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

version 1.0.1 (20.2 KB) by Gert Kruger
The Newton-Raphson approximation of the reciprocal, i.e. 1/x and square root reciprocal is provided along with accuracy testing jigs.

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Updated 29 May 2019

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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.

Cite As

Gert Kruger (2021). Newton-Raphson reciprocal approximation , 1/x and 1/sqrt(x) (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (1)

Nice implementation!

MATLAB Release Compatibility
Created with R2010a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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