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 reading/writing. > 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 ! ]. ralf [*] no ref, I decide to believe Karim+BBP on that.