// Creating a parallel multiplication Grid NPU Simulation for 4x4 Grid 11:13 03/10/2024 (c)RS

// Reference NPU Document in https://is.gd/DictionarySortJS

include <mpi.h>

include <stdio.h>

define NUM_ROWS 4

define NUM_COLS 4

int main(int argc, char* argv[]) {
int rank, size, i, j;
int data[NUMROWS][NUMCOLS];
int factor;
int localresults[NUMROWS];

MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Comm_size(MPI_COMM_WORLD, &size);

// Initialize data and factor
// ...

// Broadcast factor to all processors
MPI_Bcast(&factor, 1, MPI_INT, 0, MPI_COMM_WORLD);

// Perform local multiplication
for (i = 0; i < NUM_ROWS; i++) {
    local_results[i] = data[rank][i] * factor;
}

// Gather results from all processors
// ...

// Print results
// ...

MPI_Finalize();
return 0;

}

// # End code

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Creating a parallel multiplication with load & run in the most efficient manner, based on a 4x4 grid:

[ ]1a, [ ]2a, [ ]3a, [ ]4a
[ ]1b, [ ]2b, [ ]3b, [ ]4b
[ ]1c, [ ]2c, [ ]3c, [ ]4c
[ ]1d, [ ]2d, [ ]3d, [ ]4d
Understanding the Grid:

Each row represents a different set of data to be multiplied.

Each column represents a different factor to be multiplied by.

Parallel Multiplication Approach:

Load Data:

Assign each row to a separate processor or thread.
Load the data for each row into the corresponding processor's local memory.
Broadcast Factor:

Broadcast the factor to be multiplied by to all processors or threads.
Parallel Multiplication:

Each processor or thread performs the multiplication operation on its assigned row using the broadcasted factor.
Store Results:

Store the results of each multiplication in the corresponding processor's local memory.
Efficient Implementation:

Data Distribution:

Distribute the data across processors or threads in a way that minimizes communication overhead.

For example, if the data is already distributed across multiple memory modules,
Assign each row to a processor that has access to its corresponding data.

Factor Broadcasting:

Use efficient broadcasting mechanisms to minimize communication latency.

For example, use tree-based broadcasting or collective operations provided by MPI or other parallel programming frameworks.

Load Balancing:

Ensure that each processor or thread has a roughly equal amount of work to do.

This can be achieved by dividing the data into equal-sized chunks or by using dynamic load balancing techniques.

Memory Access Patterns:

Optimize memory access patterns to avoid cache misses and improve performance.
For example, use techniques like loop unrolling or data prefetching.

Synchronization:

Minimize synchronization overhead between processors or threads.

Use asynchronous communication or non-blocking operations whenever possible.

(c)Rupert S

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