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Square Root Function Implementation in Assembly Language (MIPS32 ISA)
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You can use Cpulator (Online Simulator) to execute this code.
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Remember to set the stack pointer beforehand, otherwise, it might throw you an 'overflow' error. The stack pointer is typically initialized to the highest address in the data segment.
li $sp, 0x7ffffffc # Setting the stack to highest stack address
Algorithm for Square Root:
First, we'll attempt to include this C logic in the MIPS assembly program for the Square Root of a number (integer).
square_root(n){
int res = n;
for(int i=0;i<(n/res);i++){
res = (res + n/res) / 2;
}
return res;
}
MIPS32 Implementation:
This is a simple program that can be implemented in MIPS32.
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We are using procedures (Functions) for Square Root, Division and Multiplication
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Check the blog for the Division and Multiplication here:
Here is the code for Square Root (MIPS32 ISA)
SQUARE_ROOT:
# res = n
# while(i < n/2)
# res = (res + n / res) / 2;
addi $sp, $sp, -20
sw $ra, 16($sp) # Saving the return address into stack
sw $s3, 12($sp) # Saving other register values
sw $s2, 8($sp)
sw $s1, 4($sp)
sw $s0, 0($sp)
add $s3, $zero, $a0 # s3 = n
add $s0, $zero, $a0 # res = n
addi $a1, $zero, 2 # A = N, B = 2
jal DIVISON # Divison(n, 2)
add $s1, $zero, $v0 # s1 = n / 2
addi $s2, $zero, 0 # idx (s2) = 0
SQUARE_ROOT_LOOP:
beq $s1, $s2, EXIT_SQUARE_ROOT # if (idx == n/2) break
add $a0, $s3, $zero # A = n
add $a1, $s0, $zero # B = res
jal DIVISION # Divison(n, res)
add $s0, $s0, $v0 # res = res + (n/res)
add $a0, $zero, $s0 # A = res + (n/res)
addi $a1, $zero, 2 # B = 2
jal DIVISION # Divison((res + (n / res), 2)
add $s0, $zero, $v0 # res = res + (n / res) / 2
addi $s2, $s2, 1 # idx++
j SQUARE_ROOT_LOOP
EXIT_SQUARE_ROOT:
lw $s0, 0($sp) # Retrieving data stored in stack
lw $s1, 4($sp)
lw $s2, 8($sp)
lw $s3, 12($sp)
lw $ra, 16($sp) # Retrieving Return Address
addi $sp, $sp, 20 # Reseting stack pointer
jr $ra
DIVISION:
# While (A >= B) A -= B; result++
add $sp, $sp, -12 # Allocating Stack Memory
sw $s2, 8($sp) # Storing register values
sw $s1, 4($sp)
sw $s0, 0($sp)
addi $s0, $zero, 0 # result (s0) = 0
add $s1, $zero, $a0 # s1 = A
add $s2, $zero, $a1 # s2 = B
DIV_LOOP:
blt $s1, $s2, EXIT_DIV # If (A < B) break
sub $s1, $s1, $s2 # A -= B
addi $s0, $s0, 1 # result++
j DIV_LOOP
EXIT_DIV:
add $v0, $zero, $s0 # v0 = result
lw $s2, 8($sp) # restoring register values
lw $s1, 4($sp)
lw $s0, 0($sp)
addi $sp, $sp, 12 # restoring stack pointer
jr $ra
Conclusion:
In this article, you have learned to implement Square Root in Mips32 ISA