Comments on: The Digits of Pi

By: Sam Kennedy

Sam Kennedy — Tue, 05 Jul 2011 16:11:44 +0000

It isn’t pretty but it works:

#!/usr/bin/perl


$| = 1;
push(@B, 0);
$counter = 3;

for($i = 0;$i<=33223;$i++){

    push(@A,$i);

    push(@remainder, 2);

    push(@B, $counter);

    $counter += 2;

}
for($x = 1; $x=1;$i--){

        $m10[$i] = $remainder[$i] * 10;

        $sum[$i] = $m10[$i] + $carried[$i];

        $remainder[$i] = $sum[$i] % $B[$i];

        $carried[$i - 1] = (($sum[$i] - $remainder[$i]) / $B[$i]) * $A[$i];

	}
    $m10[0] = $remainder[0] * 10;

    $sum[0] = $m10[0] + $carried[0];

    $remainder[0] = $sum[0]%10;

	$predigit = int($sum[0]/10);
	push(@predigits, $predigit);
	if($predigit < 9){

		for($i = 0; $i<((scalar @predigits)-1); $i++){

			print $predigits[$i];

		}

		undef @predigits;

		push(@predigits, $predigit);

	}

if($predigit == 10){ for($i = 0; $i<((scalar @predigits)-1); $i++){ if($predigits[$i] == 9) { print 0; } else { $predigits[$i] = $predigits[$i] + 1; print $predigits[$i]; } } undef @predigits; push(@predigits, 0); } }

By: Sam Kennedy

Sam Kennedy — Wed, 29 Jun 2011 13:06:08 +0000

This seems like a really interesting exercise, however I cannot understand how this spigot algorithm works. I read the PDF, but I could not follow the maths in the diagram, is there an easier explanation for someone who doesn’t have a massive background in maths?

Cheers,
-Sam

By: Graham

Graham — Tue, 17 May 2011 18:07:22 +0000

I modified the fixed-point approach for arccot found here and used it with Wikipedia's most efficient Machin-Like formula found here My submission

By: programmingpraxis

programmingpraxis — Fri, 06 Aug 2010 11:59:01 +0000

Alexander J. Yee & Shigeru Kondo recently computed five trillion digits of pi.

By: Matt Weaver

Matt Weaver — Sun, 27 Sep 2009 01:58:04 +0000

My solution, written in C:

http://codepad.org/WOEQnbTt

This version calculates the requested digit directly, based on the method described in “Computation of the nth decimal digit of pi with low memory”: http://numbers.computation.free.fr/Constants/Algorithms/nthdecimaldigit.pdf (and I must admit I also peeked a little at the implementation at http://numbers.computation.free.fr/Constants/Algorithms/nthdigit.html)

It lacks the conciseness and elegance of the spigot solution, but makes up for it in efficiency. The spigot version works well until it runs out of main memory and starts paging, at which point performance really hits a wall. On my computer that point is somewhere between the 20,000th digit (took 1:48) and the 50,000th (I killed it after 3.5 hours). For comparison, this solution returns the 50,000th digit in ~12 seconds.