1. CSCI206 - Computer Organization & Programming
Fibonacci Procedure Workshop
zyBook: 8.3

2. Factorial
int fact (int n) {
if (n < 1)
return (1);
else
return (n * fact(n-1)); }
To implement factorial, we need to use the mult instruction in MIPS.

3. Factorial (1) Stack $ra One call to fact $a0 $sp
fact: # PC == 0x c
addi $sp, $sp, -8 # create space for 2 items
sw $ra, 4($sp) # save return address
sw $a0, 0($sp) # save argument
slti $t0, $a0, 1 # $t0 = 1 if n < 1
beq $t0, $zero, Else # if n>=1, go to Else
addi $v0, $zero, 1 # return 1
addi $sp, $sp, 8 # pop 2 words off the stack
jr $ra # return to caller
Else: # PC == 0x c
addi $a0, $a0, -1 # n>=1: n = n-1
jal fact # fact(n=n-1) PC == 0x
lw $a0, 0($sp) # restore save argument n
lw $ra, 4($sp) # restore return address
mul $v0, $a0, $v0 # $v0 = n * fact(n-1)
int fact (int n) {
if (n < 1)
return (1);
else
return (n * fact(n-1)); }

4. Factorial (2) local / automatic variable, located on the stack1 2 3 4 5 6 7 8 9 10 11
int fact (int n) {
int result;
if (n < 1)
result = 1;
else
result = n * fact(n-1);
return result; }
local / automatic variable, located on the stack
single return, value from stack

5. Factorial (2) fact: addi $sp, $sp, -12 # create space for 3 items
sw $ra, 8($sp) # save return address
sw $a0, 4($sp) # save argument
slti $t0, $a0, 1 # $t0 = 1 if n < 1
beq $t0, $zero, Else # if n>=1, go to Else
li $t0, # setup for base-case
sw $t0, 0($sp) # store 1 in result
j fact_return
Else:
addi $a0, $a0, -1 # n>=1: n = n-1
jal fact # fact(n=n-1) PC = 0x0x01FC
lw $a0, 4($sp) # restore saved argument n
mul $t0, $a0, $v0 # $v0 = n * fact(n-1)
sw $t0, 0($sp) # store result on stack
#fall through to return
fact_return:
lw $ra, 8($sp) # restore return address
lw $v0, 0($sp) # get result
addi $sp, $sp, 12 # pop 3 words off the stack
jr $ra # return to caller
Factorial (2) 1 2 3 4 5 6 7 8 9 10 11
int fact (int n) {
int result;
if (n < 1)
result = 1;
else
result = n * fact(n-1);
return result; }

6. fact:
addi $sp, $sp, -8 # create space for items
sw $ra, 4($sp) # save return address
sw $a0, 0($sp) # save argument
slti $t0, $a0, 1 # $t0 = 1 if n < 1
beq $t0, $zero, Else # if n>=1, go to Else
li $v0, # setup for base-case
j fact_return
Else:
addi $a0, $a0, -1 # n>=1: n = n-1
jal fact # fact(n=n-1)
lw $a0, 0($sp) # restore saved argument n
mul $v0, $a0, $v0 # $v0 = n * fact(n-1)
#fall through to return
fact_return:
lw $ra, 4($sp) # restore return address
addi $sp, $sp, 8 # pop 2 words off the stack
jr $ra # return to caller
Factorial (2b) 1 2 3 4 5 6 7 8 9 10 11
int fact (int n) {
int result;
if (n < 1)
result = 1;
else
result = n * fact(n-1);
return result; }
Because result is assigned after all other function calls, we can use a register to hold this local variable. This is an optimization!

7. Work in groups of three (or two) on the problem of Fibonacci procedure (Activity 15)