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Groups > comp.arch > #3118 > unrolled thread
| Started by | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| First post | 2011-08-23 10:48 -0700 |
| Last post | 2011-08-29 09:18 -0700 |
| Articles | 20 on this page of 246 — 39 participants |
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Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-23 10:48 -0700
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-23 16:24 -0700
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-08-24 07:20 +0200
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-23 23:22 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-24 14:38 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-25 17:42 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-27 09:45 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-27 18:03 -0700
Re: Solving the Floating-Point Goldilocks Problem! Brett Davis <ggtgp@yahoo.com> - 2011-08-26 20:31 -0500
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-26 20:08 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-27 02:35 -0700
Re: Solving the Floating-Point Goldilocks Problem! Brett Davis <ggtgp@yahoo.com> - 2011-08-27 15:27 -0500
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-27 13:41 -0700
Re: Solving the Floating-Point Goldilocks Problem! Brett Davis <ggtgp@yahoo.com> - 2011-08-27 17:34 -0500
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-27 17:40 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-27 17:50 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-28 23:49 -0700
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-27 22:40 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-28 19:33 -0700
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-08-29 13:56 +0200
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-29 09:07 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-08-29 17:56 +0100
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-29 11:56 -0700
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-08-29 16:12 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-08-29 20:46 +0100
Re: Solving the Floating-Point Goldilocks Problem! Kalle Olavi Niemitalo <kon@iki.fi> - 2011-08-30 07:48 +0300
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-08-30 08:22 +0100
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-31 11:34 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-29 22:22 -0700
Re: Solving the Floating-Point Goldilocks Problem! Andrew Reilly <areilly---@bigpond.net.au> - 2011-08-30 11:17 +0000
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-08-30 12:35 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-30 07:02 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-08-30 15:18 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-30 15:12 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-08-31 08:30 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-01 09:54 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-01 10:09 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-01 18:01 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-01 12:25 -0700
Re: Solving the Floating-Point Goldilocks Problem! sidd <sidd@situ.com> - 2011-09-01 20:02 -0400
Re: Solving the Floating-Point Goldilocks Problem! Elliott Roper <nospam@yrl.co.uk> - 2011-09-02 10:27 +0100
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-02 11:33 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-02 08:09 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-02 08:12 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-02 15:50 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-02 08:49 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-02 17:00 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-02 15:55 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-03 18:06 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-02 07:58 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-02 15:56 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-02 07:42 -0700
Re: Solving the Floating-Point Goldilocks Problem! Andreas Eder <andreas_eder@gmx.net> - 2011-09-02 17:51 +0200
Re: Solving the Floating-Point Goldilocks Problem! sidd <sidd@situ.com> - 2011-08-31 12:11 -0400
Complex Number Representation nmm1@cam.ac.uk - 2011-09-02 21:22 +0100
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-30 07:08 -0700
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-08-31 10:39 +0200
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-31 08:00 -0700
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-08-31 18:38 +0200
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-08-31 13:18 -0400
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-31 19:09 -0700
Re: Solving the Floating-Point Goldilocks Problem! Brett Davis <ggtgp@yahoo.com> - 2011-08-30 00:19 -0500
Re: Solving the Floating-Point Goldilocks Problem! Brett Davis <ggtgp@yahoo.com> - 2011-08-31 23:46 -0500
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-31 09:56 -0700
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-09-01 08:23 +0200
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-31 14:02 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-01 04:02 -0700
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-09-01 19:42 +0200
Re: Solving the Floating-Point Goldilocks Problem! BGB <cr88192@hotmail.com> - 2011-08-31 23:20 -0700
Re: Solving the Floating-Point Goldilocks Problem! "James Van Buskirk" <not_valid@comcast.net> - 2011-09-12 15:53 -0600
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-12 22:31 +0100
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-12 22:56 +0100
Re: Solving the Floating-Point Goldilocks Problem! Walter Bushell <proto@panix.com> - 2011-09-12 21:00 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-13 10:10 +0100
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-09-13 04:58 +0200
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-01 07:25 -0400
Re: Solving the Floating-Point Goldilocks Problem! Tim Shoppa <shoppa@trailing-edge.com> - 2011-09-01 10:37 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-01 18:25 +0100
Re: Solving the Floating-Point Goldilocks Problem! Bill Findlay <yaldnif.w@blueyonder.co.uk> - 2011-09-01 19:56 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-01 12:30 -0700
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-01 12:38 -0700
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-01 17:13 -0400
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-01 14:48 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-01 22:49 +0100
Re: Solving the Floating-Point Goldilocks Problem! Robert Wessel <robertwessel2@yahoo.com> - 2011-09-01 18:08 -0500
Re: Solving the Floating-Point Goldilocks Problem! "Charlie Gibbs" <cgibbs@kltpzyxm.invalid> - 2011-09-02 00:26 -0800
Re: Solving the Floating-Point Goldilocks Problem! "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-09-02 05:06 -0700
Re: Solving the Floating-Point Goldilocks Problem! Robert Wessel <robertwessel2@yahoo.com> - 2011-09-02 10:46 -0500
Re: Solving the Floating-Point Goldilocks Problem! Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-09-02 12:08 -0700
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-02 13:54 -0700
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-03 14:57 +0000
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-03 15:33 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-03 13:42 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-04 08:46 +1000
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-04 08:05 +0100
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-04 17:44 +1000
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-04 08:56 +0100
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-04 18:52 +1000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-04 08:55 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 16:46 +0100
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-04 13:21 +0000
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 14:03 +0100
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-04 14:15 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 18:52 +0100
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-04 15:00 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 21:02 +0100
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-04 19:22 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-05 07:09 +0100
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-05 04:48 +1000
Re: Solving the Floating-Point Goldilocks Problem! Walter Bushell <proto@panix.com> - 2011-09-04 20:18 -0400
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-04 03:53 +1000
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-04 13:21 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-05 03:57 +1000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-04 08:47 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-05 04:03 +1000
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-04 14:30 -0400
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-05 04:49 +1000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-04 15:53 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-05 09:55 +1000
Re: Solving the Floating-Point Goldilocks Problem! Piotr Wyderski <peter.pan@neverland.mil> - 2011-10-19 19:17 +0200
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-04 19:54 +0100
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 20:56 +0100
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-04 19:16 -0400
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-04 16:26 -0700
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-05 13:45 +0200
Re: Solving the Floating-Point Goldilocks Problem! Bakul Shah <usenet@bitblocks.com> - 2011-09-05 12:09 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-05 20:51 +0100
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-06 10:57 +0200
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-06 19:43 +1000
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-06 10:55 +0200
Re: Solving the Floating-Point Goldilocks Problem! Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-09-06 11:36 +0100
OT English Re: Solving the Floating-Point Goldilocks Problem! wclodius@lost-alamos.pet (William Clodius) - 2011-09-05 13:33 -0600
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-05 23:12 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Charlie Gibbs" <cgibbs@kltpzyxm.invalid> - 2011-09-07 09:44 -0800
Re: Solving the Floating-Point Goldilocks Problem! Robert Wessel <robertwessel2@yahoo.com> - 2011-09-03 13:41 -0500
Re: Solving the Floating-Point Goldilocks Problem! scott@slp53.sl.home (Scott Lurndal) - 2011-09-03 21:36 +0000
Re: Solving the Floating-Point Goldilocks Problem! Robert Wessel <robertwessel2@yahoo.com> - 2011-09-03 20:18 -0500
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-04 08:31 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 13:11 +0100
Re: Solving the Floating-Point Goldilocks Problem! scott@slp53.sl.home (Scott Lurndal) - 2011-09-05 17:14 +0000
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-09-07 09:07 +0000
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-07 12:15 +0100
Re: Solving the Floating-Point Goldilocks Problem! Walter Bushell <proto@panix.com> - 2011-09-07 08:37 -0400
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-07 13:50 +0100
Re: Solving the Floating-Point Goldilocks Problem! Walter Bushell <proto@panix.com> - 2011-09-07 09:21 -0400
Re: Solving the Floating-Point Goldilocks Problem! Bernd Felsche <berfel@innovative.iinet.net.au> - 2011-09-08 08:42 +0800
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-08 14:10 +0000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-08 19:09 -0700
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-05 22:50 -0700
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-06 13:45 +0000
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-06 09:08 -0700
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-07 14:13 +0000
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-07 09:42 -0700
Re: Solving the Floating-Point Goldilocks Problem! Bernd Felsche <berfel@innovative.iinet.net.au> - 2011-09-08 09:05 +0800
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-08 14:10 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-08 04:49 +1000
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-08 14:09 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-09 03:17 +1000
Re: Solving the Floating-Point Goldilocks Problem! Gene Wirchenko <genew@ocis.net> - 2011-09-10 23:07 -0700
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-11 09:06 +0100
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-11 10:07 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-11 06:48 -0700
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-11 08:26 -0400
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-11 13:00 +0100
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-11 07:36 -0700
Re: Solving the Floating-Point Goldilocks Problem! Piotr Wyderski <peter.pan@neverland.mil> - 2011-10-19 19:15 +0200
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-10-19 14:45 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Charlie Gibbs" <cgibbs@kltpzyxm.invalid> - 2011-10-19 17:13 -0800
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-10-20 13:38 +0000
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-10-27 09:01 +0000
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-02 20:41 -0400
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-03 06:58 +0100
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-03 07:19 +0100
Re: Solving the Floating-Point Goldilocks Problem! Bakul Shah <usenet@bitblocks.com> - 2011-09-02 21:54 -0700
Re: Solving the Floating-Point Goldilocks Problem! Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-09-03 09:05 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-03 16:42 +0100
Re: Solving the Floating-Point Goldilocks Problem! scott@slp53.sl.home (Scott Lurndal) - 2011-09-03 21:00 +0000
Re: Solving the Floating-Point Goldilocks Problem! Bakul Shah <usenet@bitblocks.com> - 2011-09-03 11:01 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-03 19:18 +0100
Re: Solving the Floating-Point Goldilocks Problem! Bakul Shah <usenet@bitblocks.com> - 2011-09-03 13:05 -0700
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 08:09 +0100
Re: Solving the Floating-Point Goldilocks Problem! scott@slp53.sl.home (Scott Lurndal) - 2011-09-03 21:34 +0000
Re: Solving the Floating-Point Goldilocks Problem! Jean-Marc Bourguet <jm@bourguet.org> - 2011-09-04 22:15 +0200
Re: Solving the Floating-Point Goldilocks Problem! nmm1@cam.ac.uk - 2011-09-04 21:07 +0100
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-02 20:21 -0400
Re: Solving the Floating-Point Goldilocks Problem! Tim Shoppa <shoppa@trailing-edge.com> - 2011-09-06 09:32 -0700
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-09-07 09:09 +0000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-07 07:17 -0700
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-07 16:00 +0100
Re: Solving the Floating-Point Goldilocks Problem! Bill Findlay <yaldnif.w@blueyonder.co.uk> - 2011-09-07 16:40 +0100
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-07 09:57 -0700
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-07 09:39 -0700
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-07 20:47 +0200
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-08 14:09 +0000
Re: Solving the Floating-Point Goldilocks Problem! Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-09-08 09:13 -0700
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-08 18:59 +0200
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-09 15:21 +0000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-09 12:48 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-10 06:27 +1000
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-09 23:04 +0200
Re: Solving the Floating-Point Goldilocks Problem! Bernd Felsche <berfel@innovative.iinet.net.au> - 2011-09-08 08:57 +0800
Re: Solving the Floating-Point Goldilocks Problem! jmfbahciv <See.above@aol.com> - 2011-09-08 14:10 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Charlie Gibbs" <cgibbs@kltpzyxm.invalid> - 2011-09-08 07:50 -0800
Re: Solving the Floating-Point Goldilocks Problem! Walter Bushell <proto@panix.com> - 2011-09-08 12:07 -0400
Re: Solving the Floating-Point Goldilocks Problem! Walter Bushell <proto@panix.com> - 2011-09-08 12:10 -0400
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-08 17:38 +0100
Re: Solving the Floating-Point Goldilocks Problem! Seebs <usenet-nospam@seebs.net> - 2011-09-09 03:43 +0000
Re: Solving the Floating-Point Goldilocks Problem! Robert Wessel <robertwessel2@yahoo.com> - 2011-09-08 12:21 -0500
Re: Solving the Floating-Point Goldilocks Problem! Peter Flass <Peter_Flass@Yahoo.com> - 2011-09-01 17:09 -0400
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-02 08:59 +1000
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-09-07 09:07 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-07 20:03 +1000
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-09-08 16:55 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-09 03:52 +1000
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-10-01 15:57 +0000
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-10-02 05:51 +1100
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-10-07 11:31 +0000
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-07 14:08 +0200
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-07 14:18 +0100
Re: Solving the Floating-Point Goldilocks Problem! Huge <Huge@nowhere.much.invalid> - 2011-09-07 14:05 +0000
Re: Solving the Floating-Point Goldilocks Problem! Morten Reistad <first@last.name> - 2011-09-07 20:54 +0200
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-08 05:27 +1000
Re: Solving the Floating-Point Goldilocks Problem! timcaffrey@aol.com (Tim McCaffrey) - 2011-09-16 18:48 +0000
Re: Solving the Floating-Point Goldilocks Problem! sidd <sidd@situ.com> - 2011-09-07 18:53 -0400
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-08 04:37 +1000
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-09-08 10:19 +0200
Re: Solving the Floating-Point Goldilocks Problem! kenney@cix.compulink.co.uk - 2011-09-08 05:14 -0500
Re: Solving the Floating-Point Goldilocks Problem! Gene Wirchenko <genew@ocis.net> - 2011-09-11 12:58 -0700
Re: Solving the Floating-Point Goldilocks Problem! Ahem A Rivet's Shot <steveo@eircom.net> - 2011-09-12 10:01 +0100
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-12 19:35 +1000
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-12 09:25 -0700
Re: Solving the Floating-Point Goldilocks Problem! Michael Black <et472@ncf.ca> - 2011-09-12 13:27 -0400
Re: Solving the Floating-Point Goldilocks Problem! Ben Pfaff <blp@cs.stanford.edu> - 2011-09-12 10:41 -0700
Re: Solving the Floating-Point Goldilocks Problem! Patrick Scheible <kkt@zipcon.net> - 2011-09-12 11:34 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-13 05:40 +1000
Re: Solving the Floating-Point Goldilocks Problem! Michael Black <et472@ncf.ca> - 2011-09-12 15:53 -0400
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-12 13:08 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-08 04:14 +1000
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-09-07 11:31 -0700
Re: Solving the Floating-Point Goldilocks Problem! "Rod Speed" <rod.speed.aaa@gmail.com> - 2011-09-08 05:35 +1000
Re: Solving the Floating-Point Goldilocks Problem! Bernd Felsche <berfel@innovative.iinet.net.au> - 2011-09-08 08:40 +0800
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-09-07 20:25 +0200
Re: Solving the Floating-Point Goldilocks Problem! blmblm@myrealbox.com <blmblm.myrealbox@gmail.com> - 2011-09-08 16:58 +0000
Re: Solving the Floating-Point Goldilocks Problem! Robert Wessel <robertwessel2@yahoo.com> - 2011-09-08 12:31 -0500
Re: Solving the Floating-Point Goldilocks Problem! Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-08-30 13:46 +0200
Re: Solving the Floating-Point Goldilocks Problem! Quadibloc <jsavard@ecn.ab.ca> - 2011-08-29 09:18 -0700
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| From | Elliott Roper <nospam@yrl.co.uk> |
|---|---|
| Date | 2011-09-02 10:27 +0100 |
| Message-ID | <020920111027009199%nospam@yrl.co.uk> |
| In reply to | #3359 |
In article <j3p6e3$9m3$1@speranza.aioe.org>, sidd <sidd@situ.com> wrote: > I must agree. The Cartesian representation of the complex plane is a > very simplified version. Under exponentiation, the plane > becomes helical, and this is only a shadow of the real difficulties > in representation enforced by analyticity (Cauchy-Riemann conditions) > across branch cuts. > > Considering that floating point is an approximation to real line > anyway attempting to represent complex numbers as an ordered pair of > floating points might be considered hubris... > > The best way i have found is to do most calculation with complex > numbers is by hand, only use complex variables in a program when i > am fairly sure i know what i am doing. then when i get a ridiculous > answer, i go back and redo. > > Complex numbers are the last stop on the route from integers, thru the > rationals and the reals, before you have to give up commutativity > > ab=ba > > Then you get quarternions, and if you are willing to give up > associativity > > (ab)c=a(bc) > > you can go further... > > I would not recommend trying to do any real math for quaternions or > octonions or Clifford numbers implemented as ordered sets of floats > except under draconian supervision. Ooh mummy! If ever there was a post that raised more questions than it answered, this one wins the biscuit. I have been using quaternions a bit for combining rotations without having a clue where the pitfalls lay. And helixes for complex exponents? Yikes! Is there a gentle textbook you could recommend for an old goat that has not done that kind of maths for yonks and yonks? My idea of testing for errors in floats is to redo the calculation with higher precision and compare the answers, so the textbook really needs to be gentle. -- To de-mung my e-mail address:- fsnospam$elliott$$ PGP Fingerprint: 1A96 3CF7 637F 896B C810 E199 7E5C A9E4 8E59 E248
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-02 11:33 +0100 |
| Message-ID | <j3qbdp$4g8$1@gosset.csi.cam.ac.uk> |
| In reply to | #3364 |
In article <020920111027009199%nospam@yrl.co.uk>, Elliott Roper <nospam@yrl.co.uk> wrote: >In article <j3p6e3$9m3$1@speranza.aioe.org>, sidd <sidd@situ.com> wrote: > >> I must agree. The Cartesian representation of the complex plane is a >> very simplified version. Under exponentiation, the plane >> becomes helical, and this is only a shadow of the real difficulties >> in representation enforced by analyticity (Cauchy-Riemann conditions) >> across branch cuts. >> >> I would not recommend trying to do any real math for quaternions or >> octonions or Clifford numbers implemented as ordered sets of floats >> except under draconian supervision. > >Ooh mummy! If ever there was a post that raised more questions than it >answered, this one wins the biscuit. > >I have been using quaternions a bit for combining rotations without >having a clue where the pitfalls lay. And helixes for complex >exponents? Yikes! > >Is there a gentle textbook you could recommend for an old goat that has >not done that kind of maths for yonks and yonks? > >My idea of testing for errors in floats is to redo the calculation with >higher precision and compare the answers, so the textbook really needs >to be gentle. While I am pretty rusty, too, I should also be very interested in any such reference. I should prefer a rather less gentle one, but still several stages down from the theoretical peaks! Even though I work in an appropriate university, I am not sure where I would start looking or who to ask. This is definitely not mere undergraduate material .... Regards, Nick Maclaren.
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-02 08:09 -0700 |
| Message-ID | <671cd5c0-f82c-410e-9e21-1535b6ba11bd@t5g2000yqj.googlegroups.com> |
| In reply to | #3368 |
On Sep 2, 4:33 am, n...@cam.ac.uk wrote: > Even though I work in an appropriate university, I am not sure where > I would start looking or who to ask. This is definitely not mere > undergraduate material .... I had thought that Graves' octaves were not really used at all for anything practical, but some searching has allowed me to find that John Baez and John Huerta have been applying octonions to string theory - they even had an article about this in _Scientific American_. So I suppose one could start with their publications... John Savard
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-02 08:12 -0700 |
| Message-ID | <d16f3b1b-8852-4d15-b472-28b6fa4be258@z7g2000vbp.googlegroups.com> |
| In reply to | #3376 |
Also, look here: http://math.ucr.edu/home/baez/octonions/node1.html John Savard
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-02 15:50 +0100 |
| Message-ID | <j3qqfo$8c1$1@gosset.csi.cam.ac.uk> |
| In reply to | #3376 |
In article <671cd5c0-f82c-410e-9e21-1535b6ba11bd@t5g2000yqj.googlegroups.com>, Quadibloc <jsavard@ecn.ab.ca> wrote: > >> Even though I work in an appropriate university, I am not sure where >> I would start looking or who to ask. This is definitely not mere >> undergraduate material .... > >I had thought that Graves' octaves were not really used at all for >anything practical, but some searching has allowed me to find that >John Baez and John Huerta have been applying octonions to string >theory - they even had an article about this in _Scientific American_. >So I suppose one could start with their publications... Thanks, but that doesn't sound good. I am specifically interested in analyses of the numerical problems, and not mere examples of uses. While they MIGHT have put the effort in, the term "string theory" doesn't fill me with great confidence .... I wouldn't have much trouble doing a search, but it would be hellishly time-consuming without some definitely relevant starting points. It wouldn't be quick even for mere complex numbers :-( Regards, Nick Maclaren.
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-02 08:49 -0700 |
| Message-ID | <2be70ccd-a007-4ee0-bf30-b35d860c864d@j1g2000yqn.googlegroups.com> |
| In reply to | #3378 |
On Sep 2, 8:50 am, n...@cam.ac.uk wrote: > I wouldn't have much trouble doing a search, but it would be > hellishly time-consuming without some definitely relevant starting > points. It wouldn't be quick even for mere complex numbers :-( I've also bumped into a Google Books result for: Clifford algebras with numeric and symbolic computations By Rafał Abłamowicz, Pertti Lounesto, Josep M. Parra ... which is _sort_ of the book being sought, but it is indeed an advanced book, far beyond my level. John Savard
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-02 17:00 +0100 |
| Message-ID | <j3quj4$94v$1@gosset.csi.cam.ac.uk> |
| In reply to | #3382 |
In article <2be70ccd-a007-4ee0-bf30-b35d860c864d@j1g2000yqn.googlegroups.com>, Quadibloc <jsavard@ecn.ab.ca> wrote: > >> I wouldn't have much trouble doing a search, but it would be >> hellishly time-consuming without some definitely relevant starting >> points. It wouldn't be quick even for mere complex numbers :-( > >I've also bumped into a Google Books result for: > >Clifford algebras with numeric and symbolic computations >By Rafa=C5=82 Ab=C5=82amowicz, Pertti Lounesto, Josep M. Parra > >... which is _sort_ of the book being sought, but it is indeed an >advanced book, far beyond my level. Thanks very much! A quick look indicates that it doesn't imply that it addresses the numerical aspects, and it isn't available in the library here (and is pricey!), but the authors would be a good place to start a literature search. Amusingly, the person who I contacted first is referred to in the introduction, and he doesn't know of anything. It's rather beyond my level, but I could follow it with some help looking up the terms and results I have forgotten (the majority). Regards, Nick Maclaren.
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-02 15:55 -0700 |
| Message-ID | <08db60c0-c26a-410d-ae28-c182ddb25be6@u26g2000yqu.googlegroups.com> |
| In reply to | #3385 |
On Sep 2, 10:00 am, n...@cam.ac.uk wrote: > In article <2be70ccd-a007-4ee0-bf30-b35d860c8...@j1g2000yqn.googlegroups.com>, > > Quadibloc <jsav...@ecn.ab.ca> wrote: > > >> I wouldn't have much trouble doing a search, but it would be > >> hellishly time-consuming without some definitely relevant starting > >> points. It wouldn't be quick even for mere complex numbers :-( > > >I've also bumped into a Google Books result for: > > >Clifford algebras with numeric and symbolic computations > >By Rafa=C5=82 Ab=C5=82amowicz, Pertti Lounesto, Josep M. Parra > > >... which is _sort_ of the book being sought, but it is indeed an > >advanced book, far beyond my level. > > Thanks very much! A quick look indicates that it doesn't imply that > it addresses the numerical aspects, and it isn't available in the > library here (and is pricey!), but the authors would be a good place > to start a literature search. > > Amusingly, the person who I contacted first is referred to in the > introduction, and he doesn't know of anything. > > It's rather beyond my level, but I could follow it with some help > looking up the terms and results I have forgotten (the majority). Also, as a rather smaller thing, this web page http://www.stephenwolfram.com/publications/recent/specialfunctions/ happens to mention what happens to sin(x) = sqrt( 1 - (cos(x))^2 ) when one wishes to make it branch cut correct over the complex numbers... John Savard
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-03 18:06 -0700 |
| Message-ID | <12b8a150-1e56-4261-b1f4-5aecb11b4850@a7g2000yqb.googlegroups.com> |
| In reply to | #3385 |
Also, I've found another book which addresses the question of what is known about using quaternions and octonions in an arithmetical fashion for purposes of calculation: http://books.google.ca/books?id=H-5v6pPpyb4C With a title like "Hypercomplex Analysis", it should deal with the topic. However, it's a collection of papers. Hypercomplex Analysis and Applications is perhaps, therefore, a better choice: http://books.google.ca/books?id=-CrI7zgpoesC ... ah, no, it's also a collection of papers, not an introductory textbook. John Savard
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-02 07:58 -0700 |
| Message-ID | <2575a5eb-0339-403c-ba28-0f11b86b2dac@o26g2000vbi.googlegroups.com> |
| In reply to | #3368 |
On Sep 2, 4:33 am, n...@cam.ac.uk wrote: > Even though I work in an appropriate university, I am not sure where > I would start looking or who to ask. This is definitely not mere > undergraduate material .... One would start, I suppose, by looking for references on Clifford algebras or division algebras. What are today deservedly called octonions, incidentally, were called octaves when first invented, as someone else had swiped the name octonions for something different - a pair of quaternions. But I do suspect it would indeed be difficult to find this sort of book. Actually doing calculations even with quaternions - except for their use as a way to do a dot product and a cross product at the same time - hasn't really been found useful precisely because it does not produce meaningful results. To say it is riddled with pitfalls is misleading, as that would imply that if one is careful enough, one can produce a useful answer that means something. Beyond using quaternions for dealing with rotations after the manner of vector algebra - and going a bit further into the four-vectors of relativity - I don't think that's happened yet. The properties of division algebras are a subject of mathematical study - a largely old and neglected one - but this is abstract algebra, not applied mathematics. Not like complex numbers, which (as just one example) well represent electricity and magnetism. John Savard
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-02 15:56 +0100 |
| Message-ID | <j3qqr5$8e8$1@gosset.csi.cam.ac.uk> |
| In reply to | #3379 |
In article <2575a5eb-0339-403c-ba28-0f11b86b2dac@o26g2000vbi.googlegroups.com>, Quadibloc <jsavard@ecn.ab.ca> wrote: > >> Even though I work in an appropriate university, I am not sure where >> I would start looking or who to ask. This is definitely not mere >> undergraduate material .... > >But I do suspect it would indeed be difficult to find this sort of >book. Actually doing calculations even with quaternions - except for >their use as a way to do a dot product and a cross product at the same >time - hasn't really been found useful precisely because it does not >produce meaningful results. That is my suspicion, too. >The properties of division algebras are a subject of mathematical >study - a largely old and neglected one - but this is abstract >algebra, not applied mathematics. Not like complex numbers, which (as >just one example) well represent electricity and magnetism. Yes. Except that it's hard enough to find anything on the numerical properties of those, except for the well-thrashed overflow problem in division. Regards, Nick Maclaren.
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-02 07:42 -0700 |
| Message-ID | <0bdd755d-3528-4957-8864-94bcc964a1f3@n35g2000yqf.googlegroups.com> |
| In reply to | #3364 |
On Sep 2, 3:27 am, Elliott Roper <nos...@yrl.co.uk> wrote: > I have been using quaternions a bit for combining rotations without > having a clue where the pitfalls lay. Well, if that's _all_ you're using them for, you won't be running *into* the pitfalls. What's special about quaternions, compared to vector algebra, or a matrix representation of rotations, is that you can do real arithmetic with them - quaternions are a "division algebra", so you can divide one quaternion by another. And, in fact, one can generalize pretty much any mathematical function to work on quaternions - Hamilton called e^x, when applied to quaternions, the "ponential" function, but one could do sin, cos, tan, and even the gamma function if one likes. But there it's unclear that the results would mean anything. John Savard
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| From | Andreas Eder <andreas_eder@gmx.net> |
|---|---|
| Date | 2011-09-02 17:51 +0200 |
| Message-ID | <87mxenc58s.fsf@eder.homelinux.net> |
| In reply to | #3364 |
>>>>> "Elliott" == Elliott Roper <nospam@yrl.co.uk> writes:
Elliott> Is there a gentle textbook you could recommend for an old goat that has
Elliott> not done that kind of maths for yonks and yonks?
I can recommend 'On Quaternions and Octonions' by J.H. Conway & D.A.
Smith, A K Peters, Ltd. 2003 ISBN 1-56881-134-9
I'm not so sure about the 'gentle' but it is an interesting read.
'Andreas
--
ceterum censeo redmondinem esse delendam.
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| From | sidd <sidd@situ.com> |
|---|---|
| Date | 2011-08-31 12:11 -0400 |
| Message-ID | <j3lmfp$m81$1@speranza.aioe.org> |
| In reply to | #3287 |
On Tuesday 30 August 2011 18:12, Quadibloc wrote: > It sometimes is needed to preserve winding number - but this sounds to > me like a very specialized requirement that people would likely use > Mathematica for instead of FORTRAN. (Although what you are seeking may > indeed be a feature that does need to be added *there*.) > Mathematica has issues as well with branch cuts and winding numbers. Or at least, they did about ten years ago... When I have to handle these, i do everything in polar, as suggested above in this thread, and (very carefully) translate to and from cartesian as needed. sidd
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-02 21:22 +0100 |
| Subject | Complex Number Representation |
| Message-ID | <j3rdta$aop$1@gosset.csi.cam.ac.uk> |
| In reply to | #3274 |
This kicked me into writing some code. My test was not thorough,
but these were the results under gcc (in C++):
I could get slightly better than the built-in complex, though
I don't know why. Perhaps it used better boundary checking, or
was just poor coding.
Crude polar was, of course, dire for addition and overall.
A redundant representation (using 3 words) was over 10 times
slower in raw addition speed, though with ample scope for low-level
optimisation, but only 2-2.5 times slower on a 1000x1000 matrix
multiply. It was much faster for division.
My conclusion is that, with some trivial help from the hardware,
one could deliver comparable speed on raw codes AND get the
exception handling sane. I shall not hold my breath.
Anyone wanting my code to play further should send me a message.
Regards,
Nick Maclaren.
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| From | "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> |
|---|---|
| Date | 2011-08-30 07:08 -0700 |
| Message-ID | <4E5CEEC1.9070107@SPAM.comp-arch.net> |
| In reply to | #3261 |
On 8/30/2011 4:17 AM, Andrew Reilly wrote:
> On Mon, 29 Aug 2011 22:22:14 -0700, Andy \"Krazy\" Glew wrote:
>
>> Anyway, I am not so much interested in what I can imagine, as what has
>> already been used, which may be in somewhat wide use.
>
> I'd be very surprised if most uses weren't exactly of the form: {int data
> [N]; int scale};
I was holding my breath, hoping that somebody would post a bit
interleaved block F format:
* int11 exponent
* bit interleaved X,Y,Z
* bit 17 of X
* bit 17 of Y
* bit 17 of Z
...
* bit 0 of X
* bit 0 of Y
* bit 0 of Z
Rationale: some may be familiar with the bit interleaving scheme for
coordinates occasionally used in graphics.
Bit interleaving is hard in software om conventional machines. Not so
bad with hardware support.
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| From | Terje Mathisen <"terje.mathisen at tmsw.no"> |
|---|---|
| Date | 2011-08-31 10:39 +0200 |
| Message-ID | <ej81j8-vov2.ln1@ntp6.tmsw.no> |
| In reply to | #3270 |
Andy "Krazy" Glew wrote: > I was holding my breath, hoping that somebody would post a bit > interleaved block F format: > > * int11 exponent > * bit interleaved X,Y,Z > * bit 17 of X > * bit 17 of Y > * bit 17 of Z > ... > * bit 0 of X > * bit 0 of Y > * bit 0 of Z Hmmm... That looks like 18*3+11 = 65 bits. Are you sure that the exponent didn't use 10 bits? > > Rationale: some may be familiar with the bit interleaving scheme for > coordinates occasionally used in graphics. BTDT. Just like when you're addressing cache lines, you don't need to use all the bits like this, but it makes sense to use an interleaved index to access blocks of data, said blocks to be at least a cache line in size. > > Bit interleaving is hard in software om conventional machines. Not so > bad with hardware support. As you know LRB have two opcodes for this, to do 1:1:1:1:1 and 2:1:2:1:2:1 interleaving. With this much hw support it becomes most practical to keep the (x,y,z) indices separate and merge them before use. You can of course do strides along either axis relatively efficiently even when working with a single interleaved index: idx = (idx & yz_mask) | (((idx | yz_mask) + x_stride) & x_mask); I.e. when stepping in the X direction, make sure that all the Y&Z bits are set, add in the X increment (any carries will propagate past the YZ bit positions), save only the X bits, then merge in the original YZ bits. This is 5 operations and 4 cycles minimum latency. Terje -- - <Terje.Mathisen at tmsw.no> "almost all programming can be viewed as an exercise in caching"
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| From | "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> |
|---|---|
| Date | 2011-08-31 08:00 -0700 |
| Message-ID | <4E5E4C7E.50700@SPAM.comp-arch.net> |
| In reply to | #3296 |
On 8/31/2011 1:39 AM, Terje Mathisen wrote: > Andy "Krazy" Glew wrote: >> I was holding my breath, hoping that somebody would post a bit >> interleaved block F format: >> >> * int11 exponent >> * bit interleaved X,Y,Z >> * bit 17 of X >> * bit 17 of Y >> * bit 17 of Z >> ... >> * bit 0 of X >> * bit 0 of Y >> * bit 0 of Z > > Hmmm... That looks like 18*3+11 = 65 bits. Are you sure that the > exponent didn't use 10 bits? >> >> Rationale: some may be familiar with the bit interleaving scheme for >> coordinates occasionally used in graphics. > > BTDT. > > Just like when you're addressing cache lines, you don't need to use all > the bits like this, but it makes sense to use an interleaved index to > access blocks of data, said blocks to be at least a cache line in size. >> >> Bit interleaving is hard in software om conventional machines. Not so >> bad with hardware support. > > As you know LRB have two opcodes for this, to do 1:1:1:1:1 and > 2:1:2:1:2:1 interleaving. > > With this much hw support it becomes most practical to keep the (x,y,z) > indices separate and merge them before use. You are missing one of the other uses of bit-interleaved formats: They provide scalability. Both in online (serial) arithmetic, and in network distribution. E.g. you may want to send bit interleaved data with N bits per component around the network. At the points where you realize that this data is only ever going to be displayed on a small screen whose viewport you already know, you start truncating the bitstream. People used to build graphics devices that sent data around like this, bit serially. We may do so again. (One of my pet peeves is people assuming, for a non-lossy transformation, that A->B is necessary, but B->A is not necessary. There may not be a business case for making the reverse transformation fast. But nearly always this is a short sighted optimization.)
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| From | Terje Mathisen <"terje.mathisen at tmsw.no"> |
|---|---|
| Date | 2011-08-31 18:38 +0200 |
| Message-ID | <jk42j8-br03.ln1@ntp6.tmsw.no> |
| In reply to | #3302 |
Andy "Krazy" Glew wrote: > On 8/31/2011 1:39 AM, Terje Mathisen wrote: >> As you know LRB have two opcodes for this, to do 1:1:1:1:1 and >> 2:1:2:1:2:1 interleaving. >> >> With this much hw support it becomes most practical to keep the (x,y,z) >> indices separate and merge them before use. > > You are missing one of the other uses of bit-interleaved formats: > They provide scalability. > > Both in online (serial) arithmetic, and in network distribution. > > E.g. you may want to send bit interleaved data with N bits per component > around the network. At the points where you realize that this data is > only ever going to be displayed on a small screen whose viewport you > already know, you start truncating the bitstream. OK, that only works if your world coordinates are big endian, in something like a 0.0 to 1.0 range: In that case you can stop the transmission as soon as you have sent enough bits for the local resolution, i.e. a 640x480 screen would need the top 19 bits or so (you probably need some wiggle room for fractional pixel coords). > > People used to build graphics devices that sent data around like this, > bit serially. With unknown (to the sender) local resolution? > > We may do so again. > > (One of my pet peeves is people assuming, for a non-lossy > transformation, that A->B is necessary, but B->A is not necessary. There > may not be a business case for making the reverse transformation fast. > But nearly always this is a short sighted optimization.) So you desire unpack opcodes as well, something that can quickly extract every second or every third bit? Terje -- - <Terje.Mathisen at tmsw.no> "almost all programming can be viewed as an exercise in caching"
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| From | Peter Flass <Peter_Flass@Yahoo.com> |
|---|---|
| Date | 2011-08-31 13:18 -0400 |
| Message-ID | <j3lqcv$8g8$1@dont-email.me> |
| In reply to | #3305 |
On 8/31/2011 12:38 PM, Terje Mathisen wrote: > Andy "Krazy" Glew wrote: >> On 8/31/2011 1:39 AM, Terje Mathisen wrote: >>> As you know LRB have two opcodes for this, to do 1:1:1:1:1 and >>> 2:1:2:1:2:1 interleaving. >>> >>> With this much hw support it becomes most practical to keep the (x,y,z) >>> indices separate and merge them before use. >> >> You are missing one of the other uses of bit-interleaved formats: >> They provide scalability. >> >> Both in online (serial) arithmetic, and in network distribution. >> >> E.g. you may want to send bit interleaved data with N bits per component >> around the network. At the points where you realize that this data is >> only ever going to be displayed on a small screen whose viewport you >> already know, you start truncating the bitstream. > > OK, that only works if your world coordinates are big endian, in > something like a 0.0 to 1.0 range: In that case you can stop the > transmission as soon as you have sent enough bits for the local > resolution, i.e. a 640x480 screen would need the top 19 bits or so (you > probably need some wiggle room for fractional pixel coords). >> >> People used to build graphics devices that sent data around like this, >> bit serially. > > With unknown (to the sender) local resolution? >> >> We may do so again. >> >> (One of my pet peeves is people assuming, for a non-lossy >> transformation, that A->B is necessary, but B->A is not necessary. There >> may not be a business case for making the reverse transformation fast. >> But nearly always this is a short sighted optimization.) > > So you desire unpack opcodes as well, something that can quickly extract > every second or every third bit? > This is something that would be useful for a lot of things, but should be general-purpose. (thanks to DEC for PDP-10) have source and destination pointers in registers, with byte address, bit index and number of bits to extract, and increment in bits. Extract, e.g. an arbitrary bit field from the source and store it at an arbitrary bit position in the destination. Then update the pointers, so you could REP it, or have a repeat counter. If I had a nickle for every time I've wanted such an instruction...
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