In this assignment, you will write both serial and parallel programs to calculate the Sum using the

following formula:

Sum $=4{\displaystyle \underset{i=0}{\overset{n}{}}}\frac{(-1{)}^i}{2i+1}$

You will write a serial C program $($Sum$\_$Serial.c$)$ to calculate the sum Sum and validate the

correctness of your serial implementation. You will modify the serial program into two parallel

programs, namely Sum$\_$MPI$\_$v$1.$c and Sum$\_$MPI$\_$v$2.$c$.$ In Sum$\_$MPI$\_$v$1.$c$,$ utilize only MPI point$-$

to$-$point communication functions $($MPI$\_$Send and MPI$\_-$ Recv$){?}^{-}$for message passing. In

Sum$\_$MPI$\_2.$c$,$ implement your parallel solution using collective communication functions.

Compile and execute these programs on magnolia HPC cluster to obtain the results. The user can

specify $n$ when executing your programs.

Present your results in the following two tables. Table $1$ should include a comparison of the

Sum results obtained by three programs with respect to different n numbers. For the two parallel

programs, you can set $p=1$ and $p=8$ where $p$ is the number of processes. Ensure that the Sum

results exhibit six digits to the right of the decimal point.

Table $1$: Comparison of Sum results with respect to different $n$ and $p$ values.

In Table $2,$ analyze and compare the performance of two parallel implementations in terms of

parallel runtime $T,$ speedup $S$ and efficiency $E$ with respect to different number of processes.

Table $2$: Comparison of the parallel performance of the two parallel implementations