/usr/include/trilinos/Stokhos_CrsProductTensor.hpp is in libtrilinos-stokhos-dev 12.10.1-3.
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// ***********************************************************************
//
// Stokhos Package
// Copyright (2009) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
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// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
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//
// 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 name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "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 SANDIA CORPORATION OR THE
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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//
// Questions? Contact Eric T. Phipps (etphipp@sandia.gov).
//
// ***********************************************************************
// @HEADER
#ifndef STOKHOS_CRSPRODUCTTENSOR_HPP
#define STOKHOS_CRSPRODUCTTENSOR_HPP
#include "Kokkos_Core.hpp"
#include "Stokhos_Multiply.hpp"
#include "Stokhos_ProductBasis.hpp"
#include "Stokhos_Sparse3Tensor.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Stokhos_BlockCrsMatrix.hpp"
#include "Stokhos_StochasticProductTensor.hpp"
#include "Stokhos_TinyVec.hpp"
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
namespace Stokhos {
/** \brief Sparse product tensor with replicated entries
* to provide subsets with a given coordinate.
*
* This allows product tensor multiplication to be partitioned
* on a given coordinate values.
*
* for ( size_type i = 0 ; i < p.dimension() ; ++i ) {
* y[i] = 0 ;
* for ( size_type e = p.entry_begin(i) ;
* e < p.entry_end(i) ; ++e ) {
* const size_type j = p.coord(e,0);
* const size_type k = p.coord(e,1);
* Scalar tmp = a[j] * x[k] ; if ( j != k ) tmp += a[k] * x[j] ;
* y[i] += p.value(e) * tmp ;
* }
* }
*/
template< typename ValueType, class ExecutionSpace, class Memory = void >
class CrsProductTensor {
public:
typedef ExecutionSpace execution_space;
typedef int size_type;
typedef ValueType value_type;
typedef Memory memory_type;
typedef typename Kokkos::ViewTraits< size_type*, execution_space,void,void >::host_mirror_space host_mirror_space ;
typedef CrsProductTensor<value_type, host_mirror_space> HostMirror;
// Vectorsize used in multiply algorithm
#if defined(__AVX__)
static const size_type host_vectorsize = 32/sizeof(value_type);
static const bool use_intrinsics = true;
static const size_type num_entry_align = 1;
#elif defined(__MIC__)
static const size_type host_vectorsize = 16;
static const bool use_intrinsics = true;
static const size_type num_entry_align = 8; // avoid use of mask instructions
#else
static const size_type host_vectorsize = 2;
static const bool use_intrinsics = false;
static const size_type num_entry_align = 1;
#endif
static const size_type cuda_vectorsize = 32;
static const bool is_cuda =
#if defined( KOKKOS_HAVE_CUDA )
Kokkos::Impl::is_same<ExecutionSpace,Kokkos::Cuda>::value;
#else
false ;
#endif
static const size_type vectorsize = is_cuda ? cuda_vectorsize : host_vectorsize;
// Alignment in terms of number of entries of CRS rows
static const size_type tensor_align = vectorsize;
private:
template <class, class, class> friend class CrsProductTensor;
typedef Kokkos::View< value_type*, Kokkos::LayoutLeft, execution_space, memory_type > vec_type;
typedef Kokkos::View< size_type*, Kokkos::LayoutLeft, execution_space, memory_type > coord_array_type;
typedef Kokkos::View< size_type*[2], Kokkos::LayoutLeft, execution_space, memory_type > coord2_array_type;
typedef Kokkos::View< value_type*, Kokkos::LayoutLeft, execution_space, memory_type > value_array_type;
typedef Kokkos::View< size_type*, Kokkos::LayoutLeft, execution_space, memory_type > entry_array_type;
typedef Kokkos::View< size_type*, Kokkos::LayoutLeft, execution_space, memory_type > row_map_array_type;
coord_array_type m_coord;
coord2_array_type m_coord2;
value_array_type m_value;
entry_array_type m_num_entry;
row_map_array_type m_row_map;
size_type m_dim;
size_type m_entry_max;
size_type m_nnz;
size_type m_flops;
size_type m_avg_entries_per_row;
struct CijkRowCount {
unsigned count;
unsigned basis;
CijkRowCount()
: count(0)
, basis(0)
{}
};
struct CompareCijkRowCount {
bool operator() (const CijkRowCount& a, const CijkRowCount& b) const {
return a.count < b.count;
}
};
public:
KOKKOS_INLINE_FUNCTION
~CrsProductTensor() {}
KOKKOS_INLINE_FUNCTION
CrsProductTensor() :
m_coord(),
m_coord2(),
m_value(),
m_num_entry(),
m_row_map(),
m_dim(0),
m_entry_max(0),
m_nnz(0),
m_flops(0),
m_avg_entries_per_row(0) {}
template <class M>
KOKKOS_INLINE_FUNCTION
CrsProductTensor( const CrsProductTensor<value_type,execution_space,M> & rhs ) :
m_coord( rhs.m_coord ),
m_coord2( rhs.m_coord2 ),
m_value( rhs.m_value ),
m_num_entry( rhs.m_num_entry ),
m_row_map( rhs.m_row_map ),
m_dim( rhs.m_dim ),
m_entry_max( rhs.m_entry_max ),
m_nnz( rhs.m_nnz ),
m_flops( rhs.m_flops ),
m_avg_entries_per_row( rhs.m_avg_entries_per_row ) {}
template <class M>
KOKKOS_INLINE_FUNCTION
CrsProductTensor &
operator = ( const CrsProductTensor<value_type,execution_space,M> & rhs )
{
m_coord = rhs.m_coord;
m_coord2 = rhs.m_coord2;
m_value = rhs.m_value;
m_num_entry = rhs.m_num_entry;
m_row_map = rhs.m_row_map;
m_dim = rhs.m_dim;
m_entry_max = rhs.m_entry_max;
m_nnz = rhs.m_nnz;
m_flops = rhs.m_flops;
m_avg_entries_per_row = rhs.m_avg_entries_per_row;
return *this;
}
/** \brief Dimension of the tensor. */
KOKKOS_INLINE_FUNCTION
size_type dimension() const { return m_dim; }
/** \brief Is the tensor empty. */
KOKKOS_INLINE_FUNCTION
bool is_empty() const { return m_dim == 0; }
/** \brief Number of sparse entries. */
KOKKOS_INLINE_FUNCTION
size_type entry_count() const
{ return m_coord.dimension_0(); }
/** \brief Maximum sparse entries for any coordinate */
KOKKOS_INLINE_FUNCTION
size_type entry_maximum() const
{ return m_entry_max; }
/** \brief Begin entries with a coordinate 'i' */
KOKKOS_INLINE_FUNCTION
size_type entry_begin( size_type i ) const
{ return m_row_map[i]; }
/** \brief End entries with a coordinate 'i' */
KOKKOS_INLINE_FUNCTION
size_type entry_end( size_type i ) const
{ return m_row_map[i] + m_num_entry(i); }
/** \brief Number of entries with a coordinate 'i' */
KOKKOS_INLINE_FUNCTION
size_type num_entry( size_type i ) const
{ return m_num_entry(i); }
/** \brief Coordinates of an entry */
KOKKOS_INLINE_FUNCTION
const size_type& coord( const size_type entry, const size_type c ) const
{ return m_coord2( entry, c ); }
/** \brief Coordinates of an entry */
KOKKOS_INLINE_FUNCTION
const size_type& coord( const size_type entry ) const
{ return m_coord( entry ); }
/** \brief Value of an entry */
KOKKOS_INLINE_FUNCTION
const value_type & value( const size_type entry ) const
{ return m_value( entry ); }
/** \brief Number of non-zero's */
KOKKOS_INLINE_FUNCTION
size_type num_non_zeros() const
{ return m_nnz; }
/** \brief Number flop's per multiply-add */
KOKKOS_INLINE_FUNCTION
size_type num_flops() const
{ return m_flops; }
/** \brief Number average number of entries per row */
KOKKOS_INLINE_FUNCTION
size_type avg_entries_per_row() const
{ return m_avg_entries_per_row; }
template <typename OrdinalType>
static CrsProductTensor
create( const Stokhos::ProductBasis<OrdinalType,ValueType>& basis,
const Stokhos::Sparse3Tensor<OrdinalType,ValueType>& Cijk,
const Teuchos::ParameterList& params = Teuchos::ParameterList())
{
typedef Stokhos::Sparse3Tensor<OrdinalType,ValueType> Cijk_type;
// Note (etp 01/08/15 Commenting out the sorting as it causes a really
// weird compiler error when compiling with NVCC. It seems to think the
// < in CompareCijkRowCount() is part of a template parameter. We don't
// seem to use this option, so I am just commenting it out.
// bool sort_nnz = false;
// if (params.isParameter("Sort Nonzeros"))
// sort_nnz = params.get<bool>("Sort Nonzeros");
// Compute number of non-zeros for each i
const size_type dimension = basis.size();
std::vector< size_t > coord_work( dimension, (size_t) 0 );
size_type entry_count = 0;
for (typename Cijk_type::i_iterator i_it=Cijk.i_begin();
i_it!=Cijk.i_end(); ++i_it) {
OrdinalType i = index(i_it);
for (typename Cijk_type::ik_iterator k_it = Cijk.k_begin(i_it);
k_it != Cijk.k_end(i_it); ++k_it) {
OrdinalType k = index(k_it);
for (typename Cijk_type::ikj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
if (j >= k) {
++coord_work[i];
++entry_count;
}
}
}
}
// Compute average nonzeros per row (must be before padding)
size_type avg_entries_per_row = entry_count / dimension;
// Pad each row to have size divisible by alignment size
for ( size_type i = 0; i < dimension; ++i ) {
const size_t rem = coord_work[i] % tensor_align;
if (rem > 0) {
const size_t pad = tensor_align - rem;
coord_work[i] += pad;
entry_count += pad;
}
}
// Sort based on number of non-zeros
std::vector< CijkRowCount > row_count( dimension );
for ( size_type i = 0; i < dimension; ++i ) {
row_count[i].count = coord_work[i];
row_count[i].basis = i;
}
// Note (etp 01/08/15 See above.
// if (sort_nnz)
// std::sort( row_count.begin(), row_count.end(), CompareCijkRowCount() );
std::vector<size_type> sorted_row_map( dimension );
for ( size_type i = 0; i < dimension; ++i ) {
coord_work[i] = row_count[i].count;
sorted_row_map[ row_count[i].basis ] = i;
}
// Allocate tensor data
// coord and coord2 are initialized to zero because otherwise we get
// seg faults in the MIC algorithm when processing the tail of each
// tensor row. Not quite sure why as the coord loads are padded to
// length 16 and are masked for the remainder (unless it does load x[j]
// anyway and masks off the result, so j needs to be valid).
CrsProductTensor tensor;
tensor.m_coord = coord_array_type("tensor_coord", entry_count );
tensor.m_coord2 = coord2_array_type( "tensor_coord2", entry_count );
tensor.m_value = value_array_type( Kokkos::ViewAllocateWithoutInitializing("tensor_value"), entry_count );
tensor.m_num_entry = entry_array_type( Kokkos::ViewAllocateWithoutInitializing("tensor_num_entry"), dimension );
tensor.m_row_map = row_map_array_type( Kokkos::ViewAllocateWithoutInitializing("tensor_row_map"), dimension+1 );
tensor.m_dim = dimension;
tensor.m_entry_max = 0;
tensor.m_avg_entries_per_row = avg_entries_per_row;
// Create mirror, is a view if is host memory
typename coord_array_type::HostMirror
host_coord = Kokkos::create_mirror_view( tensor.m_coord );
typename coord2_array_type::HostMirror
host_coord2 = Kokkos::create_mirror_view( tensor.m_coord2 );
typename value_array_type::HostMirror
host_value = Kokkos::create_mirror_view( tensor.m_value );
typename entry_array_type::HostMirror
host_num_entry = Kokkos::create_mirror_view( tensor.m_num_entry );
typename entry_array_type::HostMirror
host_row_map = Kokkos::create_mirror_view( tensor.m_row_map );
// Compute row map
size_type sum = 0;
host_row_map(0) = 0;
for ( size_type i = 0; i < dimension; ++i ) {
sum += coord_work[i];
host_row_map(i+1) = sum;
host_num_entry(i) = 0;
}
for ( size_type iCoord = 0; iCoord < dimension; ++iCoord ) {
coord_work[iCoord] = host_row_map[iCoord];
}
// Initialize values and coordinates to zero since we will have extra
// ones for alignment
Kokkos::deep_copy( host_value, 0.0 );
Kokkos::deep_copy( host_coord, 0 );
Kokkos::deep_copy( host_coord2, 0 );
for (typename Cijk_type::i_iterator i_it=Cijk.i_begin();
i_it!=Cijk.i_end(); ++i_it) {
OrdinalType i = index(i_it);
const size_type row = sorted_row_map[i];
for (typename Cijk_type::ik_iterator k_it = Cijk.k_begin(i_it);
k_it != Cijk.k_end(i_it); ++k_it) {
OrdinalType k = index(k_it);
for (typename Cijk_type::ikj_iterator j_it = Cijk.j_begin(k_it);
j_it != Cijk.j_end(k_it); ++j_it) {
OrdinalType j = index(j_it);
ValueType c = Stokhos::value(j_it);
if (j >= k) {
const size_type n = coord_work[row]; ++coord_work[row];
host_value(n) = (j != k) ? c : 0.5*c;
host_coord2(n,0) = j;
host_coord2(n,1) = k;
host_coord(n) = ( k << 16 ) | j;
++host_num_entry(row);
++tensor.m_nnz;
}
}
}
// Align num_entry
host_num_entry(row) =
(host_num_entry(row) + num_entry_align-1) & ~(num_entry_align-1);
}
// Copy data to device if necessary
Kokkos::deep_copy( tensor.m_coord, host_coord );
Kokkos::deep_copy( tensor.m_coord2, host_coord2 );
Kokkos::deep_copy( tensor.m_value, host_value );
Kokkos::deep_copy( tensor.m_num_entry, host_num_entry );
Kokkos::deep_copy( tensor.m_row_map, host_row_map );
for ( size_type i = 0; i < dimension; ++i ) {
tensor.m_entry_max = std::max( tensor.m_entry_max, host_num_entry(i) );
}
tensor.m_flops = 5*tensor.m_nnz + dimension;
return tensor;
}
static CrsProductTensor createMeanBased()
{
const size_type dimension = 1;
const size_type entry_count = 1;
// Allocate tensor data
// coord and coord2 are initialized to zero because otherwise we get
// seg faults in the MIC algorithm when processing the tail of each
// tensor row. Not quite sure why as the coord loads are padded to
// length 16 and are masked for the remainder (unless it does load x[j]
// anyway and masks off the result, so j needs to be valid).
CrsProductTensor tensor;
tensor.m_coord = coord_array_type("tensor_coord", entry_count );
tensor.m_coord2 = coord2_array_type( "tensor_coord2", entry_count );
tensor.m_value = value_array_type( Kokkos::ViewAllocateWithoutInitializing("tensor_value"), entry_count );
tensor.m_num_entry = entry_array_type( Kokkos::ViewAllocateWithoutInitializing("tensor_num_entry"), dimension );
tensor.m_row_map = row_map_array_type( Kokkos::ViewAllocateWithoutInitializing("tensor_row_map"), dimension+1 );
tensor.m_dim = dimension;
tensor.m_entry_max = 1;
tensor.m_avg_entries_per_row = 1;
tensor.m_nnz = 1;
tensor.m_flops = 5*tensor.m_nnz + dimension;
// Create mirror, is a view if is host memory
typename coord_array_type::HostMirror
host_coord = Kokkos::create_mirror_view( tensor.m_coord );
typename coord2_array_type::HostMirror
host_coord2 = Kokkos::create_mirror_view( tensor.m_coord2 );
typename value_array_type::HostMirror
host_value = Kokkos::create_mirror_view( tensor.m_value );
typename entry_array_type::HostMirror
host_num_entry = Kokkos::create_mirror_view( tensor.m_num_entry );
typename entry_array_type::HostMirror
host_row_map = Kokkos::create_mirror_view( tensor.m_row_map );
// Compute row map
host_row_map(0) = 0;
host_row_map(1) = 1;
host_num_entry(0) = 1;
// Compute tensor values
host_value(0) = 0.5;
host_coord2(0,0) = 0;
host_coord2(0,1) = 0;
host_coord(0) = 0;
// Copy data to device if necessary
Kokkos::deep_copy( tensor.m_coord, host_coord );
Kokkos::deep_copy( tensor.m_coord2, host_coord2 );
Kokkos::deep_copy( tensor.m_value, host_value );
Kokkos::deep_copy( tensor.m_num_entry, host_num_entry );
Kokkos::deep_copy( tensor.m_row_map, host_row_map );
return tensor;
}
static HostMirror
create_mirror_view( const CrsProductTensor& tensor ) {
HostMirror host_tensor;
host_tensor.m_coord = Kokkos::create_mirror_view( tensor.m_coord );
host_tensor.m_coord2 = Kokkos::create_mirror_view( tensor.m_coord2 );
host_tensor.m_value = Kokkos::create_mirror_view( tensor.m_value );
host_tensor.m_num_entry = Kokkos::create_mirror_view( tensor.m_num_entry );
host_tensor.m_row_map = Kokkos::create_mirror_view( tensor.m_row_map );
host_tensor.m_dim = tensor.m_dim;
host_tensor.m_entry_max = tensor.m_entry_max;
host_tensor.m_avg_entries_per_row = tensor.m_avg_entries_per_row;
host_tensor.m_nnz = tensor.m_nnz;
host_tensor.m_flops = tensor.m_flops;
return host_tensor;
}
template < class DstDevice, class DstMemory >
static void
deep_copy( const CrsProductTensor<ValueType,DstDevice,DstMemory>& dst ,
const CrsProductTensor& src ) {
Kokkos::deep_copy( dst.m_coord, src.m_coord );
Kokkos::deep_copy( dst.m_coord2, src.m_coord2 );
Kokkos::deep_copy( dst.m_value, src.m_value );
Kokkos::deep_copy( dst.m_num_entry, src.m_num_entry );
Kokkos::deep_copy( dst.m_row_map, src.m_row_map );
}
};
template< class Device, typename OrdinalType, typename ValueType>
CrsProductTensor<ValueType, Device>
create_product_tensor(
const Stokhos::ProductBasis<OrdinalType,ValueType>& basis,
const Stokhos::Sparse3Tensor<OrdinalType,ValueType>& Cijk,
const Teuchos::ParameterList& params = Teuchos::ParameterList())
{
return CrsProductTensor<ValueType, Device>::create(basis, Cijk, params );
}
template< class Device, typename OrdinalType, typename ValueType,
class Memory >
CrsProductTensor<ValueType, Device, Memory>
create_product_tensor(
const Stokhos::ProductBasis<OrdinalType,ValueType>& basis,
const Stokhos::Sparse3Tensor<OrdinalType,ValueType>& Cijk,
const Teuchos::ParameterList& params = Teuchos::ParameterList())
{
return CrsProductTensor<ValueType, Device, Memory>::create(
basis, Cijk, params );
}
template< class Device, typename OrdinalType, typename ValueType>
CrsProductTensor<ValueType, Device>
create_mean_based_product_tensor()
{
return CrsProductTensor<ValueType, Device>::createMeanBased();
}
template< class Device, typename OrdinalType, typename ValueType,
class Memory >
CrsProductTensor<ValueType, Device, Memory>
create_mean_based_product_tensor()
{
return CrsProductTensor<ValueType, Device, Memory>::createMeanBased();
}
template < class ValueType, class Device, class Memory >
inline
typename CrsProductTensor<ValueType,Device,Memory>::HostMirror
create_mirror_view( const CrsProductTensor<ValueType,Device,Memory> & src )
{
return CrsProductTensor<ValueType,Device,Memory>::create_mirror_view( src );
}
template < class ValueType,
class DstDevice, class DstMemory,
class SrcDevice, class SrcMemory >
void
deep_copy( const CrsProductTensor<ValueType,DstDevice,DstMemory> & dst ,
const CrsProductTensor<ValueType,SrcDevice,SrcMemory> & src )
{
return CrsProductTensor<ValueType,SrcDevice,SrcMemory>::deep_copy( dst, src );
}
template < typename ValueType, typename Device >
class BlockMultiply< CrsProductTensor< ValueType , Device > >
{
public:
typedef Device execution_space;
typedef CrsProductTensor< ValueType , execution_space > tensor_type ;
typedef typename tensor_type::size_type size_type ;
// Whether to use manual or auto-vectorization
#ifdef __MIC__
#define USE_AUTO_VECTORIZATION 1
#else
#define USE_AUTO_VECTORIZATION 0
#endif
#if defined(__INTEL_COMPILER) && USE_AUTO_VECTORIZATION
// Version leveraging intel vectorization
template< typename MatrixValue , typename VectorValue >
KOKKOS_INLINE_FUNCTION
static void apply( const tensor_type & tensor ,
const MatrixValue * const a ,
const VectorValue * const x ,
VectorValue * const y ,
const VectorValue & alpha = VectorValue(1) )
{
// The intel compiler doesn't seem to be able to vectorize through
// the coord() calls, so extract pointers
const size_type * cj = &tensor.coord(0,0);
const size_type * ck = &tensor.coord(0,1);
const size_type nDim = tensor.dimension();
for ( size_type iy = 0 ; iy < nDim ; ++iy ) {
const size_type nEntry = tensor.num_entry(iy);
const size_type iEntryBeg = tensor.entry_begin(iy);
const size_type iEntryEnd = iEntryBeg + nEntry;
VectorValue ytmp = 0;
#pragma simd vectorlength(tensor_type::vectorsize)
#pragma ivdep
#pragma vector aligned
for (size_type iEntry = iEntryBeg; iEntry<iEntryEnd; ++iEntry) {
const size_type j = cj[iEntry]; //tensor.coord(iEntry,0);
const size_type k = ck[iEntry]; //tensor.coord(iEntry,1);
ytmp += tensor.value(iEntry) * ( a[j] * x[k] + a[k] * x[j] );
}
y[iy] += alpha * ytmp ;
}
}
#elif defined(__MIC__)
// Version specific to MIC architecture using manual vectorization
template< typename MatrixValue , typename VectorValue >
KOKKOS_INLINE_FUNCTION
static void apply( const tensor_type & tensor ,
const MatrixValue * const a ,
const VectorValue * const x ,
VectorValue * const y ,
const VectorValue & alpha = VectorValue(1) )
{
const size_type nDim = tensor.dimension();
for ( size_type iy = 0 ; iy < nDim ; ++iy ) {
const size_type nEntry = tensor.num_entry(iy);
const size_type iEntryBeg = tensor.entry_begin(iy);
const size_type iEntryEnd = iEntryBeg + nEntry;
size_type iEntry = iEntryBeg;
VectorValue ytmp = 0 ;
const size_type nBlock = nEntry / tensor_type::vectorsize;
const size_type nEntryB = nBlock * tensor_type::vectorsize;
const size_type iEnd = iEntryBeg + nEntryB;
typedef TinyVec<ValueType,tensor_type::vectorsize,tensor_type::use_intrinsics> TV;
TV vy;
vy.zero();
for (size_type block=0; block<nBlock; ++block, iEntry+=tensor_type::vectorsize) {
const size_type *j = &tensor.coord(iEntry,0);
const size_type *k = &tensor.coord(iEntry,1);
TV aj(a, j), ak(a, k), xj(x, j), xk(x, k),
c(&(tensor.value(iEntry)));
// vy += c * ( aj * xk + ak * xj)
aj.times_equal(xk);
aj.multiply_add(ak, xj);
vy.multiply_add(c, aj);
}
ytmp += vy.sum();
// The number of nonzeros is always constrained to be a multiple of 8
const size_type rem = iEntryEnd-iEntry;
if (rem >= 8) {
typedef TinyVec<ValueType,8,tensor_type::use_intrinsics> TV2;
const size_type *j = &tensor.coord(iEntry,0);
const size_type *k = &tensor.coord(iEntry,1);
TV2 aj(a, j), ak(a, k), xj(x, j), xk(x, k),
c(&(tensor.value(iEntry)));
// vy += c * ( aj * xk + ak * xj)
aj.times_equal(xk);
aj.multiply_add(ak, xj);
aj.times_equal(c);
ytmp += aj.sum();
}
y[iy] += alpha * ytmp ;
}
}
#else
// General version
template< typename MatrixValue , typename VectorValue >
KOKKOS_INLINE_FUNCTION
static void apply( const tensor_type & tensor ,
const MatrixValue * const a ,
const VectorValue * const x ,
VectorValue * const y ,
const VectorValue & alpha = VectorValue(1) )
{
const size_type nDim = tensor.dimension();
for ( size_type iy = 0 ; iy < nDim ; ++iy ) {
const size_type nEntry = tensor.num_entry(iy);
const size_type iEntryBeg = tensor.entry_begin(iy);
const size_type iEntryEnd = iEntryBeg + nEntry;
size_type iEntry = iEntryBeg;
VectorValue ytmp = 0 ;
// Do entries with a blocked loop of size vectorsize
if (tensor_type::vectorsize > 1 && nEntry >= tensor_type::vectorsize) {
const size_type nBlock = nEntry / tensor_type::vectorsize;
const size_type nEntryB = nBlock * tensor_type::vectorsize;
const size_type iEnd = iEntryBeg + nEntryB;
typedef TinyVec<ValueType,tensor_type::vectorsize,tensor_type::use_intrinsics> TV;
TV vy;
vy.zero();
for (; iEntry<iEnd; iEntry+=tensor_type::vectorsize) {
const size_type *j = &tensor.coord(iEntry,0);
const size_type *k = &tensor.coord(iEntry,1);
TV aj(a, j), ak(a, k), xj(x, j), xk(x, k), c(&(tensor.value(iEntry)));
// vy += c * ( aj * xk + ak * xj)
aj.times_equal(xk);
aj.multiply_add(ak, xj);
vy.multiply_add(c, aj);
}
ytmp += vy.sum();
}
// Do remaining entries with a scalar loop
for ( ; iEntry<iEntryEnd; ++iEntry) {
const size_type j = tensor.coord(iEntry,0);
const size_type k = tensor.coord(iEntry,1);
ytmp += tensor.value(iEntry) * ( a[j] * x[k] + a[k] * x[j] );
}
y[iy] += alpha * ytmp ;
}
}
#endif
KOKKOS_INLINE_FUNCTION
static size_type matrix_size( const tensor_type & tensor )
{ return tensor.dimension(); }
KOKKOS_INLINE_FUNCTION
static size_type vector_size( const tensor_type & tensor )
{ return tensor.dimension(); }
};
// Specialization of Multiply< BlockCrsMatrix< BlockSpec, ... > > > for
// CrsProductTensor, which provides a version that processes blocks of FEM
// columns together to reduce the number of global reads of the sparse 3 tensor
// Even though this isn't specific to Threads, templating on Device creates a
// duplicate specialization error for Cuda. Need to see if we can fix this,
// or put the implementation in another class easily specialized for Threads,
// OpenMP, ...
template< typename ValueType , typename MatrixValue , typename VectorValue ,
typename Device >
class MultiplyImpl {
public:
typedef Device execution_space ;
typedef CrsProductTensor< ValueType , execution_space > tensor_type;
typedef StochasticProductTensor< ValueType, tensor_type, execution_space > BlockSpec;
typedef typename BlockSpec::size_type size_type ;
typedef Kokkos::View< VectorValue** , Kokkos::LayoutLeft , execution_space > block_vector_type ;
typedef BlockCrsMatrix< BlockSpec , MatrixValue , execution_space > matrix_type ;
const matrix_type m_A ;
const block_vector_type m_x ;
const block_vector_type m_y ;
MultiplyImpl( const matrix_type & A ,
const block_vector_type & x ,
const block_vector_type & y )
: m_A( A )
, m_x( x )
, m_y( y )
{}
//--------------------------------------------------------------------------
// A( storage_size( m_A.block.size() ) , m_A.graph.row_map.size() );
// x( m_A.block.dimension() , m_A.graph.row_map.first_count() );
// y( m_A.block.dimension() , m_A.graph.row_map.first_count() );
//
KOKKOS_INLINE_FUNCTION
void operator()( const size_type iBlockRow ) const
{
// Prefer that y[ m_A.block.dimension() ] be scratch space
// on the local thread, but cannot dynamically allocate
VectorValue * const y = & m_y(0,iBlockRow);
const size_type iEntryBegin = m_A.graph.row_map[ iBlockRow ];
const size_type iEntryEnd = m_A.graph.row_map[ iBlockRow + 1 ];
// Leading dimension guaranteed contiguous for LayoutLeft
for ( size_type j = 0 ; j < m_A.block.dimension() ; ++j ) { y[j] = 0 ; }
for ( size_type iEntry = iEntryBegin ; iEntry < iEntryEnd ; ++iEntry ) {
const VectorValue * const x = & m_x( 0 , m_A.graph.entries(iEntry) );
const MatrixValue * const a = & m_A.values( 0 , iEntry );
BlockMultiply< BlockSpec >::apply( m_A.block , a , x , y );
}
}
/*
* Compute work range = (begin, end) such that adjacent threads write to
* separate cache lines
*/
KOKKOS_INLINE_FUNCTION
std::pair< size_type , size_type >
compute_work_range( const size_type work_count ,
const size_type thread_count ,
const size_type thread_rank ) const
{
enum { work_align = 64 / sizeof(VectorValue) };
enum { work_shift = Kokkos::Impl::power_of_two< work_align >::value };
enum { work_mask = work_align - 1 };
const size_type work_per_thread =
( ( ( ( work_count + work_mask ) >> work_shift ) + thread_count - 1 ) /
thread_count ) << work_shift ;
const size_type work_begin =
std::min( thread_rank * work_per_thread , work_count );
const size_type work_end =
std::min( work_begin + work_per_thread , work_count );
return std::make_pair( work_begin , work_end );
}
#if defined(__MIC__)
// A MIC-specific version of the block-multiply algorithm, where block here
// means processing multiple FEM columns at a time
KOKKOS_INLINE_FUNCTION
void operator()( const typename Kokkos::TeamPolicy< execution_space >::member_type & device ) const
{
const size_type iBlockRow = device.league_rank();
// Check for valid row
const size_type row_count = m_A.graph.row_map.dimension_0()-1;
if (iBlockRow >= row_count)
return;
const size_type num_thread = device.team_size();
const size_type thread_idx = device.team_rank();
std::pair<size_type,size_type> work_range =
compute_work_range(m_A.block.dimension(), num_thread, thread_idx);
// Prefer that y[ m_A.block.dimension() ] be scratch space
// on the local thread, but cannot dynamically allocate
VectorValue * const y = & m_y(0,iBlockRow);
// Leading dimension guaranteed contiguous for LayoutLeft
for ( size_type j = work_range.first ; j < work_range.second ; ++j )
y[j] = 0 ;
const tensor_type& tensor = m_A.block.tensor();
const size_type iBlockEntryBeg = m_A.graph.row_map[ iBlockRow ];
const size_type iBlockEntryEnd = m_A.graph.row_map[ iBlockRow + 1 ];
const size_type BlockSize = 9;
const size_type numBlock =
(iBlockEntryEnd-iBlockEntryBeg+BlockSize-1) / BlockSize;
const MatrixValue* sh_A[BlockSize];
const VectorValue* sh_x[BlockSize];
size_type iBlockEntry = iBlockEntryBeg;
for (size_type block = 0; block<numBlock; ++block, iBlockEntry+=BlockSize) {
const size_type block_size =
block == numBlock-1 ? iBlockEntryEnd-iBlockEntry : BlockSize;
for ( size_type col = 0; col < block_size; ++col ) {
const size_type iBlockColumn = m_A.graph.entries( iBlockEntry + col );
sh_x[col] = & m_x( 0 , iBlockColumn );
sh_A[col] = & m_A.values( 0 , iBlockEntry + col );
}
for ( size_type iy = work_range.first ; iy < work_range.second ; ++iy ) {
const size_type nEntry = tensor.num_entry(iy);
const size_type iEntryBeg = tensor.entry_begin(iy);
const size_type iEntryEnd = iEntryBeg + nEntry;
size_type iEntry = iEntryBeg;
VectorValue ytmp = 0 ;
// Do entries with a blocked loop of size blocksize
const size_type nBlock = nEntry / tensor_type::vectorsize;
const size_type nEntryB = nBlock * tensor_type::vectorsize;
const size_type iEnd = iEntryBeg + nEntryB;
typedef TinyVec<ValueType,tensor_type::vectorsize,tensor_type::use_intrinsics> ValTV;
typedef TinyVec<MatrixValue,tensor_type::vectorsize,tensor_type::use_intrinsics> MatTV;
typedef TinyVec<VectorValue,tensor_type::vectorsize,tensor_type::use_intrinsics> VecTV;
VecTV vy;
vy.zero();
for (size_type block=0; block<nBlock; ++block, iEntry+=tensor_type::vectorsize) {
const size_type *j = &tensor.coord(iEntry,0);
const size_type *k = &tensor.coord(iEntry,1);
ValTV c(&(tensor.value(iEntry)));
for ( size_type col = 0; col < block_size; ++col ) {
MatTV aj(sh_A[col], j), ak(sh_A[col], k);
VecTV xj(sh_x[col], j), xk(sh_x[col], k);
// vy += c * ( aj * xk + ak * xj)
aj.times_equal(xk);
aj.multiply_add(ak, xj);
vy.multiply_add(c, aj);
}
}
ytmp += vy.sum();
// The number of nonzeros is always constrained to be a multiple of 8
const size_type rem = iEntryEnd-iEntry;
if (rem >= 8) {
typedef TinyVec<ValueType,8,tensor_type::use_intrinsics> ValTV2;
typedef TinyVec<MatrixValue,8,tensor_type::use_intrinsics> MatTV2;
typedef TinyVec<VectorValue,8,tensor_type::use_intrinsics> VecTV2;
const size_type *j = &tensor.coord(iEntry,0);
const size_type *k = &tensor.coord(iEntry,1);
ValTV2 c(&(tensor.value(iEntry)));
for ( size_type col = 0; col < block_size; ++col ) {
MatTV2 aj(sh_A[col], j), ak(sh_A[col], k);
VecTV2 xj(sh_x[col], j), xk(sh_x[col], k);
// vy += c * ( aj * xk + ak * xj)
aj.times_equal(xk);
aj.multiply_add(ak, xj);
aj.times_equal(c);
ytmp += aj.sum();
}
}
y[iy] += ytmp ;
}
// Add a team barrier to keep the thread team in-sync before going on
// to the next block
device.team_barrier();
}
}
#else
// A general hand-vectorized version of the block multiply algorithm, where
// block here means processing multiple FEM columns at a time. Note that
// auto-vectorization of a block algorithm doesn't work, because the
// stochastic loop is not the inner-most loop.
KOKKOS_INLINE_FUNCTION
void operator()( const typename Kokkos::TeamPolicy< execution_space >::member_type & device ) const
{
const size_type iBlockRow = device.league_rank();
// Check for valid row
const size_type row_count = m_A.graph.row_map.dimension_0()-1;
if (iBlockRow >= row_count)
return;
const size_type num_thread = device.team_size();
const size_type thread_idx = device.team_rank();
std::pair<size_type,size_type> work_range =
compute_work_range(m_A.block.dimension(), num_thread, thread_idx);
// Prefer that y[ m_A.block.dimension() ] be scratch space
// on the local thread, but cannot dynamically allocate
VectorValue * const y = & m_y(0,iBlockRow);
// Leading dimension guaranteed contiguous for LayoutLeft
for ( size_type j = work_range.first ; j < work_range.second ; ++j )
y[j] = 0 ;
const tensor_type& tensor = m_A.block.tensor();
const size_type iBlockEntryBeg = m_A.graph.row_map[ iBlockRow ];
const size_type iBlockEntryEnd = m_A.graph.row_map[ iBlockRow + 1 ];
const size_type BlockSize = 14;
const size_type numBlock =
(iBlockEntryEnd-iBlockEntryBeg+BlockSize-1) / BlockSize;
const MatrixValue* sh_A[BlockSize];
const VectorValue* sh_x[BlockSize];
size_type iBlockEntry = iBlockEntryBeg;
for (size_type block = 0; block<numBlock; ++block, iBlockEntry+=BlockSize) {
const size_type block_size =
block == numBlock-1 ? iBlockEntryEnd-iBlockEntry : BlockSize;
for ( size_type col = 0; col < block_size; ++col ) {
const size_type iBlockColumn = m_A.graph.entries( iBlockEntry + col );
sh_x[col] = & m_x( 0 , iBlockColumn );
sh_A[col] = & m_A.values( 0 , iBlockEntry + col );
}
for ( size_type iy = work_range.first ; iy < work_range.second ; ++iy ) {
const size_type nEntry = tensor.num_entry(iy);
const size_type iEntryBeg = tensor.entry_begin(iy);
const size_type iEntryEnd = iEntryBeg + nEntry;
size_type iEntry = iEntryBeg;
VectorValue ytmp = 0 ;
// Do entries with a blocked loop of size blocksize
if (tensor_type::vectorsize > 1 && nEntry >= tensor_type::vectorsize) {
const size_type nBlock = nEntry / tensor_type::vectorsize;
const size_type nEntryB = nBlock * tensor_type::vectorsize;
const size_type iEnd = iEntryBeg + nEntryB;
typedef TinyVec<ValueType,tensor_type::vectorsize,tensor_type::use_intrinsics> ValTV;
typedef TinyVec<MatrixValue,tensor_type::vectorsize,tensor_type::use_intrinsics> MatTV;
typedef TinyVec<VectorValue,tensor_type::vectorsize,tensor_type::use_intrinsics> VecTV;
VecTV vy;
vy.zero();
for (; iEntry<iEnd; iEntry+=tensor_type::vectorsize) {
const size_type *j = &tensor.coord(iEntry,0);
const size_type *k = &tensor.coord(iEntry,1);
ValTV c(&(tensor.value(iEntry)));
for ( size_type col = 0; col < block_size; ++col ) {
MatTV aj(sh_A[col], j), ak(sh_A[col], k);
VecTV xj(sh_x[col], j), xk(sh_x[col], k);
// vy += c * ( aj * xk + ak * xj)
aj.times_equal(xk);
aj.multiply_add(ak, xj);
vy.multiply_add(c, aj);
}
}
ytmp += vy.sum();
}
// Do remaining entries with a scalar loop
for ( ; iEntry<iEntryEnd; ++iEntry) {
const size_type j = tensor.coord(iEntry,0);
const size_type k = tensor.coord(iEntry,1);
ValueType cijk = tensor.value(iEntry);
for ( size_type col = 0; col < block_size; ++col ) {
ytmp += cijk * ( sh_A[col][j] * sh_x[col][k] +
sh_A[col][k] * sh_x[col][j] );
}
}
y[iy] += ytmp ;
}
// Add a team barrier to keep the thread team in-sync before going on
// to the next block
device.team_barrier();
}
}
#endif
static void apply( const matrix_type & A ,
const block_vector_type & x ,
const block_vector_type & y )
{
// Generally the block algorithm seems to perform better on the MIC,
// as long as the stochastic size isn't too big, but doesn't perform
// any better on the CPU (probably because the CPU has a fat L3 cache
// to store the sparse 3 tensor).
#ifdef __MIC__
const bool use_block_algorithm = true;
#else
const bool use_block_algorithm = false;
#endif
const size_t row_count = A.graph.row_map.dimension_0() - 1 ;
if (use_block_algorithm) {
#ifdef __MIC__
const size_t team_size = 4; // 4 hyperthreads for MIC
#else
const size_t team_size = 2; // 2 for everything else
#endif
const size_t league_size = row_count;
Kokkos::TeamPolicy< execution_space > config(league_size, team_size);
Kokkos::parallel_for( config , MultiplyImpl(A,x,y) );
}
else {
Kokkos::parallel_for( row_count , MultiplyImpl(A,x,y) );
}
}
};
//----------------------------------------------------------------------------
} /* namespace Stokhos */
//----------------------------------------------------------------------------
//----------------------------------------------------------------------------
// Inject some functions into the Kokkos namespace
namespace Kokkos {
using Stokhos::create_mirror_view;
using Stokhos::deep_copy;
} // namespace Kokkos
#endif /* #ifndef STOKHOS_CRSPRODUCTTENSOR_HPP */
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