Ralf Stephan on Wed, 15 Jan 2003 11:02:23 +0100

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Re: Pi

Karim Belabas wrote 
> On Tue, 14 Jan 2003, Bill Allombert wrote:
> > If it is your question, there is no incremental algorithm to compute Pi
> > implemented.  Computing Pi at 12200 d.p does not use the knowledge of the 
> > first 12000 d.p.

Yes, I was thinking about Bailey/Borwein/Plouffe before having read them,
BBP is O(n\log^3n) for the nth digit but constpi() is[*] faster so...

> > I do not know if it would make sense to do that.
> It definitely would, using the log((1+i) / 2) expansion. I don't think it
> would have a major effect on running times, but if somebody wants to try it...

Now, if it wouldn't have a major effect, scratch it. I have the impression,
to fully understand the constpi() code I will have to do a little more

> Also, a different Pi formula needs to be implemented [ the current one
> was chosen so that almost all multiplication/divisions involve a single
> precision operand, which is not at all what we want now ! ].

[*] no ref, I decide to believe Karim+BBP on that.