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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 | "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> |
|---|---|
| Date | 2011-08-31 19:09 -0700 |
| Message-ID | <4E5EE93E.5090006@SPAM.comp-arch.net> |
| In reply to | #3307 |
On 8/31/2011 10:18 AM, Peter Flass wrote: > On 8/31/2011 12:38 PM, Terje Mathisen wrote: >> Andy "Krazy" Glew wrote: >>> On 8/31/2011 1:39 AM, Terje Mathisen wrote: >>> (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... I have a instruction specification that accomplishes this more efficiently than the above, but it is too big to fit in the margin of the comp.arch post.
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| From | Brett Davis <ggtgp@yahoo.com> |
|---|---|
| Date | 2011-08-30 00:19 -0500 |
| Message-ID | <ggtgp-C5DFC3.00194930082011@netnews.mchsi.com> |
| In reply to | #3239 |
In article <j3ggbl$4du$1@gosset.csi.cam.ac.uk>, nmm1@cam.ac.uk wrote: > In article <4E5BB93F.2030406@SPAM.comp-arch.net>, > Andy \"Krazy\" Glew <andy@SPAM.comp-arch.net> wrote: > >On 8/29/2011 4:56 AM, Terje Mathisen wrote: > >> > >> Block fp formats have been quite common afaik in the embedded world, > >> where you would store an array of (integer) mantissas, all sharing a > >> common exponent. > >> > >> With a few guard bits to reduce the need for block renormalization this > >> seems like an efficient layout. > > > >I'd appreciate any references to block FP. > > > >BGB provided a few. > > > >(Hell, I'd love it if you could/would just post, although my current > >wiki security kerfuffle may delay that a bit.) > > Modern Computing Methods, 1948 :-) > > More seriously, it's just an example of scaled fixed-point, which > was in widespread use until the 1960s. The Playstation One did not support floating point, all that 3D math for graphics was fixed point. The Playstation first shipped in 1994, so people are still re-inventing all that 1940's knowledge. > It lost out because it's more hassle to use. The math chip had 32 registers made up of 16 bits halves. (1:3:12,1:3:12) You would load up a transform and light matrix and feed in XYZ values into one and a half registers and call microcode that gave you the results in ~14 cycles, in the result registers. You then copied the results into a DMA list for the graphics chip, which was also primitive. The very definition of hassle to use.
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| From | Brett Davis <ggtgp@yahoo.com> |
|---|---|
| Date | 2011-08-31 23:46 -0500 |
| Message-ID | <ggtgp-C47A0C.23461831082011@netnews.mchsi.com> |
| In reply to | #3258 |
In article <ggtgp-C5DFC3.00194930082011@netnews.mchsi.com>, Brett Davis <ggtgp@yahoo.com> wrote: > In article <j3ggbl$4du$1@gosset.csi.cam.ac.uk>, nmm1@cam.ac.uk wrote: > > > In article <4E5BB93F.2030406@SPAM.comp-arch.net>, > > Andy \"Krazy\" Glew <andy@SPAM.comp-arch.net> wrote: > > >On 8/29/2011 4:56 AM, Terje Mathisen wrote: > > >> > > >> Block fp formats have been quite common afaik in the embedded world, > > >> where you would store an array of (integer) mantissas, all sharing a > > >> common exponent. > > >> > > >> With a few guard bits to reduce the need for block renormalization this > > >> seems like an efficient layout. > > > > > >I'd appreciate any references to block FP. > > > > > >BGB provided a few. > > > > > >(Hell, I'd love it if you could/would just post, although my current > > >wiki security kerfuffle may delay that a bit.) > > > > Modern Computing Methods, 1948 :-) > > > > More seriously, it's just an example of scaled fixed-point, which > > was in widespread use until the 1960s. > > The Playstation One did not support floating point, all that 3D math > for graphics was fixed point. > The Playstation first shipped in 1994, so people are still re-inventing > all that 1940's knowledge. > > > It lost out because it's more hassle to use. > > The math chip had 32 registers made up of 16 bits halves. (1:3:12,1:3:12) A delayed ECC interrupt in my brain kicked off, data recovery indicates that the data format was scaled ints, with 4 bit fraction. So signed 12.4 ints, computed two per 32 bit register. > You would load up a transform and light matrix and feed in XYZ > values into one and a half registers and call microcode that > gave you the results in ~14 cycles, in the result registers. > > You then copied the results into a DMA list for the graphics > chip, which was also primitive. > > The very definition of hassle to use.
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| From | BGB <cr88192@hotmail.com> |
|---|---|
| Date | 2011-08-31 09:56 -0700 |
| Message-ID | <j3n39q$oc1$1@news.albasani.net> |
| In reply to | #3258 |
On 8/29/2011 10:19 PM, Brett Davis wrote: > In article<j3ggbl$4du$1@gosset.csi.cam.ac.uk>, nmm1@cam.ac.uk wrote: > >> In article<4E5BB93F.2030406@SPAM.comp-arch.net>, >> Andy \"Krazy\" Glew<andy@SPAM.comp-arch.net> wrote: >>> On 8/29/2011 4:56 AM, Terje Mathisen wrote: >>>> >>>> Block fp formats have been quite common afaik in the embedded world, >>>> where you would store an array of (integer) mantissas, all sharing a >>>> common exponent. >>>> >>>> With a few guard bits to reduce the need for block renormalization this >>>> seems like an efficient layout. >>> >>> I'd appreciate any references to block FP. >>> >>> BGB provided a few. >>> >>> (Hell, I'd love it if you could/would just post, although my current >>> wiki security kerfuffle may delay that a bit.) >> >> Modern Computing Methods, 1948 :-) >> >> More seriously, it's just an example of scaled fixed-point, which >> was in widespread use until the 1960s. > > The Playstation One did not support floating point, all that 3D math > for graphics was fixed point. > The Playstation first shipped in 1994, so people are still re-inventing > all that 1940's knowledge. > many/most 90s era games included some amount of fixed point math. Doom 1/2 were all integer and fixed-point (given they were written for 386 and 486 systems where an FPU was a novelty). Quake used floating point, but was still fixed-point in many places as well. Quake 2 was similar, except more of the fixed point had gone away. some fundamental limitations of both Quake 1 and 2 were due to the use of 16-bit fixed point values, and the possibility of them overflowing and wrapping around. Quake3 popularized a certain mathematical trick involving treating a float as an integer and doing arithmetic on it (involving magic numbers and shifts), so in this sense fixed point is still not entirely dead. even long after the FPU stopped being so much of a novelty, it has often been *slow* vs the use of integer math (and is also potentially a notable reason fixed-point is still commonly found in audio and video codecs and signal processing tasks). >> It lost out because it's more hassle to use. > > The math chip had 32 registers made up of 16 bits halves. (1:3:12,1:3:12) > You would load up a transform and light matrix and feed in XYZ > values into one and a half registers and call microcode that > gave you the results in ~14 cycles, in the result registers. > > You then copied the results into a DMA list for the graphics > chip, which was also primitive. > > The very definition of hassle to use. yep. half idea: 128 8 bit registers; 64 16 bit registers; 32 32 bit registers; 16 64 bit registers; 8 128 bit registers. single 8 bit register field: 0..127: 8 bit register; 128..191: 16 bit register; 192..223: 32 bit register; 224..239: 64 bit register; 240..247: 128-bit register. then, one has a choice between lots of individual small registers (they all overlap), and a fewer large registers. also like SIMD types, but where one can easily access individual components. or such...
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| From | Terje Mathisen <"terje.mathisen at tmsw.no"> |
|---|---|
| Date | 2011-09-01 08:23 +0200 |
| Message-ID | <ivk3j8-9b1.ln1@ntp6.tmsw.no> |
| In reply to | #3317 |
BGB wrote: > Quake3 popularized a certain mathematical trick involving treating a > float as an integer and doing arithmetic on it (involving magic numbers > and shifts), so in this sense fixed point is still not entirely dead. > Probably the invsqrt() trick, using a subtract of a shift on the fp bit pattern, this has been superseded by SIMD sqrt and invsqrt parallel lookup instructions. > > even long after the FPU stopped being so much of a novelty, it has often > been *slow* vs the use of integer math (and is also potentially a > notable reason fixed-point is still commonly found in audio and video > codecs and signal processing tasks). On a codec like Ogg Vorbis, the integer code is all in the encoding/decoding of the bitstream; all the actual audio processing uses fp IMDCTs. (Just like pretty much all current audio codecs, actually.) > half idea: > 128 8 bit registers; > 64 16 bit registers; > 32 32 bit registers; > 16 64 bit registers; > 8 128 bit registers. > > single 8 bit register field: > 0..127: 8 bit register; > 128..191: 16 bit register; > 192..223: 32 bit register; > 224..239: 64 bit register; > 240..247: 128-bit register. Nice: A huffman encoding for register numbers. :-) Terje -- - <Terje.Mathisen at tmsw.no> "almost all programming can be viewed as an exercise in caching"
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| From | BGB <cr88192@hotmail.com> |
|---|---|
| Date | 2011-08-31 14:02 -0700 |
| Message-ID | <j3nhmt$ldr$1@news.albasani.net> |
| In reply to | #3318 |
On 8/31/2011 11:23 PM, Terje Mathisen wrote: > BGB wrote: >> Quake3 popularized a certain mathematical trick involving treating a >> float as an integer and doing arithmetic on it (involving magic numbers >> and shifts), so in this sense fixed point is still not entirely dead. >> > > Probably the invsqrt() trick, using a subtract of a shift on the fp bit > pattern, this has been superseded by SIMD sqrt and invsqrt parallel > lookup instructions. > yep. >> >> even long after the FPU stopped being so much of a novelty, it has often >> been *slow* vs the use of integer math (and is also potentially a >> notable reason fixed-point is still commonly found in audio and video >> codecs and signal processing tasks). > > On a codec like Ogg Vorbis, the integer code is all in the > encoding/decoding of the bitstream; all the actual audio processing uses > fp IMDCTs. (Just like pretty much all current audio codecs, actually.) > actually, the Ogg/Vorbis decoder I am using (Tremor) uses fixed-point for the IMDCT. however, at this point in time it is probably not such a big issue anymore on most HW. my own implementation of FLAC uses fixed point. as well, my JPEG decoder uses fixed point for the IDCT. >> half idea: >> 128 8 bit registers; >> 64 16 bit registers; >> 32 32 bit registers; >> 16 64 bit registers; >> 8 128 bit registers. >> >> single 8 bit register field: >> 0..127: 8 bit register; >> 128..191: 16 bit register; >> 192..223: 32 bit register; >> 224..239: 64 bit register; >> 240..247: 128-bit register. > > Nice: A huffman encoding for register numbers. :-) > yep. it is a trick to both encode the register size and deal with the issue of there being more smaller than larger registers if all smaller registers map to parts of bigger ones.
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-01 04:02 -0700 |
| Message-ID | <cdd48889-5524-4d12-a38e-2fce99787ce7@h11g2000vbc.googlegroups.com> |
| In reply to | #3318 |
On Sep 1, 12:23 am, Terje Mathisen <"terje.mathisen at tmsw.no"> wrote: > BGB wrote: > > Quake3 popularized a certain mathematical trick involving treating a > > float as an integer and doing arithmetic on it (involving magic numbers > > and shifts), so in this sense fixed point is still not entirely dead. > > Probably the invsqrt() trick, using a subtract of a shift on the fp bit > pattern, this has been superseded by SIMD sqrt and invsqrt parallel > lookup instructions. Not knowing what you were referring to, I did a Google search, which, fortunately, brought me quickly to: http://en.wikipedia.org/wiki/Fast_inverse_square_root John Savard
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| From | Terje Mathisen <"terje.mathisen at tmsw.no"> |
|---|---|
| Date | 2011-09-01 19:42 +0200 |
| Message-ID | <pos4j8-vo2.ln1@ntp6.tmsw.no> |
| In reply to | #3320 |
Quadibloc wrote: > On Sep 1, 12:23 am, Terje Mathisen<"terje.mathisen at tmsw.no"> > wrote: >> BGB wrote: >>> Quake3 popularized a certain mathematical trick involving treating a >>> float as an integer and doing arithmetic on it (involving magic numbers >>> and shifts), so in this sense fixed point is still not entirely dead. >> >> Probably the invsqrt() trick, using a subtract of a shift on the fp bit >> pattern, this has been superseded by SIMD sqrt and invsqrt parallel >> lookup instructions. > > Not knowing what you were referring to, I did a Google search, which, > fortunately, brought me quickly to: > > http://en.wikipedia.org/wiki/Fast_inverse_square_root The original beyond3d article is unfortunately gone, that one had much more of the history. :-( Terje -- - <Terje.Mathisen at tmsw.no> "almost all programming can be viewed as an exercise in caching"
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| From | BGB <cr88192@hotmail.com> |
|---|---|
| Date | 2011-08-31 23:20 -0700 |
| Message-ID | <j3oido$18s$1@news.albasani.net> |
| In reply to | #3320 |
On 9/1/2011 4:02 AM, Quadibloc wrote:
> On Sep 1, 12:23 am, Terje Mathisen<"terje.mathisen at tmsw.no">
> wrote:
>> BGB wrote:
>>> Quake3 popularized a certain mathematical trick involving treating a
>>> float as an integer and doing arithmetic on it (involving magic numbers
>>> and shifts), so in this sense fixed point is still not entirely dead.
>>
>> Probably the invsqrt() trick, using a subtract of a shift on the fp bit
>> pattern, this has been superseded by SIMD sqrt and invsqrt parallel
>> lookup instructions.
>
> Not knowing what you were referring to, I did a Google search, which,
> fortunately, brought me quickly to:
>
> http://en.wikipedia.org/wiki/Fast_inverse_square_root
>
yep, here is the version from my own 3D engine:
static INLINE float frsqrt(float x)
{
float xh, y;
s32 i;
xh=x*0.5F; y=x;
i=*(s32 *)(&y);
i=0x5F375A86-(i>>1);
y=*(float *)(&i);
y=y*(1.5F-(xh*y*y));
return(y);
}
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| From | "James Van Buskirk" <not_valid@comcast.net> |
|---|---|
| Date | 2011-09-12 15:53 -0600 |
| Message-ID | <j4lv0u$crf$1@dont-email.me> |
| In reply to | #3320 |
"Quadibloc" <jsavard@ecn.ab.ca> wrote in message news:cdd48889-5524-4d12-a38e-2fce99787ce7@h11g2000vbc.googlegroups.com... > Not knowing what you were referring to, I did a Google search, which, > fortunately, brought me quickly to: > http://en.wikipedia.org/wiki/Fast_inverse_square_root That article says the algorithm didn't appear on Usenet until 2002, but see: http://groups.google.com/group/comp.lang.asm.x86/msg/2581f8457100f7a4?hl=en -- write(*,*) transfer((/17.392111325966148d0,6.5794487871554595D-85, & 6.0134700243160014d-154/),(/'x'/)); end
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-12 22:31 +0100 |
| Message-ID | <j4ltna$udm$1@gosset.csi.cam.ac.uk> |
| In reply to | #3647 |
In article <j4lv0u$crf$1@dont-email.me>,
James Van Buskirk <not_valid@comcast.net> wrote:
>"Quadibloc" <jsavard@ecn.ab.ca> wrote in message
>news:cdd48889-5524-4d12-a38e-2fce99787ce7@h11g2000vbc.googlegroups.com...
>
>> Not knowing what you were referring to, I did a Google search, which,
>> fortunately, brought me quickly to:
>
>> http://en.wikipedia.org/wiki/Fast_inverse_square_root
>
>That article says the algorithm didn't appear on Usenet until 2002,
Solely because the kiddies that wrote that hadn't spoken to anyone
who was doing that in the 1950s or 1960s. Of the three aspects:
The algorithm was extensively used in the 1950s, as many
machines did not have hardware floating-point division.
I don't know when the application of that to integers started,
but I knew about it in the late 1960s - I may have seen it, or may
have reinvented it.
The use of magic numbers to get initial starting points again
dates from the 1950s, though the numbers are architecture-specific.
Publish? Why? It's all bloody obvious!
Regards,
Nick Maclaren.
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-12 22:56 +0100 |
| Message-ID | <j4lv6m$ujs$1@gosset.csi.cam.ac.uk> |
| In reply to | #3648 |
In article <j4ltna$udm$1@gosset.csi.cam.ac.uk>, <nmm1@cam.ac.uk> wrote: >In article <j4lv0u$crf$1@dont-email.me>, >James Van Buskirk <not_valid@comcast.net> wrote: >>"Quadibloc" <jsavard@ecn.ab.ca> wrote in message >>news:cdd48889-5524-4d12-a38e-2fce99787ce7@h11g2000vbc.googlegroups.com... >> >>> Not knowing what you were referring to, I did a Google search, which, >>> fortunately, brought me quickly to: >> >>> http://en.wikipedia.org/wiki/Fast_inverse_square_root >> >>That article says the algorithm didn't appear on Usenet until 2002, > > The algorithm was extensively used in the 1950s, as many >machines did not have hardware floating-point division. > > I don't know when the application of that to integers started, >but I knew about it in the late 1960s - I may have seen it, or may >have reinvented it. Oops. I am getting forgetful. Make that 1920s in both cases. It was how you did square roots on an electromechanical calculator if you knew what you were up to. It is by far the fastest for the usual precisions on such machines. My Modern Computing Methods is at work, but it might be in that. Regards, Nick Maclaren.
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| From | Walter Bushell <proto@panix.com> |
|---|---|
| Date | 2011-09-12 21:00 -0400 |
| Message-ID | <proto-A04772.21003812092011@news.panix.com> |
| In reply to | #3649 |
In article <j4lv6m$ujs$1@gosset.csi.cam.ac.uk>, nmm1@cam.ac.uk wrote: > In article <j4ltna$udm$1@gosset.csi.cam.ac.uk>, <nmm1@cam.ac.uk> wrote: > >In article <j4lv0u$crf$1@dont-email.me>, > >James Van Buskirk <not_valid@comcast.net> wrote: > >>"Quadibloc" <jsavard@ecn.ab.ca> wrote in message > >>news:cdd48889-5524-4d12-a38e-2fce99787ce7@h11g2000vbc.googlegroups.com... > >> > >>> Not knowing what you were referring to, I did a Google search, which, > >>> fortunately, brought me quickly to: > >> > >>> http://en.wikipedia.org/wiki/Fast_inverse_square_root > >> > >>That article says the algorithm didn't appear on Usenet until 2002, > > > > The algorithm was extensively used in the 1950s, as many > >machines did not have hardware floating-point division. > > > > I don't know when the application of that to integers started, > >but I knew about it in the late 1960s - I may have seen it, or may > >have reinvented it. > > Oops. I am getting forgetful. Make that 1920s in both cases. > It was how you did square roots on an electromechanical calculator > if you knew what you were up to. It is by far the fastest for the > usual precisions on such machines. > > My Modern Computing Methods is at work, but it might be in that. > > > Regards, > Nick Maclaren. There were square root Frieden electromechanical calculators. I used one on a summer job in 1962. And yes I used the square root function. At that time Nixie tubes with ultra cool. They were used in, for example, the control room of a research nuclear reactor. -- Ignorance is no protection against reality. -- Paul J Gans
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-13 10:10 +0100 |
| Message-ID | <j4n6lu$1ss$1@gosset.csi.cam.ac.uk> |
| In reply to | #3650 |
In article <proto-A04772.21003812092011@news.panix.com>, Walter Bushell <proto@panix.com> wrote: > >There were square root Frieden electromechanical calculators. I used one >on a summer job in 1962. And yes I used the square root function. At >that time Nixie tubes with ultra cool. They were used in, for example, >the control room of a research nuclear reactor. Well, yes, but the majority didn't have it and you had to do it by hand. Regards, Nick Maclaren.
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| From | Terje Mathisen <"terje.mathisen at tmsw.no"> |
|---|---|
| Date | 2011-09-13 04:58 +0200 |
| Message-ID | <cft2k8-grh1.ln1@ntp6.tmsw.no> |
| In reply to | #3647 |
James Van Buskirk wrote: > "Quadibloc"<jsavard@ecn.ab.ca> wrote in message > news:cdd48889-5524-4d12-a38e-2fce99787ce7@h11g2000vbc.googlegroups.com... > >> Not knowing what you were referring to, I did a Google search, which, >> fortunately, brought me quickly to: > >> http://en.wikipedia.org/wiki/Fast_inverse_square_root > > That article says the algorithm didn't appear on Usenet until 2002, > but see: > > http://groups.google.com/group/comp.lang.asm.x86/msg/2581f8457100f7a4?hl=en > Hello again James. :-) Terje -- - <Terje.Mathisen at tmsw.no> "almost all programming can be viewed as an exercise in caching"
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| From | Peter Flass <Peter_Flass@Yahoo.com> |
|---|---|
| Date | 2011-09-01 07:25 -0400 |
| Message-ID | <j3nq2o$po9$1@dont-email.me> |
| In reply to | #3317 |
On 8/31/2011 12:56 PM, BGB wrote: > On 8/29/2011 10:19 PM, Brett Davis wrote: >> In article<j3ggbl$4du$1@gosset.csi.cam.ac.uk>, nmm1@cam.ac.uk wrote: >> >>> In article<4E5BB93F.2030406@SPAM.comp-arch.net>, >>> Andy \"Krazy\" Glew<andy@SPAM.comp-arch.net> wrote: >>>> On 8/29/2011 4:56 AM, Terje Mathisen wrote: >>>>> >>>>> Block fp formats have been quite common afaik in the embedded world, >>>>> where you would store an array of (integer) mantissas, all sharing a >>>>> common exponent. >>>>> >>>>> With a few guard bits to reduce the need for block renormalization >>>>> this >>>>> seems like an efficient layout. >>>> >>>> I'd appreciate any references to block FP. >>>> >>>> BGB provided a few. >>>> >>>> (Hell, I'd love it if you could/would just post, although my current >>>> wiki security kerfuffle may delay that a bit.) >>> >>> Modern Computing Methods, 1948 :-) >>> >>> More seriously, it's just an example of scaled fixed-point, which >>> was in widespread use until the 1960s. >> >> The Playstation One did not support floating point, all that 3D math >> for graphics was fixed point. >> The Playstation first shipped in 1994, so people are still re-inventing >> all that 1940's knowledge. >> > > many/most 90s era games included some amount of fixed point math. > > Doom 1/2 were all integer and fixed-point (given they were written for > 386 and 486 systems where an FPU was a novelty). > > Quake used floating point, but was still fixed-point in many places as > well. Quake 2 was similar, except more of the fixed point had gone away. > > some fundamental limitations of both Quake 1 and 2 were due to the use > of 16-bit fixed point values, and the possibility of them overflowing > and wrapping around. > > Quake3 popularized a certain mathematical trick involving treating a > float as an integer and doing arithmetic on it (involving magic numbers > and shifts), so in this sense fixed point is still not entirely dead. A lot of the Xerox stuff used "rational numbers", stored as an integer numerator and an integer denominator.
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| From | Tim Shoppa <shoppa@trailing-edge.com> |
|---|---|
| Date | 2011-09-01 10:37 -0700 |
| Message-ID | <1c679456-72d6-4231-9a6d-20f0c9060799@bl1g2000vbb.googlegroups.com> |
| In reply to | #3321 |
On Sep 1, 7:25 am, Peter Flass <Peter_Fl...@Yahoo.com> wrote: > On 8/31/2011 12:56 PM, BGB wrote: > > > > > > > > > > > On 8/29/2011 10:19 PM, Brett Davis wrote: > >> In article<j3ggbl$4d...@gosset.csi.cam.ac.uk>, n...@cam.ac.uk wrote: > > >>> In article<4E5BB93F.2030...@SPAM.comp-arch.net>, > >>> Andy \"Krazy\" Glew<a...@SPAM.comp-arch.net> wrote: > >>>> On 8/29/2011 4:56 AM, Terje Mathisen wrote: > > >>>>> Block fp formats have been quite common afaik in the embedded world, > >>>>> where you would store an array of (integer) mantissas, all sharing a > >>>>> common exponent. > > >>>>> With a few guard bits to reduce the need for block renormalization > >>>>> this > >>>>> seems like an efficient layout. > > >>>> I'd appreciate any references to block FP. > > >>>> BGB provided a few. > > >>>> (Hell, I'd love it if you could/would just post, although my current > >>>> wiki security kerfuffle may delay that a bit.) > > >>> Modern Computing Methods, 1948 :-) > > >>> More seriously, it's just an example of scaled fixed-point, which > >>> was in widespread use until the 1960s. > > >> The Playstation One did not support floating point, all that 3D math > >> for graphics was fixed point. > >> The Playstation first shipped in 1994, so people are still re-inventing > >> all that 1940's knowledge. > > > many/most 90s era games included some amount of fixed point math. > > > Doom 1/2 were all integer and fixed-point (given they were written for > > 386 and 486 systems where an FPU was a novelty). > > > Quake used floating point, but was still fixed-point in many places as > > well. Quake 2 was similar, except more of the fixed point had gone away. > > > some fundamental limitations of both Quake 1 and 2 were due to the use > > of 16-bit fixed point values, and the possibility of them overflowing > > and wrapping around. > > > Quake3 popularized a certain mathematical trick involving treating a > > float as an integer and doing arithmetic on it (involving magic numbers > > and shifts), so in this sense fixed point is still not entirely dead. > > A lot of the Xerox stuff used "rational numbers", stored as an integer > numerator and an integer denominator. Not sure what Xerox stuff this is. SDS/XDS, Alto, Star, or something I never heard of :-). I know there was some academic overlap between Interlisp/Smalltalk and the Star communities. I wonder if this was done for bignum or mathematica style stuff, or if it was a different tack than fixed-point Cobol style math to approach financial accounting. I know folks from across the pond could teach me a lot about how to do math with twelfths and twentieths for pennies/shillings/pounds and I can see this driving some interesting British computer representations... Tim.
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| From | nmm1@cam.ac.uk |
|---|---|
| Date | 2011-09-01 18:25 +0100 |
| Message-ID | <j3of5s$gad$1@gosset.csi.cam.ac.uk> |
| In reply to | #3335 |
In article <1c679456-72d6-4231-9a6d-20f0c9060799@bl1g2000vbb.googlegroups.com>,
Tim Shoppa <shoppa@trailing-edge.com> wrote:
>On Sep 1, 7:25=A0am, Peter Flass <Peter_Fl...@Yahoo.com> wrote:
>>
>> A lot of the Xerox stuff used "rational numbers", stored as an integer
>> numerator and an integer denominator.
>
>Not sure what Xerox stuff this is. SDS/XDS, Alto, Star, or something I
>never heard of :-). I know there was some academic overlap between
>Interlisp/Smalltalk and the Star communities.
>
>I wonder if this was done for bignum or mathematica style stuff, or if
>it was a different tack than fixed-point Cobol style math to approach
>financial accounting.
Look up "fixed slash" arithmetic - I don't know what Xerox did, but I
mention that in my computer arithmetic course. I have just added an
equally brief reference to quaternions :-)
http://www-uxsup.csx.cam.ac.uk/courses/Arithmetic/index.html
>I know folks from across the pond could teach me a lot about how to do
>math with twelfths and twentieths for pennies/shillings/pounds and I
>can see this driving some interesting British computer
>representations...
Nah. We weren't insane, and represented such numbers as integers,
with appropriate conversion functions! When I were a lad, we were
required to do mental arithmetic involving currency, and I go back
to the days of farthings. That skill has disappeared, which has
had the disadvantage that most people no longer have the 'feel' for
numbers that used to be normal.
Regards,
Nick Maclaren.
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| From | Bill Findlay <yaldnif.w@blueyonder.co.uk> |
|---|---|
| Date | 2011-09-01 19:56 +0100 |
| Message-ID | <CA8593FF.355E%yaldnif.w@blueyonder.co.uk> |
| In reply to | #3337 |
On 01/09/2011 18:25, in article j3of5s$gad$1@gosset.csi.cam.ac.uk, "nmm1@cam.ac.uk" <nmm1@cam.ac.uk> wrote: > In article > <1c679456-72d6-4231-9a6d-20f0c9060799@bl1g2000vbb.googlegroups.com>, > Tim Shoppa <shoppa@trailing-edge.com> wrote: > >> I know folks from across the pond could teach me a lot about how to do >> math with twelfths and twentieths for pennies/shillings/pounds and I >> can see this driving some interesting British computer >> representations... > > Nah. We weren't insane, and represented such numbers as integers, > with appropriate conversion functions! For the most part, yes; but there were a few machines that did mixed-radix arithmetic. The Ferranti Perseus and the LEO 3 range spring to mind. > When I were a lad, we were > required to do mental arithmetic involving currency, and I go back > to the days of farthings. That skill has disappeared, which has > had the disadvantage that most people no longer have the 'feel' for > numbers that used to be normal. Yup. -- Bill Findlay with blueyonder.co.uk; use surname & forename;
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| From | Quadibloc <jsavard@ecn.ab.ca> |
|---|---|
| Date | 2011-09-01 12:30 -0700 |
| Message-ID | <cf3834e8-ac6b-4f5e-b94b-54e576c1f3cc@g30g2000vbu.googlegroups.com> |
| In reply to | #3337 |
On Sep 1, 11:25 am, n...@cam.ac.uk wrote: > In article <1c679456-72d6-4231-9a6d-20f0c9060...@bl1g2000vbb.googlegroups.com>, > Tim Shoppa <sho...@trailing-edge.com> wrote: > >I know folks from across the pond could teach me a lot about how to do > >math with twelfths and twentieths for pennies/shillings/pounds and I > >can see this driving some interesting British computer > >representations... > > Nah. We weren't insane, and represented such numbers as integers, > with appropriate conversion functions! When I were a lad, we were > required to do mental arithmetic involving currency, and I go back > to the days of farthings. That skill has disappeared, which has > had the disadvantage that most people no longer have the 'feel' for > numbers that used to be normal. As it happens, I had recently read about a very early British computer, which happened to be (at least at the time) the _only_ one that, in addition to, like many commercial computers, doing decimal arithmetic, actually did internally represent pounds, shillings, and pence (with twelve pence to the shilling and twenty shillings to the pound) and perform arithmetic natively on them. Since it was one of a kind, though, it's quite true that in general the British computer industry was not insane. John Savard
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