Root finding using the Bisection Method - comments on the logic

In my previous blog entry I described one way in which to implement the bisection method. Most programmers would probably be aghast at my liberal use of the Goto command, but in this situation I think it is required.

There are necessarily two calculations of the function f(x) in different places of the logic; f(a) at the beginning of the program and f(c) during the iterations. As I only want to have the function in one place in the program (to make it easier to edit) I needed to have a subroutine, but the fx-50F doesn't have this functionality. To make matters worse, the control structures such as While/WhileEnd do not allow you to jump in and out of them using a Goto command and they also cannot be nested. So in the end I had to go back to basics and use Goto commands with a structure similar to a subroutine and a While/WhileEnd loop.

The 'subroutine' can be found at the end of the logic after the statement Display X (this is the actual end-point of the program). I have included another memory variable X which counts the number of iterations that were needed to obtain the root to the required accuracy. Conveniently, X has been used to identify where in the program the subroutine has been called from.

The function that appears in this subroutine is f(x)=x-cos(x) and I will say more about this in a later blog.