Raising to a power

Archiver

I need to raise a word (in the range 0:1023) to the power n, where n
will be < 1, for example:

y = x**.23


I've read Tracy's math stuff, but didn't see anything there that was
directly applicable. Other than table lookup, anyone got any good
ideas?

Thanks

Larry

Archiver

This will be tough to do well with integer math. The trick is to keep in
mind that what you really want is a root. So if you say 5**.5 you are
really asking for the square root (1/2 = .5).

Of course, this can be done with a log table (think slide rule) or just
a pure look up table, but for 1024 entries that's somewhat large.
Another answer would be a PAK-II or one of its related coprocessors.
http://www.al-williams.com/pak1.htm
This has the extra advantage that you can get the fractional part as
accurate as you like subject to the 32-bit floating point number (24
bits of significant value).

Do you need just one root, or is the exponent also variable?

Al Williams
AWC
* Floating point math for the Stamp, PIC, SX, or any microcontroller
http://www.al-williams.com/awce/pak1.htm



>

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Original Message

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> From: ve3crx [noparse]/noparse]mailto:[url=http://forums.parallaxinc.com/group/basicstamps/post?postID=x1JsMx0HzqzQTKFx-aRsqffEFBszGJxu2EzsYFfaqtDS88SckHm4fg_x-KeqGAzFeRFDXdI]ve3crx@r...[/url
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> Subject: [noparse][[/noparse]JUNK] [noparse][[/noparse]basicstamps] Raising to a power
>
>
> I need to raise a word (in the range 0:1023) to the power n, where n
> will be < 1, for example:
>
> y = x**.23
>
>
> I've read Tracy's math stuff, but didn't see anything there that was
> directly applicable. Other than table lookup, anyone got any good
> ideas?
>
> Thanks
>
> Larry
>
>
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Archiver

>I need to raise a word (in the range 0:1023) to the power n, where n
>will be < 1, for example:
>
>y = x**.23
>
>
>I've read Tracy's math stuff, but didn't see anything there that was
>directly applicable. Other than table lookup, anyone got any good
>ideas?
>
>Thanks
>
>Larry


If n is a variable, too, then a table lookup/interpolation is not feasible.

I would approach it as
lg y = n * lg x
where lg is log base 2. There is a an iterative algorithm for that
on my web site. Having that, you can multiply (n * lg x) using the
** operator, and the result will be an integer part (characteristic)
and a fractional part (mantissa) equal to lg y. The characteristic
brackets the possible values of y between two integer powers of two.
Then to narrow it down it would not be hard to put lg y in a loop and
converge quickly on the solution. By quickly, I mean 10s of
milliseconds altogether!

I have not done the Stamp antilog explicitly (maybe someday).


-- best regards
Tracy Allen
electronically monitored ecosystems
http://www.emesystems.com
mailto:tracy@e...

Archiver

Hi again Larry,

Another thought on this,
y = x**.23
computed using lg (log base 2)
lg y = .23 * lg x
y = 2 to the power (.23 * lg x)

if you need more speed and not so much accuracy (??), you could use
the bitlog and its inverse (2 to the power of..) from
http://www.emesys.com/BS2math3.htm#bitlog
Bitlog is a very fast interpolation scheme to find logs and antilogs.

-- Tracy


>>I need to raise a word (in the range 0:1023) to the power n, where n
>>will be < 1, for example:
>>
>>y = x**.23
>>
>>
>>I've read Tracy's math stuff, but didn't see anything there that was
>>directly applicable. Other than table lookup, anyone got any good
>>ideas?
>>
>>Thanks
>>
>>Larry
>
>
>If n is a variable, too, then a table lookup/interpolation is not feasible.
>
>I would approach it as
> lg y = n * lg x
>where lg is log base 2. There is a an iterative algorithm for that
>on my web site. Having that, you can multiply (n * lg x) using the
>** operator, and the result will be an integer part (characteristic)
>and a fractional part (mantissa) equal to lg y. The characteristic
>brackets the possible values of y between two integer powers of two.
>Then to narrow it down it would not be hard to put lg y in a loop
>and converge quickly on the solution. By quickly, I mean 10s of
>milliseconds altogether!
>
>I have not done the Stamp antilog explicitly (maybe someday).
>
>
> -- best regards
> Tracy Allen
> electronically monitored ecosystems
> http://www.emesystems.com
> mailto:tracy@e...
>
>
>

Archiver

Tracy (and Al)

The power is a constant within a given system (It is an amp-hour
meter for my sailboat; the available power in a battery depends on
the actual current drain raised to a power; the number is a constant
for a particular brand of battery.

A general method would of course be best; then I can just change the
constant for different batteries.

Actually, the real version of this is going to be built using a PIC
16F877 rather than a STAMP. The stamp is real nice for playing around
with concepts. The real device will probably be programmed using
PicBasic Pro.

I'll look at the web site again for your log stuff, Tracy.

Thanks

Larry