Newton-Raphson reciprocal approximation , 1/x and 1/sqrt(x)
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.
Citation pour cette source
Gert Kruger (2024). Newton-Raphson reciprocal approximation , 1/x and 1/sqrt(x) (https://www.mathworks.com/matlabcentral/fileexchange/71675-newton-raphson-reciprocal-approximation-1-x-and-1-sqrt-x), MATLAB Central File Exchange. Récupéré le .
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Version | Publié le | Notes de version | |
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1.0.1 | Removed an unnecessary variable from the reciprocal calculation which was used for performance analysis. The functions are now suitable for use (copy and paste). |
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1.0.0 |