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/*
* This is an extension of the original CUSP csr_vector.h SPMV implementation. * It is based on the Code and incorporates changes as to cope with the details * of the StoRM code. * As this is mostly copy & paste, the original license still applies. */
/*
* Copyright 2008-2009 NVIDIA Corporation * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0
* * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */
#pragma once
#include <limits>
#include <cstdint>
#include <algorithm>
#include <math_functions.h>
#include <cusp/detail/device/spmv/csr_vector.h>
namespace cusp { namespace detail { namespace device {
//////////////////////////////////////////////////////////////////////////////
// CSR SpMV kernels based on a vector model (one warp per row)
//////////////////////////////////////////////////////////////////////////////
//
// spmv_csr_vector_device
// Each row of the CSR matrix is assigned to a warp. The warp computes
// y[i] = A[i,:] * x, i.e. the dot product of the i-th row of A with
// the x vector, in parallel. This division of work implies that
// the CSR index and data arrays (Aj and Ax) are accessed in a contiguous
// manner (but generally not aligned). On GT200 these accesses are
// coalesced, unlike kernels based on the one-row-per-thread division of
// work. Since an entire 32-thread warp is assigned to each row, many
// threads will remain idle when their row contains a small number
// of elements. This code relies on implicit synchronization among
// threads in a warp.
//
// spmv_csr_vector_tex_device
// Same as spmv_csr_vector_tex_device, except that the texture cache is
// used for accessing the x vector.
//
// Note: THREADS_PER_VECTOR must be one of [2,4,8,16,32]
template <unsigned int VECTORS_PER_BLOCK, unsigned int THREADS_PER_VECTOR, bool UseCache> __launch_bounds__(VECTORS_PER_BLOCK * THREADS_PER_VECTOR,1) __global__ void storm_cuda_opt_spmv_csr_vector_kernel_double(const uint_fast64_t num_rows, const uint_fast64_t * __restrict__ matrixRowIndices, const double * __restrict__ matrixColumnIndicesAndValues, const double * __restrict__ x, double * __restrict__ y) { __shared__ volatile double sdata[VECTORS_PER_BLOCK * THREADS_PER_VECTOR + THREADS_PER_VECTOR / 2]; // padded to avoid reduction conditionals
__shared__ volatile uint_fast64_t ptrs[VECTORS_PER_BLOCK][2]; const uint_fast64_t THREADS_PER_BLOCK = VECTORS_PER_BLOCK * THREADS_PER_VECTOR;
const uint_fast64_t thread_id = THREADS_PER_BLOCK * blockIdx.x + threadIdx.x; // global thread index
const uint_fast64_t thread_lane = threadIdx.x & (THREADS_PER_VECTOR - 1); // thread index within the vector
const uint_fast64_t vector_id = thread_id / THREADS_PER_VECTOR; // global vector index
const uint_fast64_t vector_lane = threadIdx.x / THREADS_PER_VECTOR; // vector index within the block
const uint_fast64_t num_vectors = VECTORS_PER_BLOCK * gridDim.x; // total number of active vectors
for(uint_fast64_t row = vector_id; row < num_rows; row += num_vectors) { // use two threads to fetch Ap[row] and Ap[row+1]
// this is considerably faster than the straightforward version
if(thread_lane < 2) ptrs[vector_lane][thread_lane] = matrixRowIndices[row + thread_lane];
const uint_fast64_t row_start = ptrs[vector_lane][0]; //same as: row_start = Ap[row];
const uint_fast64_t row_end = ptrs[vector_lane][1]; //same as: row_end = Ap[row+1];
// initialize local sum
double sum = 0; if (THREADS_PER_VECTOR == 32 && row_end - row_start > 32) { // ensure aligned memory access to Aj and Ax
uint_fast64_t jj = row_start - (row_start & (THREADS_PER_VECTOR - 1)) + thread_lane;
// accumulate local sums
if(jj >= row_start && jj < row_end) { sum += matrixColumnIndicesAndValues[2 * jj + 1] * fetch_x<UseCache>(*reinterpret_cast<uint_fast64_t const*>(matrixColumnIndicesAndValues + 2 * jj), x); //sum += reinterpret_cast<ValueType const*>(matrixColumnIndicesAndValues)[2*jj + 1] * fetch_x<UseCache>(matrixColumnIndicesAndValues[2*jj], x);
} // accumulate local sums
for(jj += THREADS_PER_VECTOR; jj < row_end; jj += THREADS_PER_VECTOR) { //sum += reinterpret_cast<ValueType const*>(matrixColumnIndicesAndValues)[2*jj + 1] * fetch_x<UseCache>(matrixColumnIndicesAndValues[2*jj], x);
sum += matrixColumnIndicesAndValues[2 * jj + 1] * fetch_x<UseCache>(*reinterpret_cast<uint_fast64_t const*>(matrixColumnIndicesAndValues + 2 * jj), x); } } else { // accumulate local sums
for(uint_fast64_t jj = row_start + thread_lane; jj < row_end; jj += THREADS_PER_VECTOR) { //sum += reinterpret_cast<ValueType const*>(matrixColumnIndicesAndValues)[2*jj + 1] * fetch_x<UseCache>(matrixColumnIndicesAndValues[2*jj], x);
sum += matrixColumnIndicesAndValues[2 * jj + 1] * fetch_x<UseCache>(*reinterpret_cast<uint_fast64_t const*>(matrixColumnIndicesAndValues + 2 * jj), x); } }
// store local sum in shared memory
sdata[threadIdx.x] = sum; // reduce local sums to row sum
if (THREADS_PER_VECTOR > 16) sdata[threadIdx.x] = sum = sum + sdata[threadIdx.x + 16]; if (THREADS_PER_VECTOR > 8) sdata[threadIdx.x] = sum = sum + sdata[threadIdx.x + 8]; if (THREADS_PER_VECTOR > 4) sdata[threadIdx.x] = sum = sum + sdata[threadIdx.x + 4]; if (THREADS_PER_VECTOR > 2) sdata[threadIdx.x] = sum = sum + sdata[threadIdx.x + 2]; if (THREADS_PER_VECTOR > 1) sdata[threadIdx.x] = sum = sum + sdata[threadIdx.x + 1]; // first thread writes the result
if (thread_lane == 0) y[row] = sdata[threadIdx.x]; } }
template <unsigned int ROWS_PER_BLOCK, unsigned int THREADS_PER_ROW, bool Minimize> __launch_bounds__(ROWS_PER_BLOCK * THREADS_PER_ROW,1) __global__ void storm_cuda_opt_vector_reduce_kernel_double(const uint_fast64_t num_rows, const uint_fast64_t * __restrict__ nondeterministicChoiceIndices, double * __restrict__ x, const double * __restrict__ y, const double minMaxInitializer) { __shared__ volatile double sdata[ROWS_PER_BLOCK * THREADS_PER_ROW + THREADS_PER_ROW / 2]; // padded to avoid reduction conditionals
__shared__ volatile uint_fast64_t ptrs[ROWS_PER_BLOCK][2]; const uint_fast64_t THREADS_PER_BLOCK = ROWS_PER_BLOCK * THREADS_PER_ROW;
const uint_fast64_t thread_id = THREADS_PER_BLOCK * blockIdx.x + threadIdx.x; // global thread index
const uint_fast64_t thread_lane = threadIdx.x & (THREADS_PER_ROW - 1); // thread index within the vector
const uint_fast64_t vector_id = thread_id / THREADS_PER_ROW; // global vector index
const uint_fast64_t vector_lane = threadIdx.x / THREADS_PER_ROW; // vector index within the block
const uint_fast64_t num_vectors = ROWS_PER_BLOCK * gridDim.x; // total number of active vectors
for(uint_fast64_t row = vector_id; row < num_rows; row += num_vectors) { // use two threads to fetch Ap[row] and Ap[row+1]
// this is considerably faster than the straightforward version
if(thread_lane < 2) ptrs[vector_lane][thread_lane] = nondeterministicChoiceIndices[row + thread_lane];
const uint_fast64_t row_start = ptrs[vector_lane][0]; //same as: row_start = Ap[row];
const uint_fast64_t row_end = ptrs[vector_lane][1]; //same as: row_end = Ap[row+1];
// initialize local Min/Max
double localMinMaxElement = minMaxInitializer;
if (THREADS_PER_ROW == 32 && row_end - row_start > 32) { // ensure aligned memory access to Aj and Ax
uint_fast64_t jj = row_start - (row_start & (THREADS_PER_ROW - 1)) + thread_lane;
// accumulate local sums
if(jj >= row_start && jj < row_end) { if(Minimize) { localMinMaxElement = min(localMinMaxElement, y[jj]); //localMinMaxElement = (localMinMaxElement > y[jj]) ? y[jj] : localMinMaxElement;
} else { localMinMaxElement = max(localMinMaxElement, y[jj]); //localMinMaxElement = (localMinMaxElement < y[jj]) ? y[jj] : localMinMaxElement;
} }
// accumulate local sums
for(jj += THREADS_PER_ROW; jj < row_end; jj += THREADS_PER_ROW) if(Minimize) { localMinMaxElement = min(localMinMaxElement, y[jj]); //localMinMaxElement = (localMinMaxElement > y[jj]) ? y[jj] : localMinMaxElement;
} else { localMinMaxElement = max(localMinMaxElement, y[jj]); //localMinMaxElement = (localMinMaxElement < y[jj]) ? y[jj] : localMinMaxElement;
} } else { // accumulate local sums
for(uint_fast64_t jj = row_start + thread_lane; jj < row_end; jj += THREADS_PER_ROW) if(Minimize) { localMinMaxElement = min(localMinMaxElement, y[jj]); //localMinMaxElement = (localMinMaxElement > y[jj]) ? y[jj] : localMinMaxElement;
} else { localMinMaxElement = max(localMinMaxElement, y[jj]); //localMinMaxElement = (localMinMaxElement < y[jj]) ? y[jj] : localMinMaxElement;
} }
// store local sum in shared memory
sdata[threadIdx.x] = localMinMaxElement; // reduce local min/max to row min/max
if (Minimize) { /*if (THREADS_PER_ROW > 16) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement > sdata[threadIdx.x + 16]) ? sdata[threadIdx.x + 16] : localMinMaxElement);
if (THREADS_PER_ROW > 8) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement > sdata[threadIdx.x + 8]) ? sdata[threadIdx.x + 8] : localMinMaxElement); if (THREADS_PER_ROW > 4) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement > sdata[threadIdx.x + 4]) ? sdata[threadIdx.x + 4] : localMinMaxElement); if (THREADS_PER_ROW > 2) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement > sdata[threadIdx.x + 2]) ? sdata[threadIdx.x + 2] : localMinMaxElement); if (THREADS_PER_ROW > 1) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement > sdata[threadIdx.x + 1]) ? sdata[threadIdx.x + 1] : localMinMaxElement);*/
if (THREADS_PER_ROW > 16) sdata[threadIdx.x] = localMinMaxElement = min(localMinMaxElement, sdata[threadIdx.x + 16]); if (THREADS_PER_ROW > 8) sdata[threadIdx.x] = localMinMaxElement = min(localMinMaxElement, sdata[threadIdx.x + 8]); if (THREADS_PER_ROW > 4) sdata[threadIdx.x] = localMinMaxElement = min(localMinMaxElement, sdata[threadIdx.x + 4]); if (THREADS_PER_ROW > 2) sdata[threadIdx.x] = localMinMaxElement = min(localMinMaxElement, sdata[threadIdx.x + 2]); if (THREADS_PER_ROW > 1) sdata[threadIdx.x] = localMinMaxElement = min(localMinMaxElement, sdata[threadIdx.x + 1]); } else { /*if (THREADS_PER_ROW > 16) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement < sdata[threadIdx.x + 16]) ? sdata[threadIdx.x + 16] : localMinMaxElement);
if (THREADS_PER_ROW > 8) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement < sdata[threadIdx.x + 8]) ? sdata[threadIdx.x + 8] : localMinMaxElement); if (THREADS_PER_ROW > 4) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement < sdata[threadIdx.x + 4]) ? sdata[threadIdx.x + 4] : localMinMaxElement); if (THREADS_PER_ROW > 2) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement < sdata[threadIdx.x + 2]) ? sdata[threadIdx.x + 2] : localMinMaxElement); if (THREADS_PER_ROW > 1) sdata[threadIdx.x] = localMinMaxElement = ((localMinMaxElement < sdata[threadIdx.x + 1]) ? sdata[threadIdx.x + 1] : localMinMaxElement);*/ if (THREADS_PER_ROW > 16) sdata[threadIdx.x] = localMinMaxElement = max(localMinMaxElement, sdata[threadIdx.x + 16]); if (THREADS_PER_ROW > 8) sdata[threadIdx.x] = localMinMaxElement = max(localMinMaxElement, sdata[threadIdx.x + 8]); if (THREADS_PER_ROW > 4) sdata[threadIdx.x] = localMinMaxElement = max(localMinMaxElement, sdata[threadIdx.x + 4]); if (THREADS_PER_ROW > 2) sdata[threadIdx.x] = localMinMaxElement = max(localMinMaxElement, sdata[threadIdx.x + 2]); if (THREADS_PER_ROW > 1) sdata[threadIdx.x] = localMinMaxElement = max(localMinMaxElement, sdata[threadIdx.x + 1]); } // first thread writes the result
if (thread_lane == 0) x[row] = sdata[threadIdx.x]; } }
template <bool Minimize, unsigned int THREADS_PER_VECTOR> void __storm_cuda_opt_vector_reduce_double(const uint_fast64_t num_rows, const uint_fast64_t * nondeterministicChoiceIndices, double * x, const double * y) { double __minMaxInitializer = -std::numeric_limits<double>::max(); if (Minimize) { __minMaxInitializer = std::numeric_limits<double>::max(); } const double minMaxInitializer = __minMaxInitializer;
const size_t THREADS_PER_BLOCK = 128; const size_t VECTORS_PER_BLOCK = THREADS_PER_BLOCK / THREADS_PER_VECTOR;
const size_t MAX_BLOCKS = cusp::detail::device::arch::max_active_blocks(storm_cuda_opt_vector_reduce_kernel_double<VECTORS_PER_BLOCK, THREADS_PER_VECTOR, Minimize>, THREADS_PER_BLOCK, (size_t) 0); const size_t NUM_BLOCKS = std::min<size_t>(MAX_BLOCKS, DIVIDE_INTO(num_rows, VECTORS_PER_BLOCK));
storm_cuda_opt_vector_reduce_kernel_double<VECTORS_PER_BLOCK, THREADS_PER_VECTOR, Minimize> <<<NUM_BLOCKS, THREADS_PER_BLOCK>>> (num_rows, nondeterministicChoiceIndices, x, y, minMaxInitializer); }
template <bool Minimize> void storm_cuda_opt_vector_reduce_double(const uint_fast64_t num_rows, const uint_fast64_t num_entries, const uint_fast64_t * nondeterministicChoiceIndices, double * x, const double * y) { const uint_fast64_t rows_per_group = num_entries / num_rows;
if (rows_per_group <= 2) { __storm_cuda_opt_vector_reduce_double<Minimize, 2>(num_rows, nondeterministicChoiceIndices, x, y); return; } if (rows_per_group <= 4) { __storm_cuda_opt_vector_reduce_double<Minimize, 4>(num_rows, nondeterministicChoiceIndices, x, y); return; } if (rows_per_group <= 8) { __storm_cuda_opt_vector_reduce_double<Minimize, 8>(num_rows, nondeterministicChoiceIndices, x, y); return; } if (rows_per_group <= 16) { __storm_cuda_opt_vector_reduce_double<Minimize,16>(num_rows, nondeterministicChoiceIndices, x, y); return; } __storm_cuda_opt_vector_reduce_double<Minimize,32>(num_rows, nondeterministicChoiceIndices, x, y); }
template <bool UseCache, unsigned int THREADS_PER_VECTOR> void __storm_cuda_opt_spmv_csr_vector_double(const uint_fast64_t num_rows, const uint_fast64_t * matrixRowIndices, const double * matrixColumnIndicesAndValues, const double* x, double* y) { const size_t THREADS_PER_BLOCK = 128; const size_t VECTORS_PER_BLOCK = THREADS_PER_BLOCK / THREADS_PER_VECTOR;
const size_t MAX_BLOCKS = cusp::detail::device::arch::max_active_blocks(storm_cuda_opt_spmv_csr_vector_kernel_double<VECTORS_PER_BLOCK, THREADS_PER_VECTOR, UseCache>, THREADS_PER_BLOCK, (size_t) 0); const size_t NUM_BLOCKS = std::min<size_t>(MAX_BLOCKS, DIVIDE_INTO(num_rows, VECTORS_PER_BLOCK)); if (UseCache) bind_x(x);
storm_cuda_opt_spmv_csr_vector_kernel_double<VECTORS_PER_BLOCK, THREADS_PER_VECTOR, UseCache> <<<NUM_BLOCKS, THREADS_PER_BLOCK>>> (num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y);
if (UseCache) unbind_x(x); }
void storm_cuda_opt_spmv_csr_vector_double(const uint_fast64_t num_rows, const uint_fast64_t num_entries, const uint_fast64_t * matrixRowIndices, const double * matrixColumnIndicesAndValues, const double* x, double* y) { const uint_fast64_t nnz_per_row = num_entries / num_rows;
if (nnz_per_row <= 2) { __storm_cuda_opt_spmv_csr_vector_double<false, 2>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } if (nnz_per_row <= 4) { __storm_cuda_opt_spmv_csr_vector_double<false, 4>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } if (nnz_per_row <= 8) { __storm_cuda_opt_spmv_csr_vector_double<false, 8>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } if (nnz_per_row <= 16) { __storm_cuda_opt_spmv_csr_vector_double<false,16>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } __storm_cuda_opt_spmv_csr_vector_double<false,32>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); }
void storm_cuda_opt_spmv_csr_vector_tex(const uint_fast64_t num_rows, const uint_fast64_t num_entries, const uint_fast64_t * matrixRowIndices, const double * matrixColumnIndicesAndValues, const double* x, double* y) { const uint_fast64_t nnz_per_row = num_entries / num_rows;
if (nnz_per_row <= 2) { __storm_cuda_opt_spmv_csr_vector_double<true, 2>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } if (nnz_per_row <= 4) { __storm_cuda_opt_spmv_csr_vector_double<true, 4>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } if (nnz_per_row <= 8) { __storm_cuda_opt_spmv_csr_vector_double<true, 8>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; } if (nnz_per_row <= 16) { __storm_cuda_opt_spmv_csr_vector_double<true,16>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); return; }
__storm_cuda_opt_spmv_csr_vector_double<true,32>(num_rows, matrixRowIndices, matrixColumnIndicesAndValues, x, y); }
// NON-OPT
template <bool UseCache, unsigned int THREADS_PER_VECTOR> void __storm_cuda_spmv_csr_vector_double(const uint_fast64_t num_rows, const uint_fast64_t * matrixRowIndices, const uint_fast64_t * matrixColumnIndices, const double * matrixValues, const double* x, double* y) { const size_t THREADS_PER_BLOCK = 128; const size_t VECTORS_PER_BLOCK = THREADS_PER_BLOCK / THREADS_PER_VECTOR;
const size_t MAX_BLOCKS = cusp::detail::device::arch::max_active_blocks(spmv_csr_vector_kernel<uint_fast64_t, double, VECTORS_PER_BLOCK, THREADS_PER_VECTOR, UseCache>, THREADS_PER_BLOCK, (size_t) 0); const size_t NUM_BLOCKS = std::min<size_t>(MAX_BLOCKS, DIVIDE_INTO(num_rows, VECTORS_PER_BLOCK)); if (UseCache) bind_x(x);
spmv_csr_vector_kernel<uint_fast64_t, double, VECTORS_PER_BLOCK, THREADS_PER_VECTOR, UseCache> <<<NUM_BLOCKS, THREADS_PER_BLOCK>>> (num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y);
if (UseCache) unbind_x(x); }
void storm_cuda_spmv_csr_vector_double(const uint_fast64_t num_rows, const uint_fast64_t num_entries, const uint_fast64_t * matrixRowIndices, const uint_fast64_t * matrixColumnIndices, const double * matrixValues, const double* x, double* y) { const uint_fast64_t nnz_per_row = num_entries / num_rows;
if (nnz_per_row <= 2) { __storm_cuda_spmv_csr_vector_double<false, 2>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } if (nnz_per_row <= 4) { __storm_cuda_spmv_csr_vector_double<false, 4>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } if (nnz_per_row <= 8) { __storm_cuda_spmv_csr_vector_double<false, 8>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } if (nnz_per_row <= 16) { __storm_cuda_spmv_csr_vector_double<false,16>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } __storm_cuda_spmv_csr_vector_double<false,32>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); }
void storm_cuda_spmv_csr_vector_tex_double(const uint_fast64_t num_rows, const uint_fast64_t num_entries, const uint_fast64_t * matrixRowIndices, const uint_fast64_t * matrixColumnIndices, const double * matrixValues, const double* x, double* y) { const uint_fast64_t nnz_per_row = num_entries / num_rows;
if (nnz_per_row <= 2) { __storm_cuda_spmv_csr_vector_double<true, 2>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } if (nnz_per_row <= 4) { __storm_cuda_spmv_csr_vector_double<true, 4>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } if (nnz_per_row <= 8) { __storm_cuda_spmv_csr_vector_double<true, 8>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; } if (nnz_per_row <= 16) { __storm_cuda_spmv_csr_vector_double<true,16>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); return; }
__storm_cuda_spmv_csr_vector_double<true,32>(num_rows, matrixRowIndices, matrixColumnIndices, matrixValues, x, y); }
} // end namespace device
} // end namespace detail
} // end namespace cusp
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