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Re: Multiple precisions of floating-point arithmetic




On Feb 26, 2006, at 2:00 PM, bear wrote:

On Sun, 26 Feb 2006, Bradley Lucier wrote:

Then Colin Percival published his paper "Rapid multiplication modulo
the sum and difference of highly composite numbers",

www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/
S0025-5718-02-01419-9.pdf

which gives new bounds for the error in FFTs implemented in floating-
point arithmetic.  This allows you to use FFTs to implement bignum
arithmetic with inputs of size 256 * (1024)^2 bits in 64-bit IEEE
arithmetic with proven accuracy.

This is a very interesting potential implementation technique.
Is there a URL for this article that someone who is not a member
of the American Mathematical Society can access?  Or a publication
we can find at a local print library?

					Bear


Sorry, I didn't realize that that link was restricted to AMS members. You can also get it at

http://www.daemonology.net/papers/

The citation is

Colin Percival, Rapid multiplication modulo the sum and difference of highly composite numbers, Mathematics of Computation, Volume 72, Number 241, Pages 387-395, 2002.

The bignum implementation of Gambit-C uses this technique (hopefully correctly ;-).

Brad