Answer the following questions about MPI.

a$.[6]$ Suppose we have an MPI program where we have four processes.

MPI$\_$Comm$\_$Split$()$ is called once. How many ranks can each process have after that

call? If there are several answers, specify them all and justify your answer.

b$.$ For the following piece of code $($assume very large number of cores$)$:

int main$()\{$

int globalnum $=0$;

int numprocs, rank;

int $i=0$;

MPI$\_$Init$($NULL$,$ NULL$)$;

MPI$\_$Comm$\_$size$($MPI$\_$COMM$\_$WORLD, &numprocs$)$;

MPI$\_$Comm$\_$rank$($MPI$\_$COMM$\_$WORLD, &rank$)$;

#pragma omp parallel for reduction$(+$:globalnum$)$

for$(i=0$; rank ;$i++$

$\{$

globalnum $++$;

$...$rest of loop body $...$

$\}$

MPI$\_$Finalize$()$;

$...$

$\}$

We execute the above code with: mpirun $-$n $5./$progname

$[5]$ What is the maximum number of threads we will end up having in the

whole system? Explain.

$[5]$ Just before executing MPI$\_$Finalize$(),$ how many instances of globalnum

do we have in the system? Justify.

$[5]$ Just after executing MPI$\_$Finalize$(),$ and before exiting main$()$ how many

instances of globalnum do we have in the system? Justify

c$.[9]$ Suppose we have three processes. Each process has an array p of integers of $3$

elements as follows. Process $0$ has $[1,2,3],$ process $1$ has $4,5,7,$ and process $2$ has $[7,$

$8,9.$ Suppose all the processes execute the following API:

MPI$\_$Reduce$($p$,$ q$,3,$ MPI$\_$INT, MPI$\_$BAND, $1,$ MPI$\_$COMM$\_$WORLD$)$;

Where $p$ is a pointer to the array and $q$ is a pointer to a receiving array. Assume the

receiving array $q$ is initially $0,0,0$ for all processes. After executing the above function,

what will be the content of $q$ for each process.