Pi Formulas, Algorithms and Computations

Pi Computation

(Dec 31 2009)
2700 billion decimal digits of Pi computed with a desktop computer.

Formulas and Algorithms

(Jan 20 1997)
A new and faster formula to compute the n'th binary digit of Pi. The article (Jan 20 1997) in html or in PDF pi_bin.pdf (revised edition, Feb 2007). A systematic way to find similar formulas is presented here.

(Jan 10 1997)
Simon Plouffe has found an algorithm to compute the n'th digit of Pi in any base in O(n^3log(n)^3) with little memory. We give here an improvement of his algorithm to get a speed of O(n^2). The postscript file of the alpha version of the article: pi_n2.ps , the html version, and the corresponding implementation in C: pi.c . (Feb 27 1997) A faster implementation which uses the Gosper formula : pi1.c .

(Feb 4 1997)
While testing some numerical relations with the PSLQ algorithm , I found this exotic formula for Pi:


(Aug 2003)Boris Gourevitch and Jesus Guillera show how to demonstrate similar formulas.

Related information

Fabrice Bellard - http://bellard.org/