Newton-Raphson reciprocal approximation , 1/x and 1/sqrt(x)

The Newton-Raphson approximation of the reciprocal, i.e. 1/x and square root reciprocal is provided along with accuracy testing jigs.

The reciprocal calculation in a real-time controller is quite computationally expensive. The Newton-Raphson approximation of the reciprocal saves on the computational cost at the expense of accuracy. If the reciprocal of an input signal is calculated, with the signal itself having a limited change from one execution cycle to the next, then the previously calculated Newton-Raphson reciprocal serves as an initial "guess" to the new the iteration. This results in a large improvement in accuracy.

The number of iterations can be modified according to the required accuracy.

An analysis can be found in:
Fowler, D. L., and James E. Smith. "An accurate, high speed implementation of division by reciprocal approximation." Proceedings of 9th Symposium on Computer Arithmetic. IEEE, 1989.