$1$a$.$ Write a function combination which implements the combinatorial function $nCr$ in MIPS assembler.

A straightforward Java implementation without checks is given here:

int combinations$($int $n,$ int $r$

int $c=1$;

for$($int $i=r+1$;$in$;$i++)$

$c^{**}=i$;

for$($int $i=1$;$i$ n$-$r; $i++$

$\frac{c}{?}=i$;

return $c$;

$\}$

$1$b$.$ The assemble instructions for multiplication and division, respectively, are mul and div.

Use the non$-$recursive factorial example with loops from the class as a starting point.

Write a main function which calls combinations twice with hardcoded $n$ and $r$ as follows:

a$.n=10,r=5($The answer is $252.)$

b$.n=100,r=10($The answer is $17,310,309,456,440$ which takes more than $32$ bits to represent!$)$

Exit your program with the proper syscall.

$1$c$.$ Test and run your program. Provide a screenshot of test runs for the two cases.

$($I haven't learned mflo or mfhi.$)$

data

result: $.$word $0$

$.$text

main:

Call combinations with $n=10,r=5$

$li$ $$a0,10$

$li$ $$a1,5$

jal combinations

Display result for $n=10,r=5$

li $$v,1$

move $$a0,$$$v0$

syscall

# Call combinations with $n=100,r=10$

li $$a,100$

jal combinations

# Display result for $n=100,r=10$

li $ve$,1$

move $$a0,$ $$v0$

syscall

exit: $l{i}_{\text{s}\text{y}\text{s}\text{c}\text{a}\text{l}\text{l}}$$$v0,10,$# exit with syscall $10$

# subroutine FACTORIAL$(n)$

# calculates $n**(n-1)**(n-2)**dots**1$

# IN: $,$$ a $=n,$ as unsigned integer

# OUT: $,$$ V$0=$ FACTORIAL $(n)$

# CHANGES:

$to$,$ $t$1,$ $ve

combinations:

#Function proglogue

addiu $sp$,$ $sp$,-8$

Sw $$ra,0($$$sp)$

Sw $,$$$s0,4($$$sp)$

# Initialize result to $1$

li $$50,1$

# Calculate $nCr$ numerator $)$

move $t$0,$ $a$0$

# Save $n$

# Loop to calculate $nCr$ numerator $(n**(n-1)**dots**(n-r+1))$

loop$\_$num:

addiu $$a0,$$$a0,-1,$ # Decrement $n$

bltu $a$0,$ $a$1,$ end$\_$num #Exit if $$v0,$$$a0nCrrr$$$s0,$$$$se$$$t0,$$$t0,-1$$$50,0$$$s0,4($$$sp)$$$sp,$$$sp,8n$

mult $$v0,$$$a0$

mflo $$v0$

$jloo{p}_{n}um$

$en{d}_{n}um$:

# Calculate $nCr$ denominator $(r!)$

move $$a0,$ $$a1$ #Set $a0tor$

jal factorial # Call factorial function

div $$v0,$ $$v0,$ $$a0$ # Divide numerator $by$ denominator

mflo $$v0$ #Store the result $invo$

$jr$ $$ra$ #Return

$loo{p}_d$enom:

mult $$s0,$$ $to$

mflo $$se$

addiu $$t0,$$$t0,-1$

bltu $$t0,$ $zero, $en{d}_c$ombinations

$jloo{p}_d$enom

#Function epilogue

$en{d}_c$ombinations:

# Store the result

$sw$ $$50,0(result)$

# Function epilogue

$lw$ $$ra,o($$$sp)$

$lw$ $$s0,4($$$sp)$

addiu $$sp,$$$sp,8$

$jr$ $$ra$

Error line $75$ column $24$: "result": operand $isof$ incorrect type