A quick precision test
06-05-2014, 02:00 AM
Post: #40
 Paul Dale Senior Member Posts: 1,770 Joined: Dec 2013
RE: A quick precision test
(06-05-2014 01:18 AM)Claudio L. Wrote:  I'd love to test some corner cases to see how the algorithms behave (like that case that needs 1600 digits, do you have any links to good material on this subject?). I did some tests of my own but I don't know what the corner cases are. I'd like to have some literature where they list cases that I can use to stress the algorithms and see the results.

I doubt that the 1600 bits (not digits) is actually required in reality. I suspect rather, that a proof was devised that this was sufficient for all possible input values rather than finding the absolute worst case. There has been a fair bit of work done on actually locating the worst cases in the past few years.

For binary: http://hal.inria.fr/inria-00072594/PS/RR-4044.ps
For decimal: http://perso.ens-lyon.fr/damien.stehle/d...malexp.pdf

There are plenty of others a search away.

The example at the bottom of the second page of the second paper is interesting. Forty seven correct decimal digits being required to correctly round towards zero -- 34 plus 9 guards won't get this right and this is only a 16 digit input, a 34 digit one would be worse.

As I've said many times, "numerical analysis is hard".

- Pauli
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 Messages In This Thread A quick precision test - pito - 06-02-2014, 10:37 PM RE: A quick precison test - Paul Dale - 06-02-2014, 11:04 PM RE: A quick precison test - pito - 06-03-2014, 12:07 AM RE: A quick precison test - Paul Dale - 06-03-2014, 12:13 AM RE: A quick precison test - pito - 06-03-2014, 12:27 AM RE: A quick precison test - Paul Dale - 06-03-2014, 12:36 AM RE: A quick precision test - Claudio L. - 06-04-2014, 01:25 PM RE: A quick precision test - walter b - 06-04-2014, 01:33 PM RE: A quick precision test - Claudio L. - 06-04-2014, 01:42 PM RE: A quick precision test - Paul Dale - 06-04-2014, 09:47 PM RE: A quick precison test - Gerson W. Barbosa - 06-03-2014, 01:51 AM RE: A quick precison test - Massimo Gnerucci - 06-03-2014, 06:21 AM RE: A quick precison test - walter b - 06-03-2014, 11:24 AM RE: A quick precison test - Massimo Gnerucci - 06-03-2014, 11:31 AM RE: A quick precision test - Gerson W. Barbosa - 06-03-2014, 10:20 PM RE: A quick precision test - Didier Lachieze - 06-03-2014, 10:38 PM RE: A quick precision test - Gerson W. Barbosa - 06-04-2014, 05:07 AM RE: A quick precision test - Dieter - 06-04-2014, 01:08 PM RE: A quick precision test - walter b - 06-04-2014, 01:23 PM RE: A quick precison test - HP67 - 06-03-2014, 09:06 AM RE: A quick precison test - Massimo Gnerucci - 06-03-2014, 09:15 AM RE: A quick precision test - everettr - 06-03-2014, 02:11 PM RE: A quick precision test - Gerson W. Barbosa - 06-03-2014, 09:39 PM RE: A quick precision test - Massimo Gnerucci - 06-03-2014, 10:06 PM RE: A quick precision test - Gerson W. Barbosa - 06-08-2014, 02:10 AM RE: A quick precison test - pito - 06-03-2014, 07:23 AM RE: A quick precison test - HP67 - 06-03-2014, 11:50 AM RE: A quick precison test - Paul Dale - 06-03-2014, 12:25 PM RE: A quick precision test - Massimo Gnerucci - 06-03-2014, 12:57 PM RE: A quick precision test - walter b - 06-03-2014, 01:52 PM RE: A quick precision test - Paul Dale - 06-03-2014, 10:10 PM RE: A quick precison test - HP67 - 06-03-2014, 12:41 PM RE: A quick precision test - HP67 - 06-03-2014, 01:01 PM RE: A quick precision test - walter b - 06-03-2014, 01:56 PM RE: A quick precision test - pito - 06-04-2014, 01:38 PM RE: A quick precision test - Claudio L. - 06-04-2014, 02:17 PM RE: A quick precision test - Paul Dale - 06-04-2014, 10:09 PM RE: A quick precision test - Claudio L. - 06-05-2014, 01:18 AM RE: A quick precision test - Paul Dale - 06-05-2014 02:00 AM RE: A quick precision test - Claudio L. - 06-05-2014, 11:03 AM RE: A quick precision test - Dieter - 06-05-2014, 11:23 AM RE: A quick precision test - Paul Dale - 06-05-2014, 12:06 PM RE: A quick precision test - Claudio L. - 06-05-2014, 09:08 PM RE: A quick precision test - Paul Dale - 06-05-2014, 10:09 PM RE: A quick precision test - Claudio L. - 06-06-2014, 12:57 AM RE: A quick precision test - Claudio L. - 06-06-2014, 01:15 AM RE: A quick precision test - Paul Dale - 06-06-2014, 01:35 AM RE: A quick precision test - pito - 06-06-2014, 11:16 AM RE: A quick precision test - Claudio L. - 06-06-2014, 12:04 PM RE: A quick precision test - Paul Dale - 06-06-2014, 10:55 PM RE: A quick precision test - pito - 06-07-2014, 11:56 AM RE: A quick precision test - Paul Dale - 06-07-2014, 12:20 PM RE: A quick precision test - pito - 06-07-2014, 04:44 PM RE: A quick precision test - walter b - 06-08-2014, 05:28 PM RE: A quick precision test - Claudio L. - 06-05-2014, 09:25 PM RE: A quick precision test - Paul Dale - 06-05-2014, 10:20 PM RE: A quick precision test - Claudio L. - 06-06-2014, 01:03 AM RE: A quick precision test - Paul Dale - 06-06-2014, 01:46 AM RE: A quick precision test - pito - 06-04-2014, 02:12 PM RE: A quick precision test - pito - 06-04-2014, 02:31 PM RE: A quick precision test - pito - 06-05-2014, 08:49 PM RE: A quick precision test - walter b - 06-05-2014, 09:07 PM RE: A quick precision test - pito - 06-05-2014, 09:13 PM RE: A quick precision test - Mark Hardman - 06-05-2014, 09:21 PM RE: A quick precision test - pito - 06-06-2014, 12:19 PM RE: A quick precision test - pito - 06-08-2014, 12:44 PM RE: A quick precision test - walter b - 06-08-2014, 01:57 PM RE: A quick precision test - pito - 06-08-2014, 02:07 PM RE: A quick precision test - walter b - 06-08-2014, 03:00 PM RE: A quick precision test - Paul Dale - 06-08-2014, 10:46 PM

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