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DMatEvalExpr.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_EXPRESSIONS_DMATEVALEXPR_H_
36 #define _BLAZE_MATH_EXPRESSIONS_DMATEVALEXPR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <cmath>
60 #include <blaze/util/Assert.h>
62 #include <blaze/util/EnableIf.h>
63 #include <blaze/util/InvalidType.h>
65 #include <blaze/util/SelectType.h>
66 #include <blaze/util/Types.h>
67 
68 
69 namespace blaze {
70 
71 //=================================================================================================
72 //
73 // CLASS DMATEVALEXPR
74 //
75 //=================================================================================================
76 
77 //*************************************************************************************************
84 template< typename MT // Type of the dense matrix
85  , bool SO > // Storage order
86 class DMatEvalExpr : public DenseMatrix< DMatEvalExpr<MT,SO>, SO >
87  , private MatEvalExpr
88  , private Computation
89 {
90  public:
91  //**Type definitions****************************************************************************
93  typedef typename MT::ResultType ResultType;
94  typedef typename MT::OppositeType OppositeType;
95  typedef typename MT::TransposeType TransposeType;
96  typedef typename MT::ElementType ElementType;
97  typedef typename MT::ReturnType ReturnType;
98 
100  typedef const ResultType CompositeType;
101 
103  typedef typename SelectType< IsExpression<MT>::value, const MT, const MT& >::Type Operand;
104  //**********************************************************************************************
105 
106  //**Compilation flags***************************************************************************
108  enum { vectorizable = 0 };
109 
111  enum { smpAssignable = MT::smpAssignable };
112  //**********************************************************************************************
113 
114  //**Constructor*********************************************************************************
119  explicit inline DMatEvalExpr( const MT& dm )
120  : dm_( dm ) // Dense matrix of the evaluation expression
121  {}
122  //**********************************************************************************************
123 
124  //**Access operator*****************************************************************************
131  inline ReturnType operator()( size_t i, size_t j ) const {
132  BLAZE_INTERNAL_ASSERT( i < dm_.rows() , "Invalid row access index" );
133  BLAZE_INTERNAL_ASSERT( j < dm_.columns(), "Invalid column access index" );
134  return dm_(i,j);
135  }
136  //**********************************************************************************************
137 
138  //**Rows function*******************************************************************************
143  inline size_t rows() const {
144  return dm_.rows();
145  }
146  //**********************************************************************************************
147 
148  //**Columns function****************************************************************************
153  inline size_t columns() const {
154  return dm_.columns();
155  }
156  //**********************************************************************************************
157 
158  //**Operand access******************************************************************************
163  inline Operand operand() const {
164  return dm_;
165  }
166  //**********************************************************************************************
167 
168  //**********************************************************************************************
174  template< typename T >
175  inline bool canAlias( const T* alias ) const {
176  return dm_.canAlias( alias );
177  }
178  //**********************************************************************************************
179 
180  //**********************************************************************************************
186  template< typename T >
187  inline bool isAliased( const T* alias ) const {
188  return dm_.isAliased( alias );
189  }
190  //**********************************************************************************************
191 
192  //**********************************************************************************************
197  inline bool isAligned() const {
198  return dm_.isAligned();
199  }
200  //**********************************************************************************************
201 
202  //**********************************************************************************************
207  inline bool canSMPAssign() const {
208  return dm_.canSMPAssign();
209  }
210  //**********************************************************************************************
211 
212  private:
213  //**Member variables****************************************************************************
215  //**********************************************************************************************
216 
217  //**Assignment to dense matrices****************************************************************
229  template< typename MT2 // Type of the target dense matrix
230  , bool SO2 > // Storage order of the target dense matrix
231  friend inline void assign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
232  {
234 
235  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
236  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
237 
238  assign( ~lhs, rhs.dm_ );
239  }
241  //**********************************************************************************************
242 
243  //**Assignment to sparse matrices***************************************************************
255  template< typename MT2 // Type of the target sparse matrix
256  , bool SO2 > // Storage order of the target dense matrix
257  friend inline void assign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
258  {
260 
261  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
262  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
263 
264  assign( ~lhs, rhs.dm_ );
265  }
267  //**********************************************************************************************
268 
269  //**Addition assignment to dense matrices*******************************************************
281  template< typename MT2 // Type of the target dense matrix
282  , bool SO2 > // Storage order of the target dense matrix
283  friend inline void addAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
284  {
286 
287  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
288  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
289 
290  addAssign( ~lhs, rhs.dm_ );
291  }
293  //**********************************************************************************************
294 
295  //**Addition assignment to sparse matrices******************************************************
307  template< typename MT2 // Type of the target sparse matrix
308  , bool SO2 > // Storage order of the target dense matrix
309  friend inline void addAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
310  {
312 
313  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
314  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
315 
316  addAssign( ~lhs, rhs.dm_ );
317  }
319  //**********************************************************************************************
320 
321  //**Subtraction assignment to dense matrices****************************************************
333  template< typename MT2 // Type of the target dense matrix
334  , bool SO2 > // Storage order of the target dense matrix
335  friend inline void subAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
336  {
338 
339  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
340  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
341 
342  subAssign( ~lhs, rhs.dm_ );
343  }
345  //**********************************************************************************************
346 
347  //**Subtraction assignment to sparse matrices***************************************************
359  template< typename MT2 // Type of the target sparse matrix
360  , bool SO2 > // Storage order of the target dense matrix
361  friend inline void subAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
362  {
364 
365  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
366  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
367 
368  subAssign( ~lhs, rhs.dm_ );
369  }
371  //**********************************************************************************************
372 
373  //**Multiplication assignment to dense matrices*************************************************
385  template< typename MT2 // Type of the target dense matrix
386  , bool SO2 > // Storage order of the target dense matrix
387  friend inline void multAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
388  {
390 
391  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
392  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
393 
394  multAssign( ~lhs, rhs.dm_ );
395  }
397  //**********************************************************************************************
398 
399  //**Multiplication assignment to sparse matrices************************************************
411  template< typename MT2 // Type of the target sparse matrix
412  , bool SO2 > // Storage order of the target dense matrix
413  friend inline void multAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
414  {
416 
417  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
418  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
419 
420  multAssign( ~lhs, rhs.dm_ );
421  }
423  //**********************************************************************************************
424 
425  //**SMP assignment to dense matrices************************************************************
437  template< typename MT2 // Type of the target dense matrix
438  , bool SO2 > // Storage order of the target dense matrix
439  friend inline void smpAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
440  {
442 
443  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
444  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
445 
446  smpAssign( ~lhs, rhs.dm_ );
447  }
449  //**********************************************************************************************
450 
451  //**SMP assignment to sparse matrices***********************************************************
463  template< typename MT2 // Type of the target sparse matrix
464  , bool SO2 > // Storage order of the target dense matrix
465  friend inline void smpAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
466  {
468 
469  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
470  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
471 
472  smpAssign( ~lhs, rhs.dm_ );
473  }
475  //**********************************************************************************************
476 
477  //**SMP addition assignment to dense matrices***************************************************
489  template< typename MT2 // Type of the target dense matrix
490  , bool SO2 > // Storage order of the target dense matrix
491  friend inline void smpAddAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
492  {
494 
495  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
496  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
497 
498  smpAddAssign( ~lhs, rhs.dm_ );
499  }
501  //**********************************************************************************************
502 
503  //**SMP addition assignment to sparse matrices**************************************************
515  template< typename MT2 // Type of the target sparse matrix
516  , bool SO2 > // Storage order of the target dense matrix
517  friend inline void smpAddAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
518  {
520 
521  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
522  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
523 
524  smpAddAssign( ~lhs, rhs.dm_ );
525  }
527  //**********************************************************************************************
528 
529  //**SMP subtraction assignment to dense matrices************************************************
541  template< typename MT2 // Type of the target dense matrix
542  , bool SO2 > // Storage order of the target dense matrix
543  friend inline void smpSubAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
544  {
546 
547  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
548  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
549 
550  smpSubAssign( ~lhs, rhs.dm_ );
551  }
553  //**********************************************************************************************
554 
555  //**SMP subtraction assignment to sparse matrices***********************************************
567  template< typename MT2 // Type of the target sparse matrix
568  , bool SO2 > // Storage order of the target dense matrix
569  friend inline void smpSubAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
570  {
572 
573  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
574  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
575 
576  smpSubAssign( ~lhs, rhs.dm_ );
577  }
579  //**********************************************************************************************
580 
581  //**SMP multiplication assignment to dense matrices*********************************************
594  template< typename MT2 // Type of the target dense matrix
595  , bool SO2 > // Storage order of the target dense matrix
596  friend inline void smpMultAssign( DenseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
597  {
599 
600  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
601  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
602 
603  smpMultAssign( ~lhs, rhs.dm_ );
604  }
606  //**********************************************************************************************
607 
608  //**SMP multiplication assignment to sparse matrices********************************************
621  template< typename MT2 // Type of the target sparse matrix
622  , bool SO2 > // Storage order of the target dense matrix
623  friend inline void smpMultAssign( SparseMatrix<MT2,SO2>& lhs, const DMatEvalExpr& rhs )
624  {
626 
627  BLAZE_INTERNAL_ASSERT( (~lhs).rows() == rhs.rows() , "Invalid number of rows" );
628  BLAZE_INTERNAL_ASSERT( (~lhs).columns() == rhs.columns(), "Invalid number of columns" );
629 
630  smpMultAssign( ~lhs, rhs.dm_ );
631  }
633  //**********************************************************************************************
634 
635  //**Compile time checks*************************************************************************
640  //**********************************************************************************************
641 };
642 //*************************************************************************************************
643 
644 
645 
646 
647 //=================================================================================================
648 //
649 // GLOBAL FUNCTIONS
650 //
651 //=================================================================================================
652 
653 //*************************************************************************************************
670 template< typename MT // Type of the dense matrix
671  , bool SO > // Storage order
672 inline const DMatEvalExpr<MT,SO> eval( const DenseMatrix<MT,SO>& dm )
673 {
675 
676  return DMatEvalExpr<MT,SO>( ~dm );
677 }
678 //*************************************************************************************************
679 
680 
681 
682 
683 //=================================================================================================
684 //
685 // GLOBAL RESTRUCTURING FUNCTIONS
686 //
687 //=================================================================================================
688 
689 //*************************************************************************************************
700 template< typename MT // Type of the dense matrix
701  , bool SO > // Storage order
702 inline const DMatEvalExpr<MT,SO> eval( const DMatEvalExpr<MT,SO>& dm )
703 {
704  return dm;
705 }
707 //*************************************************************************************************
708 
709 
710 
711 
712 //=================================================================================================
713 //
714 // EXPRESSION TRAIT SPECIALIZATIONS
715 //
716 //=================================================================================================
717 
718 //*************************************************************************************************
720 template< typename MT >
721 struct DMatEvalExprTrait< DMatEvalExpr<MT,false> >
722 {
723  public:
724  //**********************************************************************************************
725  typedef typename SelectType< IsDenseMatrix<MT>::value && IsRowMajorMatrix<MT>::value
726  , DMatEvalExpr<MT,false>
727  , INVALID_TYPE >::Type Type;
728  //**********************************************************************************************
729 };
731 //*************************************************************************************************
732 
733 
734 //*************************************************************************************************
736 template< typename MT >
737 struct TDMatEvalExprTrait< DMatEvalExpr<MT,true> >
738 {
739  public:
740  //**********************************************************************************************
741  typedef typename SelectType< IsDenseMatrix<MT>::value && IsColumnMajorMatrix<MT>::value
742  , DMatEvalExpr<MT,true>
743  , INVALID_TYPE >::Type Type;
744  //**********************************************************************************************
745 };
747 //*************************************************************************************************
748 
749 
750 //*************************************************************************************************
752 template< typename MT, bool SO, bool AF >
753 struct SubmatrixExprTrait< DMatEvalExpr<MT,SO>, AF >
754 {
755  public:
756  //**********************************************************************************************
757  typedef typename EvalExprTrait< typename SubmatrixExprTrait<const MT,AF>::Type >::Type Type;
758  //**********************************************************************************************
759 };
761 //*************************************************************************************************
762 
763 
764 //*************************************************************************************************
766 template< typename MT, bool SO >
767 struct RowExprTrait< DMatEvalExpr<MT,SO> >
768 {
769  public:
770  //**********************************************************************************************
771  typedef typename EvalExprTrait< typename RowExprTrait<const MT>::Type >::Type Type;
772  //**********************************************************************************************
773 };
775 //*************************************************************************************************
776 
777 
778 //*************************************************************************************************
780 template< typename MT, bool SO >
781 struct ColumnExprTrait< DMatEvalExpr<MT,SO> >
782 {
783  public:
784  //**********************************************************************************************
785  typedef typename EvalExprTrait< typename ColumnExprTrait<const MT>::Type >::Type Type;
786  //**********************************************************************************************
787 };
789 //*************************************************************************************************
790 
791 } // namespace blaze
792 
793 #endif
Header file for the DMatEvalExprTrait class template.
void smpSubAssign(DenseMatrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP subtraction assignment of a matrix to dense matrix.
Definition: DenseMatrix.h:152
#define BLAZE_CONSTRAINT_MUST_BE_MATRIX_WITH_STORAGE_ORDER(T, SO)
Constraint on the data type.In case the given data type T is not a dense or sparse matrix type and in...
Definition: StorageOrder.h:242
size_t rows() const
Returns the current number of rows of the matrix.
Definition: DMatEvalExpr.h:143
#define BLAZE_CONSTRAINT_MUST_BE_DENSE_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is not a dense, N-dimensional matrix type...
Definition: DenseMatrix.h:79
void smpMultAssign(DenseVector< VT1, TF1 > &lhs, const Vector< VT2, TF2 > &rhs)
Default implementation of the SMP multiplication assignment of a vector to a dense vector...
Definition: DenseVector.h:179
Header file for the ColumnExprTrait class template.
Header file for the IsColumnMajorMatrix type trait.
Header file for the MatEvalExpr base class.
Header file for the Computation base class.
CompressedMatrix< Type, false > OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: CompressedMatrix.h:2404
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:70
Base class for sparse matrices.The SparseMatrix class is a base class for all sparse matrix classes...
Definition: Forward.h:107
Constraint on the data type.
Operand operand() const
Returns the dense matrix operand.
Definition: DMatEvalExpr.h:163
Constraint on the data type.
void smpAddAssign(DenseMatrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP addition assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:122
DMatEvalExpr< MT, SO > This
Type of this DMatEvalExpr instance.
Definition: DMatEvalExpr.h:92
SelectType< IsExpression< MT >::value, const MT, const MT & >::Type Operand
Composite data type of the dense matrix expression.
Definition: DMatEvalExpr.h:103
Compile time type selection.The SelectType class template selects one of the two given types T1 and T...
Definition: SelectType.h:59
DMatEvalExpr(const MT &dm)
Constructor for the DMatEvalExpr class.
Definition: DMatEvalExpr.h:119
bool isAligned() const
Returns whether the operands of the expression are properly aligned in memory.
Definition: DMatEvalExpr.h:197
Header file for the DenseMatrix base class.
void assign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the assignment of a matrix to a matrix.
Definition: Matrix.h:271
MT::OppositeType OppositeType
Result type with opposite storage order for expression template evaluations.
Definition: DMatEvalExpr.h:94
const ResultType CompositeType
Data type for composite expression templates.
Definition: DMatEvalExpr.h:100
CompressedMatrix< Type, false > TransposeType
Transpose type for expression template evaluations.
Definition: CompressedMatrix.h:2405
Constraints on the storage order of matrix types.
Type ElementType
Type of the sparse matrix elements.
Definition: CompressedMatrix.h:2406
void multAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the multiplication assignment of a matrix to a matrix.
Definition: Matrix.h:361
bool canAlias(const T *alias) const
Returns whether the expression can alias with the given address alias.
Definition: DMatEvalExpr.h:175
Header file for the SelectType class template.
Header file for the RowExprTrait class template.
Header file for all forward declarations for expression class templates.
Header file for the IsDenseMatrix type trait.
Header file for the EnableIf class template.
Operand dm_
Dense matrix of the evaluation expression.
Definition: DMatEvalExpr.h:214
void smpAssign(DenseMatrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the SMP assignment of a matrix to a dense matrix.
Definition: DenseMatrix.h:92
MT::ReturnType ReturnType
Return type for expression template evaluations.
Definition: DMatEvalExpr.h:97
MT::ElementType ElementType
Resulting element type.
Definition: DMatEvalExpr.h:96
Header file for the SubmatrixExprTrait class template.
const Type & ReturnType
Return type for expression template evaluations.
Definition: CompressedMatrix.h:2407
Header file for run time assertion macros.
Utility type for generic codes.
void addAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the addition assignment of a matrix to a matrix.
Definition: Matrix.h:301
Header file for the EvalExprTrait class template.
Base class for all matrix evaluation expression templates.The MatEvalExpr class serves as a tag for a...
Definition: MatEvalExpr.h:65
void subAssign(Matrix< MT1, SO1 > &lhs, const Matrix< MT2, SO2 > &rhs)
Default implementation of the subtraction assignment of a matrix to matrix.
Definition: Matrix.h:331
bool isAliased(const T *alias) const
Returns whether the expression is aliased with the given address alias.
Definition: DMatEvalExpr.h:187
const DMatEvalExpr< MT, SO > eval(const DenseMatrix< MT, SO > &dm)
Forces the evaluation of the given dense matrix expression dm.
Definition: DMatEvalExpr.h:672
Header file for the IsRowMajorMatrix type trait.
MT::TransposeType TransposeType
Transpose type for expression template evaluations.
Definition: DMatEvalExpr.h:95
Expression object for the forced evaluation of dense matrices.The DMatEvalExpr class represents the c...
Definition: DMatEvalExpr.h:86
Base class for all compute expression templates.The Computation class serves as a tag for all computa...
Definition: Computation.h:59
bool canSMPAssign() const
Returns whether the expression can be used in SMP assignments.
Definition: DMatEvalExpr.h:207
#define BLAZE_FUNCTION_TRACE
Function trace macro.This macro can be used to reliably trace function calls. In case function tracin...
Definition: FunctionTrace.h:157
Header file for the TDMatEvalExprTrait class template.
This ResultType
Result type for expression template evaluations.
Definition: CompressedMatrix.h:2403
Header file for basic type definitions.
size_t columns() const
Returns the current number of columns of the matrix.
Definition: DMatEvalExpr.h:153
ReturnType operator()(size_t i, size_t j) const
2D-access to the matrix elements.
Definition: DMatEvalExpr.h:131
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression, the program execution is terminated. The BLAZE_INTERNAL_ASSERT macro can be disabled by setting the BLAZE_USER_ASSERTION flag to zero or by defining NDEBUG during the compilation.
Definition: Assert.h:101
MT::ResultType ResultType
Result type for expression template evaluations.
Definition: DMatEvalExpr.h:93
Header file for the IsExpression type trait class.
Header file for the FunctionTrace class.