Assignment Instructions:
1) The Factorial The factorial of a non-negative integer ??,denoted by ??!, is the product of all positive integers less thanor equal to ??. The textbook has an example of a recursive MIPSimplementation of factorial. Additionally, a simplified version ofthe MIPS assembly language recursive implementation of thefactorial function is attached. Trace the factorial examplecarefully using QTSPIM
2) Recursive definition of multiplication The function??????????(??, ??) for two positive integers 1 ? ??, and 1 ? ??, isdefined as the following: ??????????(??, 1) = ??; ??????????(??,??) = ?? + ??????????(??, ?? ? 1) Write a recursive version of??????????() in C or C++ and a pseudo C program (based on chapter 2in the book) then use these programs to develop a MIPS program thatgets as input two integers 0 < ?? ? 255, and 0 < ?? ? 255,and returns the result of ??????????(??, ??) in $v1. Yourdeliverable should be the pseudo C and the assembly levelfunction
Given code file:
#####################################################################################
# Functional Description: Main program to test Factorialfunction # Enter a negative number to terminate run
#####################################################################################
.data
.align 2
prompt:Â Â .asciiz \"\n\n Give me a value for \\"N\\" :\"
msg: .asciiz \" N factorial is: \"
bye: .asciiz \" \n *** Good-Bye ***\"
.text
main: addiu $sp, $sp, -8 #Allocate space
mloop:
li $v0, 4
la $a0, prompt
syscall
li $v0, 5 #Get value for N
syscall
bltz $v0, quit
sw $v0, 0 ($sp)
jal Fac # Call factorial
li $v0, 4 # Print message
la $a0, msg
syscall
lw $a0, 4($sp) #Get result
li $v0, 1
syscall #Print factorial
b mloop
quit:
addiu $sp, 8 # Deallocate space
li $v0, 4 la $a0, bye
syscall li $v0, 10
syscall
#####################################################################################
# Functional Description: Recursive Factorial Fac (N: in, N!:out)
#####################################################################################
Fac:
lw $a0, 0 ($sp)
bltz $a0, Problem
addi $t1, $a0, -13
bgtz $t1, Problem # 13 is largest value we can
# accept
addiu $sp, $sp, -16 # Allocate
sw $ra, 12 ($sp) # Save return address
sw $a0, 8($sp)
slti $t0, $a0, 2 # If N is 1 or 0, then return the value 1
beqz $t0, Go
li $v0, 1
b facret
Go:
addi $a0, $a0, -1 #
sw $a0, 0 ($sp) # Pass N-1 to factorial function
jal Fac # Recursive call
lw $v0, 4($sp) # Get (N-1) ! back.
lw $ra, 12 ($sp)
lw $a0, 8 ($sp)
mult $v0, $a0 # N* (N-1) !
mflo $v0
facret:
addiu $sp, $sp, 16 # Deallocate
sw $v0, 4 ($sp)
jr $ra
Problem:
sw $0, 4 ($sp)
jr $ra
Second give code file:
#####################################################################################
# Functional Description: Main program to test Factorialfunction # Enter a negative number to terminate run
#####################################################################################
.data
.align 2
.text
main: addiu $sp, $sp, -8 # Allocate space
mloop:
li $v0, 4 # Get value for N
sw $v0, 0 ($sp)
jal Fac # Call factorial
or $v1, $v0, $0
addiu $sp, 8 # Deallocate space
li $v0, 10
syscall
#####################################################################################
# Functional Description: Recursive Factorial Fac (N: in, N!:out)
#####################################################################################
Fac:
lw $a0, 0 ($sp)
addiu $sp, $sp, -16 # Allocate
sw $ra, 12 ($sp) # Save return address
sw $a0, 8($sp)
slti $t0, $a0, 2 # If N is 1 or 0, then return the value 1
eqz $t0, Go
li $v0, 1
b facret
Go:
addi $a0, $a0, -1 #
sw $a0, 0 ($sp) # Pass N-1 to factorial function
jal Fac # Recursive call
lw $v0, 4($sp) # Get (N-1) ! back.
lw $ra, 12 ($sp)
lw $a0, 8 ($sp)
mult $v0, $a0 # N* (N-1) !
mflo $v0
facret:
addiu $sp, $sp, 16 # Deallocate
sw $v0, 4 ($sp)
jr $ra
