See below.
## x' = (1/2)(x + n/x)
## $f0 --- n
## $f1 --- 1.0
## $f2 --- 2.0
## $f3 --- x : current approx.
## $f4 --- x' : next approx.
## $f8 --- temp
## $f10 --- small value
loop:
mov.s $f4,$f0 # x' = n
div.s $f4,$f4,$f3 # x' = n/x
add.s $f4,$f3,$f4 # x' = x + n/x
div.s $f3,$f4,$f2 # x = (1/2)(x + n/x)
# test if loop should end
After calculating a new approximation check if the loop should end. This is more work than the actual calculation.
We can't test if we have the exact answer,
because that may never happen.
Instead test if the current x is
close to the square root of n
Say that x is very close to n0.5.
What do you think will be the value of n/(x*x)?