CompilerConstruction-ex4/vsl_programs/newton.vsl

// Approximate square root by the Newton/Raphson method for f(x) = x^2 - n
// f(x) = x^2 - n = 0
// f'(x) = 2x
// x{n+1} = x{n} - (x^2-n) / 2x 

def newton ( n )
begin
    print "The square root of", n, "is", improve ( n, 1 )
    return 0
end

def improve ( n, estimate )
begin
    var next
    next := estimate - ( (estimate * estimate - n) / ( 2 * estimate ) )
    if next - estimate = 0 then
        // Integer precision converges at smallest int greater than the square
        return next-1
    else
        return improve ( n, next )
end