As far as I see the page http://www.sciencenews.org/20021214/mathtrek.asp doesn't say that Kanada actually used pi = 16 arctan(1/5) - 4 arctan(1/239) It only says he used two different _formulas_ (unclear even whether arctan-type). I'd guess he used binary splitting and ramanujan-type formulas. Judging from the quality of the past Kanada information I wouldn't be surprised if he will never tell us. The necessity (or advantage) using binsplit and a series isn't clear to me. Number theoretic transforms (with CRT) and the AGM would IMHO do it, too. Btw. five years for coding is quite ridiculous. However, having seen some of the Kanada's code I am not exactly surprised about that. Quite amazing how someone with that resources (staff, machinery and time) can restrict himself to the mere announcement "done nnn digits" every now and then. * Simon Plouffe <simon.plouffe@sympatico.ca> [Jan 09. 2003 13:10]:
hello,
there is more, Kanada used Machin formula and another one(?) to verify the computation apparently and made basic statistics about the distribution of digits (0 to 9), that's about it.
see the article of Peterson in : http://www.sciencenews.org/20021214/mathtrek.asp
see also : http://www.super-computing.org/
I find it surprising that he took that formula which is by far not the best.
Simon Plouffe
-- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.