text: //=================================================================================================
  /*!
  //  \file blaze/math/expressions/DMatDMatEqualExpr.h
  //  \brief Header file for the dense matrix/dense matrix equality comparison expression
  //
  //  Copyright (C) 2012-2018 Klaus Iglberger - All Rights Reserved
  //
  //  This file is part of the Blaze library. You can redistribute it and/or modify it under
  //  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
  //  forms, with or without modification, are permitted provided that the following conditions
  //  are met:
  //
  //  1. Redistributions of source code must retain the above copyright notice, this list of
  //     conditions and the following disclaimer.
  //  2. Redistributions in binary form must reproduce the above copyright notice, this list
  //     of conditions and the following disclaimer in the documentation and/or other materials
  //     provided with the distribution.
  //  3. Neither the names of the Blaze development group nor the names of its contributors
  //     may be used to endorse or promote products derived from this software without specific
  //     prior written permission.
  //
  //  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
  //  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  //  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
  //  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  //  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
  //  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
  //  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  //  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  //  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
  //  DAMAGE.
  */
  //=================================================================================================
  
  #ifndef _BLAZE_MATH_EXPRESSIONS_DMATDMATEQUALEXPR_H_
  #define _BLAZE_MATH_EXPRESSIONS_DMATDMATEQUALEXPR_H_
  
  
  //*************************************************************************************************
  // Includes
  //*************************************************************************************************
  
  #include <blaze/math/Aliases.h>
  #include <blaze/math/expressions/DenseMatrix.h>
  #include <blaze/math/RelaxationFlag.h>
  #include <blaze/math/shims/Equal.h>
  #include <blaze/math/SIMD.h>
  #include <blaze/math/typetraits/HasSIMDEqual.h>
  #include <blaze/math/typetraits/IsPadded.h>
  #include <blaze/system/Blocking.h>
  #include <blaze/system/Optimizations.h>
  #include <blaze/util/DisableIf.h>
  #include <blaze/util/EnableIf.h>
  #include <blaze/util/Types.h>
  #include <blaze/util/typetraits/RemoveReference.h>
  
  
  namespace blaze {
  
  //=================================================================================================
  //
  //  CLASS DEFINITION
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Auxiliary helper struct for the dense matrix/dense matrix equality comparison.
  // \ingroup dense_matrix
  */
  template< typename MT1    // Type of the left-hand side dense matrix
          , typename MT2 >  // Type of the right-hand side dense matrix
  struct DMatDMatEqualExprHelper
  {
     //**Type definitions****************************************************************************
     //! Composite type of the left-hand side dense matrix expression.
     using CT1 = RemoveReference_t< CompositeType_t<MT1> >;
  
     //! Composite type of the right-hand side dense matrix expression.
     using CT2 = RemoveReference_t< CompositeType_t<MT2> >;
     //**********************************************************************************************
  
     //**********************************************************************************************
     static constexpr bool value =
        ( useOptimizedKernels &&
          CT1::simdEnabled &&
          CT2::simdEnabled &&
          HasSIMDEqual_v< ElementType_t<CT1>, ElementType_t<CT2> > );
     //**********************************************************************************************
  };
  /*! \endcond */
  //*************************************************************************************************
  
  
  
  
  //=================================================================================================
  //
  //  GLOBAL BINARY RELATIONAL OPERATORS
  //
  //=================================================================================================
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default equality check of two row-major dense matrices.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the comparison.
  // \param rhs The right-hand side dense matrix for the comparison.
  // \return \a true if the two matrices are equal, \a false if not.
  //
  // Equal function for the comparison of two dense matrices. Due to the limited machine accuracy,
  // a direct comparison of two floating point numbers should be avoided. This function offers the
  // possibility to compare two floating-point matrices with a certain accuracy margin.
  */
  template< bool RF         // Relaxation flag
          , typename MT1    // Type of the left-hand side dense matrix
          , typename MT2 >  // Type of the right-hand side dense matrix
  inline DisableIf_t< DMatDMatEqualExprHelper<MT1,MT2>::value, bool >
     equal( const DenseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,false>& rhs )
  {
     using CT1 = CompositeType_t<MT1>;
     using CT2 = CompositeType_t<MT2>;
  
     // Early exit in case the matrix sizes don't match
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() )
        return false;
  
     // Evaluation of the two dense matrix operands
     CT1 A( ~lhs );
     CT2 B( ~rhs );
  
     // In order to compare the two matrices, the data values of the lower-order data
     // type are converted to the higher-order data type within the equal function.
     for( size_t i=0UL; i<A.rows(); ++i ) {
        for( size_t j=0UL; j<A.columns(); ++j ) {
           if( !equal( A(i,j), B(i,j) ) ) return false;
        }
     }
  
     return true;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief SIMD optimized equality check of two row-major dense matrices.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the comparison.
  // \param rhs The right-hand side dense matrix for the comparison.
  // \return \a true if the two matrices are equal, \a false if not.
  //
  // Equal function for the comparison of two dense matrices. Due to the limited machine accuracy,
  // a direct comparison of two floating point numbers should be avoided. This function offers the
  // possibility to compare two floating-point matrices with a certain accuracy margin.
  */
  template< bool RF         // Relaxation flag
          , typename MT1    // Type of the left-hand side dense matrix
          , typename MT2 >  // Type of the right-hand side dense matrix
  inline EnableIf_t< DMatDMatEqualExprHelper<MT1,MT2>::value, bool >
     equal( const DenseMatrix<MT1,false>& lhs, const DenseMatrix<MT2,false>& rhs )
  {
     using CT1 = CompositeType_t<MT1>;
     using CT2 = CompositeType_t<MT2>;
     using XT1 = RemoveReference_t<CT1>;
     using XT2 = RemoveReference_t<CT2>;
  
     // Early exit in case the matrix sizes don't match
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() )
        return false;
  
     // Evaluation of the two dense matrix operands
     CT1 A( ~lhs );
     CT2 B( ~rhs );
  
     constexpr size_t SIMDSIZE = SIMDTrait< ElementType_t<MT1> >::size;
     constexpr bool remainder( !usePadding || !IsPadded_v<XT1> || !IsPadded_v<XT2> );
  
     const size_t M( A.rows()    );
     const size_t N( A.columns() );
  
     const size_t jpos( ( remainder )?( N & size_t(-SIMDSIZE) ):( N ) );
     BLAZE_INTERNAL_ASSERT( !remainder || ( N - ( N % SIMDSIZE ) ) == jpos, "Invalid end calculation" );
  
     for( size_t i=0UL; i<M; ++i )
     {
        size_t j( 0UL );
  
        for( ; (j+SIMDSIZE*3UL) < jpos; j+=SIMDSIZE*4UL ) {
           if( !equal( A.load(i,j             ), B.load(i,j             ) ) ) return false;
           if( !equal( A.load(i,j+SIMDSIZE    ), B.load(i,j+SIMDSIZE    ) ) ) return false;
           if( !equal( A.load(i,j+SIMDSIZE*2UL), B.load(i,j+SIMDSIZE*2UL) ) ) return false;
           if( !equal( A.load(i,j+SIMDSIZE*3UL), B.load(i,j+SIMDSIZE*3UL) ) ) return false;
        }
        for( ; (j+SIMDSIZE) < jpos; j+=SIMDSIZE*2UL ) {
           if( !equal( A.load(i,j         ), B.load(i,j         ) ) ) return false;
           if( !equal( A.load(i,j+SIMDSIZE), B.load(i,j+SIMDSIZE) ) ) return false;
        }
        for( ; j<jpos; j+=SIMDSIZE ) {
           if( !equal( A.load(i,j), B.load(i,j) ) ) return false;
        }
        for( ; remainder && j<A.columns(); ++j ) {
           if( !equal( A(i,j), B(i,j) ) ) return false;
        }
     }
  
     return true;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Default equality check of two column-major dense matrices.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the comparison.
  // \param rhs The right-hand side dense matrix for the comparison.
  // \return \a true if the two matrices are equal, \a false if not.
  //
  // Equal function for the comparison of two dense matrices. Due to the limited machine accuracy,
  // a direct comparison of two floating point numbers should be avoided. This function offers the
  // possibility to compare two floating-point matrices with a certain accuracy margin.
  */
  template< bool RF         // Relaxation flag
          , typename MT1    // Type of the left-hand side dense matrix
          , typename MT2 >  // Type of the right-hand side dense matrix
  inline DisableIf_t< DMatDMatEqualExprHelper<MT1,MT2>::value, bool >
     equal( const DenseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
  {
     using CT1 = CompositeType_t<MT1>;
     using CT2 = CompositeType_t<MT2>;
  
     // Early exit in case the matrix sizes don't match
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() )
        return false;
  
     // Evaluation of the two dense matrix operands
     CT1 A( ~lhs );
     CT2 B( ~rhs );
  
     // In order to compare the two matrices, the data values of the lower-order data
     // type are converted to the higher-order data type within the equal function.
     for( size_t j=0UL; j<A.columns(); ++j ) {
        for( size_t i=0UL; i<A.rows(); ++i ) {
           if( !equal( A(i,j), B(i,j) ) ) return false;
        }
     }
  
     return true;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief SIMD optimized equality check of two column-major dense matrices.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the comparison.
  // \param rhs The right-hand side dense matrix for the comparison.
  // \return \a true if the two matrices are equal, \a false if not.
  //
  // Equal function for the comparison of two dense matrices. Due to the limited machine accuracy,
  // a direct comparison of two floating point numbers should be avoided. This function offers the
  // possibility to compare two floating-point matrices with a certain accuracy margin.
  */
  template< bool RF         // Relaxation flag
          , typename MT1    // Type of the left-hand side dense matrix
          , typename MT2 >  // Type of the right-hand side dense matrix
  inline EnableIf_t< DMatDMatEqualExprHelper<MT1,MT2>::value, bool >
     equal( const DenseMatrix<MT1,true>& lhs, const DenseMatrix<MT2,true>& rhs )
  {
     using CT1 = CompositeType_t<MT1>;
     using CT2 = CompositeType_t<MT2>;
     using XT1 = RemoveReference_t<CT1>;
     using XT2 = RemoveReference_t<CT2>;
  
     // Early exit in case the matrix sizes don't match
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() )
        return false;
  
     // Evaluation of the two dense matrix operands
     CT1 A( ~lhs );
     CT2 B( ~rhs );
  
     constexpr size_t SIMDSIZE = SIMDTrait< ElementType_t<MT1> >::size;
     constexpr bool remainder( !usePadding || !IsPadded_v<XT1> || !IsPadded_v<XT2> );
  
     const size_t M( A.rows()    );
     const size_t N( A.columns() );
  
     const size_t ipos( ( remainder )?( M & size_t(-SIMDSIZE) ):( M ) );
     BLAZE_INTERNAL_ASSERT( !remainder || ( M - ( M % SIMDSIZE ) ) == ipos, "Invalid end calculation" );
  
     for( size_t j=0UL; j<N; ++j )
     {
        size_t i( 0UL );
  
        for( ; (i+SIMDSIZE*3UL) < ipos; i+=SIMDSIZE*4UL ) {
           if( !equal( A.load(i             ,j), B.load(i             ,j) ) ) return false;
           if( !equal( A.load(i+SIMDSIZE    ,j), B.load(i+SIMDSIZE    ,j) ) ) return false;
           if( !equal( A.load(i+SIMDSIZE*2UL,j), B.load(i+SIMDSIZE*2UL,j) ) ) return false;
           if( !equal( A.load(i+SIMDSIZE*3UL,j), B.load(i+SIMDSIZE*3UL,j) ) ) return false;
        }
        for( ; (i+SIMDSIZE) < ipos; i+=SIMDSIZE*2UL ) {
           if( !equal( A.load(i         ,j), B.load(i         ,j) ) ) return false;
           if( !equal( A.load(i+SIMDSIZE,j), B.load(i+SIMDSIZE,j) ) ) return false;
        }
        for( ; i<ipos; i+=SIMDSIZE ) {
           if( !equal( A.load(i,j), B.load(i,j) ) ) return false;
        }
        for( ; remainder && i<M; ++i ) {
           if( !equal( A(i,j), B(i,j) ) ) return false;
        }
     }
  
     return true;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*! \cond BLAZE_INTERNAL */
  /*!\brief Equality check of two dense matrices with different storage order.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the comparison.
  // \param rhs The right-hand side dense matrix for the comparison.
  // \return \a true if the two matrices are equal, \a false if not.
  //
  // Equal function for the comparison of two dense matrices. Due to the limited machine accuracy,
  // a direct comparison of two floating point numbers should be avoided. This function offers the
  // possibility to compare two floating-point matrices with a certain accuracy margin.
  */
  template< bool RF       // Relaxation flag
          , typename MT1  // Type of the left-hand side dense matrix
          , typename MT2  // Type of the right-hand side dense matrix
          , bool SO >     // Storage order
  inline bool equal( const DenseMatrix<MT1,SO>& lhs, const DenseMatrix<MT2,!SO>& rhs )
  {
     using CT1 = CompositeType_t<MT1>;
     using CT2 = CompositeType_t<MT2>;
  
     // Early exit in case the matrix sizes don't match
     if( (~lhs).rows() != (~rhs).rows() || (~lhs).columns() != (~rhs).columns() )
        return false;
  
     // Evaluation of the two dense matrix operands
     CT1 A( ~lhs );
     CT2 B( ~rhs );
  
     // In order to compare the two matrices, the data values of the lower-order data
     // type are converted to the higher-order data type within the equal function.
     const size_t rows   ( A.rows() );
     const size_t columns( A.columns() );
     const size_t block  ( BLOCK_SIZE );
  
     for( size_t ii=0UL; ii<rows; ii+=block ) {
        const size_t iend( ( rows < ii+block )?( rows ):( ii+block ) );
        for( size_t jj=0UL; jj<columns; jj+=block ) {
           const size_t jend( ( columns < jj+block )?( columns ):( jj+block ) );
           for( size_t i=ii; i<iend; ++i ) {
              for( size_t j=jj; j<jend; ++j ) {
                 if( !equal( A(i,j), B(i,j) ) ) return false;
              }
           }
        }
     }
  
     return true;
  }
  /*! \endcond */
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Equality operator for the comparison of two dense matrices.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side matrix for the comparison.
  // \param rhs The right-hand side matrix for the comparison.
  // \return \a true if the two matrices are equal, \a false if not.
  */
  template< typename MT1  // Type of the left-hand side dense matrix
          , bool SO1      // Storage order of the left-hand side dense matrix
          , typename MT2  // Type of the right-hand side dense matrix
          , bool SO2 >    // Storage order of the right-hand side dense matrix
  inline bool operator==( const DenseMatrix<MT1,SO1>& lhs, const DenseMatrix<MT2,SO2>& rhs )
  {
     return equal<relaxed>( lhs, rhs );
  }
  //*************************************************************************************************
  
  
  //*************************************************************************************************
  /*!\brief Inequality operator for the comparison of two dense matrices.
  // \ingroup dense_matrix
  //
  // \param lhs The left-hand side dense matrix for the comparison.
  // \param rhs The right-hand side dense matrix for the comparison.
  // \return \a true if the two matrices are not equal, \a false if they are equal.
  */
  template< typename MT1  // Type of the left-hand side dense matrix
          , bool SO1      // Storage order of the left-hand side dense matrix
          , typename MT2  // Type of the right-hand side dense matrix
          , bool SO2 >    // Storage order of the right-hand side dense matrix
  inline bool operator!=( const DenseMatrix<MT1,SO1>& lhs, const DenseMatrix<MT2,SO2>& rhs )
  {
     return !equal<relaxed>( lhs, rhs );
  }
  //*************************************************************************************************
  
  } // namespace blaze
  
  #endif
  