doc/html/Stokhos__Cuda__TiledCrsProductTensor_8hpp_source.html

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 #ifndef STOKHOS_CUDA_TILED_CRS_PRODUCT_TENSOR_HPP

 #define STOKHOS_CUDA_TILED_CRS_PRODUCT_TENSOR_HPP


 #include <iostream>


 #include "Kokkos_Core.hpp"


 #include "Stokhos_Multiply.hpp"

 #include "Stokhos_BlockCrsMatrix.hpp"

 #include "Stokhos_TiledCrsProductTensor.hpp"


 #include "cuda_profiler_api.h"


 namespace Stokhos {


 #if 1


 //----------------------------------------------------------------------------


 template< typename TensorScalar ,

           typename MatrixScalar ,

           typename VectorScalar >

 class Multiply<

   BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >,

                   MatrixScalar, Kokkos::Cuda >,

   Kokkos::View<VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda>,

   Kokkos::View<VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda> >

 {

 public:


   typedef Kokkos::Cuda  execution_space ;

   typedef execution_space::size_type size_type ;


   typedef TiledCrsProductTensor< TensorScalar, execution_space > tensor_type ;

   typedef BlockCrsMatrix< tensor_type, MatrixScalar, execution_space > matrix_type ;

   typedef Kokkos::View< VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda >  vector_type ;


   class ProductTensorLoop {

   public:


     const matrix_type m_A;

     const vector_type m_x;

     const vector_type m_y;

     const size_type m_block_size ;


     ProductTensorLoop( const matrix_type & A,

                        const vector_type & x,

                        const vector_type & y,

                        const size_type block_size )

       : m_A( A ), m_x( x ), m_y( y ), m_block_size(block_size) {}


     __device__

     void operator()(void) const

     {

       const size_type WarpSize = Kokkos::Impl::CudaTraits::WarpSize;


       // Number of bases in the stochastic system:

       const size_type dim = m_A.block.dimension();


       // Number of Cijk tiles

       const size_type n_tile = m_A.block.num_tiles();

       const size_type tile_size = m_A.block.tile_size();

       const size_type tile_dim = n_tile == 1 ? dim : tile_size;

       //const size_type tile_dim = tile_size;


       VectorScalar * const sh_x_k =

         kokkos_impl_cuda_shared_memory<VectorScalar>();

       VectorScalar * const sh_x_j =

         n_tile == 1 ? sh_x_k : sh_x_k + m_block_size*tile_dim;

       VectorScalar * const sh_A_k =

         sh_x_j + m_block_size*tile_dim;

       VectorScalar * const sh_A_j =

         n_tile == 1 ? sh_A_k : sh_A_k + m_block_size*tile_dim;

       VectorScalar * const sh_y   = sh_A_j + m_block_size*tile_dim;

       volatile VectorScalar * const sh_t = sh_y + tile_dim;


       const size_type nid = blockDim.x * blockDim.y;

       const size_type tid = threadIdx.x + blockDim.x * threadIdx.y;


       // blockIdx.x == row in the deterministic (finite element) system

       const size_type iBlockEntryBeg = m_A.graph.row_map[ blockIdx.x ];

       const size_type iBlockEntryEnd = m_A.graph.row_map[ blockIdx.x + 1 ];

       size_type numBlock = (iBlockEntryEnd-iBlockEntryBeg) / m_block_size;

       const size_type remBlock = (iBlockEntryEnd-iBlockEntryBeg) % m_block_size;

       if (remBlock > 0) ++numBlock;


       // Zero y

       for (size_type i=tid; i<dim; i+=nid) {

         m_y(i,blockIdx.x) = 0.0;

       }


       // Loop over Cijk tiles

       for (size_type tile = 0; tile<n_tile; ++tile) {


         const size_type i_offset = m_A.block.offset(tile, 0);

         const size_type j_offset = m_A.block.offset(tile, 1);

         const size_type k_offset = m_A.block.offset(tile, 2);

         const size_type i_range  = m_A.block.range(tile, 0);

         const size_type j_range  = m_A.block.range(tile, 1);

         const size_type k_range  = m_A.block.range(tile, 2);

         const size_type n_row    = m_A.block.num_rows(tile);


         // Zero y

         for (size_type i=tid; i<i_range; i+=nid) {

           sh_y[i] = 0.0;

         }


         // Loop over finite element column blocks.

         size_type iBlockEntry = iBlockEntryBeg;

         for (size_type block=0; block<numBlock;

              ++block, iBlockEntry+=m_block_size) {


           const size_type block_size =

             (block == numBlock-1 && remBlock > 0) ? remBlock : m_block_size;


           // Wait for X and A to be used in the previous iteration

           // before reading new values.

           __syncthreads();


           // Coalesced read blocks of X and A into shared memory

           for (size_type col=0; col<block_size; ++col) {


             const size_type iBlockColumn =

               m_A.graph.entries( iBlockEntry + col );

             const VectorScalar * const x_k = & m_x( k_offset , iBlockColumn );

             const VectorScalar * const x_j = & m_x( j_offset , iBlockColumn );

             const MatrixScalar * const A_k = & m_A.values( k_offset , iBlockEntry + col );

             const MatrixScalar * const A_j = & m_A.values( j_offset , iBlockEntry + col );


             for (size_type j=tid; j<j_range; j+=nid) {

               sh_x_j[col+j*m_block_size] = x_j[j];

               sh_A_j[col+j*m_block_size] = A_j[j];

             }

             if (n_tile > 1) {

               for (size_type k=tid; k<k_range; k+=nid) {

                 sh_x_k[col+k*m_block_size] = x_k[k];

                 sh_A_k[col+k*m_block_size] = A_k[k];

               }

             }


           }


           __syncthreads(); // wait for X and A to be read


           // Loop over stochastic rows in this tile

           for (size_type i=threadIdx.y; i<i_range; i+=blockDim.y) {

             VectorScalar s = 0;


             // Product tensor entries which this warp will iterate:

             const size_type lBeg = m_A.block.entry_begin(tile, i);

             const size_type lEnd = m_A.block.entry_end(tile, i);


             // Loop through sparse tensor contributions with coalesced reads.

             for (size_type l=lBeg+threadIdx.x; l<lEnd; l+=blockDim.x) {


               const size_type kj   = m_A.block.coord( l );

               const TensorScalar v = m_A.block.value( l );

               const size_type j    = ( kj & 0x0ffff ) * m_block_size ;

               const size_type k    = ( kj >> 16     ) * m_block_size ;


               for ( size_type col = 0; col < block_size; ++col ) {

                 s += v * ( sh_A_j[col+j] * sh_x_k[col+k] + sh_A_k[col+k] * sh_x_j[col+j] );

               }


             }


             // Reduction of 'y' within 'CudaTraits::WarpSize'

             sh_t[tid] = s;

             if ( threadIdx.x + 16 < WarpSize ) sh_t[tid] += sh_t[tid+16];

             if ( threadIdx.x +  8 < WarpSize ) sh_t[tid] += sh_t[tid+ 8];

             if ( threadIdx.x +  4 < WarpSize ) sh_t[tid] += sh_t[tid+ 4];

             if ( threadIdx.x +  2 < WarpSize ) sh_t[tid] += sh_t[tid+ 2];

             if ( threadIdx.x +  1 < WarpSize ) sh_t[tid] += sh_t[tid+ 1];

             if ( threadIdx.x == 0 ) sh_y[i] += sh_t[tid];


           }


         }


         // Wait for all threads to complete the tile

         __syncthreads();


         // Store partial sum for this tile back in global memory

         for (size_type i=tid; i<i_range; i+=nid) {

           m_y( i+i_offset , blockIdx.x ) += sh_y[i];

         }

       }


     }

   };


   //------------------------------------


   static void apply( const matrix_type & A ,

                      const vector_type & x ,

                      const vector_type & y )

   {

     const size_type row_count = A.graph.row_map.extent(0) - 1;

     const size_type tensor_dimension = A.block.dimension();

     const size_type tile_size = A.block.tile_size();

     const size_type num_tiles = A.block.num_tiles();

     //const size_type tile_dim = std::min(tensor_dimension, tile_size);

     const size_type tile_dim = tile_size;


 #ifdef STOKHOS_DEBUG

     const size_type nWarp = 12; // Use fewer warps in debug mode to prevent

                                 // launch failures

 #else

     const size_type nWarp = 16;

 #endif

     const dim3 dBlock( Kokkos::Impl::CudaTraits::WarpSize , nWarp , 1 );

     const dim3 dGrid( row_count , 1 , 1 );


     const size_type shmem_factor = num_tiles == 1 ? 2 : 4;

     const size_type tensor_align = num_tiles == 1 ? tensor_dimension : tile_dim;

     const size_type shcap =

       Kokkos::Cuda().impl_internal_space_instance()->m_maxShmemPerBlock / 2;

     size_type bs = ((shcap / sizeof(VectorScalar) - dBlock.x*dBlock.y) / tensor_align - 1) / shmem_factor;

     if (bs % 2 == 0)

       --bs;

     const size_type block_size_max = 31;

     const size_type block_size = std::min(bs, block_size_max);

     // const int block_size = 9;

     const size_type shmem =

       sizeof(VectorScalar) * ((shmem_factor*block_size+1) * tensor_align + dBlock.x*dBlock.y);


     /*

     //const size_type shcap = Kokkos::Impl::CudaTraits::SharedMemoryCapacity;

     const size_type block_size = 9;

     size_type shmem;

     if (num_tiles > 1)

       shmem = sizeof(VectorScalar) * ((4*block_size+1)*tile_dim + dBlock.x*dBlock.y);

     else

       shmem = sizeof(VectorScalar) * ((2*block_size+1)*tensor_dimension + dBlock.x*dBlock.y);

     */


 #if 0


     std::cout << "Multiply< BlockCrsMatrix< CrsProductTensor ... > >::apply"

               << std::endl

               << "  grid(" << dGrid.x << "," << dGrid.y << ")" << std::endl

               << "  block(" << dBlock.x << "," << dBlock.y << ")" << std::endl

               << "  block_size(" << block_size << ")" << std::endl

               << "  shmem(" << shmem/1024 << " kB)" << std::endl

               << "  row_count(" << row_count << ")" << std::endl

               << "  tensor_dimension(" << tensor_dimension << ")" << std::endl

               << "  tile_size(" << tile_size << ")" << std::endl

               << "  num_tiles(" << num_tiles << ")" << std::endl

              ;

 #endif

     //cudaProfilerStart();

     Kokkos::Impl::cuda_parallel_launch_local_memory<<< dGrid , dBlock , shmem >>>

       ( ProductTensorLoop( A , x , y, block_size ) );

     //cudaProfilerStop();

   }

 };


 #elif 0


 //----------------------------------------------------------------------------


 template< typename TensorScalar ,

           typename MatrixScalar ,

           typename VectorScalar >

 class Multiply<

   BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >,

                   MatrixScalar, Kokkos::Cuda >,

   Kokkos::View<VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda>,

   Kokkos::View<VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda> >

 {

 public:


   typedef Kokkos::Cuda  execution_space ;

   typedef execution_space::size_type size_type ;


   typedef TiledCrsProductTensor< TensorScalar, execution_space > tensor_type ;

   typedef BlockCrsMatrix< tensor_type, MatrixScalar, execution_space > matrix_type ;

   typedef Kokkos::View< VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda >  vector_type ;


   class ProductTensorLoop {

   public:


     const matrix_type m_A;

     const vector_type m_x;

     const vector_type m_y;

     const size_type m_tile;


     ProductTensorLoop( const matrix_type & A,

                        const vector_type & x,

                        const vector_type & y,

                        const size_type tile )

       : m_A( A ), m_x( x ), m_y( y ), m_tile(tile) {}


     __device__

     void operator()(void) const

     {

       const size_type WarpSize = Kokkos::Impl::CudaTraits::WarpSize;


       // Number of bases in the stochastic system:

       const size_type dim = m_A.block.dimension();

       const size_type tile_size = m_A.block.tile_size();


       VectorScalar * const sh_x_k =

         kokkos_impl_cuda_shared_memory<VectorScalar>();

       VectorScalar * const sh_x_j = sh_x_k + tile_size;

       VectorScalar * const sh_A_k = sh_x_j + tile_size;

       VectorScalar * const sh_A_j = sh_A_k + tile_size;

       VectorScalar * const sh_y   = sh_A_j + tile_size;

       volatile VectorScalar * const sh_t = sh_y + tile_size;


       const size_type nid = blockDim.x * blockDim.y;

       const size_type tid = threadIdx.x + blockDim.x * threadIdx.y;


       // Divide warps into 4 groups for reading x_j, x_k, A_j, and A_k

       // const size_type warps_per_group = blockDim.y / 4;

       // const size_type group_lane = threadIdx.y % warps_per_group;

       // const size_type gid = threadIdx.x + blockDim.x * group_lane;

       // const size_type ngid = warps_per_group * blockDim.x;

       // const size_type group = threadIdx.y / warps_per_group;


       const size_type i_offset = m_A.block.offset(m_tile, 0);

       const size_type j_offset = m_A.block.offset(m_tile, 1);

       const size_type k_offset = m_A.block.offset(m_tile, 2);

       const size_type i_range  = m_A.block.range(m_tile, 0);

       const size_type j_range  = m_A.block.range(m_tile, 1);

       const size_type k_range  = m_A.block.range(m_tile, 2);

       const size_type n_row    = m_A.block.num_rows(m_tile);


       // blockIdx.x == row in the deterministic (finite element) system

       const size_type iBlockEntryBeg = m_A.graph.row_map[ blockIdx.x ];

       const size_type iBlockEntryEnd = m_A.graph.row_map[ blockIdx.x + 1 ];


       // Zero y

       for (size_type i=tid; i<i_range; i+=nid) {

         sh_y[i] = 0.0;

       }


       const size_type * __restrict cijk_j = &m_A.block.coord(0,0);

       const size_type * __restrict cijk_k = &m_A.block.coord(0,1);

       const TensorScalar * __restrict cijk_v = &m_A.block.value(0);


       // Loop over finite element column blocks.

       for (size_type iBlockEntry = iBlockEntryBeg; iBlockEntry<iBlockEntryEnd;

            ++iBlockEntry) {


         __syncthreads(); // wait for threads from previous iteration to finish


         // Coalesced read blocks of X and A into shared memory

         const size_type iBlockColumn = m_A.graph.entries( iBlockEntry );

         const VectorScalar * const x_k = & m_x( k_offset , iBlockColumn );

         const VectorScalar * const x_j = & m_x( j_offset , iBlockColumn );

         const MatrixScalar * const A_k = & m_A.values( k_offset , iBlockEntry );

         const MatrixScalar * const A_j = & m_A.values( j_offset , iBlockEntry );


         for (size_type j=tid; j<j_range; j+=nid) {

           sh_x_j[j] = x_j[j];

           sh_A_j[j] = A_j[j];

         }

         for (size_type k=tid; k<k_range; k+=nid) {

           sh_x_k[k] = x_k[k];

           sh_A_k[k] = A_k[k];

         }

         // if (group == 0)

         //   for (size_type j=gid; j<j_range; j+=ngid) sh_x_j[j] = x_j[j];

         // if (group == 1)

         //   for (size_type j=gid; j<j_range; j+=ngid) sh_A_j[j] = A_j[j];

         // if (group == 2)

         //   for (size_type k=gid; k<k_range; k+=ngid) sh_x_k[k] = x_k[k];

         // if (group == 3)

         //   for (size_type k=gid; k<k_range; k+=ngid) sh_A_k[k] = A_k[k];


         __syncthreads(); // wait for X and A to be read


         // Loop over stochastic rows in this tile

         for (size_type i=threadIdx.y; i<i_range; i+=blockDim.y) {

           VectorScalar s = 0;


           // Product tensor entries which this warp will iterate:

           const size_type lBeg = m_A.block.entry_begin(m_tile, i);

           const size_type lEnd = m_A.block.entry_end(m_tile, i);


           // Loop through sparse tensor contributions with coalesced reads.

           for (size_type l=lBeg+threadIdx.x; l<lEnd; l+=blockDim.x) {


             // Read entries from the tensor

             // const int j = m_A.block.coord(l,0);

             // const int k = m_A.block.coord(l,1);

             // const MatrixScalar v = m_A.block.value(l);

             const size_type j = cijk_j[l];

             const size_type k = cijk_k[l];

             const TensorScalar v = cijk_v[l];


             s += v * ( sh_A_j[j] * sh_x_k[k] + sh_A_k[k] * sh_x_j[j] );


           }


           // Reduction of 'y' within 'CudaTraits::WarpSize'

           sh_t[tid] = s;

           if ( threadIdx.x + 16 < WarpSize ) sh_t[tid] += sh_t[tid+16];

           if ( threadIdx.x +  8 < WarpSize ) sh_t[tid] += sh_t[tid+ 8];

           if ( threadIdx.x +  4 < WarpSize ) sh_t[tid] += sh_t[tid+ 4];

           if ( threadIdx.x +  2 < WarpSize ) sh_t[tid] += sh_t[tid+ 2];

           if ( threadIdx.x +  1 < WarpSize ) sh_t[tid] += sh_t[tid+ 1];

           if ( threadIdx.x == 0 ) sh_y[i] += sh_t[tid];


         }


       }


       // Wait for all threads to complete the tile

       __syncthreads();


       // Store partial sum for this tile back in global memory

       for (size_type i=tid; i<i_range; i+=nid) {

         m_y( i+i_offset , blockIdx.x ) += sh_y[i];

       }


     }

   };


   class Zero {

   public:

     typedef typename vector_type::value_type value_type;

     typedef typename vector_type::execution_space execution_space;

     typedef typename execution_space::size_type size_type;


     Zero( const vector_type & x ) : m_x( x ), m_d(x.extent(0)) {}


     KOKKOS_INLINE_FUNCTION

     void operator()( const size_type j ) const {

       for (size_type i=0; i<m_d; ++i)

         m_x(i,j) = 0.0;

     }


   private:

     const vector_type m_x;

     const size_type m_d;


   };


   //------------------------------------


   static void apply( const matrix_type & A ,

                      const vector_type & x ,

                      const vector_type & y )

   {

     const size_type row_count = A.graph.row_map.extent(0) - 1;

     const size_type tensor_dimension = A.block.dimension();

     const size_type tile_size = A.block.tile_size();

     const size_type num_tiles = A.block.num_tiles();


     const size_type nWarp = 16;

     const dim3 dBlock( Kokkos::Impl::CudaTraits::WarpSize , nWarp , 1 );

     const dim3 dGrid( row_count , 1 , 1 );


     const size_type shmem =

       sizeof(VectorScalar) * (5*tile_size + dBlock.x*dBlock.y);


 #if 1


     std::cout << "Multiply< BlockCrsMatrix< CrsProductTensor ... > >::apply"

               << std::endl

               << "  grid(" << dGrid.x << "," << dGrid.y << ")" << std::endl

               << "  block(" << dBlock.x << "," << dBlock.y << ")" << std::endl

               << "  shmem(" << shmem/1024 << " kB)" << std::endl

               << "  row_count(" << row_count << ")" << std::endl

               << "  tensor_dimension(" << tensor_dimension << ")" << std::endl

               << "  tile_size(" << tile_size << ")" << std::endl

               << "  num_tiles(" << num_tiles << ")" << std::endl

              ;

 #endif

     //cudaProfilerStart();

     // Zero y

     Kokkos::parallel_for( row_count , Zero(y) );


     // Loop over Cijk tiles

     for (size_type tile = 0; tile<num_tiles; ++tile) {

       Kokkos::Impl::cuda_parallel_launch_local_memory<<< dGrid , dBlock , shmem >>>

         ( ProductTensorLoop( A , x , y, tile ) );

     }

     //cudaProfilerStop();

   }

 };


 #else


 //----------------------------------------------------------------------------


 // #define MAX_TENSOR_OFFSETS 2000

 // __constant__ Kokkos::Cuda::size_type tensor_row_begin[MAX_TENSOR_OFFSETS];


 template< typename TensorScalar ,

           typename MatrixScalar ,

           typename VectorScalar >

 class Multiply<

   BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >,

                   MatrixScalar, Kokkos::Cuda >,

   Kokkos::View<VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda>,

   Kokkos::View<VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda> >

 {

 public:


   typedef Kokkos::Cuda  execution_space ;

   typedef execution_space::size_type size_type ;


   typedef TiledCrsProductTensor< TensorScalar, execution_space > tensor_type ;

   typedef BlockCrsMatrix< tensor_type, MatrixScalar, execution_space > matrix_type ;

   typedef Kokkos::View< VectorScalar**, Kokkos::LayoutLeft, Kokkos::Cuda >  vector_type ;


   class ProductTensorLoop {

   public:


     const matrix_type m_A;

     const vector_type m_x;

     const vector_type m_y;


     ProductTensorLoop( const matrix_type & A,

                        const vector_type & x,

                        const vector_type & y )

       : m_A( A ), m_x( x ), m_y( y ) {}


     __device__

     void operator()(void) const

     {

       const size_type WarpSize = Kokkos::Impl::CudaTraits::WarpSize;


       // Number of bases in the stochastic system:

       const size_type dim = m_A.block.dimension();

       const size_type tile_size = m_A.block.tile_size();

       const size_type max_num_rows = m_A.block.max_num_rows();


       const size_type nid = blockDim.x * blockDim.y * blockDim.z;

       const size_type tid =

         threadIdx.x + blockDim.x * ( threadIdx.y + blockDim.y * threadIdx.z );

       const size_type thread_lane = threadIdx.x + blockDim.x * threadIdx.y;


       // blockDim.x == FEM column block-size

       VectorScalar * const sh_x_k =

         kokkos_impl_cuda_shared_memory<VectorScalar>();

       //VectorScalar * const sh_x_j = sh_x_k + blockDim.x*tile_size;

       VectorScalar * const sh_x_j = sh_x_k;

       VectorScalar * const sh_A_k = sh_x_j + blockDim.x*tile_size;

       //VectorScalar * const sh_A_j = sh_A_k + blockDim.x*tile_size;

       VectorScalar * const sh_A_j = sh_A_k;

       VectorScalar * const sh_y   = sh_A_j + blockDim.x*tile_size;

       volatile VectorScalar * const sh_t = sh_y + tile_size;

       //volatile VectorScalar * const sh_v = sh_t + nid;

       size_type * const sh_j = (size_type*) (sh_t + nid);

       size_type * const sh_k = (size_type*) (sh_j + nid);


       // blockIdx.x == row in the deterministic (finite element) system

       // These are not coalesced, but there is nothing we can do about it

       // since we only do one row per block

       const size_type iBlockEntryBeg = m_A.graph.row_map[ blockIdx.x ];

       const size_type iBlockEntryEnd = m_A.graph.row_map[ blockIdx.x + 1 ];

       size_type numBlock = (iBlockEntryEnd-iBlockEntryBeg) / blockDim.x;

       const size_type remBlock = (iBlockEntryEnd-iBlockEntryBeg) % blockDim.x;

       if (remBlock > 0) ++numBlock;


       // Zero y

       for (size_type i=tid; i<dim; i+=nid) {

         m_y(i,blockIdx.x) = 0.0;

       }


       // Number of Cijk tiles

       const size_type n_tile = m_A.block.num_tiles();


       // Loop over Cijk tiles

       for (size_type tile = 0; tile<n_tile; ++tile) {


         // These are not coalesced

         const size_type i_offset = m_A.block.offset(tile, 0);

         const size_type j_offset = m_A.block.offset(tile, 1);

         const size_type k_offset = m_A.block.offset(tile, 2);

         const size_type i_range  = m_A.block.range(tile, 0);

         const size_type j_range  = m_A.block.range(tile, 1);

         const size_type k_range  = m_A.block.range(tile, 2);

         const size_type n_row    = m_A.block.num_rows(tile);


         // Zero y

         for (size_type i=tid; i<i_range; i+=nid) {

           sh_y[i] = 0.0;

         }


         // Loop over finite element column blocks.

         // threadIdx.x == FEM column within current block

         size_type iBlockEntry = iBlockEntryBeg;

         for (size_type block=0; block<numBlock;

              ++block, iBlockEntry+=blockDim.x) {


           const size_type block_size =

             (block == numBlock-1 && remBlock > 0) ? remBlock : blockDim.x;


           // Coalesced read blocks of X and A into shared memory

           for (size_type col=0; col<block_size; ++col) {


             // This is not a coalesced read

             const size_type iBlockColumn =

               m_A.graph.entries( iBlockEntry + col );


             const VectorScalar * const x_k = & m_x( k_offset , iBlockColumn );

             const VectorScalar * const x_j = & m_x( j_offset , iBlockColumn );

             const MatrixScalar * const A_k =

               & m_A.values( k_offset , iBlockEntry + col );

             const MatrixScalar * const A_j =

               & m_A.values( j_offset , iBlockEntry + col );

             for (size_type j=tid; j<j_range; j+=nid) {

               sh_x_j[col+j*blockDim.x] = x_j[j];

               sh_A_j[col+j*blockDim.x] = A_j[j];

             }

             // for (size_type k=tid; k<k_range; k+=nid) {

             //   sh_x_k[col+k*blockDim.x] = x_k[k];

             //   sh_A_k[col+k*blockDim.x] = A_k[k];

             // }


           }


           __syncthreads(); // wait for X and A to be read


           // Loop over stochastic rows in this tile

           for (size_type i=threadIdx.z; i<i_range; i+=blockDim.z) {

             VectorScalar s = 0;


             // Product tensor entries which this warp will iterate:

             // These are not coalesced

             const size_type lBeg = m_A.block.entry_begin(tile, i);

             const size_type lEnd = m_A.block.entry_end(tile, i);

             // const size_type lBeg = tensor_row_begin[tile*(max_num_rows+1)+i];

             // const size_type lEnd = tensor_row_begin[tile*(max_num_rows+1)+i+1];


             // Loop through sparse tensor contributions with coalesced reads.

             for (size_type l=lBeg; l<lEnd; l+=WarpSize) {

               //for (size_type l=lBeg+threadIdx.y; l<lEnd; l+=blockDim.y) {


               // Read entries from the tensor

               if (l+thread_lane < lEnd) {

                 sh_j[tid] = m_A.block.coord(l+thread_lane,0);

                 sh_k[tid] = m_A.block.coord(l+thread_lane,1);

                 sh_t[tid] = m_A.block.value(l+thread_lane);

               }


               const int mm = (l+WarpSize<lEnd) ? WarpSize : lEnd-l;

               for (size_type m=threadIdx.y; m<mm; m+=blockDim.y) {


                 if (threadIdx.x < block_size) {

                   // const int j = m_A.block.coord(l+m,0);

                   // const int k = m_A.block.coord(l+m,1);

                   // const MatrixScalar v = m_A.block.value(l+m);

                   const size_type j = sh_j[m+WarpSize*threadIdx.z];

                   const size_type k = sh_k[m+WarpSize*threadIdx.z];

                   const TensorScalar v = sh_t[m+WarpSize*threadIdx.z];

                   const size_type jj = threadIdx.x + j*blockDim.x;

                   const size_type kk = threadIdx.x + k*blockDim.x;

                   s += v * ( sh_A_j[jj] * sh_x_k[kk] + sh_A_k[kk] * sh_x_j[jj] );

                 }


               }


             }


             // Reduction of 'y' within 'CudaTraits::WarpSize'

             sh_t[tid] = s;

             if ( thread_lane + 16 < WarpSize ) sh_t[tid] += sh_t[tid+16];

             if ( thread_lane +  8 < WarpSize ) sh_t[tid] += sh_t[tid+ 8];

             if ( thread_lane +  4 < WarpSize ) sh_t[tid] += sh_t[tid+ 4];

             if ( thread_lane +  2 < WarpSize ) sh_t[tid] += sh_t[tid+ 2];

             if ( thread_lane +  1 < WarpSize ) sh_t[tid] += sh_t[tid+ 1];

             if ( thread_lane == 0 ) sh_y[i] += sh_t[tid];


           }


         }


         // Wait for all threads to complete the tile

         __syncthreads();


         // Store partial sum for this tile back in global memory

         for (size_type i=tid; i<i_range; i+=nid) {

           m_y( i+i_offset , blockIdx.x ) += sh_y[i];

         }

       }


     }

   };


   //------------------------------------


   static void apply( const matrix_type & A ,

                      const vector_type & x ,

                      const vector_type & y )

   {

     const size_type row_count = A.graph.row_map.extent(0) - 1;

     const size_type tensor_dimension = A.block.dimension();

     const size_type tile_size = A.block.tile_size();

     const size_type num_tiles = A.block.num_tiles();

     const size_type max_num_rows = A.block.max_num_rows();


     const size_type warp_size = Kokkos::Impl::CudaTraits::WarpSize;

     const size_type block_size = 8;

     const size_type nWarp = 16;

     const dim3 dBlock( block_size, warp_size / block_size, nWarp );

     const dim3 dGrid( row_count , 1 , 1 );


     const size_type shmem =

       sizeof(VectorScalar) * ( (2*block_size+1)*tile_size +

                                dBlock.x*dBlock.y*dBlock.z ) +

       sizeof(size_type) * 2 * dBlock.x*dBlock.y*dBlock.z;


     const size_type cmem = sizeof(size_type)*(max_num_rows+1)*num_tiles;


 #if 1


     std::cout << "Multiply< BlockCrsMatrix< CrsProductTensor ... > >::apply"

               << std::endl

               << "  grid(" << dGrid.x << "," << dGrid.y << ")" << std::endl

               << "  block(" << dBlock.x << "," << dBlock.y << "," << dBlock.z

               << ")" << std::endl

               << "  block_size(" << block_size << ")" << std::endl

               << "  shmem(" << shmem/1024 << " kB)" << std::endl

               << "  row_count(" << row_count << ")" << std::endl

               << "  tensor_dimension(" << tensor_dimension << ")" << std::endl

               << "  tile_size(" << tile_size << ")" << std::endl

               << "  num_tiles(" << num_tiles << ")" << std::endl

               << "  cmem(" << cmem/1024 << " kB)" << std::endl

              ;

 #endif


     // Copy tensor row offsets to constant device memory

     // cudaMemcpyToSymbol(tensor_row_begin, A.block.row_map_ptr(), cmem, 0,

     //                    cudaMemcpyDeviceToDevice);


     //cudaProfilerStart();

     Kokkos::Impl::cuda_parallel_launch_local_memory<<< dGrid , dBlock , shmem >>>

       ( ProductTensorLoop( A , x , y ) );

     //cudaProfilerStop();

   }

 };


 #endif


 //----------------------------------------------------------------------------

 //----------------------------------------------------------------------------


 } // namespace Stokhos


 #endif /* #ifndef STOKHOS_CUDA_TILED_CRS_PRODUCT_TENSOR_HPP */

Stokhos_Multiply.hpp

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::matrix_type
BlockCrsMatrix< tensor_type, MatrixScalar, execution_space > matrix_type
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:76

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::ProductTensorLoop::m_y
const vector_type m_y
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:84

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::ProductTensorLoop::m_block_size
const size_type m_block_size
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:85

Stokhos::BlockCrsMatrix::block
block_spec block
Definition: Stokhos_BlockCrsMatrix.hpp:76

Stokhos_BlockCrsMatrix.hpp

DynamicVecTest::execution_space
Kokkos::DefaultExecutionSpace execution_space
Definition: Stokhos_SacadoMPVectorCommTests.cpp:682

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::vector_type
Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > vector_type
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:77

Zero

A

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::apply
static void apply(const matrix_type &A, const vector_type &x, const vector_type &y)
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:235

Sacado::UQ::min
KOKKOS_INLINE_FUNCTION PCE< Storage > min(const typename PCE< Storage >::value_type &a, const PCE< Storage > &b)
Definition: Sacado_UQ_PCE_Imp.hpp:1247

j
j
Definition: Sacado_Fad_Exp_MP_Vector.hpp:527

TotalOrderBasisUnitTest::value_type
double value_type
Definition: Stokhos_LexicographicTreeBasisUnitTest.cpp:70

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::tensor_type
TiledCrsProductTensor< TensorScalar, execution_space > tensor_type
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:75

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::execution_space
Kokkos::Cuda execution_space
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:72

Stokhos::BlockCrsMatrix::graph
graph_type graph
Definition: Stokhos_BlockCrsMatrix.hpp:75

Stokhos::BlockCrsMatrix
CRS matrix of dense blocks.
Definition: Stokhos_BlockCrsMatrix.hpp:64

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::ProductTensorLoop::m_x
const vector_type m_x
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:83

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::size_type
execution_space::size_type size_type
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:73

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::ProductTensorLoop::m_A
const matrix_type m_A
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:82

Stokhos::TiledCrsProductTensor
Definition: Stokhos_TiledCrsProductTensor.hpp:61

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::ProductTensorLoop::operator()
__device__ void operator()(void) const
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:94

Stokhos_TiledCrsProductTensor.hpp

Stokhos::Multiply< BlockCrsMatrix< TiledCrsProductTensor< TensorScalar, Kokkos::Cuda >, MatrixScalar, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda >, Kokkos::View< VectorScalar **, Kokkos::LayoutLeft, Kokkos::Cuda > >::ProductTensorLoop::ProductTensorLoop
ProductTensorLoop(const matrix_type &A, const vector_type &x, const vector_type &y, const size_type block_size)
Definition: Stokhos_Cuda_TiledCrsProductTensor.hpp:87

Stokhos::Multiply
Definition: Stokhos_Multiply.hpp:73