On Fri, 14 Mar 2003, Russell McMahon wrote:

> Wanted:
>
>             Algorithm for A = B ^ X         0 < X < 1
>
> I have a sensor output that I wish to raise to a fractional power (about
> 0.85 in this case but this will vary).
>
> While there are probably any number of algorithms or methods available to do
> this, somebody may have a favourite that is especially effective in some
> manner. Neither speed or memory capacity are critical - it would just be
> nice to find some "easy" way to do this well. This will be implemented on a
> non-PIC processor (but PIC seemed the best tag). Precision of any algorithm
> should be algorithm independent but I will need at least 8 bit and possibly
> up to about 12. Implementation will be in machine language. Standard fixed
> point, 4 function arithmetic routines are already available. Anything more
> complex (eg log) would need to be added.

I have two suggestions:

1) Feynman's Power Algorithm

  - See Vol 1 of TAOCP, Chapter 1 problem 28

2) Lookup tables with interpolation

  - This will be easier to implement

The power function for powers close to one (like 0.85) is very "smooth".
I can't really quantify (other than saying that the error is somewhat
proportional to the first derivative). However if both X and B vary then
the lookup table isn't too useful.

Scott

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