Finding polynamial roots using Newton-Raphson takes more time than in-built 'roots' function

Dear users,

I would like to find roots of a cubic equation in Simulink[ver: 8.0]

INPUTs to embedded Matlab function block: * initial guess (x0) and * coefficient vector.[a, b, c, d]

Matlab in-built 'roots' does the job, though, accuracy is an issue.

I went on finding roots manually using Newton-Raphson's method. Though, it really slows down the simulation. Here is the code I use:

-------------------------------------
            function x1 = fcn(x0,a,b,c,d)
            %#codegen
            x1=x0;
            flag=0;
            while(flag==0)

                  fx=(a*(x1^3))+(b*(x1^2))+(c*x1)+d;
                  fdx=(3*a*(x1^2))+(2*b*x1)+c;
                  x1=x1-(fx/fdx);
                  diff=abs(x1-x0);
                  x0=x1;
                  if diff<=0.00000000001
                      flag=1;
                  end
              end
  ------------------------

Do you have any suggestions to make it faster OR any better(accurate+fast) method to get roots in Simulink?

Looking forward to hearing.

Thank you.

[Amit Doshi]

sample time for the model is 0.01

[Javier]

Accurate desired goes again faster desired. I made a tic toc on your code and was ok (time elapsed: 1.9829e-05). A more accurate result can be achieved via lower diff or other search method.