fild [eax]        ; put epsilon on stack
fild [ebx]        ; put x on top of stack
fild [ecx]        ; put guess (y_0) on top of stack
test:
fld st(0)         ; copy y_i on top of stack again, so that:
fmul              ; st(0) := y_i ^ 2
fsub st(2)        ; st(0) := y_i ^ 2 - x
fabs              ;
fcomp st(3)       ; if st(0) < epsilon
jc done           ; jump to done
improve:
fld st(0)         ; copy y_i
fdivr st(2) st(0) ; st(0) := x / y_i
fadd              ; st(0) := y_i + (x/y_i)
fld1
fld1
fadd              ; push 2 onto stack
fdivr st(1) st(0) ; st(0) := (y_i + (x/y_i))/2
jmp test
done:
fistp [eax]       ; return result
fstp st(0) 
fstp st(0)
fstp st(0)        ; cleanup

float FindBabylonianSqRoot( float x, float epsilon, float initial = 0 ) {
    
    var guess = Math.Abs(initial);
    
    while( epsilon < Math.Abs(x - guess * guess) ) {
        guess = ((x / guess) + guess) / 2.0f;
    }

    return guess;
}