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
25namespace Eigen {
26
27typedef EIGEN_DEFAULT_DENSE_INDEX_TYPE DenseIndex;
28
29namespace internal {
30
31//classes inheriting no_assignment_operator don't generate a default operator=.
32class 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 */
39template<typename I1, typename I2>
40struct 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  */
49template<typename T, int Value> class variable_if_dynamic
50{
51  public:
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)); }
54    static T value() { return T(Value); }
55    void setValue(T) {}
56};
57
58template<typename T> class variable_if_dynamic<T, Dynamic>
59{
60    T m_value;
61    variable_if_dynamic() { assert(false); }
62  public:
63    explicit variable_if_dynamic(T value) : m_value(value) {}
64    T value() const { return m_value; }
65    void setValue(T value) { m_value = value; }
66};
67
68/** \internal like variable_if_dynamic but for DynamicIndex
69  */
70template<typename T, int Value> class variable_if_dynamicindex
71{
72  public:
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)); }
75    static T value() { return T(Value); }
76    void setValue(T) {}
77};
78
79template<typename T> class variable_if_dynamicindex<T, DynamicIndex>
80{
81    T m_value;
82    variable_if_dynamicindex() { assert(false); }
83  public:
84    explicit variable_if_dynamicindex(T value) : m_value(value) {}
85    T value() const { return m_value; }
86    void setValue(T value) { m_value = value; }
87};
88
89template<typename T> struct functor_traits
90{
91  enum
92  {
93    Cost = 10,
94    PacketAccess = false,
95    IsRepeatable = false
96  };
97};
98
99template<typename T> struct packet_traits;
100
101template<typename T> struct unpacket_traits
102{
103  typedef T type;
104  enum {size=1};
105};
106
107template<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
127template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
128class 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
161template<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
170template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct plain_matrix_type;
171template<typename T, typename BaseClassType> struct plain_matrix_type_dense;
172template<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
177template<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
188template<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
203template<typename T, typename StorageKind = typename traits<T>::StorageKind> struct eval;
204
205template<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
219template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
220struct eval<Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>, Dense>
221{
222  typedef const Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>& type;
223};
224
225template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
226struct 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 */
235template<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 */
253template<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
270template<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. */
275template <typename T>
276struct 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 */
286template<typename T1, typename T2>
287struct 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  */
316template<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
343template<typename T>
344T* const_cast_ptr(const T* ptr)
345{
346  return const_cast<T*>(ptr);
347}
348
349template<typename Derived, typename XprKind = typename traits<Derived>::XprKind>
350struct 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
355template<typename Derived>
356struct dense_xpr_base<Derived, MatrixXpr>
357{
358  typedef MatrixBase<Derived> type;
359};
360
361template<typename Derived>
362struct 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 */
369template<typename Derived,typename Scalar,typename OtherScalar,
370         bool EnableIt = !is_same<Scalar,OtherScalar>::value >
371struct 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
378template<typename Derived,typename Scalar,typename OtherScalar>
379struct 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
393template<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
402template <typename A, typename B> struct promote_storage_type;
403
404template <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  */
412template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
413struct 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
427template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
428struct 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
442template<typename ExpressionType, typename Scalar = typename ExpressionType::Scalar>
443struct 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
458template<typename ExpressionType>
459struct 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