#include

#include

#include

#include

double Trap(double a, double b, int n, double h){ //a, b, n will have copy of local_a, local_b, local_n

double approx, x_i;

approx= (exp(a)+ exp(b))/2.0;

for (int i=1; i< n; i++){

x_i = a + i*h;

approx += exp(x_i);

}

approx = h * approx;

return approx;

}

int main(int argc, char** argv) {

int n, local_n, p;

double a, b, h, local_a, local_b;

double local_int, total_int;

// Initialize the MPI environment

MPI_Init(NULL, NULL);

// Get the number of processes

int world_size;

MPI_Comm_size(MPI_COMM_WORLD, &world_size);

// Get the rank of the process

int my_rank;

MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);

if(my_rank == 0){

printf("Please enter a, b, n:");

fflush(stdout);

scanf("%lf %lf %d", &a, &b, &n);

}

fflush(stdout);

MPI_Bcast(&a, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);

MPI_Bcast(&b, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);

MPI_Bcast(&n, 1, MPI_INT, 0, MPI_COMM_WORLD);

h = (b-a)/n;

local_n = n/world_size;

local_a = a + my_rank*local_n*h;

local_b = local_a + local_n*h;

local_int = Trap(local_a, local_b, local_n, h);

if(my_rank != 0){

MPI_Send(&local_int, 1, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD);

}

else{

total_int = local_int;

for(p=1; p < world_size;p++){

MPI_Recv(&local_int, 1, MPI_DOUBLE, p, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);

total_int +=local_int;

}

}

if (my_rank ==0){

printf("With n = % d trapezoids, our estimate ", n);

printf("of the integral from %f to %f = %f ", a, b, total_int);

}

// Finalize the MPI environment.

MPI_Finalize();

return 0;

}

Write C program and parallelize it using MPI that that compute area under the curve using the trapezoidal role. Let each process compute area under the curve for subinterval and then sum (i.e. reduce operation) in process 0. In example 5, we read a, b, and n from user using scanf through process0, then process 0 broadcast them to all other processes. In this labwork, replace lines from 59 68 with MPI_Reduce collective communication. Here, we will use MPI_SUM operator. Time the parallel code (start timing before Trap function and end timing after MPI_Reduce) and run it using 1, 2, 4, 8 processes (nodes) and report execution time, and speedup = Tserial/Tparallel, and efficiency = speedup/#threads Please consider these values for a=0, b=10, n=100000000