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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 isColin 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 ;-).