Functors.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_FUNCTORS_H
11 #define EIGEN_FUNCTORS_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 // associative functors:
18 
24 template<typename Scalar> struct scalar_sum_op {
25  EIGEN_EMPTY_STRUCT_CTOR(scalar_sum_op)
26  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a + b; }
27  template<typename Packet>
28  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
29  { return internal::padd(a,b); }
30  template<typename Packet>
31  EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
32  { return internal::predux(a); }
33 };
34 template<typename Scalar>
35 struct functor_traits<scalar_sum_op<Scalar> > {
36  enum {
37  Cost = NumTraits<Scalar>::AddCost,
38  PacketAccess = packet_traits<Scalar>::HasAdd
39  };
40 };
41 
47 template<typename LhsScalar,typename RhsScalar> struct scalar_product_op {
48  enum {
49  // TODO vectorize mixed product
50  Vectorizable = is_same<LhsScalar,RhsScalar>::value && packet_traits<LhsScalar>::HasMul && packet_traits<RhsScalar>::HasMul
51  };
52  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
53  EIGEN_EMPTY_STRUCT_CTOR(scalar_product_op)
54  EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a * b; }
55  template<typename Packet>
56  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
57  { return internal::pmul(a,b); }
58  template<typename Packet>
59  EIGEN_STRONG_INLINE const result_type predux(const Packet& a) const
60  { return internal::predux_mul(a); }
61 };
62 template<typename LhsScalar,typename RhsScalar>
63 struct functor_traits<scalar_product_op<LhsScalar,RhsScalar> > {
64  enum {
65  Cost = (NumTraits<LhsScalar>::MulCost + NumTraits<RhsScalar>::MulCost)/2, // rough estimate!
66  PacketAccess = scalar_product_op<LhsScalar,RhsScalar>::Vectorizable
67  };
68 };
69 
75 template<typename LhsScalar,typename RhsScalar> struct scalar_conj_product_op {
76 
77  enum {
78  Conj = NumTraits<LhsScalar>::IsComplex
79  };
80 
81  typedef typename scalar_product_traits<LhsScalar,RhsScalar>::ReturnType result_type;
82 
83  EIGEN_EMPTY_STRUCT_CTOR(scalar_conj_product_op)
84  EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const
85  { return conj_helper<LhsScalar,RhsScalar,Conj,false>().pmul(a,b); }
86 
87  template<typename Packet>
88  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
89  { return conj_helper<Packet,Packet,Conj,false>().pmul(a,b); }
90 };
91 template<typename LhsScalar,typename RhsScalar>
92 struct functor_traits<scalar_conj_product_op<LhsScalar,RhsScalar> > {
93  enum {
94  Cost = NumTraits<LhsScalar>::MulCost,
95  PacketAccess = internal::is_same<LhsScalar, RhsScalar>::value && packet_traits<LhsScalar>::HasMul
96  };
97 };
98 
104 template<typename Scalar> struct scalar_min_op {
105  EIGEN_EMPTY_STRUCT_CTOR(scalar_min_op)
106  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::min; return (min)(a, b); }
107  template<typename Packet>
108  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
109  { return internal::pmin(a,b); }
110  template<typename Packet>
111  EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
112  { return internal::predux_min(a); }
113 };
114 template<typename Scalar>
115 struct functor_traits<scalar_min_op<Scalar> > {
116  enum {
117  Cost = NumTraits<Scalar>::AddCost,
118  PacketAccess = packet_traits<Scalar>::HasMin
119  };
120 };
121 
127 template<typename Scalar> struct scalar_max_op {
128  EIGEN_EMPTY_STRUCT_CTOR(scalar_max_op)
129  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { using std::max; return (max)(a, b); }
130  template<typename Packet>
131  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
132  { return internal::pmax(a,b); }
133  template<typename Packet>
134  EIGEN_STRONG_INLINE const Scalar predux(const Packet& a) const
135  { return internal::predux_max(a); }
136 };
137 template<typename Scalar>
138 struct functor_traits<scalar_max_op<Scalar> > {
139  enum {
140  Cost = NumTraits<Scalar>::AddCost,
141  PacketAccess = packet_traits<Scalar>::HasMax
142  };
143 };
144 
150 template<typename Scalar> struct scalar_hypot_op {
151  EIGEN_EMPTY_STRUCT_CTOR(scalar_hypot_op)
152 // typedef typename NumTraits<Scalar>::Real result_type;
153  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& _x, const Scalar& _y) const
154  {
155  using std::max;
156  using std::min;
157  Scalar p = (max)(_x, _y);
158  Scalar q = (min)(_x, _y);
159  Scalar qp = q/p;
160  return p * sqrt(Scalar(1) + qp*qp);
161  }
162 };
163 template<typename Scalar>
164 struct functor_traits<scalar_hypot_op<Scalar> > {
165  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess=0 };
166 };
167 
171 template<typename Scalar, typename OtherScalar> struct scalar_binary_pow_op {
172  EIGEN_EMPTY_STRUCT_CTOR(scalar_binary_pow_op)
173  inline Scalar operator() (const Scalar& a, const OtherScalar& b) const { return internal::pow(a, b); }
174 };
175 template<typename Scalar, typename OtherScalar>
176 struct functor_traits<scalar_binary_pow_op<Scalar,OtherScalar> > {
177  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
178 };
179 
180 // other binary functors:
181 
187 template<typename Scalar> struct scalar_difference_op {
188  EIGEN_EMPTY_STRUCT_CTOR(scalar_difference_op)
189  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a - b; }
190  template<typename Packet>
191  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
192  { return internal::psub(a,b); }
193 };
194 template<typename Scalar>
195 struct functor_traits<scalar_difference_op<Scalar> > {
196  enum {
197  Cost = NumTraits<Scalar>::AddCost,
198  PacketAccess = packet_traits<Scalar>::HasSub
199  };
200 };
201 
207 template<typename Scalar> struct scalar_quotient_op {
208  EIGEN_EMPTY_STRUCT_CTOR(scalar_quotient_op)
209  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& b) const { return a / b; }
210  template<typename Packet>
211  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& b) const
212  { return internal::pdiv(a,b); }
213 };
214 template<typename Scalar>
215 struct functor_traits<scalar_quotient_op<Scalar> > {
216  enum {
217  Cost = 2 * NumTraits<Scalar>::MulCost,
218  PacketAccess = packet_traits<Scalar>::HasDiv
219  };
220 };
221 
227 struct scalar_boolean_and_op {
228  EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_and_op)
229  EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a && b; }
230 };
231 template<> struct functor_traits<scalar_boolean_and_op> {
232  enum {
233  Cost = NumTraits<bool>::AddCost,
234  PacketAccess = false
235  };
236 };
237 
243 struct scalar_boolean_or_op {
244  EIGEN_EMPTY_STRUCT_CTOR(scalar_boolean_or_op)
245  EIGEN_STRONG_INLINE bool operator() (const bool& a, const bool& b) const { return a || b; }
246 };
247 template<> struct functor_traits<scalar_boolean_or_op> {
248  enum {
249  Cost = NumTraits<bool>::AddCost,
250  PacketAccess = false
251  };
252 };
253 
254 // unary functors:
255 
261 template<typename Scalar> struct scalar_opposite_op {
262  EIGEN_EMPTY_STRUCT_CTOR(scalar_opposite_op)
263  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
264  template<typename Packet>
265  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
266  { return internal::pnegate(a); }
267 };
268 template<typename Scalar>
269 struct functor_traits<scalar_opposite_op<Scalar> >
270 { enum {
271  Cost = NumTraits<Scalar>::AddCost,
272  PacketAccess = packet_traits<Scalar>::HasNegate };
273 };
274 
280 template<typename Scalar> struct scalar_abs_op {
281  EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
282  typedef typename NumTraits<Scalar>::Real result_type;
283  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs(a); }
284  template<typename Packet>
285  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
286  { return internal::pabs(a); }
287 };
288 template<typename Scalar>
289 struct functor_traits<scalar_abs_op<Scalar> >
290 {
291  enum {
292  Cost = NumTraits<Scalar>::AddCost,
293  PacketAccess = packet_traits<Scalar>::HasAbs
294  };
295 };
296 
302 template<typename Scalar> struct scalar_abs2_op {
303  EIGEN_EMPTY_STRUCT_CTOR(scalar_abs2_op)
304  typedef typename NumTraits<Scalar>::Real result_type;
305  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs2(a); }
306  template<typename Packet>
307  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
308  { return internal::pmul(a,a); }
309 };
310 template<typename Scalar>
311 struct functor_traits<scalar_abs2_op<Scalar> >
312 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };
313 
319 template<typename Scalar> struct scalar_conjugate_op {
320  EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
321  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return internal::conj(a); }
322  template<typename Packet>
323  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
324 };
325 template<typename Scalar>
326 struct functor_traits<scalar_conjugate_op<Scalar> >
327 {
328  enum {
329  Cost = NumTraits<Scalar>::IsComplex ? NumTraits<Scalar>::AddCost : 0,
330  PacketAccess = packet_traits<Scalar>::HasConj
331  };
332 };
333 
339 template<typename Scalar, typename NewType>
340 struct scalar_cast_op {
341  EIGEN_EMPTY_STRUCT_CTOR(scalar_cast_op)
342  typedef NewType result_type;
343  EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
344 };
345 template<typename Scalar, typename NewType>
346 struct functor_traits<scalar_cast_op<Scalar,NewType> >
347 { enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };
348 
354 template<typename Scalar>
355 struct scalar_real_op {
356  EIGEN_EMPTY_STRUCT_CTOR(scalar_real_op)
357  typedef typename NumTraits<Scalar>::Real result_type;
358  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::real(a); }
359 };
360 template<typename Scalar>
361 struct functor_traits<scalar_real_op<Scalar> >
362 { enum { Cost = 0, PacketAccess = false }; };
363 
369 template<typename Scalar>
370 struct scalar_imag_op {
371  EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_op)
372  typedef typename NumTraits<Scalar>::Real result_type;
373  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return internal::imag(a); }
374 };
375 template<typename Scalar>
376 struct functor_traits<scalar_imag_op<Scalar> >
377 { enum { Cost = 0, PacketAccess = false }; };
378 
384 template<typename Scalar>
385 struct scalar_real_ref_op {
386  EIGEN_EMPTY_STRUCT_CTOR(scalar_real_ref_op)
387  typedef typename NumTraits<Scalar>::Real result_type;
388  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::real_ref(*const_cast<Scalar*>(&a)); }
389 };
390 template<typename Scalar>
391 struct functor_traits<scalar_real_ref_op<Scalar> >
392 { enum { Cost = 0, PacketAccess = false }; };
393 
399 template<typename Scalar>
400 struct scalar_imag_ref_op {
401  EIGEN_EMPTY_STRUCT_CTOR(scalar_imag_ref_op)
402  typedef typename NumTraits<Scalar>::Real result_type;
403  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return internal::imag_ref(*const_cast<Scalar*>(&a)); }
404 };
405 template<typename Scalar>
406 struct functor_traits<scalar_imag_ref_op<Scalar> >
407 { enum { Cost = 0, PacketAccess = false }; };
408 
415 template<typename Scalar> struct scalar_exp_op {
416  EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
417  inline const Scalar operator() (const Scalar& a) const { return internal::exp(a); }
418  typedef typename packet_traits<Scalar>::type Packet;
419  inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
420 };
421 template<typename Scalar>
422 struct functor_traits<scalar_exp_op<Scalar> >
423 { enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasExp }; };
424 
431 template<typename Scalar> struct scalar_log_op {
432  EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
433  inline const Scalar operator() (const Scalar& a) const { return internal::log(a); }
434  typedef typename packet_traits<Scalar>::type Packet;
435  inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
436 };
437 template<typename Scalar>
438 struct functor_traits<scalar_log_op<Scalar> >
439 { enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };
440 
446 /* NOTE why doing the pset1() in packetOp *is* an optimization ?
447  * indeed it seems better to declare m_other as a Packet and do the pset1() once
448  * in the constructor. However, in practice:
449  * - GCC does not like m_other as a Packet and generate a load every time it needs it
450  * - on the other hand GCC is able to moves the pset1() outside the loop :)
451  * - simpler code ;)
452  * (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y)
453  */
454 template<typename Scalar>
455 struct scalar_multiple_op {
456  typedef typename packet_traits<Scalar>::type Packet;
457  // FIXME default copy constructors seems bugged with std::complex<>
458  EIGEN_STRONG_INLINE scalar_multiple_op(const scalar_multiple_op& other) : m_other(other.m_other) { }
459  EIGEN_STRONG_INLINE scalar_multiple_op(const Scalar& other) : m_other(other) { }
460  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; }
461  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
462  { return internal::pmul(a, pset1<Packet>(m_other)); }
463  typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
464 };
465 template<typename Scalar>
466 struct functor_traits<scalar_multiple_op<Scalar> >
467 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
468 
469 template<typename Scalar1, typename Scalar2>
470 struct scalar_multiple2_op {
471  typedef typename scalar_product_traits<Scalar1,Scalar2>::ReturnType result_type;
472  EIGEN_STRONG_INLINE scalar_multiple2_op(const scalar_multiple2_op& other) : m_other(other.m_other) { }
473  EIGEN_STRONG_INLINE scalar_multiple2_op(const Scalar2& other) : m_other(other) { }
474  EIGEN_STRONG_INLINE result_type operator() (const Scalar1& a) const { return a * m_other; }
475  typename add_const_on_value_type<typename NumTraits<Scalar2>::Nested>::type m_other;
476 };
477 template<typename Scalar1,typename Scalar2>
478 struct functor_traits<scalar_multiple2_op<Scalar1,Scalar2> >
479 { enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
480 
489 template<typename Scalar>
490 struct scalar_quotient1_op {
491  typedef typename packet_traits<Scalar>::type Packet;
492  // FIXME default copy constructors seems bugged with std::complex<>
493  EIGEN_STRONG_INLINE scalar_quotient1_op(const scalar_quotient1_op& other) : m_other(other.m_other) { }
494  EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other) : m_other(other) {}
495  EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; }
496  EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
497  { return internal::pdiv(a, pset1<Packet>(m_other)); }
498  typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
499 };
500 template<typename Scalar>
501 struct functor_traits<scalar_quotient1_op<Scalar> >
502 { enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
503 
504 // nullary functors
505 
506 template<typename Scalar>
507 struct scalar_constant_op {
508  typedef typename packet_traits<Scalar>::type Packet;
509  EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }
510  EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }
511  template<typename Index>
512  EIGEN_STRONG_INLINE const Scalar operator() (Index, Index = 0) const { return m_other; }
513  template<typename Index>
514  EIGEN_STRONG_INLINE const Packet packetOp(Index, Index = 0) const { return internal::pset1<Packet>(m_other); }
515  const Scalar m_other;
516 };
517 template<typename Scalar>
518 struct functor_traits<scalar_constant_op<Scalar> >
519 // FIXME replace this packet test by a safe one
520 { enum { Cost = 1, PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
521 
522 template<typename Scalar> struct scalar_identity_op {
523  EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)
524  template<typename Index>
525  EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const { return row==col ? Scalar(1) : Scalar(0); }
526 };
527 template<typename Scalar>
528 struct functor_traits<scalar_identity_op<Scalar> >
529 { enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
530 
531 template <typename Scalar, bool RandomAccess> struct linspaced_op_impl;
532 
533 // linear access for packet ops:
534 // 1) initialization
535 // base = [low, ..., low] + ([step, ..., step] * [-size, ..., 0])
536 // 2) each step (where size is 1 for coeff access or PacketSize for packet access)
537 // base += [size*step, ..., size*step]
538 //
539 // TODO: Perhaps it's better to initialize lazily (so not in the constructor but in packetOp)
540 // in order to avoid the padd() in operator() ?
541 template <typename Scalar>
542 struct linspaced_op_impl<Scalar,false>
543 {
544  typedef typename packet_traits<Scalar>::type Packet;
545 
546  linspaced_op_impl(Scalar low, Scalar step) :
547  m_low(low), m_step(step),
548  m_packetStep(pset1<Packet>(packet_traits<Scalar>::size*step)),
549  m_base(padd(pset1<Packet>(low), pmul(pset1<Packet>(step),plset<Scalar>(-packet_traits<Scalar>::size)))) {}
550 
551  template<typename Index>
552  EIGEN_STRONG_INLINE const Scalar operator() (Index i) const
553  {
554  m_base = padd(m_base, pset1<Packet>(m_step));
555  return m_low+i*m_step;
556  }
557 
558  template<typename Index>
559  EIGEN_STRONG_INLINE const Packet packetOp(Index) const { return m_base = padd(m_base,m_packetStep); }
560 
561  const Scalar m_low;
562  const Scalar m_step;
563  const Packet m_packetStep;
564  mutable Packet m_base;
565 };
566 
567 // random access for packet ops:
568 // 1) each step
569 // [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
570 template <typename Scalar>
571 struct linspaced_op_impl<Scalar,true>
572 {
573  typedef typename packet_traits<Scalar>::type Packet;
574 
575  linspaced_op_impl(Scalar low, Scalar step) :
576  m_low(low), m_step(step),
577  m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Scalar>(0)) {}
578 
579  template<typename Index>
580  EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
581 
582  template<typename Index>
583  EIGEN_STRONG_INLINE const Packet packetOp(Index i) const
584  { return internal::padd(m_lowPacket, pmul(m_stepPacket, padd(pset1<Packet>(i),m_interPacket))); }
585 
586  const Scalar m_low;
587  const Scalar m_step;
588  const Packet m_lowPacket;
589  const Packet m_stepPacket;
590  const Packet m_interPacket;
591 };
592 
593 // ----- Linspace functor ----------------------------------------------------------------
594 
595 // Forward declaration (we default to random access which does not really give
596 // us a speed gain when using packet access but it allows to use the functor in
597 // nested expressions).
598 template <typename Scalar, bool RandomAccess = true> struct linspaced_op;
599 template <typename Scalar, bool RandomAccess> struct functor_traits< linspaced_op<Scalar,RandomAccess> >
600 { enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasSetLinear, IsRepeatable = true }; };
601 template <typename Scalar, bool RandomAccess> struct linspaced_op
602 {
603  typedef typename packet_traits<Scalar>::type Packet;
604  linspaced_op(Scalar low, Scalar high, int num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/(num_steps-1))) {}
605 
606  template<typename Index>
607  EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }
608 
609  // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
610  // there row==0 and col is used for the actual iteration.
611  template<typename Index>
612  EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const
613  {
614  eigen_assert(col==0 || row==0);
615  return impl(col + row);
616  }
617 
618  template<typename Index>
619  EIGEN_STRONG_INLINE const Packet packetOp(Index i) const { return impl.packetOp(i); }
620 
621  // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
622  // there row==0 and col is used for the actual iteration.
623  template<typename Index>
624  EIGEN_STRONG_INLINE const Packet packetOp(Index row, Index col) const
625  {
626  eigen_assert(col==0 || row==0);
627  return impl.packetOp(col + row);
628  }
629 
630  // This proxy object handles the actual required temporaries, the different
631  // implementations (random vs. sequential access) as well as the
632  // correct piping to size 2/4 packet operations.
633  const linspaced_op_impl<Scalar,RandomAccess> impl;
634 };
635 
636 // all functors allow linear access, except scalar_identity_op. So we fix here a quick meta
637 // to indicate whether a functor allows linear access, just always answering 'yes' except for
638 // scalar_identity_op.
639 // FIXME move this to functor_traits adding a functor_default
640 template<typename Functor> struct functor_has_linear_access { enum { ret = 1 }; };
641 template<typename Scalar> struct functor_has_linear_access<scalar_identity_op<Scalar> > { enum { ret = 0 }; };
642 
643 // in CwiseBinaryOp, we require the Lhs and Rhs to have the same scalar type, except for multiplication
644 // where we only require them to have the same _real_ scalar type so one may multiply, say, float by complex<float>.
645 // FIXME move this to functor_traits adding a functor_default
646 template<typename Functor> struct functor_allows_mixing_real_and_complex { enum { ret = 0 }; };
647 template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
648 template<typename LhsScalar,typename RhsScalar> struct functor_allows_mixing_real_and_complex<scalar_conj_product_op<LhsScalar,RhsScalar> > { enum { ret = 1 }; };
649 
650 
655 /* If you wonder why doing the pset1() in packetOp() is an optimization check scalar_multiple_op */
656 template<typename Scalar>
657 struct scalar_add_op {
658  typedef typename packet_traits<Scalar>::type Packet;
659  // FIXME default copy constructors seems bugged with std::complex<>
660  inline scalar_add_op(const scalar_add_op& other) : m_other(other.m_other) { }
661  inline scalar_add_op(const Scalar& other) : m_other(other) { }
662  inline Scalar operator() (const Scalar& a) const { return a + m_other; }
663  inline const Packet packetOp(const Packet& a) const
664  { return internal::padd(a, pset1<Packet>(m_other)); }
665  const Scalar m_other;
666 };
667 template<typename Scalar>
668 struct functor_traits<scalar_add_op<Scalar> >
669 { enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasAdd }; };
670 
675 template<typename Scalar> struct scalar_sqrt_op {
676  EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
677  inline const Scalar operator() (const Scalar& a) const { return internal::sqrt(a); }
678  typedef typename packet_traits<Scalar>::type Packet;
679  inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
680 };
681 template<typename Scalar>
682 struct functor_traits<scalar_sqrt_op<Scalar> >
683 { enum {
684  Cost = 5 * NumTraits<Scalar>::MulCost,
685  PacketAccess = packet_traits<Scalar>::HasSqrt
686  };
687 };
688 
693 template<typename Scalar> struct scalar_cos_op {
694  EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)
695  inline Scalar operator() (const Scalar& a) const { return internal::cos(a); }
696  typedef typename packet_traits<Scalar>::type Packet;
697  inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
698 };
699 template<typename Scalar>
700 struct functor_traits<scalar_cos_op<Scalar> >
701 {
702  enum {
703  Cost = 5 * NumTraits<Scalar>::MulCost,
704  PacketAccess = packet_traits<Scalar>::HasCos
705  };
706 };
707 
712 template<typename Scalar> struct scalar_sin_op {
713  EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)
714  inline const Scalar operator() (const Scalar& a) const { return internal::sin(a); }
715  typedef typename packet_traits<Scalar>::type Packet;
716  inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
717 };
718 template<typename Scalar>
719 struct functor_traits<scalar_sin_op<Scalar> >
720 {
721  enum {
722  Cost = 5 * NumTraits<Scalar>::MulCost,
723  PacketAccess = packet_traits<Scalar>::HasSin
724  };
725 };
726 
727 
732 template<typename Scalar> struct scalar_tan_op {
733  EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)
734  inline const Scalar operator() (const Scalar& a) const { return internal::tan(a); }
735  typedef typename packet_traits<Scalar>::type Packet;
736  inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
737 };
738 template<typename Scalar>
739 struct functor_traits<scalar_tan_op<Scalar> >
740 {
741  enum {
742  Cost = 5 * NumTraits<Scalar>::MulCost,
743  PacketAccess = packet_traits<Scalar>::HasTan
744  };
745 };
746 
751 template<typename Scalar> struct scalar_acos_op {
752  EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)
753  inline const Scalar operator() (const Scalar& a) const { return internal::acos(a); }
754  typedef typename packet_traits<Scalar>::type Packet;
755  inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
756 };
757 template<typename Scalar>
758 struct functor_traits<scalar_acos_op<Scalar> >
759 {
760  enum {
761  Cost = 5 * NumTraits<Scalar>::MulCost,
762  PacketAccess = packet_traits<Scalar>::HasACos
763  };
764 };
765 
770 template<typename Scalar> struct scalar_asin_op {
771  EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)
772  inline const Scalar operator() (const Scalar& a) const { return internal::asin(a); }
773  typedef typename packet_traits<Scalar>::type Packet;
774  inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
775 };
776 template<typename Scalar>
777 struct functor_traits<scalar_asin_op<Scalar> >
778 {
779  enum {
780  Cost = 5 * NumTraits<Scalar>::MulCost,
781  PacketAccess = packet_traits<Scalar>::HasASin
782  };
783 };
784 
789 template<typename Scalar>
790 struct scalar_pow_op {
791  // FIXME default copy constructors seems bugged with std::complex<>
792  inline scalar_pow_op(const scalar_pow_op& other) : m_exponent(other.m_exponent) { }
793  inline scalar_pow_op(const Scalar& exponent) : m_exponent(exponent) {}
794  inline Scalar operator() (const Scalar& a) const { return internal::pow(a, m_exponent); }
795  const Scalar m_exponent;
796 };
797 template<typename Scalar>
798 struct functor_traits<scalar_pow_op<Scalar> >
799 { enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
800 
805 template<typename Scalar>
806 struct scalar_inverse_mult_op {
807  scalar_inverse_mult_op(const Scalar& other) : m_other(other) {}
808  inline Scalar operator() (const Scalar& a) const { return m_other / a; }
809  template<typename Packet>
810  inline const Packet packetOp(const Packet& a) const
811  { return internal::pdiv(pset1<Packet>(m_other),a); }
812  Scalar m_other;
813 };
814 
819 template<typename Scalar>
820 struct scalar_inverse_op {
821  EIGEN_EMPTY_STRUCT_CTOR(scalar_inverse_op)
822  inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
823  template<typename Packet>
824  inline const Packet packetOp(const Packet& a) const
825  { return internal::pdiv(pset1<Packet>(Scalar(1)),a); }
826 };
827 template<typename Scalar>
828 struct functor_traits<scalar_inverse_op<Scalar> >
829 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
830 
835 template<typename Scalar>
836 struct scalar_square_op {
837  EIGEN_EMPTY_STRUCT_CTOR(scalar_square_op)
838  inline Scalar operator() (const Scalar& a) const { return a*a; }
839  template<typename Packet>
840  inline const Packet packetOp(const Packet& a) const
841  { return internal::pmul(a,a); }
842 };
843 template<typename Scalar>
844 struct functor_traits<scalar_square_op<Scalar> >
845 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
846 
851 template<typename Scalar>
852 struct scalar_cube_op {
853  EIGEN_EMPTY_STRUCT_CTOR(scalar_cube_op)
854  inline Scalar operator() (const Scalar& a) const { return a*a*a; }
855  template<typename Packet>
856  inline const Packet packetOp(const Packet& a) const
857  { return internal::pmul(a,pmul(a,a)); }
858 };
859 template<typename Scalar>
860 struct functor_traits<scalar_cube_op<Scalar> >
861 { enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
862 
863 // default functor traits for STL functors:
864 
865 template<typename T>
866 struct functor_traits<std::multiplies<T> >
867 { enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
868 
869 template<typename T>
870 struct functor_traits<std::divides<T> >
871 { enum { Cost = NumTraits<T>::MulCost, PacketAccess = false }; };
872 
873 template<typename T>
874 struct functor_traits<std::plus<T> >
875 { enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
876 
877 template<typename T>
878 struct functor_traits<std::minus<T> >
879 { enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
880 
881 template<typename T>
882 struct functor_traits<std::negate<T> >
883 { enum { Cost = NumTraits<T>::AddCost, PacketAccess = false }; };
884 
885 template<typename T>
886 struct functor_traits<std::logical_or<T> >
887 { enum { Cost = 1, PacketAccess = false }; };
888 
889 template<typename T>
890 struct functor_traits<std::logical_and<T> >
891 { enum { Cost = 1, PacketAccess = false }; };
892 
893 template<typename T>
894 struct functor_traits<std::logical_not<T> >
895 { enum { Cost = 1, PacketAccess = false }; };
896 
897 template<typename T>
898 struct functor_traits<std::greater<T> >
899 { enum { Cost = 1, PacketAccess = false }; };
900 
901 template<typename T>
902 struct functor_traits<std::less<T> >
903 { enum { Cost = 1, PacketAccess = false }; };
904 
905 template<typename T>
906 struct functor_traits<std::greater_equal<T> >
907 { enum { Cost = 1, PacketAccess = false }; };
908 
909 template<typename T>
910 struct functor_traits<std::less_equal<T> >
911 { enum { Cost = 1, PacketAccess = false }; };
912 
913 template<typename T>
914 struct functor_traits<std::equal_to<T> >
915 { enum { Cost = 1, PacketAccess = false }; };
916 
917 template<typename T>
918 struct functor_traits<std::not_equal_to<T> >
919 { enum { Cost = 1, PacketAccess = false }; };
920 
921 template<typename T>
922 struct functor_traits<std::binder2nd<T> >
923 { enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
924 
925 template<typename T>
926 struct functor_traits<std::binder1st<T> >
927 { enum { Cost = functor_traits<T>::Cost, PacketAccess = false }; };
928 
929 template<typename T>
930 struct functor_traits<std::unary_negate<T> >
931 { enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
932 
933 template<typename T>
934 struct functor_traits<std::binary_negate<T> >
935 { enum { Cost = 1 + functor_traits<T>::Cost, PacketAccess = false }; };
936 
937 #ifdef EIGEN_STDEXT_SUPPORT
938 
939 template<typename T0,typename T1>
940 struct functor_traits<std::project1st<T0,T1> >
941 { enum { Cost = 0, PacketAccess = false }; };
942 
943 template<typename T0,typename T1>
944 struct functor_traits<std::project2nd<T0,T1> >
945 { enum { Cost = 0, PacketAccess = false }; };
946 
947 template<typename T0,typename T1>
948 struct functor_traits<std::select2nd<std::pair<T0,T1> > >
949 { enum { Cost = 0, PacketAccess = false }; };
950 
951 template<typename T0,typename T1>
952 struct functor_traits<std::select1st<std::pair<T0,T1> > >
953 { enum { Cost = 0, PacketAccess = false }; };
954 
955 template<typename T0,typename T1>
956 struct functor_traits<std::unary_compose<T0,T1> >
957 { enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost, PacketAccess = false }; };
958 
959 template<typename T0,typename T1,typename T2>
960 struct functor_traits<std::binary_compose<T0,T1,T2> >
961 { enum { Cost = functor_traits<T0>::Cost + functor_traits<T1>::Cost + functor_traits<T2>::Cost, PacketAccess = false }; };
962 
963 #endif // EIGEN_STDEXT_SUPPORT
964 
965 // allow to add new functors and specializations of functor_traits from outside Eigen.
966 // this macro is really needed because functor_traits must be specialized after it is declared but before it is used...
967 #ifdef EIGEN_FUNCTORS_PLUGIN
968 #include EIGEN_FUNCTORS_PLUGIN
969 #endif
970 
971 } // end namespace internal
972 
973 } // end namespace Eigen
974 
975 #endif // EIGEN_FUNCTORS_H