/* Copyright (c) 2021, NVIDIA CORPORATION. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 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. * * Neither the name of NVIDIA CORPORATION 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 ``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 OWNER 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. */ #include #include #include #include #include "jacobi.h" namespace cg = cooperative_groups; // 8 Rows of square-matrix A processed by each CTA. // This can be max 32 and only power of 2 (i.e., 2/4/8/16/32). #define ROWS_PER_CTA 8 #if !defined(__CUDA_ARCH__) || __CUDA_ARCH__ >= 600 #else __device__ double atomicAdd(double *address, double val) { unsigned long long int *address_as_ull = (unsigned long long int *)address; unsigned long long int old = *address_as_ull, assumed; do { assumed = old; old = atomicCAS(address_as_ull, assumed, __double_as_longlong(val + __longlong_as_double(assumed))); // Note: uses integer comparison to avoid hang in case of NaN (since NaN != // NaN) } while (assumed != old); return __longlong_as_double(old); } #endif static __global__ void JacobiMethod(const float *A, const double *b, const float conv_threshold, double *x, double *x_new, double *sum) { // Handle to thread block group cg::thread_block cta = cg::this_thread_block(); __shared__ double x_shared[N_ROWS]; // N_ROWS == n __shared__ double b_shared[ROWS_PER_CTA + 1]; for (int i = threadIdx.x; i < N_ROWS; i += blockDim.x) { x_shared[i] = x[i]; } if (threadIdx.x < ROWS_PER_CTA) { int k = threadIdx.x; for (int i = k + (blockIdx.x * ROWS_PER_CTA); (k < ROWS_PER_CTA) && (i < N_ROWS); k += ROWS_PER_CTA, i += ROWS_PER_CTA) { b_shared[i % (ROWS_PER_CTA + 1)] = b[i]; } } cg::sync(cta); cg::thread_block_tile<32> tile32 = cg::tiled_partition<32>(cta); for (int k = 0, i = blockIdx.x * ROWS_PER_CTA; (k < ROWS_PER_CTA) && (i < N_ROWS); k++, i++) { double rowThreadSum = 0.0; for (int j = threadIdx.x; j < N_ROWS; j += blockDim.x) { rowThreadSum += (A[i * N_ROWS + j] * x_shared[j]); } for (int offset = tile32.size() / 2; offset > 0; offset /= 2) { rowThreadSum += tile32.shfl_down(rowThreadSum, offset); } if (tile32.thread_rank() == 0) { atomicAdd(&b_shared[i % (ROWS_PER_CTA + 1)], -rowThreadSum); } } cg::sync(cta); if (threadIdx.x < ROWS_PER_CTA) { cg::thread_block_tile tile8 = cg::tiled_partition(cta); double temp_sum = 0.0; int k = threadIdx.x; for (int i = k + (blockIdx.x * ROWS_PER_CTA); (k < ROWS_PER_CTA) && (i < N_ROWS); k += ROWS_PER_CTA, i += ROWS_PER_CTA) { double dx = b_shared[i % (ROWS_PER_CTA + 1)]; dx /= A[i * N_ROWS + i]; x_new[i] = (x_shared[i] + dx); temp_sum += fabs(dx); } for (int offset = tile8.size() / 2; offset > 0; offset /= 2) { temp_sum += tile8.shfl_down(temp_sum, offset); } if (tile8.thread_rank() == 0) { atomicAdd(sum, temp_sum); } } } // Thread block size for finalError kernel should be multiple of 32 static __global__ void finalError(double *x, double *g_sum) { // Handle to thread block group cg::thread_block cta = cg::this_thread_block(); extern __shared__ double warpSum[]; double sum = 0.0; int globalThreadId = blockIdx.x * blockDim.x + threadIdx.x; for (int i = globalThreadId; i < N_ROWS; i += blockDim.x * gridDim.x) { double d = x[i] - 1.0; sum += fabs(d); } cg::thread_block_tile<32> tile32 = cg::tiled_partition<32>(cta); for (int offset = tile32.size() / 2; offset > 0; offset /= 2) { sum += tile32.shfl_down(sum, offset); } if (tile32.thread_rank() == 0) { warpSum[threadIdx.x / warpSize] = sum; } cg::sync(cta); double blockSum = 0.0; if (threadIdx.x < (blockDim.x / warpSize)) { blockSum = warpSum[threadIdx.x]; } if (threadIdx.x < 32) { for (int offset = tile32.size() / 2; offset > 0; offset /= 2) { blockSum += tile32.shfl_down(blockSum, offset); } if (tile32.thread_rank() == 0) { atomicAdd(g_sum, blockSum); } } } double JacobiMethodGpuCudaGraphExecKernelSetParams( const float *A, const double *b, const float conv_threshold, const int max_iter, double *x, double *x_new, cudaStream_t stream) { // CTA size dim3 nthreads(256, 1, 1); // grid size dim3 nblocks((N_ROWS / ROWS_PER_CTA) + 2, 1, 1); cudaGraph_t graph; cudaGraphExec_t graphExec = NULL; double sum = 0.0; double *d_sum = NULL; checkCudaErrors(cudaMalloc(&d_sum, sizeof(double))); std::vector nodeDependencies; cudaGraphNode_t memcpyNode, jacobiKernelNode, memsetNode; cudaMemcpy3DParms memcpyParams = {0}; cudaMemsetParams memsetParams = {0}; memsetParams.dst = (void *)d_sum; memsetParams.value = 0; memsetParams.pitch = 0; // elementSize can be max 4 bytes, so we take sizeof(float) and width=2 memsetParams.elementSize = sizeof(float); memsetParams.width = 2; memsetParams.height = 1; checkCudaErrors(cudaGraphCreate(&graph, 0)); checkCudaErrors( cudaGraphAddMemsetNode(&memsetNode, graph, NULL, 0, &memsetParams)); nodeDependencies.push_back(memsetNode); cudaKernelNodeParams NodeParams0, NodeParams1; NodeParams0.func = (void *)JacobiMethod; NodeParams0.gridDim = nblocks; NodeParams0.blockDim = nthreads; NodeParams0.sharedMemBytes = 0; void *kernelArgs0[6] = {(void *)&A, (void *)&b, (void *)&conv_threshold, (void *)&x, (void *)&x_new, (void *)&d_sum}; NodeParams0.kernelParams = kernelArgs0; NodeParams0.extra = NULL; checkCudaErrors( cudaGraphAddKernelNode(&jacobiKernelNode, graph, nodeDependencies.data(), nodeDependencies.size(), &NodeParams0)); nodeDependencies.clear(); nodeDependencies.push_back(jacobiKernelNode); memcpyParams.srcArray = NULL; memcpyParams.srcPos = make_cudaPos(0, 0, 0); memcpyParams.srcPtr = make_cudaPitchedPtr(d_sum, sizeof(double), 1, 1); memcpyParams.dstArray = NULL; memcpyParams.dstPos = make_cudaPos(0, 0, 0); memcpyParams.dstPtr = make_cudaPitchedPtr(&sum, sizeof(double), 1, 1); memcpyParams.extent = make_cudaExtent(sizeof(double), 1, 1); memcpyParams.kind = cudaMemcpyDeviceToHost; checkCudaErrors( cudaGraphAddMemcpyNode(&memcpyNode, graph, nodeDependencies.data(), nodeDependencies.size(), &memcpyParams)); checkCudaErrors(cudaGraphInstantiate(&graphExec, graph, NULL, NULL, 0)); NodeParams1.func = (void *)JacobiMethod; NodeParams1.gridDim = nblocks; NodeParams1.blockDim = nthreads; NodeParams1.sharedMemBytes = 0; void *kernelArgs1[6] = {(void *)&A, (void *)&b, (void *)&conv_threshold, (void *)&x_new, (void *)&x, (void *)&d_sum}; NodeParams1.kernelParams = kernelArgs1; NodeParams1.extra = NULL; int k = 0; for (k = 0; k < max_iter; k++) { checkCudaErrors(cudaGraphExecKernelNodeSetParams( graphExec, jacobiKernelNode, ((k & 1) == 0) ? &NodeParams0 : &NodeParams1)); checkCudaErrors(cudaGraphLaunch(graphExec, stream)); checkCudaErrors(cudaStreamSynchronize(stream)); if (sum <= conv_threshold) { checkCudaErrors(cudaMemsetAsync(d_sum, 0, sizeof(double), stream)); nblocks.x = (N_ROWS / nthreads.x) + 1; size_t sharedMemSize = ((nthreads.x / 32) + 1) * sizeof(double); if ((k & 1) == 0) { finalError<<>>(x_new, d_sum); } else { finalError<<>>(x, d_sum); } checkCudaErrors(cudaMemcpyAsync(&sum, d_sum, sizeof(double), cudaMemcpyDeviceToHost, stream)); checkCudaErrors(cudaStreamSynchronize(stream)); printf("GPU iterations : %d\n", k + 1); printf("GPU error : %.3e\n", sum); break; } } checkCudaErrors(cudaFree(d_sum)); return sum; } double JacobiMethodGpuCudaGraphExecUpdate(const float *A, const double *b, const float conv_threshold, const int max_iter, double *x, double *x_new, cudaStream_t stream) { // CTA size dim3 nthreads(256, 1, 1); // grid size dim3 nblocks((N_ROWS / ROWS_PER_CTA) + 2, 1, 1); cudaGraph_t graph; cudaGraphExec_t graphExec = NULL; double sum = 0.0; double *d_sum; checkCudaErrors(cudaMalloc(&d_sum, sizeof(double))); int k = 0; for (k = 0; k < max_iter; k++) { checkCudaErrors( cudaStreamBeginCapture(stream, cudaStreamCaptureModeGlobal)); checkCudaErrors(cudaMemsetAsync(d_sum, 0, sizeof(double), stream)); if ((k & 1) == 0) { JacobiMethod<<>>(A, b, conv_threshold, x, x_new, d_sum); } else { JacobiMethod<<>>(A, b, conv_threshold, x_new, x, d_sum); } checkCudaErrors(cudaMemcpyAsync(&sum, d_sum, sizeof(double), cudaMemcpyDeviceToHost, stream)); checkCudaErrors(cudaStreamEndCapture(stream, &graph)); if (graphExec == NULL) { checkCudaErrors(cudaGraphInstantiate(&graphExec, graph, NULL, NULL, 0)); } else { cudaGraphExecUpdateResult updateResult_out; checkCudaErrors( cudaGraphExecUpdate(graphExec, graph, NULL, &updateResult_out)); if (updateResult_out != cudaGraphExecUpdateSuccess) { if (graphExec != NULL) { checkCudaErrors(cudaGraphExecDestroy(graphExec)); } printf("k = %d graph update failed with error - %d\n", k, updateResult_out); checkCudaErrors(cudaGraphInstantiate(&graphExec, graph, NULL, NULL, 0)); } } checkCudaErrors(cudaGraphLaunch(graphExec, stream)); checkCudaErrors(cudaStreamSynchronize(stream)); if (sum <= conv_threshold) { checkCudaErrors(cudaMemsetAsync(d_sum, 0, sizeof(double), stream)); nblocks.x = (N_ROWS / nthreads.x) + 1; size_t sharedMemSize = ((nthreads.x / 32) + 1) * sizeof(double); if ((k & 1) == 0) { finalError<<>>(x_new, d_sum); } else { finalError<<>>(x, d_sum); } checkCudaErrors(cudaMemcpyAsync(&sum, d_sum, sizeof(double), cudaMemcpyDeviceToHost, stream)); checkCudaErrors(cudaStreamSynchronize(stream)); printf("GPU iterations : %d\n", k + 1); printf("GPU error : %.3e\n", sum); break; } } checkCudaErrors(cudaFree(d_sum)); return sum; } double JacobiMethodGpu(const float *A, const double *b, const float conv_threshold, const int max_iter, double *x, double *x_new, cudaStream_t stream) { // CTA size dim3 nthreads(256, 1, 1); // grid size dim3 nblocks((N_ROWS / ROWS_PER_CTA) + 2, 1, 1); double sum = 0.0; double *d_sum; checkCudaErrors(cudaMalloc(&d_sum, sizeof(double))); int k = 0; for (k = 0; k < max_iter; k++) { checkCudaErrors(cudaMemsetAsync(d_sum, 0, sizeof(double), stream)); if ((k & 1) == 0) { JacobiMethod<<>>(A, b, conv_threshold, x, x_new, d_sum); } else { JacobiMethod<<>>(A, b, conv_threshold, x_new, x, d_sum); } checkCudaErrors(cudaMemcpyAsync(&sum, d_sum, sizeof(double), cudaMemcpyDeviceToHost, stream)); checkCudaErrors(cudaStreamSynchronize(stream)); if (sum <= conv_threshold) { checkCudaErrors(cudaMemsetAsync(d_sum, 0, sizeof(double), stream)); nblocks.x = (N_ROWS / nthreads.x) + 1; size_t sharedMemSize = ((nthreads.x / 32) + 1) * sizeof(double); if ((k & 1) == 0) { finalError<<>>(x_new, d_sum); } else { finalError<<>>(x, d_sum); } checkCudaErrors(cudaMemcpyAsync(&sum, d_sum, sizeof(double), cudaMemcpyDeviceToHost, stream)); checkCudaErrors(cudaStreamSynchronize(stream)); printf("GPU iterations : %d\n", k + 1); printf("GPU error : %.3e\n", sum); break; } } checkCudaErrors(cudaFree(d_sum)); return sum; }