https://bellard.org/pi/

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.
[pi10]

(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:
[c7n2n1]
with
[c7n2n2]

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

Related information

  * Numbers, constants and computation, by Xavier Gourdon
    and Pascal Sebah
  * The Pi entry in Wolfram MathWorld.
  * Jorg Arndt's home page .
  * Favorite Mathematical Constants from Steven Finch.
  * L'univers de Pi, by Boris Gourevitch.
  * Simon Plouffe's home page .                            [couv_pi2]
  * A French book about Pi: Le fascinant nombre Pi ,
    Jean-Paul Delahaye, Editions Belin / Pour La Science,
    Paris, 1997, ISSN 0224-5159 ISBN 2-9029-1825-9. 
  * A German book about Pi by Jorg Arndt:  Pi -
    Algorithmen, Computer, Arithmetik, Springer-Verlag
    Heidelberg, ISBN 3-540-63419-3. English translation to
    come.

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Fabrice Bellard - http://bellard.org/