Write a OpenMP-CUDA program to Compute the value of pie value by Numerical Integration using OpenMP directives and CUDA

This is an openMP implementation on host-CPU using p threads of OpenMP and computation on device-GPU. One approach is to partition the data among the processes. That is we partition the interval of integration [0,1] among the OpenMP threads, and each thread estimates local integral over its number of subinterval on GPU using CUDA APIs. The comptuations on GPU produced by the individual OpenMP thread are transformed back to host-CPU . These results are combined on host-CPU to produce the final result. On host-CPU, prints the result.

To perform this integration numerically, divide the interval from 0 to 1 into n subintervals and add up the areas of the rectangles as shown in the Figure 1 (n = 5). Large values of n give more accurate approximations of pi . Use MPI point-to-point communication library calls.

We assume that n is total number of subintervals, p is the number of processes and p < n. One simple way to distribute the total number of subintervals to each process is to dividen by p. There are two kinds of mappings that balance the load. One is a block mapping, partitions the array elements into blocks of consecutive entries and assigns the block to the processes. The other mapping is a cyclic mapping. It assigns the first element to the first process, the second element to the second, and so on. If n > p, we get back to the first process, and repeat the assignment process for remaining elements. This process is repeated until all the elements are assigned. We have used a cyclic mapping for partition of interval [0,1] ontop processes.

CUDA API used:

To Allocate memory on device-GPU :
cudaMalloc(void** array, int size)

To Free memory allocated on device-GPU:
cudaFree(void* array)

To transfer from host-CPU to device-GPU:
cudaMemcpy((void*)device_array, (void*)host_array, size, cudaMemcpyHostToDevice)

To transfer from device-GPU to host-GPU:
cudaMemcpy((void*)host_array, (void*)device_array, size, cudaMemcpyDeviceToHost)

Write a OpenMP-CUDA program to Matrix vector multiplication based on OpenMP & CUDA directives and use CUBLAS1 library funcation calls to compute vector vector multiplication

This is an openMP implementation on host-CPU using p threads of OpenMP and computation on device-GPU. This is an implementation of Matrix-Vector multiplication using the block striped partitioning algorithm on host-CPU and device-GPU. Each OpenMP thread gets the block of rows of the matrix and each transfers the block of its rows and vector to the device-GPU from host-CPU. On each device-GPU,the elements of the row of a bock matrix with the vector by calling the CUDA kernel Vector-VectorMultiplication i.e. CUBLAS1 Library call and writes the partial product into the result vector. The result vector is transfered from device-GPU to host-CPU. on host-CPU to the output array.

For local block matrix of rows into vector on GPU, please refer CUDA enabled NVIDIA GPU i.e. gpu-comp-cublas-cuda-numerical.html

CUDA API used:

To Allocate memory on device-GPU :
cudaMalloc(void** array, int size)

To Free memory allocated on device-GPU:
cudaFree(void* array)

To transfer from host-CPU to device-GPU:
cudaMemcpy((void*)device_array, (void*)host_array, size, cudaMemcpyHostToDevice)

To transfer from device-GPU to host-GPU:
cudaMemcpy((void*)host_array, (void*)device_array, size, cudaMemcpyDeviceToHost)

Write a OpenMP program to Matrix vector multiplication based on OpenMP & CUDA directives and use CUBLAS2 library funcation calls to compute matrix vector multiplication

This is an openMP implementation on host-CPU using p threads of OpenMP and computation on device-GPU. This is an implementation of Matrix-Vector multiplication using the block striped partitioning algorithm on host-CPU and device-GPU. Each OpenMP thread gets the block of rows of the matrix and each transfers the block of its rows and vector to the device-GPU from host-CPU. Then each device-GPU multiplies the corresponding block matrix with the vector by calling the CUDA kernel MatrixVectorMultiplication CUBLAS2 library and writes the partial product into the result vector. The result vector is transfered from device-GPU to host-CPU. on host-CPU to the output array.

For local block matrix of rows into vector on GPU, please refer CUDA enabled NVIDIA GPU i.e. gpu-comp-cublas-cuda-numerical.html

CUDA API used:

To Allocate memory on device-GPU :
cudaMalloc(void** array, int size)

To Free memory allocated on device-GPU:
cudaFree(void* array)

To transfer from host-CPU to device-GPU:
cudaMemcpy((void*)device_array, (void*)host_array, size, cudaMemcpyHostToDevice)

To transfer from device-GPU to host-GPU:
cudaMemcpy((void*)host_array, (void*)device_array, size, cudaMemcpyDeviceToHost)

Write a OpenMP-CUDA program to Matrix Matrix multiplication based on OpenMP & CUDA directives and use CUBLAS3 library funcation calls to compute matrix matrix multiplication

This is an openMP implementation Matrix-Matrix multiplication on host-CPU using p threads of OpenMP and computation on device-GPU in which block striped partitioning of the both input matrices on host-CPU is performance and on device-GPU, the CUDA BLAS3 library call us used to compute block matrix-matrix multiplication algorithm. Each OpenMP thread gets the block of rows of the input matrix A and a block of columns of input matrix B. Each OpenMP threads transfers the respective block of matrices of A and B from host-CPU to device-GPU. Then each device-GPU multiplies the corresponding block matrices by calling the CUDA kernel MatrixMatrixMultiplication CUBLAS3 library and writes the partial output matrix i.e., C . The result block matrix C is transfered from device-GPU to host-CPU.

For block matrix matix multiplication on GPU, please refer CUDA enabled NVIDIA GPU i.e. gpu-comp-cublas-cuda-numerical.html

CUDA API used:

To Allocate memory on device-GPU :
cudaMalloc(void** array, int size)

To Free memory allocated on device-GPU:
cudaFree(void* array)

To transfer from host-CPU to device-GPU:
cudaMemcpy((void*)device_array, (void*)host_array, size, cudaMemcpyHostToDevice)

To transfer from device-GPU to host-GPU:
cudaMemcpy((void*)host_array, (void*)device_array, size, cudaMemcpyDeviceToHost)

Write a OpenMP program to Matrix Matrix multiplication based on OpenMP & CUDA directives and use CUBLAS3 library funcation calls to compute matrix matrix multiplication

This is an openMP implementation Matrix-Matrix multiplication on host-CPU using p threads of OpenMP and computation on device-GPU in which block striped partitioning of the both input matrices on host-CPU is performance and on device-GPU, the CUDA BLAS3 library call us used to compute block matrix-matrix multiplication algorithm. Each OpenMP thread gets the block of rows of the input matrix A and a block of columns of input matrix B. Computations of block matrices are performed on host-CPU using tuned mathematical libraries. The other OpenMP thread transfers the remaining block of matrices of A and B from host-CPU to device-GPU. Then, one device-GPU multiplies the corresponding block matrices by calling the CUDA kernel MatrixMatrixMultiplication CUBLAS3 library and writes the partial output matrix i.e., C . The result block matrix C is transfered from device-GPU to host-CPU.

For block matrix matix multiplication on GPU, please refer CUDA enabled NVIDIA GPU i.e. gpu-comp-cublas-cuda-numerical.html

CUDA API used:

To Allocate memory on device-GPU :
cudaMalloc(void** array, int size)

To Free memory allocated on device-GPU:
cudaFree(void* array)

To transfer from host-CPU to device-GPU:
cudaMemcpy((void*)device_array, (void*)host_array, size, cudaMemcpyHostToDevice)

To transfer from device-GPU to host-GPU:
cudaMemcpy((void*)host_array, (void*)device_array, size, cudaMemcpyDeviceToHost)