Bellard's formula

Bellard's formula

Bellard's formula, as used by PiHex, the now-completed distributed computing project, is used to calculate the "n"th digit of π in base 2. It is a faster version (about 43% faster [ [http://oldweb.cecm.sfu.ca/projects/pihex/credits.html PiHex Credits ] ] ) of the BBP formula. Bellard's formula was discovered by Fabrice Bellard.

Formula

pi=frac1{2^6,{sum_{n=0}^infty {frac({-1})}^n}{2^10}, n},{left(frac{-{2^54, n}+1-{frac14, n}+3+{frac{2^8}{10}, n}+1-{frac{2^6}{10}, n}+3-{frac{2^2}{10}, n}+5-{frac{2^2}{10}, n}+7+{frac1{10}, n}+9} ight)}

Notes

External links

* [http://fabrice.bellard.free.fr/pi/ Fabrice Bellard's PI page]
* [http://oldweb.cecm.sfu.ca/projects/pihex/ PiHex web site]
* [http://denistn.mine.nu/pdf2html.php?url=http://oldweb.cecm.sfu.ca/projects/pihex/p123.pdf David Bailey, Peter Borwein, and Simon Plouffe's BBP formula ("On the rapid computation of various polylogarithmic constants") (PDF)]


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