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MathGroup Archive 2002

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36821] RE: [mg36806] Re: Could someone verify a long Pi calculation in Version 4 for me?
  • From: "DrBob" <drbob at bigfoot.com>
  • Date: Fri, 27 Sep 2002 04:15:23 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

>>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

-----Original Message-----
From: zeno [mailto:zeno1234 at mindspring.com] 
To: mathgroup at smc.vnet.net
Subject: [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





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