Exercise 2.20 This exercise deals with recursive procedure calls. For the following problems, the table has an assembly code fragment that computes the factorial of a number.

However, the entries in the table have errors, and you will be asked to fi x these errors.

a. FACT: addi $sp, $sp, –8 sw $ra, 4($sp)

sw $a0, 0($sp)

slti $t0, $a0, 1 beq $t0, $0, L1 addi $v0, $0, 1 addi $sp, $sp, 8 jr $ra L1: addi $a0, $a0, –1 jal FACT lw $a0, 4($sp)

lw $ra, 0($sp)

addi $sp, $sp, 8 mul $v0, $a0, $v0 jr $ra

b. FACT: addi $sp, $sp, –8 sw $ra, 4($sp)

sw $a0, 0($sp)

slti $t0, $a0, 1 beq $t0, $0, L1 addi $v0, $0, 1 addi $sp, $sp, 8 jr $ra L1: addi $t0, $t0, –1 jal FACT lw $a0, 4($sp)

lw $ra, 0($sp)

addi $sp, $sp, 8 mul $v0, $a0, $v0 jr $ra 2.20.1 [5] <2.8> The MIPS assembly program above computes the factorial of a given input. The integer input is passed through register $a0, and the result is returned in register $v0. In the assembly code, there are a few errors. Correct the MIPS errors.

2.20.2 [10] <2.8> For the recursive factorial MIPS program above, assume that the input is 4. Rewrite the factorial program to operate in a nonrecursive manner.

Restrict your register usage to registers $s0-$s7. What is the total number of instructions used to execute your solution from 2.20.2 versus the recursive version of the factorial program?
2.20.3 [5] <2.8> Show the contents of the stack after each function call, assuming that the input is 4.
For the following problems, the table has an assembly code fragment that computes a Fibonacci number. However, the entries in the table have errors, and you will be asked to fi x these errors.

a. FIB: addi $sp,$sp, –12 sw $ra, 0($sp)
sw $s1, 4($sp)
sw $a0, 8($sp)
slti $t0, $a0, 1 beq $t0, $0, L1 addi $v0,$a0, $0 j EXIT L1: addi $a0,$a0, –1 jal FIB addi $s1,$v0, $0 addi $a0,$a0, –1 jal FIB add $v0, $v0, $s1 EXIT: lw $ra, 0($sp)
lw $a0, 8($sp)
lw $s1, 4($sp)
addi $sp, $sp, 12 jr $ra

b. FIB: addi $sp,$sp, –12 sw $ra, 0($sp)
sw $s1, 4($sp)
sw $a0, 8($sp)
slti $t0, $a0, 1 beq $t0, $0, L1 addi $v0,$a0, $0 j EXIT L1: addi $a0,$a0, –1 jal FIB addi $s1,$v0, $0 addi $a0,$a0, –1 jal FIB add $v0, $v0, $s1 EXIT: lw $ra, 0($sp)
lw $a0, 8($sp)
lw $s1, 4($sp)
addi $sp, $sp, 12 jr $ra 2.20.4 [5] <2.8> The MIPS assembly program above computes the Fibonacci of a given input. The integer input is passed through register $a0, and the result is returned in register $v0. In the assembly code, there are a few errors. Correct the MIPS errors.
2.20.5 [10] <2.8> For the recursive Fibonacci MIPS program above, assume that the input is 4. Rewrite the Fibonacci program to operate in a nonrecursive manner.
Restrict your register usage to registers $s0-$s7. What is the total number of instructions used to execute your solution from 2.20.2 versus the recursive version of the factorial program?
2.20.6 [5] <2.8> Show the contents of the stack after each function call, assuming that the input is 4.