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'[PIC]: Algortithm sort  raising to a power'
2003\03\13@194603
by
Russell McMahon

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
nonPIC 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.
Russell McMahon

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2003\03\13@213940
by
Scott Dattalo

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
> nonPIC 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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