$***$Please make sure you do not use la$,$ beqz, bgtz$,$ blez, and syscall.$***$ Write a MIPS program using $*$Recursive Procedure Execution to perform the following tasks: $*$Note:$*$ If your code runs perfectly, but you didn't use Procedure Execution correctly, you will be given zero points.

Write the following functions in MIPS.

main

inputs: integers a$,$ b

task: Compute the integer: a $*$ F$(|$a$+$b$|,|$a$-$b$|)-$ b $*$ F$(|$b$-$a$|,|$b$+$a$|).$

recursion F$($x$,$ y$)$

inputs: integers x$,$ y$.$

task:

F$($x$,$ y$)=$ F$($x$-1,$ y$)+$ F$($x$,$ y$-1),$ if x$,$ y $>0$

F$($x$,$ y$)=$ y if x y $>0$

F$($x$,$ y$)=$ x if y x $>0$

F$($x$,$ y$)=0$ if x$,$ y

Following is a sample C code segment. You may modify the code for the functions, but the task performed should not be changed, i$.$e$.,$ you should use recursive procedure calls.

int main$($int a$,$ int b$)\{$

int result $=$ a $*$ recursion$($abs$($a$+$b$),$ abs$($a$-$b$))-$ b $*$ recursion$($abs$($b$-$a$),$ abs$($b$+$a$))$;

$\}$

int recursion$($int x$,$ int y$)\{$

if $($x && y

return$(0)$;

else if $($x $>0$ && y

return$($x$)$;

else if $($x && y $>0)$

return$($y$)$;

else

return$($recursion$($x$-1,$ y$)+$ recursion$($x$,$ y$-1))$;

$\}$

Registers Variables

$s$0$ a

$s$1$ b

$s$2$ result

Example Test: If the values of $s$1$ and $s$2$ are initialized in the simulator as:

$($Use the $\text{'}+\text{'}$ button under the Registers display to initialize register values for $s$1,$ $s$2.)$

Registers Data

$s$01$

$s$12$

$s$20$

The resultant registers are:

Registers Data

$s$01$

$s$12$

$s$2-7$

Example Test: If the values of $$s1$ and $$s2$ are initialized in the simulator as:

$($Use the $\text{'}+\text{'}$ button under the Registers display to initialize register values for $s$1,$ $s$2.)$

The resultant registers are: