Has anyone coded spece efficient replacements for pow() and log()? The BasicX library versions of these consume so much stack that they are basically useless. Has anyone coded a Taylor's expansion for these that they's like to share?

# pow() and log() replacements?

Started by ●February 19, 2006

Reply by ●February 19, 20062006-02-19

cfrancois_55116 wrote: > Has anyone coded spece efficient replacements for pow() and log()? The > BasicX library versions of these consume so much stack that they are > basically useless. Has anyone coded a Taylor's expansion for these > that they's like to share? How did you come to the conclusion that these functions are wasteful of RAM? They are but for exact measurements see part 4 of my series of articles on the Internals of BasicX. In section 4.4.6 I show how to replace the code for Sin() using an abbreviated Taylor series. The following webpage gives some algorithms for calculating log() and log10() - http://www.dattalo.com/technical/theory/logs.html. You should be able to do some space enhancements for pwr() along the same lines as documented in section 4.4 of the article and by reusing some of the code from that section - see also section 4.3.5 to see what needs rewriting. Mike http://home.austin.rr.com/perks/micros/Articles/

Reply by ●February 20, 20062006-02-20

I used bxdism. log() uses 63 bytes of stack while pow() uses an astonishing 100, probably because it calls log() in a Taylor's expansion. http://www.efunda.com/math/taylor_series/logarithmic.cfm has several Taylor's series for these but I was hoping someone already went to the trouble of coding. Maybe I'm missing something, but to use 63 and 100 bytes, they must be coded with almost complete disregard for stack usage. At 100 bytes, it pretty much rules out using pow() in a multi-task app. BTW, I've been looking through your articles- good stuff. STACK USAGE ANALYSIS =================== Length Parameters Returns Local Vars Stack Usage Total Stack Name of Routine ------ ---------- ------- ---------- ----------- ----------- --------- ------ 251 4 4 26 39 63 sys~mathlibrary.sys~log 100 8 4 8 34 100 sys~mathlibrary.sys~pow --- In basicx@basi..., Mike Perks <basicx@...> wrote: > > cfrancois_55116 wrote: > > > Has anyone coded spece efficient replacements for pow() and log ()? The > > BasicX library versions of these consume so much stack that they are > > basically useless. Has anyone coded a Taylor's expansion for these > > that they's like to share? > > How did you come to the conclusion that these functions are wasteful of > RAM? They are but for exact measurements see part 4 of my series of > articles on the Internals of BasicX. In section 4.4.6 I show how to > replace the code for Sin() using an abbreviated Taylor series. > > The following webpage gives some algorithms for calculating log() and > log10() - http://www.dattalo.com/technical/theory/logs.html. You should > be able to do some space enhancements for pwr() along the same lines as > documented in section 4.4 of the article and by reusing some of the code > from that section - see also section 4.3.5 to see what needs rewriting. > > Mike > http://home.austin.rr.com/perks/micros/Articles/ >

Reply by ●February 20, 20062006-02-20

cfrancois_55116 wrote: > I used bxdism. log() uses 63 bytes of stack while pow() uses an > astonishing 100, probably because it calls log() in a Taylor's > expansion. http://www.efunda.com/math/taylor_series/logarithmic.cfm > has several Taylor's series for these but I was hoping someone already > went to the trouble of coding. Maybe I'm missing something, but to > use 63 and 100 bytes, they must be coded with almost complete > disregard for stack usage. At 100 bytes, it pretty much rules out > using pow() in a multi-task app. > > BTW, I've been looking through your articles- good stuff. This is quite straightforward coding with just a little optimization for the stack. I have posted some code on my Experiments page ( http://home.austin.rr.com/perks/micros/Experiments/ ) that implements the Log function (which I call Ln). I only used the first six terms from the Taylor expansion and achieved an accuracy better than 0.0001%. Here is the extract from bxDism: Length ... Local Vars Stack Usage Total Stack Name of Routine ------ ---------- ----------- ----------- --------------- 276 14 26 26 log.ln 251 26 39 63 sys~mathlibrary.sys~log The function is slightly longer (could probably be improved) but it only uses 26 bytes on the stack versus 63. In addition a welcome improvement is that it seems to be more than 3 times faster than the BasicX code. This performance improvement is surprising but nonetheless very welcome. Try the code for yourself and verify both the results and that my implementation is correct. Mike BasicX, ZBasic and AVR expert http://home.austin.rr.com/perks/micros/