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 (at) inria.fr> 5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1 (at) 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: 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 58 template<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 */ 70 template<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 79 template<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 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 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
