# MPI Calculate Polynom Using Pipeline

An MPI program in English to calculate a polynomial using a pipeline approach. In this example, we'll compute a polynomial of the form f(x) = ax^2 + bx + c, where a, b and c are coefficients and x is the variable.

We will use three MPI processes, each corresponding to one term of the polynomial.

The first process will calculate ax^2, the second will calculate bx and the third will calculate c. Each process will add its result to a running total passed along the pipeline. The last process will output the final result.

- pipeline-polynom.c
#include <mpi.h> #include <stdio.h> int main(int argc, char** argv) { // Initialize the MPI environment MPI_Init(NULL, NULL); // Get the rank of the process int world_rank; MPI_Comm_rank(MPI_COMM_WORLD, &world_rank); // Define the coefficients and the value of x int coefficients[3] = {1, 2, 1}; // Coefficients for x^2, x, and constant term int x = 2; // The value of x // Each process performs its part of the calculation int local_result = 0; if (world_rank == 0) { // First process calculates ax^2 local_result = coefficients[0] * x * x; } else if (world_rank == 1) { // Second process calculates bx local_result = coefficients[1] * x; } else if (world_rank == 2) { // Third process calculates c local_result = coefficients[2]; } // Pipeline to sum up the results int sum = 0; if (world_rank != 0) { MPI_Recv(&sum, 1, MPI_INT, world_rank - 1, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE); } sum += local_result; if (world_rank != 2) { MPI_Send(&sum, 1, MPI_INT, world_rank + 1, 0, MPI_COMM_WORLD); } // The last process prints the final result if (world_rank == 2) { printf("The result of the polynomial is %d\n", sum); } // Finalize the MPI environment MPI_Finalize(); return 0; }

**Initialization**: The MPI environment is initialized.
**Calculation**: Each MPI process calculates a part of the polynomial based on its rank.

- Process 0 calculates ax^2
- Process 1 calculates bx
- Process 2 calculates c

**Pipeline Communication**: The processes use MPI **send** and receive calls to pass along a running sum.
Each process, except the first, receives a sum from the previous process, adds its local result, and sends the new sum to the next process.

**Final Result**: The last process (rank 2) outputs the final result of the polynomial calculation.

**Finalization**: The MPI environment is finalized.

You should specify exactly three processes. The output will be the result of the polynomial calculation given the coefficients and the value of x.