Could you tell us about your timing results? On what computer and which
lisp?
Comppi does not use bigfloats at all.
I think it uses only integer calculations, though there is a "quotient"
which is like truncate, I think.
I think that there are fast results from Chudnovskys, but I think there is a
more recent survey of such results in
"Experimental Mathematics" by Bailey et al.
Similarly, fpexp1 uses a taylor series, so your comment that you changed it
seems to require some justification (timing, accuracy, etc.)
I think that changes to code that works already should be held to extremely
high standards.
Regards
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of van Nek
> Sent: Sunday, November 04, 2007 1:32 PM
> To: fateman at cs.berkeley.edu
> Cc: Maxima at math.utexas.edu
> Subject: Re: [Maxima] comppi
>
> Am 13 Oct 2007 um 22:01 hat Richard Fateman geschrieben:
>
> > I haven't looked at it, but I think I copied it from some
> continued fraction
> > approximation in Hakmem, probably written out by Bill Gosper.
> > There are likely faster-converging formulas known now.
>
> It took me some time to find out, what series it was.
> I found, that it was the Newton series based on
> pi = 6*asin(1/2)
>
> Meanwhile I was looking for a faster way to compute PI in Maxima.
> The best I found is a some kind of Ramanujan series by
> Chudnovsky & Chudnovsky.
> The computation mainly uses bignum calculations and is
> therefor faster than other
> algorithms which are based on bigfloat calculations (e.g.
> Borwein's recursive algorithms).
>
> I changed float.lisp/comppi and also wrote a new function
> float.lisp/compe which computes
> E by some modified Taylor series.
>
> Volker van Nek
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