, a1+a5, a2+a6, a3+a7}
328  * For packet-size smaller or equal to 4, this boils down to a noop.
329  */
330template<typename Packet> EIGEN_DEVICE_FUNC inline
331typename conditional<(unpacket_traits<Packet>::size%8)==0,typename unpacket_traits<Packet>::half,Packet>::type
332predux_downto4(const Packet& a)
333{ return a; }
334
335/** \internal \returns the product of the elements of \a a*/
336template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
337{ return a; }
338
339/** \internal \returns the min of the elements of \a a*/
340template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
341{ return a; }
342
343/** \internal \returns the max of the elements of \a a*/
344template<typename Packet> EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
345{ return a; }
346
347/** \internal \returns the reversed elements of \a a*/
348template<typename Packet> EIGEN_DEVICE_FUNC inline Packet preverse(const Packet& a)
349{ return a; }
350
351/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
352template<typename Packet> EIGEN_DEVICE_FUNC inline Packet pcplxflip(const Packet& a)
353{
354  // FIXME: uncomment the following in case we drop the internal imag and real functions.
355//   using std::imag;
356//   using std::real;
357  return Packet(imag(a),real(a));
358}
359
360/**************************
361* Special math functions
362***************************/
363
364/** \internal \returns the sine of \a a (coeff-wise) */
365template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
366Packet psin(const Packet& a) { using std::sin; return sin(a); }
367
368/** \internal \returns the cosine of \a a (coeff-wise) */
369template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
370Packet pcos(const Packet& a) { using std::cos; return cos(a); }
371
372/** \internal \returns the tan of \a a (coeff-wise) */
373template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
374Packet ptan(const Packet& a) { using std::tan; return tan(a); }
375
376/** \internal \returns the arc sine of \a a (coeff-wise) */
377template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
378Packet pasin(const Packet& a) { using std::asin; return asin(a); }
379
380/** \internal \returns the arc cosine of \a a (coeff-wise) */
381template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
382Packet pacos(const Packet& a) { using std::acos; return acos(a); }
383
384/** \internal \returns the arc tangent of \a a (coeff-wise) */
385template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
386Packet patan(const Packet& a) { using std::atan; return atan(a); }
387
388/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */
389template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
390Packet psinh(const Packet& a) { using std::sinh; return sinh(a); }
391
392/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */
393template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
394Packet pcosh(const Packet& a) { using std::cosh; return cosh(a); }
395
396/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */
397template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
398Packet ptanh(const Packet& a) { using std::tanh; return tanh(a); }
399
400/** \internal \returns the exp of \a a (coeff-wise) */
401template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
402Packet pexp(const Packet& a) { using std::exp; return exp(a); }
403
404/** \internal \returns the log of \a a (coeff-wise) */
405template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
406Packet plog(const Packet& a) { using std::log; return log(a); }
407
408/** \internal \returns the log1p of \a a (coeff-wise) */
409template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
410Packet plog1p(const Packet& a) { return numext::log1p(a); }
411
412/** \internal \returns the log10 of \a a (coeff-wise) */
413template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
414Packet plog10(const Packet& a) { using std::log10; return log10(a); }
415
416/** \internal \returns the square-root of \a a (coeff-wise) */
417template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
418Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
419
420/** \internal \returns the reciprocal square-root of \a a (coeff-wise) */
421template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
422Packet prsqrt(const Packet& a) {
423  return pdiv(pset1<Packet>(1), psqrt(a));
424}
425
426/** \internal \returns the rounded value of \a a (coeff-wise) */
427template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
428Packet pround(const Packet& a) { using numext::round; return round(a); }
429
430/** \internal \returns the floor of \a a (coeff-wise) */
431template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
432Packet pfloor(const Packet& a) { using numext::floor; return floor(a); }
433
434/** \internal \returns the ceil of \a a (coeff-wise) */
435template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
436Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); }
437
438/***************************************************************************
439* The following functions might not have to be overwritten for vectorized types
440***************************************************************************/
441
442/** \internal copy a packet with constant coeficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */
443// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
444template<typename Packet>
445inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
446{
447  pstore(to, pset1<Packet>(a));
448}
449
450/** \internal \returns a * b + c (coeff-wise) */
451template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
452pmadd(const Packet&  a,
453         const Packet&  b,
454         const Packet&  c)
455{ return padd(pmul(a, b),c); }
456
457/** \internal \returns a packet version of \a *from.
458  * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
459template<typename Packet, int Alignment>
460EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt(const typename unpacket_traits<Packet>::type* from)
461{
462  if(Alignment >= unpacket_traits<Packet>::alignment)
463    return pload<Packet>(from);
464  else
465    return ploadu<Packet>(from);
466}
467
468/** \internal copy the packet \a from to \a *to.
469  * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
470template<typename Scalar, typename Packet, int Alignment>
471EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pstoret(Scalar* to, const Packet& from)
472{
473  if(Alignment >= unpacket_traits<Packet>::alignment)
474    pstore(to, from);
475  else
476    pstoreu(to, from);
477}
478
479/** \internal \returns a packet version of \a *from.
480  * Unlike ploadt, ploadt_ro takes advantage of the read-only memory path on the
481  * hardware if available to speedup the loading of data that won't be modified
482  * by the current computation.
483  */
484template<typename Packet, int LoadMode>
485EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet ploadt_ro(const typename unpacket_traits<Packet>::type* from)
486{
487  return ploadt<Packet, LoadMode>(from);
488}
489
490/** \internal default implementation of palign() allowing partial specialization */
491template<int Offset,typename PacketType>
492struct palign_impl
493{
494  // by default data are aligned, so there is nothing to be done :)
495  static inline void run(PacketType&, const PacketType&) {}
496};
497
498/** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements
499  * of \a first and \a Offset first elements of \a second.
500  *
501  * This function is currently only used to optimize matrix-vector products on unligned matrices.
502  * It takes 2 packets that represent a contiguous memory array, and returns a packet starting
503  * at the position \a Offset. For instance, for packets of 4 elements, we have:
504  *  Input:
505  *  - first = {f0,f1,f2,f3}
506  *  - second = {s0,s1,s2,s3}
507  * Output:
508  *   - if Offset==0 then {f0,f1,f2,f3}
509  *   - if Offset==1 then {f1,f2,f3,s0}
510  *   - if Offset==2 then {f2,f3,s0,s1}
511  *   - if Offset==3 then {f3,s0,s1,s3}
512  */
513template<int Offset,typename PacketType>
514inline void palign(PacketType& first, const PacketType& second)
515{
516  palign_impl<Offset,PacketType>::run(first,second);
517}
518
519/***************************************************************************
520* Fast complex products (GCC generates a function call which is very slow)
521***************************************************************************/
522
523// Eigen+CUDA does not support complexes.
524#ifndef __CUDACC__
525
526template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
527{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
528
529template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
530{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
531
532#endif
533
534
535/***************************************************************************
536 * PacketBlock, that is a collection of N packets where the number of words
537 * in the packet is a multiple of N.
538***************************************************************************/
539template <typename Packet,int N=unpacket_traits<Packet>::size> struct PacketBlock {
540  Packet packet[N];
541};
542
543template<typename Packet> EIGEN_DEVICE_FUNC inline void
544ptranspose(PacketBlock<Packet,1>& /*kernel*/) {
545  // Nothing to do in the scalar case, i.e. a 1x1 matrix.
546}
547
548/***************************************************************************
549 * Selector, i.e. vector of N boolean values used to select (i.e. blend)
550 * words from 2 packets.
551***************************************************************************/
552template <size_t N> struct Selector {
553  bool select[N];
554};
555
556template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
557pblend(const Selector<unpacket_traits<Packet>::size>& ifPacket, const Packet& thenPacket, const Packet& elsePacket) {
558  return ifPacket.select[0] ? thenPacket : elsePacket;
559}
560
561/** \internal \returns \a a with the first coefficient replaced by the scalar b */
562template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
563pinsertfirst(const Packet& a, typename unpacket_traits<Packet>::type b)
564{
565  // Default implementation based on pblend.
566  // It must be specialized for higher performance.
567  Selector<unpacket_traits<Packet>::size> mask;
568  mask.select[0] = true;
569  // This for loop should be optimized away by the compiler.
570  for(Index i=1; i<unpacket_traits<Packet>::size; ++i)
571    mask.select[i] = false;
572  return pblend(mask, pset1<Packet>(b), a);
573}
574
575/** \internal \returns \a a with the last coefficient replaced by the scalar b */
576template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
577pinsertlast(const Packet& a, typename unpacket_traits<Packet>::type b)
578{
579  // Default implementation based on pblend.
580  // It must be specialized for higher performance.
581  Selector<unpacket_traits<Packet>::size> mask;
582  // This for loop should be optimized away by the compiler.
583  for(Index i=0; i<unpacket_traits<Packet>::size-1; ++i)
584    mask.select[i] = false;
585  mask.select[unpacket_traits<Packet>::size-1] = true;
586  return pblend(mask, pset1<Packet>(b), a);
587}
588
589} // end namespace internal
590
591} // end namespace Eigen
592
593#endif // EIGEN_GENERIC_PACKET_MATH_H
594