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_REDUX_H
12#define EIGEN_REDUX_H
13
14namespace Eigen {
15
16namespace internal {
17
18// TODO
19// * implement other kind of vectorization
20// * factorize code
21
22/***************************************************************************
23* Part 1 : the logic deciding a strategy for vectorization and unrolling
24***************************************************************************/
25
26template<typename Func, typename Derived>
27struct redux_traits
28{
29public:
30 typedef typename find_best_packet<typename Derived::Scalar,Derived::SizeAtCompileTime>::type PacketType;
31 enum {
32 PacketSize = unpacket_traits<PacketType>::size,
33 InnerMaxSize = int(Derived::IsRowMajor)
34 ? Derived::MaxColsAtCompileTime
35 : Derived::MaxRowsAtCompileTime
36 };
37
38 enum {
39 MightVectorize = (int(Derived::Flags)&ActualPacketAccessBit)
40 && (functor_traits<Func>::PacketAccess),
41 MayLinearVectorize = bool(MightVectorize) && (int(Derived::Flags)&LinearAccessBit),
42 MaySliceVectorize = bool(MightVectorize) && int(InnerMaxSize)>=3*PacketSize
43 };
44
45public:
46 enum {
47 Traversal = int(MayLinearVectorize) ? int(LinearVectorizedTraversal)
48 : int(MaySliceVectorize) ? int(SliceVectorizedTraversal)
49 : int(DefaultTraversal)
50 };
51
52public:
53 enum {
54 Cost = Derived::SizeAtCompileTime == Dynamic ? HugeCost
55 : Derived::SizeAtCompileTime * Derived::CoeffReadCost + (Derived::SizeAtCompileTime-1) * functor_traits<Func>::Cost,
56 UnrollingLimit = EIGEN_UNROLLING_LIMIT * (int(Traversal) == int(DefaultTraversal) ? 1 : int(PacketSize))
57 };
58
59public:
60 enum {
61 Unrolling = Cost <= UnrollingLimit ? CompleteUnrolling : NoUnrolling
62 };
63
64#ifdef EIGEN_DEBUG_ASSIGN
65 static void debug()
66 {
67 std::cerr << "Xpr: " << typeid(typename Derived::XprType).name() << std::endl;
68 std::cerr.setf(std::ios::hex, std::ios::basefield);
69 EIGEN_DEBUG_VAR(Derived::Flags)
70 std::cerr.unsetf(std::ios::hex);
71 EIGEN_DEBUG_VAR(InnerMaxSize)
72 EIGEN_DEBUG_VAR(PacketSize)
73 EIGEN_DEBUG_VAR(MightVectorize)
74 EIGEN_DEBUG_VAR(MayLinearVectorize)
75 EIGEN_DEBUG_VAR(MaySliceVectorize)
76 EIGEN_DEBUG_VAR(Traversal)
77 EIGEN_DEBUG_VAR(UnrollingLimit)
78 EIGEN_DEBUG_VAR(Unrolling)
79 std::cerr << std::endl;
80 }
81#endif
82};
83
84/***************************************************************************
85* Part 2 : unrollers
86***************************************************************************/
87
88/*** no vectorization ***/
89
90template<typename Func, typename Derived, int Start, int Length>
91struct redux_novec_unroller
92{
93 enum {
94 HalfLength = Length/2
95 };
96
97 typedef typename Derived::Scalar Scalar;
98
99 EIGEN_DEVICE_FUNC
100 static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)
101 {
102 return func(redux_novec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
103 redux_novec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func));
104 }
105};
106
107template<typename Func, typename Derived, int Start>
108struct redux_novec_unroller<Func, Derived, Start, 1>
109{
110 enum {
111 outer = Start / Derived::InnerSizeAtCompileTime,
112 inner = Start % Derived::InnerSizeAtCompileTime
113 };
114
115 typedef typename Derived::Scalar Scalar;
116
117 EIGEN_DEVICE_FUNC
118 static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func&)
119 {
120 return mat.coeffByOuterInner(outer, inner);
121 }
122};
123
124// This is actually dead code and will never be called. It is required
125// to prevent false warnings regarding failed inlining though
126// for 0 length run() will never be called at all.
127template<typename Func, typename Derived, int Start>
128struct redux_novec_unroller<Func, Derived, Start, 0>
129{
130 typedef typename Derived::Scalar Scalar;
131 EIGEN_DEVICE_FUNC
132 static EIGEN_STRONG_INLINE Scalar run(const Derived&, const Func&) { return Scalar(); }
133};
134
135/*** vectorization ***/
136
137template<typename Func, typename Derived, int Start, int Length>
138struct redux_vec_unroller
139{
140 enum {
141 PacketSize = redux_traits<Func, Derived>::PacketSize,
142 HalfLength = Length/2
143 };
144
145 typedef typename Derived::Scalar Scalar;
146 typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;
147
148 static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func& func)
149 {
150 return func.packetOp(
151 redux_vec_unroller<Func, Derived, Start, HalfLength>::run(mat,func),
152 redux_vec_unroller<Func, Derived, Start+HalfLength, Length-HalfLength>::run(mat,func) );
153 }
154};
155
156template<typename Func, typename Derived, int Start>
157struct redux_vec_unroller<Func, Derived, Start, 1>
158{
159 enum {
160 index = Start * redux_traits<Func, Derived>::PacketSize,
161 outer = index / int(Derived::InnerSizeAtCompileTime),
162 inner = index % int(Derived::InnerSizeAtCompileTime),
163 alignment = Derived::Alignment
164 };
165
166 typedef typename Derived::Scalar Scalar;
167 typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;
168
169 static EIGEN_STRONG_INLINE PacketScalar run(const Derived &mat, const Func&)
170 {
171 return mat.template packetByOuterInner<alignment,PacketScalar>(outer, inner);
172 }
173};
174
175/***************************************************************************
176* Part 3 : implementation of all cases
177***************************************************************************/
178
179template<typename Func, typename Derived,
180 int Traversal = redux_traits<Func, Derived>::Traversal,
181 int Unrolling = redux_traits<Func, Derived>::Unrolling
182>
183struct redux_impl;
184
185template<typename Func, typename Derived>
186struct redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>
187{
188 typedef typename Derived::Scalar Scalar;
189 EIGEN_DEVICE_FUNC
190 static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)
191 {
192 eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
193 Scalar res;
194 res = mat.coeffByOuterInner(0, 0);
195 for(Index i = 1; i < mat.innerSize(); ++i)
196 res = func(res, mat.coeffByOuterInner(0, i));
197 for(Index i = 1; i < mat.outerSize(); ++i)
198 for(Index j = 0; j < mat.innerSize(); ++j)
199 res = func(res, mat.coeffByOuterInner(i, j));
200 return res;
201 }
202};
203
204template<typename Func, typename Derived>
205struct redux_impl<Func,Derived, DefaultTraversal, CompleteUnrolling>
206 : public redux_novec_unroller<Func,Derived, 0, Derived::SizeAtCompileTime>
207{};
208
209template<typename Func, typename Derived>
210struct redux_impl<Func, Derived, LinearVectorizedTraversal, NoUnrolling>
211{
212 typedef typename Derived::Scalar Scalar;
213 typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;
214
215 static Scalar run(const Derived &mat, const Func& func)
216 {
217 const Index size = mat.size();
218
219 const Index packetSize = redux_traits<Func, Derived>::PacketSize;
220 const int packetAlignment = unpacket_traits<PacketScalar>::alignment;
221 enum {
222 alignment0 = (bool(Derived::Flags & DirectAccessBit) && bool(packet_traits<Scalar>::AlignedOnScalar)) ? int(packetAlignment) : int(Unaligned),
223 alignment = EIGEN_PLAIN_ENUM_MAX(alignment0, Derived::Alignment)
224 };
225 const Index alignedStart = internal::first_default_aligned(mat.nestedExpression());
226 const Index alignedSize2 = ((size-alignedStart)/(2*packetSize))*(2*packetSize);
227 const Index alignedSize = ((size-alignedStart)/(packetSize))*(packetSize);
228 const Index alignedEnd2 = alignedStart + alignedSize2;
229 const Index alignedEnd = alignedStart + alignedSize;
230 Scalar res;
231 if(alignedSize)
232 {
233 PacketScalar packet_res0 = mat.template packet<alignment,PacketScalar>(alignedStart);
234 if(alignedSize>packetSize) // we have at least two packets to partly unroll the loop
235 {
236 PacketScalar packet_res1 = mat.template packet<alignment,PacketScalar>(alignedStart+packetSize);
237 for(Index index = alignedStart + 2*packetSize; index < alignedEnd2; index += 2*packetSize)
238 {
239 packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment,PacketScalar>(index));
240 packet_res1 = func.packetOp(packet_res1, mat.template packet<alignment,PacketScalar>(index+packetSize));
241 }
242
243 packet_res0 = func.packetOp(packet_res0,packet_res1);
244 if(alignedEnd>alignedEnd2)
245 packet_res0 = func.packetOp(packet_res0, mat.template packet<alignment,PacketScalar>(alignedEnd2));
246 }
247 res = func.predux(packet_res0);
248
249 for(Index index = 0; index < alignedStart; ++index)
250 res = func(res,mat.coeff(index));
251
252 for(Index index = alignedEnd; index < size; ++index)
253 res = func(res,mat.coeff(index));
254 }
255 else // too small to vectorize anything.
256 // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
257 {
258 res = mat.coeff(0);
259 for(Index index = 1; index < size; ++index)
260 res = func(res,mat.coeff(index));
261 }
262
263 return res;
264 }
265};
266
267// NOTE: for SliceVectorizedTraversal we simply bypass unrolling
268template<typename Func, typename Derived, int Unrolling>
269struct redux_impl<Func, Derived, SliceVectorizedTraversal, Unrolling>
270{
271 typedef typename Derived::Scalar Scalar;
272 typedef typename redux_traits<Func, Derived>::PacketType PacketType;
273
274 EIGEN_DEVICE_FUNC static Scalar run(const Derived &mat, const Func& func)
275 {
276 eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
277 const Index innerSize = mat.innerSize();
278 const Index outerSize = mat.outerSize();
279 enum {
280 packetSize = redux_traits<Func, Derived>::PacketSize
281 };
282 const Index packetedInnerSize = ((innerSize)/packetSize)*packetSize;
283 Scalar res;
284 if(packetedInnerSize)
285 {
286 PacketType packet_res = mat.template packet<Unaligned,PacketType>(0,0);
287 for(Index j=0; j<outerSize; ++j)
288 for(Index i=(j==0?packetSize:0); i<packetedInnerSize; i+=Index(packetSize))
289 packet_res = func.packetOp(packet_res, mat.template packetByOuterInner<Unaligned,PacketType>(j,i));
290
291 res = func.predux(packet_res);
292 for(Index j=0; j<outerSize; ++j)
293 for(Index i=packetedInnerSize; i<innerSize; ++i)
294 res = func(res, mat.coeffByOuterInner(j,i));
295 }
296 else // too small to vectorize anything.
297 // since this is dynamic-size hence inefficient anyway for such small sizes, don't try to optimize.
298 {
299 res = redux_impl<Func, Derived, DefaultTraversal, NoUnrolling>::run(mat, func);
300 }
301
302 return res;
303 }
304};
305
306template<typename Func, typename Derived>
307struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
308{
309 typedef typename Derived::Scalar Scalar;
310
311 typedef typename redux_traits<Func, Derived>::PacketType PacketScalar;
312 enum {
313 PacketSize = redux_traits<Func, Derived>::PacketSize,
314 Size = Derived::SizeAtCompileTime,
315 VectorizedSize = (Size / PacketSize) * PacketSize
316 };
317 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Scalar run(const Derived &mat, const Func& func)
318 {
319 eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
320 if (VectorizedSize > 0) {
321 Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
322 if (VectorizedSize != Size)
323 res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
324 return res;
325 }
326 else {
327 return redux_novec_unroller<Func, Derived, 0, Size>::run(mat,func);
328 }
329 }
330};
331
332// evaluator adaptor
333template<typename _XprType>
334class redux_evaluator
335{
336public:
337 typedef _XprType XprType;
338 EIGEN_DEVICE_FUNC explicit redux_evaluator(const XprType &xpr) : m_evaluator(xpr), m_xpr(xpr) {}
339
340 typedef typename XprType::Scalar Scalar;
341 typedef typename XprType::CoeffReturnType CoeffReturnType;
342 typedef typename XprType::PacketScalar PacketScalar;
343 typedef typename XprType::PacketReturnType PacketReturnType;
344
345 enum {
346 MaxRowsAtCompileTime = XprType::MaxRowsAtCompileTime,
347 MaxColsAtCompileTime = XprType::MaxColsAtCompileTime,
348 // TODO we should not remove DirectAccessBit and rather find an elegant way to query the alignment offset at runtime from the evaluator
349 Flags = evaluator<XprType>::Flags & ~DirectAccessBit,
350 IsRowMajor = XprType::IsRowMajor,
351 SizeAtCompileTime = XprType::SizeAtCompileTime,
352 InnerSizeAtCompileTime = XprType::InnerSizeAtCompileTime,
353 CoeffReadCost = evaluator<XprType>::CoeffReadCost,
354 Alignment = evaluator<XprType>::Alignment
355 };
356
357 EIGEN_DEVICE_FUNC Index rows() const { return m_xpr.rows(); }
358 EIGEN_DEVICE_FUNC Index cols() const { return m_xpr.cols(); }
359 EIGEN_DEVICE_FUNC Index size() const { return m_xpr.size(); }
360 EIGEN_DEVICE_FUNC Index innerSize() const { return m_xpr.innerSize(); }
361 EIGEN_DEVICE_FUNC Index outerSize() const { return m_xpr.outerSize(); }
362
363 EIGEN_DEVICE_FUNC
364 CoeffReturnType coeff(Index row, Index col) const
365 { return m_evaluator.coeff(row, col); }
366
367 EIGEN_DEVICE_FUNC
368 CoeffReturnType coeff(Index index) const
369 { return m_evaluator.coeff(index); }
370
371 template<int LoadMode, typename PacketType>
372 PacketType packet(Index row, Index col) const
373 { return m_evaluator.template packet<LoadMode,PacketType>(row, col); }
374
375 template<int LoadMode, typename PacketType>
376 PacketType packet(Index index) const
377 { return m_evaluator.template packet<LoadMode,PacketType>(index); }
378
379 EIGEN_DEVICE_FUNC
380 CoeffReturnType coeffByOuterInner(Index outer, Index inner) const
381 { return m_evaluator.coeff(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }
382
383 template<int LoadMode, typename PacketType>
384 PacketType packetByOuterInner(Index outer, Index inner) const
385 { return m_evaluator.template packet<LoadMode,PacketType>(IsRowMajor ? outer : inner, IsRowMajor ? inner : outer); }
386
387 const XprType & nestedExpression() const { return m_xpr; }
388
389protected:
390 internal::evaluator<XprType> m_evaluator;
391 const XprType &m_xpr;
392};
393
394} // end namespace internal
395
396/***************************************************************************
397* Part 4 : public API
398***************************************************************************/
399
400
401/** \returns the result of a full redux operation on the whole matrix or vector using \a func
402 *
403 * The template parameter \a BinaryOp is the type of the functor \a func which must be
404 * an associative operator. Both current C++98 and C++11 functor styles are handled.
405 *
406 * \sa DenseBase::sum(), DenseBase::minCoeff(), DenseBase::maxCoeff(), MatrixBase::colwise(), MatrixBase::rowwise()
407 */
408template<typename Derived>
409template<typename Func>
410EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
411DenseBase<Derived>::redux(const Func& func) const
412{
413 eigen_assert(this->rows()>0 && this->cols()>0 && "you are using an empty matrix");
414
415 typedef typename internal::redux_evaluator<Derived> ThisEvaluator;
416 ThisEvaluator thisEval(derived());
417
418 return internal::redux_impl<Func, ThisEvaluator>::run(thisEval, func);
419}
420
421/** \returns the minimum of all coefficients of \c *this.
422 * \warning the result is undefined if \c *this contains NaN.
423 */
424template<typename Derived>
425EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
426DenseBase<Derived>::minCoeff() const
427{
428 return derived().redux(Eigen::internal::scalar_min_op<Scalar,Scalar>());
429}
430
431/** \returns the maximum of all coefficients of \c *this.
432 * \warning the result is undefined if \c *this contains NaN.
433 */
434template<typename Derived>
435EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
436DenseBase<Derived>::maxCoeff() const
437{
438 return derived().redux(Eigen::internal::scalar_max_op<Scalar,Scalar>());
439}
440
441/** \returns the sum of all coefficients of \c *this
442 *
443 * If \c *this is empty, then the value 0 is returned.
444 *
445 * \sa trace(), prod(), mean()
446 */
447template<typename Derived>
448EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
449DenseBase<Derived>::sum() const
450{
451 if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
452 return Scalar(0);
453 return derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>());
454}
455
456/** \returns the mean of all coefficients of *this
457*
458* \sa trace(), prod(), sum()
459*/
460template<typename Derived>
461EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
462DenseBase<Derived>::mean() const
463{
464#ifdef __INTEL_COMPILER
465 #pragma warning push
466 #pragma warning ( disable : 2259 )
467#endif
468 return Scalar(derived().redux(Eigen::internal::scalar_sum_op<Scalar,Scalar>())) / Scalar(this->size());
469#ifdef __INTEL_COMPILER
470 #pragma warning pop
471#endif
472}
473
474/** \returns the product of all coefficients of *this
475 *
476 * Example: \include MatrixBase_prod.cpp
477 * Output: \verbinclude MatrixBase_prod.out
478 *
479 * \sa sum(), mean(), trace()
480 */
481template<typename Derived>
482EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
483DenseBase<Derived>::prod() const
484{
485 if(SizeAtCompileTime==0 || (SizeAtCompileTime==Dynamic && size()==0))
486 return Scalar(1);
487 return derived().redux(Eigen::internal::scalar_product_op<Scalar>());
488}
489
490/** \returns the trace of \c *this, i.e. the sum of the coefficients on the main diagonal.
491 *
492 * \c *this can be any matrix, not necessarily square.
493 *
494 * \sa diagonal(), sum()
495 */
496template<typename Derived>
497EIGEN_STRONG_INLINE typename internal::traits<Derived>::Scalar
498MatrixBase<Derived>::trace() const
499{
500 return derived().diagonal().sum();
501}
502
503} // end namespace Eigen
504
505#endif // EIGEN_REDUX_H
506