RE: RE: Re: Could someone verify a long Pi calculation in Version 4 for me?

*To*: mathgroup at smc.vnet.net*Subject*: [mg36840] RE: [mg36821] RE: [mg36806] Re: Could someone verify a long Pi calculation in Version 4 for me?*From*: "DrBob" <drbob at bigfoot.com>*Date*: Sat, 28 Sep 2002 04:34:45 -0400 (EDT)*Reply-to*: <drbob at bigfoot.com>*Sender*: owner-wri-mathgroup at wolfram.com

>>I believe the complexity is O(n log n), so this should be good enough. Umm ..."good enough"? I understand the words individually, but the phrase makes no sense to me. Bobby Treat -----Original Message----- From: dterr at wolfram.com [mailto:dterr at wolfram.com] To: mathgroup at smc.vnet.net Subject: [mg36840] Re: [mg36821] RE: [mg36806] Re: Could someone verify a long Pi calculation in Version 4 for me? DrBob wrote: > >>So would it take about the same amont of time for the complete > printout > of digits? Of course it would take a few additional seconds to format > the output... > > I think it would take FAR more time for a complete printout, and might > crash the Front End. I was thinking about the fact that I calculated > all those digits and then threw them away. I could save them with Save > or DumpSave, and read them in with Get the next time I wanted any of > them, although the file would be close to 70 MB (if not more). I may do > that, in fact -- I have plenty of disk space. > > The next step would be to somehow reuse the stored digits if I wanted > MORE digits. But how? > > The Bailey-Borwein-Plouffe Pi algorithm is an avenue of attack, since it > can calculate digits far from the decimal point, without calculating > those in between. Unfortunately, it calculates hexadecimal digits in > that way, not decimal digits. (That's true for the version I've seen, > anyway.) Still, I could take the stored digits, convert to hexadecimal, > add more hexadecimal digits with the B-B-P algorithm, and then convert > back to decimal. In both conversions, I'd have to be very cognizant of > how much precision I end up with, but that shouldn't be too difficult. > It might go faster if I store hexadecimal digits, as well as decimal > digits, to eliminate one of those conversions at each increase in the > number of digits. > > The next step would be to set up an application that allowed anyone to > ping for digits across the Internet, and would return them if they're > stored. > > Hasn't someone already done that? It seems as if someone would have. > > Bobby Treat If you're interested in decimal digits, I don't think the BBP algorithm is the way to go. In order to get the nth decimal digit of Pi you need to compute the previous n-1 digits, since base conversion is global, not local. The algorithm Mathematica uses for computing Pi is quite fast - I believe the complexity is O(n log n), so this should be good enough. David > > > -----Original Message----- > From: zeno [mailto:zeno1234 at mindspring.com] To: mathgroup at smc.vnet.net > Subject: [mg36840] [mg36821] [mg36806] Re: Could someone verify a long Pi calculation in > Version 4 for me? > > So would it take about the same amont of time for the complete printout > of digits? Of course it would take a few additional seconds to format > the output... > > Or does Mathematica take alot less time when it truncates the output? > > In article <amris4$576$1 at smc.vnet.net>, Tom Burton <tburton at brahea.com> > wrote: > > > Hello, > > > > On 9/23/02 12:19 AM, in article ammfi5$lk7$1 at smc.vnet.net, "zeno" > > <zeno1234 at mindspring.com> wrote: > > > > > Could you tell me the CPU you used and its speed etc...i am curious, > > > thanks. It would be interesting to compare Version 4s Pi performance > to > > > other programs out there. > > > > I used one processor of a dual 1GH Mac and got the same answer with > the > > following speed: > > > > $Version > > 4.2 for Mac OS X (June 4, 2002) > > oldmax = $MaxPrecision > > 6 > > 1. 10 > > $MaxPrecision = Infinity > > Infinity > > With[{n = 2^26}, Timing[ > > pd = RealDigits[N[Pi, n + 1], 10, 20, > > 19 - n]; ]] > > {28794.1 Second, Null} > > MaxMemoryUsed[] > > 512055204 > > pd > > {{3, 3, 8, 6, 3, 2, 2, 0, 8, 9, 6, 2, 2, 3, > > > > 4, 0, 9, 8, 0, 3}, -67108844} > > > > Tom Burton