Start of the Program

Now using x = 2.5 in the formula yields:

x' = (1/2)(2.5 + 4/2.5) = (1/2)(2.5 + 1.6) = (1/2)(4.1) = 2.05

This is a better yet approximation, and could be fed back into the formula to get an even better approximation.

The example program implements this procedure. It repeatedly uses the formula to calculate increasingly accurate approximations to the square root. Here is the start of the program:

## newton.asm -- compute sqrt(n) 

## given an approximation x to sqrt(n),
## an improved approximation is:

## 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 ---  accuracy limit, a small value

        .text
        .globl main

main:   

        l.s     $f0,n               # get n
        li.s    $f1,1.0             # constant 1.0
        li.s    $f2,2.0             # constant 2.0
        li.s    $f3,1.0             # x == first approx.
        li.s    $f10,1.0e-5         # accuracy limit
loop:

The program will be written so that it stops looping when no further improvement is possible. We can't expect to get the answer exactly correct.