1. Csci136 Computer Architecture II Lab#4. - Stack and Nested Procedures
Csci136 Computer Architecture II Lab#4 - Stack and Nested Procedures - Project#1: due on Feb 13, Quiz#1 Feb.9, 2005

2. Stack and Nested Procedures
Why? -may be modified by others…
Must be saved before you go!
Return address
Local parameters
Others
How? -save to stacks!
Before you go…
addi $sp,$sp, -framesize
sw $ra, framesize-4($sp) # save $ra
save other regs if need be
Before you return…
restore other regs if need be
lw $ra, framesize-4($sp) # restore $ra
addi $sp,$sp, framesize
jr $ra

3. Example: Fibonacci Numbers 1/7
Definition:
F(n) = F(n – 1) + F(n – 2), F(0) and F(1) are defined to be 1.
C Programming:
int fib(int n) {
if(n == 0) { return 1; }  
if(n == 1) { return 1; }  
return (fib(n - 1) + fib(n - 2)); }

4. Example: Fibonacci Numbers 2/7
Now, let’s translate this to MIPS!
You will need space for three words on the stack
Why three?
Return addr($ra)
n($a0)
temp sum($s0)
Write the Prologue:
# Space for three words
# Save the return address
# Save $s0
addi $sp, $sp, -12
sw $ra, 8($sp)
sw $s0, 4($sp)
fib:
___________________

5. Example: Fibonacci Numbers 3/7
Now write the Epilogue:
lw $s0, 4($sp)
lw $ra, 8($sp)
addi $sp, $sp, 12
# Restore $s0
# Restore return address
# Pop the stack frame
# Return to caller
fin:
___________________
jr $ra_____________

6. Example: Fibonacci Numbers 4/7
Finally, write the body. The C code is below. Start by translating the lines indicated in the comments
int fib(int n) {
if(n == 0) { return 1; } /*Translate Me!*/
if(n == 1) { return 1; } /*Translate Me!*/
return (fib(n - 1) + fib(n - 2)); }
# $v0 = 1 #
# $t0 = 1
addi $v0, $zero, 1_
_______, _____,_fin
addi $t0, $zero, 1_
_______,______,_fin
Continued on next slide
beq $a0 $zero
beq $a0 $t0
___________________
__if (n == 0)
______ ____________
__if (n == 1)

7. Example: Fibonacci Numbers 5/7
Finally, write the body. The C code is below. Start by translating the lines indicated in the comments
int fib(int n) { …
return (fib(n - 1) + fib(n - 2)); }
# $a0 = n - 1 #
addi $a0, $a0, -1__
sw____, ___________
___________________
lw____,____________
addi $a0, ___,_____
$a0 0($sp)
jal fib
$a0, -1
Continued on next slide
___________________
__Need $a0 after jal
_ fib(n – 1) ______
__Restore $a0______
__$a0 = n – 2_________

8. Example: Fibonacci Numbers 6/7
Remember that $v0 is caller saved!
int fib(int n) {
return (fib(n - 1) + fib(n - 2)); }
# Place fib(n – 1)
# somewhere it won’t get
# clobbered #
add $s0,_ ___,______
___________________
add $v0, $v0, $s0__
To the epilogue and beyond
_______ $v0 $zero
jal fib
____________________
__fib(n – 2) __________
__$v0 = fib(n-1) + fib(n-2)

9. Example: Fibonacci Numbers 7/7
Here’s the complete code for reference
fib:
addi $sp, $sp, -12
sw $ra, 8($sp)
sw $s0, 4($sp)
addi $v0, $zero, 1
beq $a0, $zero, fin
addi $t0, $zero, 1
beq $a0, $t0, fin
addi $a0, $a0, -1
sw $a0, 0($sp)
jal fib
lw $a0, 0($sp)
addi $a0, $a0, -1
add $s0, $v0, $zero
jal fib
add $v0, $v0, $s0
fin:
lw $s0, 4($sp)
lw $ra, 8($sp)
addi $sp, $sp, 12
jr $ra

10. Exercise Show the content of the stack when computing Fib(2).
Assume the top of the stack is at address 0x7FFF and initially the stack is empty.
fib(2)=fib(1)+fib(0)
fib(1)=fib(0)=1

11. Project#1: MergeSort
Procedure Mergesort (input A[1:n], i,j; output B[1:n])
begin
Datatype C[1:n];
If i=j then B[i] = A[i]; Return; endif
Mergesort (A,i,(i+j)/2;C); /* sorts the first half*/
Mergesort (A,(i+j)/2 +1,j;C); /* sorts the second half*/
Merge(C,i,j;B); /*merges the two sorted halves *
*into a single sorted list */
end

12. Project#1: MergeSort
Example:

13. Project#1: MergeSort

14. Quiz#1
Give the MIPS code to load a large constant number 0xABCD9876 into register $s0.
Why not lw?
Compile the C code A[5]=A[4]+100 into MIPS code, where A is an integer array.
MIPS Addressing mode
Immediate addressing
Register addressing
Base/Displacement addressing
PC-relative addressing

15. Quiz#1
Specify the types of the following MIPS instructions. Describe the changes to PC after each instruction is executed.
Lw $s5, 8($sp)
Jr $31
Beq $1, $2, 100
J, Jr, Jal …

16. Quiz#1 if(b == 0) { return 0; } if (even(b)) return fmult(2*a,b/2);
Fast multiplication:
int fmult(int a,b) {
if(b == 0) { return 0; }
if (even(b)) return fmult(2*a,b/2);
if (odd(b)) return (a+fmult(a, b-1)); }
Use stack in your programming!
Nested Procedures