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_XPRHELPER_H
12 #define EIGEN_XPRHELPER_H
13 
14 // just a workaround because GCC seems to not really like empty structs
15 // FIXME: gcc 4.3 generates bad code when strict-aliasing is enabled
16 // so currently we simply disable this optimization for gcc 4.3
17 #if (defined __GNUG__) && !((__GNUC__==4) && (__GNUC_MINOR__==3))
18   #define EIGEN_EMPTY_STRUCT_CTOR(X) \
19     EIGEN_STRONG_INLINE X() {} \
20     EIGEN_STRONG_INLINE X(const X& ) {}
21 #else
22   #define EIGEN_EMPTY_STRUCT_CTOR(X)
23 #endif
24 
25 namespace Eigen {
26 
27 typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
28 
29 namespace internal {
30 
31 //classes inheriting no_assignment_operator don't generate a default operator=.
32 class no_assignment_operator
33 {
34   private:
35     no_assignment_operator& operator=(const no_assignment_operator&);
36 };
37 
38 /** \internal return the index type with the largest number of bits */
39 template<typename I1, typename I2>
40 struct promote_index_type
41 {
42   typedef typename conditional<(sizeof(I1)<sizeof(I2)), I2, I1>::type type;
43 };
44 
45 /** \internal If the template parameter Value is Dynamic, this class is just a wrapper around a T variable that
46   * can be accessed using value() and setValue().
47   * Otherwise, this class is an empty structure and value() just returns the template parameter Value.
48   */
49 template<typename T, int Value> class variable_if_dynamic
50 {
51   public:
EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamic)52     EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamic)
53     explicit variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
value()54     static T value() { return T(Value); }
setValue(T)55     void setValue(T) {}
56 };
57 
58 template<typename T> class variable_if_dynamic<T, Dynamic>
59 {
60     T m_value;
variable_if_dynamic()61     variable_if_dynamic() { assert(false); }
62   public:
variable_if_dynamic(T value)63     explicit variable_if_dynamic(T value) : m_value(value) {}
value()64     T value() const { return m_value; }
setValue(T value)65     void setValue(T value) { m_value = value; }
66 };
67 
68 /** \internal like variable_if_dynamic but for DynamicIndex
69   */
70 template<typename T, int Value> class variable_if_dynamicindex
71 {
72   public:
EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamicindex)73     EIGEN_EMPTY_STRUCT_CTOR(variable_if_dynamicindex)
74     explicit variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); assert(v == T(Value)); }
value()75     static T value() { return T(Value); }
setValue(T)76     void setValue(T) {}
77 };
78 
79 template<typename T> class variable_if_dynamicindex<T, DynamicIndex>
80 {
81     T m_value;
variable_if_dynamicindex()82     variable_if_dynamicindex() { assert(false); }
83   public:
variable_if_dynamicindex(T value)84     explicit variable_if_dynamicindex(T value) : m_value(value) {}
value()85     T value() const { return m_value; }
setValue(T value)86     void setValue(T value) { m_value = value; }
87 };
88 
89 template<typename T> struct functor_traits
90 {
91   enum
92   {
93     Cost = 10,
94     PacketAccess = false,
95     IsRepeatable = false
96   };
97 };
98 
99 template<typename T> struct packet_traits;
100 
101 template<typename T> struct unpacket_traits
102 {
103   typedef T type;
104   enum {size=1};
105 };
106 
107 template<typename _Scalar, int _Rows, int _Cols,
108          int _Options = AutoAlign |
109                           ( (_Rows==1 && _Cols!=1) ? RowMajor
110                           : (_Cols==1 && _Rows!=1) ? ColMajor
111                           : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),
112          int _MaxRows = _Rows,
113          int _MaxCols = _Cols
114 > class make_proper_matrix_type
115 {
116     enum {
117       IsColVector = _Cols==1 && _Rows!=1,
118       IsRowVector = _Rows==1 && _Cols!=1,
119       Options = IsColVector ? (_Options | ColMajor) & ~RowMajor
120               : IsRowVector ? (_Options | RowMajor) & ~ColMajor
121               : _Options
122     };
123   public:
124     typedef Matrix<_Scalar, _Rows, _Cols, Options, _MaxRows, _MaxCols> type;
125 };
126 
127 template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
128 class compute_matrix_flags
129 {
130     enum {
131       row_major_bit = Options&RowMajor ? RowMajorBit : 0,
132       is_dynamic_size_storage = MaxRows==Dynamic || MaxCols==Dynamic,
133 
134       aligned_bit =
135       (
136             ((Options&DontAlign)==0)
137         && (
138 #if EIGEN_ALIGN_STATICALLY
139              ((!is_dynamic_size_storage) && (((MaxCols*MaxRows*int(sizeof(Scalar))) % 16) == 0))
140 #else
141              0
142 #endif
143 
144           ||
145 
146 #if EIGEN_ALIGN
147              is_dynamic_size_storage
148 #else
149              0
150 #endif
151 
152           )
153       ) ? AlignedBit : 0,
154       packet_access_bit = packet_traits<Scalar>::Vectorizable && aligned_bit ? PacketAccessBit : 0
155     };
156 
157   public:
158     enum { ret = LinearAccessBit | LvalueBit | DirectAccessBit | NestByRefBit | packet_access_bit | row_major_bit | aligned_bit };
159 };
160 
161 template<int _Rows, int _Cols> struct size_at_compile_time
162 {
163   enum { ret = (_Rows==Dynamic || _Cols==Dynamic) ? Dynamic : _Rows * _Cols };
164 };
165 
166 /* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,
167  * whereas eval is a const reference in the case of a matrix
168  */
169 
170 template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;
171 template<typename T, typename BaseClassType> struct plain_matrix_type_dense;
172 template<typename T> struct plain_matrix_type<T,Dense>
173 {
174   typedef typename plain_matrix_type_dense<T,typename traits<T>::XprKind>::type type;
175 };
176 
177 template<typename T> struct plain_matrix_type_dense<T,MatrixXpr>
178 {
179   typedef Matrix<typename traits<T>::Scalar,
180                 traits<T>::RowsAtCompileTime,
181                 traits<T>::ColsAtCompileTime,
182                 AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
183                 traits<T>::MaxRowsAtCompileTime,
184                 traits<T>::MaxColsAtCompileTime
185           > type;
186 };
187 
188 template<typename T> struct plain_matrix_type_dense<T,ArrayXpr>
189 {
190   typedef Array<typename traits<T>::Scalar,
191                 traits<T>::RowsAtCompileTime,
192                 traits<T>::ColsAtCompileTime,
193                 AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
194                 traits<T>::MaxRowsAtCompileTime,
195                 traits<T>::MaxColsAtCompileTime
196           > type;
197 };
198 
199 /* eval : the return type of eval(). For matrices, this is just a const reference
200  * in order to avoid a useless copy
201  */
202 
203 template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval;
204 
205 template<typename T> struct eval<T,Dense>
206 {
207   typedef typename plain_matrix_type<T>::type type;
208 //   typedef typename T::PlainObject type;
209 //   typedef T::Matrix<typename traits<T>::Scalar,
210 //                 traits<T>::RowsAtCompileTime,
211 //                 traits<T>::ColsAtCompileTime,
212 //                 AutoAlign | (traits<T>::Flags&RowMajorBit ? RowMajor : ColMajor),
213 //                 traits<T>::MaxRowsAtCompileTime,
214 //                 traits<T>::MaxColsAtCompileTime
215 //           > type;
216 };
217 
218 // for matrices, no need to evaluate, just use a const reference to avoid a useless copy
219 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
220 struct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
221 {
222   typedef const Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
223 };
224 
225 template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
226 struct eval<Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
227 {
228   typedef const Array<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
229 };
230 
231 
232 
233 /* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major
234  */
235 template<typename T> struct plain_matrix_type_column_major
236 {
237   enum { Rows = traits<T>::RowsAtCompileTime,
238          Cols = traits<T>::ColsAtCompileTime,
239          MaxRows = traits<T>::MaxRowsAtCompileTime,
240          MaxCols = traits<T>::MaxColsAtCompileTime
241   };
242   typedef Matrix<typename traits<T>::Scalar,
243                 Rows,
244                 Cols,
245                 (MaxRows==1&&MaxCols!=1) ? RowMajor : ColMajor,
246                 MaxRows,
247                 MaxCols
248           > type;
249 };
250 
251 /* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major
252  */
253 template<typename T> struct plain_matrix_type_row_major
254 {
255   enum { Rows = traits<T>::RowsAtCompileTime,
256          Cols = traits<T>::ColsAtCompileTime,
257          MaxRows = traits<T>::MaxRowsAtCompileTime,
258          MaxCols = traits<T>::MaxColsAtCompileTime
259   };
260   typedef Matrix<typename traits<T>::Scalar,
261                 Rows,
262                 Cols,
263                 (MaxCols==1&&MaxRows!=1) ? RowMajor : ColMajor,
264                 MaxRows,
265                 MaxCols
266           > type;
267 };
268 
269 // we should be able to get rid of this one too
270 template<typename T> struct must_nest_by_value { enum { ret = false }; };
271 
272 /** \internal The reference selector for template expressions. The idea is that we don't
273   * need to use references for expressions since they are light weight proxy
274   * objects which should generate no copying overhead. */
275 template <typename T>
276 struct ref_selector
277 {
278   typedef typename conditional<
279     bool(traits<T>::Flags & NestByRefBit),
280     T const&,
281     const T
282   >::type type;
283 };
284 
285 /** \internal Adds the const qualifier on the value-type of T2 if and only if T1 is a const type */
286 template<typename T1, typename T2>
287 struct transfer_constness
288 {
289   typedef typename conditional<
290     bool(internal::is_const<T1>::value),
291     typename internal::add_const_on_value_type<T2>::type,
292     T2
293   >::type type;
294 };
295 
296 /** \internal Determines how a given expression should be nested into another one.
297   * For example, when you do a * (b+c), Eigen will determine how the expression b+c should be
298   * nested into the bigger product expression. The choice is between nesting the expression b+c as-is, or
299   * evaluating that expression b+c into a temporary variable d, and nest d so that the resulting expression is
300   * a*d. Evaluating can be beneficial for example if every coefficient access in the resulting expression causes
301   * many coefficient accesses in the nested expressions -- as is the case with matrix product for example.
302   *
303   * \param T the type of the expression being nested
304   * \param n the number of coefficient accesses in the nested expression for each coefficient access in the bigger expression.
305   *
306   * Note that if no evaluation occur, then the constness of T is preserved.
307   *
308   * Example. Suppose that a, b, and c are of type Matrix3d. The user forms the expression a*(b+c).
309   * b+c is an expression "sum of matrices", which we will denote by S. In order to determine how to nest it,
310   * the Product expression uses: nested<S, 3>::ret, which turns out to be Matrix3d because the internal logic of
311   * nested determined that in this case it was better to evaluate the expression b+c into a temporary. On the other hand,
312   * since a is of type Matrix3d, the Product expression nests it as nested<Matrix3d, 3>::ret, which turns out to be
313   * const Matrix3d&, because the internal logic of nested determined that since a was already a matrix, there was no point
314   * in copying it into another matrix.
315   */
316 template<typename T, int n=1, typename PlainObject = typename eval<T>::type> struct nested
317 {
318   enum {
319     // for the purpose of this test, to keep it reasonably simple, we arbitrarily choose a value of Dynamic values.
320     // the choice of 10000 makes it larger than any practical fixed value and even most dynamic values.
321     // in extreme cases where these assumptions would be wrong, we would still at worst suffer performance issues
322     // (poor choice of temporaries).
323     // it's important that this value can still be squared without integer overflowing.
324     DynamicAsInteger = 10000,
325     ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,
326     ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost),
327     CoeffReadCost = traits<T>::CoeffReadCost,
328     CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? int(DynamicAsInteger) : int(CoeffReadCost),
329     NAsInteger = n == Dynamic ? int(DynamicAsInteger) : n,
330     CostEvalAsInteger   = (NAsInteger+1) * ScalarReadCostAsInteger + CoeffReadCostAsInteger,
331     CostNoEvalAsInteger = NAsInteger * CoeffReadCostAsInteger
332   };
333 
334   typedef typename conditional<
335       ( (int(traits<T>::Flags) & EvalBeforeNestingBit) ||
336         int(CostEvalAsInteger) < int(CostNoEvalAsInteger)
337       ),
338       PlainObject,
339       typename ref_selector<T>::type
340   >::type type;
341 };
342 
343 template<typename T>
344 inline T* const_cast_ptr(const T* ptr)
345 {
346   return const_cast<T*>(ptr);
347 }
348 
349 template<typename Derived, typename XprKind = typename traits<Derived>::XprKind>
350 struct dense_xpr_base
351 {
352   /* dense_xpr_base should only ever be used on dense expressions, thus falling either into the MatrixXpr or into the ArrayXpr cases */
353 };
354 
355 template<typename Derived>
356 struct dense_xpr_base<Derived, MatrixXpr>
357 {
358   typedef MatrixBase<Derived> type;
359 };
360 
361 template<typename Derived>
362 struct dense_xpr_base<Derived, ArrayXpr>
363 {
364   typedef ArrayBase<Derived> type;
365 };
366 
367 /** \internal Helper base class to add a scalar multiple operator
368   * overloads for complex types */
369 template<typename Derived,typename Scalar,typename OtherScalar,
370          bool EnableIt = !is_same<Scalar,OtherScalar>::value >
371 struct special_scalar_op_base : public DenseCoeffsBase<Derived>
372 {
373   // dummy operator* so that the
374   // "using special_scalar_op_base::operator*" compiles
375   void operator*() const;
376 };
377 
378 template<typename Derived,typename Scalar,typename OtherScalar>
379 struct special_scalar_op_base<Derived,Scalar,OtherScalar,true>  : public DenseCoeffsBase<Derived>
380 {
381   const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
382   operator*(const OtherScalar& scalar) const
383   {
384     return CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
385       (*static_cast<const Derived*>(this), scalar_multiple2_op<Scalar,OtherScalar>(scalar));
386   }
387 
388   inline friend const CwiseUnaryOp<scalar_multiple2_op<Scalar,OtherScalar>, Derived>
389   operator*(const OtherScalar& scalar, const Derived& matrix)
390   { return static_cast<const special_scalar_op_base&>(matrix).operator*(scalar); }
391 };
392 
393 template<typename XprType, typename CastType> struct cast_return_type
394 {
395   typedef typename XprType::Scalar CurrentScalarType;
396   typedef typename remove_all<CastType>::type _CastType;
397   typedef typename _CastType::Scalar NewScalarType;
398   typedef typename conditional<is_same<CurrentScalarType,NewScalarType>::value,
399                               const XprType&,CastType>::type type;
400 };
401 
402 template <typename A, typename B> struct promote_storage_type;
403 
404 template <typename A> struct promote_storage_type<A,A>
405 {
406   typedef A ret;
407 };
408 
409 /** \internal gives the plain matrix or array type to store a row/column/diagonal of a matrix type.
410   * \param Scalar optional parameter allowing to pass a different scalar type than the one of the MatrixType.
411   */
412 template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
413 struct plain_row_type
414 {
415   typedef Matrix<Scalar, 1, ExpressionType::ColsAtCompileTime,
416                  ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> MatrixRowType;
417   typedef Array<Scalar, 1, ExpressionType::ColsAtCompileTime,
418                  ExpressionType::PlainObject::Options | RowMajor, 1, ExpressionType::MaxColsAtCompileTime> ArrayRowType;
419 
420   typedef typename conditional<
421     is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
422     MatrixRowType,
423     ArrayRowType
424   >::type type;
425 };
426 
427 template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
428 struct plain_col_type
429 {
430   typedef Matrix<Scalar, ExpressionType::RowsAtCompileTime, 1,
431                  ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> MatrixColType;
432   typedef Array<Scalar, ExpressionType::RowsAtCompileTime, 1,
433                  ExpressionType::PlainObject::Options & ~RowMajor, ExpressionType::MaxRowsAtCompileTime, 1> ArrayColType;
434 
435   typedef typename conditional<
436     is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
437     MatrixColType,
438     ArrayColType
439   >::type type;
440 };
441 
442 template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
443 struct plain_diag_type
444 {
445   enum { diag_size = EIGEN_SIZE_MIN_PREFER_DYNAMIC(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime),
446          max_diag_size = EIGEN_SIZE_MIN_PREFER_FIXED(ExpressionType::MaxRowsAtCompileTime, ExpressionType::MaxColsAtCompileTime)
447   };
448   typedef Matrix<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> MatrixDiagType;
449   typedef Array<Scalar, diag_size, 1, ExpressionType::PlainObject::Options & ~RowMajor, max_diag_size, 1> ArrayDiagType;
450 
451   typedef typename conditional<
452     is_same< typename traits<ExpressionType>::XprKind, MatrixXpr >::value,
453     MatrixDiagType,
454     ArrayDiagType
455   >::type type;
456 };
457 
458 template<typename ExpressionType>
459 struct is_lvalue
460 {
461   enum { value = !bool(is_const<ExpressionType>::value) &&
462                  bool(traits<ExpressionType>::Flags & LvalueBit) };
463 };
464 
465 } // end namespace internal
466 
467 } // end namespace Eigen
468 
469 #endif // EIGEN_XPRHELPER_H
470