INTIAL

Question1/Makefile

+# Makefile for MPI program
+
+# Source file
+SRC = question1.c
+
+# number of process
+NP = 4
+
+# Compiler
+CC = mpicc
+
+# Executable name
+EXE = ./out
+
+all: $(EXE) 
+
+$(EXE): $(SRC)
+	$(CC) -o $(EXE) $(SRC)
+
+clean:
+	rm -f $(EXE)
+
+run:
+	mpirun -np $(NP) -f mpihost $(EXE) 
\ No newline at end of file

Question1/mpihost

+master
+slave1 user=mpiuser
+slave2 user=mpiuser

Question1/question1.c

+#include <mpi.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <math.h>  
+#include <stdbool.h>
+
+void prefix_mpi(int* block_array, int block_size, int* block_prefix, MPI_Comm communicator)
+{
+    int my_rank, com_size;
+    MPI_Comm_rank(communicator, &my_rank);
+    MPI_Comm_size(communicator, &com_size);
+
+    // Step 1: Parallel sum within each block
+    int block_sum = 0;
+    for (int i = 0; i < block_size; i++)
+        block_sum += block_array[i];
+
+    // Step 2: Sequential prefix sum over block sums
+    int* all_block_sums = (int*)malloc(com_size * sizeof(int));
+    MPI_Allgather(&block_sum, 1, MPI_INT, all_block_sums, 1, MPI_INT, communicator);
+
+    int block_prefix_sum = 0;
+    for (int i = 0; i < my_rank; i++)
+        block_prefix_sum += all_block_sums[i];
+
+    // Step 3: Parallel prefix sum within each block
+    block_prefix[0] = block_prefix_sum;
+    for (int i = 1; i < block_size; i++)
+        block_prefix[i] = block_prefix[i - 1] + block_array[i - 1];
+
+    free(all_block_sums);
+}
+
+
+int main(int argc, char** args)
+{
+    MPI_Init(&argc, &args);
+
+    int my_rank;
+    int com_size;
+    MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
+    MPI_Comm_size(MPI_COMM_WORLD, &com_size);
+
+    int total_array_size = 2048;
+
+    if (total_array_size % com_size != 0)
+        total_array_size = (total_array_size / com_size + 1) * com_size;
+
+
+    int block_size = total_array_size / com_size;
+    int* total_array = NULL;
+    int* total_prefix = NULL;
+
+    if (my_rank == 0)
+    {
+        total_array = (int*)malloc(total_array_size * sizeof(int));
+        total_prefix = (int*)malloc(total_array_size * sizeof(int));
+        for (int i = 0; i < total_array_size; i++)
+            total_array[i] = rand() % 11;
+    }
+
+    int* block_array = (int*)malloc(block_size * sizeof(int));
+    int* block_prefix = (int*)malloc(block_size * sizeof(int));
+
+    MPI_Scatter(total_array, block_size, MPI_INT,
+        block_array, block_size, MPI_INT, 0, MPI_COMM_WORLD);
+
+    prefix_mpi(block_array, block_size, block_prefix, MPI_COMM_WORLD);
+
+    MPI_Gather(block_prefix, block_size, MPI_INT,
+        total_prefix, block_size, MPI_INT, 0, MPI_COMM_WORLD);
+
+    int accum = 0;
+    if (my_rank == 0)
+    {
+        for (int i = 1; i < total_array_size; i++)
+        {
+            accum += total_array[i-1];
+            if (total_prefix[i] != accum)
+                printf("Error at index %i: %i expected, %i computed\n", i, accum, total_prefix[i]);
+        }
+
+        printf("Test completed!\n"); 
+        free(total_array);
+        free(total_prefix);
+    }
+    free(block_array);
+    free(block_prefix);
+
+    MPI_Finalize();
+    
+    return 0;
+}

Question2/Makefile

+# Makefile for MPI program
+
+# Source file
+SRC = question2.c
+
+# number of process
+NP = 8
+
+# Compiler
+CC = mpicc
+
+# Executable name
+EXE = ./out
+
+all: $(EXE) 
+
+$(EXE): $(SRC)
+	$(CC) -o $(EXE) $(SRC)
+
+clean:
+	rm -f $(EXE)
+
+run:
+	mpirun -np $(NP) -f mpihost $(EXE) 
\ No newline at end of file

Question2/mpihost

+master
+slave1 user=mpiuser
+slave2 user=mpiuser

Question2/question2.c

+#include <mpi.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <math.h>  
+#include <stdbool.h>
+
+void perform_reduction_step(int* local_result, int* received_data, int count) {
+    // Perform the reduction operation (sum in this case)
+    for (int i = 0; i < count; i++) {
+        local_result[i] += received_data[i];
+    }
+}
+
+void reduce_tree(int* send_data, int* recv_data, int count, MPI_Comm communicator) {
+    int my_rank, size;
+    MPI_Comm_rank(communicator, &my_rank);
+    MPI_Comm_size(communicator, &size);
+
+    // Allocate memory for local reduction
+    int* local_result = (int*)malloc(count * sizeof(int));
+    memcpy(local_result, send_data, count * sizeof(int));
+
+    int step = 1;
+    while (step < size) {
+        if (my_rank % (2 * step) == 0) {
+            int source = my_rank + step;
+            if (source < size) {
+                int* received_data = (int*)malloc(count * sizeof(int));
+                MPI_Recv(received_data, count, MPI_INT, source, 0, communicator, MPI_STATUS_IGNORE);
+
+                // Perform the reduction operation (sum in this case)
+                perform_reduction_step(local_result, received_data, count);  
+                free(received_data);
+            }
+        } else {
+            int destination = my_rank - step;
+            MPI_Send(local_result, count, MPI_INT, destination, 0, communicator);
+            break;
+        }
+
+        step *= 2;
+    }
+
+    // Copy the final result to the recv_data buffer for the root process
+    if (my_rank == 0) {
+        memcpy(recv_data, local_result, count * sizeof(int));
+    }
+
+    free(local_result);
+}
+
+void reduce_sequential(
+    int* send_data,
+    int* recv_data,
+    int count,
+    MPI_Comm communicator)
+{
+    int my_rank;
+    int com_size;
+    MPI_Comm_rank(communicator, &my_rank);
+    MPI_Comm_size(communicator, &com_size);
+
+    int* gather_buffer = NULL;
+    if (my_rank == 0)
+    {
+        gather_buffer = (int*) calloc(count * com_size, sizeof(int));
+    }
+
+    MPI_Gather(send_data, count, MPI_INT, gather_buffer, count, MPI_INT, 0, communicator);
+
+    if (my_rank == 0)
+    {
+        memset(recv_data, 0, count * sizeof(int));
+        for (int p = 0; p < com_size; p++)
+            for (int i = 0; i < count; i++)
+                recv_data[i] += gather_buffer[count * p + i];
+        free(gather_buffer);
+    }
+}
+
+int main(int argc, char** args)
+{
+    MPI_Init(&argc, &args);
+    int count = 50;
+    int* recv_array_tree = NULL;
+    int* recv_array_sequential = NULL;
+
+    int my_rank;
+    MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
+    if (my_rank == 0)
+    {
+        recv_array_tree = (int*) malloc(count * sizeof(int));
+        recv_array_sequential = (int*) malloc(count * sizeof(int));
+    }
+
+    int* send_array = (int*)malloc(count * sizeof(int));
+    for (int i = 0; i < count; i++)
+        send_array[i] = my_rank;
+
+    // Measure time for tree-based reduction
+    double start_tree = MPI_Wtime();
+    reduce_tree(send_array, recv_array_tree, count, MPI_COMM_WORLD);
+    double end_tree = MPI_Wtime();
+
+    // Measure time for sequential reduction
+    double start_sequential = MPI_Wtime();
+    reduce_sequential(send_array, recv_array_sequential, count, MPI_COMM_WORLD);
+    double end_sequential = MPI_Wtime();
+
+    if (my_rank == 0)
+    {
+        for (int i = 0; i < count; i++)
+            if (recv_array_tree[i] == recv_array_sequential[i])
+                printf("At index %i: reduce_tree is %i, reduce_sequential is %i\n",
+                    i, recv_array_tree[i], recv_array_sequential[i]);
+
+        printf("Time taken by reduce_tree: %f seconds\n", end_tree - start_tree);
+        printf("Time taken by reduce_sequential: %f seconds\n", end_sequential - start_sequential);
+
+        free(recv_array_tree);
+        free(recv_array_sequential);
+    }
+    free(send_array);
+    MPI_Finalize();
+    return 0;
+}