what are the shared variables in the program below $($note: A variable x is shared if and only if multiple threads reference some instance of x$.)$ and what is the output of the program when the number of threads is $8$ and number of elements per thread is $1?$ what about the case when number of threads is $1$ and the number of elements per thread is $8?$ comment on the relative performance of these two cases:

#include "csapp.h$"$

#define MAXTHREADS $32$

void $*$sum$\_$mutex$($void $*$vargp$)$;

long gsum $=0$; $//$ Global variable automatically initialized to $0$

long nelems$\_$per$\_$thread;

sem$\_$t mutex;

int main$($int argc, char $*$argv$[])\{$

long i$,$ nelems, log$\_$nelems, nthreads, myid$[$MAXTHREADS$]$;

pthread$\_$t tid$[$MAXTHREADS$]$;

$//$ Get input arguments

if $($argc $!=3)\{$

printf$("$Usage: $\%$s

$",$ argv$[0])$;

exit$(0)$;

$\}$

nthreads $=$ atoi$($argv$[1])$;

log$\_$nelems $=$ atol$($argv$[2])$;

nelems $=(1$L $<<$ log$\_$nelems$)$;

$//$ Check input arguments

if $(($nelems $\%$ nthreads$)!=0||$ log$\_$nelems $>31)\{$

printf$("$Error: invalid nelems

$")$;

exit$(0)$;

$\}$

$//$ Begin psumutex

nelems$\_$per$\_$thread $=$ nelems $/$ nthreads;

sem$\_$init$($&mutex, $0,1)$;

$//$ Create peer threads and wait for them to finish

for $($i $=0$; i $<$ nthreads; i$++)\{$

myid$[$i$]=$ i;

pthread$\_$create$($&tid$[$i$],$ NULL, sum$\_$mutex, &myid$[$i$])$;

$\}$

for $($i $=0$; i $<$ nthreads; i$++)\{$

pthread$\_$join$($tid$[$i$],$ NULL$)$;

$\}$

$//$ Print final answer

printf$("$result$=\%$ld

$",$ gsum$)$;

exit$(0)$;

$\}$

void $*$sum$\_$mutex$($void $*$vargp$)\{$

long myid $=*(($long $*)$vargp$)$;

long start $=$ myid $*$ nelems$\_$per$\_$thread;

long end $=$ start $+$ nelems$\_$per$\_$thread;

long i;

for $($i $=$ start; i $<$ end; i$++)\{$

P$($&mutex$)$;

gsum $+=$ i;

V$($&mutex$)$;

$\}$

return NULL;

$\}$