Consumer GPUs do single-precision floating point very fast but tend to do double-precision, half-precision (16-bit), and integer operations much less quickly. And GPUs are where you get your OPs these days (FLOPS or otherwise). On Sun, Mar 26, 2017 at 6:36 PM, Bill Gosper <billgosper@gmail.com> wrote:

I think the early largest Mersenne primes were found using a bignum package built on floating point. (E.g. Brillhart's 11213(?)). -------- Original Message -------- Date: 2017-03-26 18:07 From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>

At 01:02 PM 3/26/2017, Gareth McCaughan wrote: This has the drawback that essentially no integers other than

...

0 and +-1 are *exactly* represented, unless I'm missing something. I'm not sure how much that matters, but it would be quite a departure from conventional floating-point representations.

I'm not so sure that anyone cares about this anymore.

I may have been one of the few people trying to do integer calculations using a floating point unit:

January 1992

http://home.pipeline.com/~hbaker1/AB-mod-N.html

http://home.pipeline.com/~hbaker1/AB-mod-N.pdf

"We show how to compute A*B (mod N) efficiently, for single-precision A,B, and N, on a modern RISC architecture (Intel 80860) in ANSI C. On this architecture, our method computes A*B (mod N) faster than ANSI C computes A%N, for unsigned longs A and N." _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

-- -- http://cube20.org/ -- http://golly.sf.net/ --