Pi Computation

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

Formulas and Algorithms

(Jan 20 1997)
A modern and sooner system 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 methodology to search out the same formulas is presented right here.

(Jan 10 1997)
Simon Plouffe has
found an algorithm to compute the n’th digit of Pi in any unsuitable in
O(n^3log(n)^3) with little memory. We give right here an enchancment of his algorithm
to obtain a flee 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 sooner implementation which
makes use of the Gosper system : pi1.c .

(Feb 4 1997)

While making an strive out some numerical family with the PSLQ
algorithm
, I found this abnormal system for Pi:



with

(Aug 2003)Boris Gourevitch and Jesus Guillera
show how to uncover the same formulas.

Linked data

Numbers, constants and computation, by Xavier Gourdon and Pascal Sebah The Pi entry in Wolfram MathWorld. Jörg Arndt’s dwelling page . Favourite Mathematical Constants from Steven Finch. L’univers de Pi, by Boris Gourevitch. Simon Plouffe’s dwelling page . A French e-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 e-book about Pi by Jörg Arndt:  Pi – Algorithmen, Computer, Arithmetik, Springer-Verlag Heidelberg, ISBN 3-540-63419-3. English translation to advance relief.

---

Fabrice Bellard –
http://bellard.org/