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Groups > comp.lang.c > #400968 > unrolled thread
| Started by | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| First post | 2026-08-11 03:01 -0500 |
| Last post | 2026-08-18 11:32 +0200 |
| Articles | 20 on this page of 191 — 17 participants |
Back to article view | Back to comp.lang.c
why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 03:01 -0500
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 13:11 +0200
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 12:45 +0100
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 14:34 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 14:55 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 15:19 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 15:27 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 16:08 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 16:18 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:11 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:20 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:32 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:39 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 18:33 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 18:39 +0200
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-11 23:31 +0300
Re: why is there not a ipow version of pow? James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-11 11:46 -0400
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 18:35 +0200
Re: why is there not a ipow version of pow? antispam@fricas.org (Waldek Hebisch) - 2026-08-11 22:53 +0000
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-12 10:08 +0200
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-12 03:58 -0700
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-12 13:31 +0200
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-12 22:43 +0300
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-12 13:44 -0700
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-13 00:24 +0300
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-12 16:49 -0500
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-13 08:38 +0200
Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) scott@slp53.sl.home (Scott Lurndal) - 2026-08-13 14:36 +0000
Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) David Brown <david.brown@hesbynett.no> - 2026-08-13 17:07 +0200
Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-13 19:07 +0200
Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) David Brown <david.brown@hesbynett.no> - 2026-08-13 22:24 +0200
Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-13 16:36 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-13 18:59 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-13 18:51 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 00:58 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:08 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 15:48 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 13:51 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 16:40 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 19:24 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 22:51 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 22:33 -0700
Re: why is there not a ipow version of pow? Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-15 10:40 -0700
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-15 11:41 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 14:48 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-16 14:58 -0700
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-14 08:57 +0200
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:46 -0700
Calculation of sine with tables (was Re: why is there not a ipow version of pow?) Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-13 14:45 +0200
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-15 13:00 -0700
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-15 23:17 +0300
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-17 10:07 -0700
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-18 00:35 +0300
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-18 11:22 +0200
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-18 22:22 +0300
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-18 21:59 +0200
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-18 08:38 -0700
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-18 22:17 +0300
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-18 15:42 -0700
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-18 17:44 -0700
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-19 21:55 +0300
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-19 18:25 -0700
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-20 22:03 +0300
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-19 04:53 +0800
Re: why is there not a ipow version of pow? James Kuyper <jameskuyper@alumni.caltech.edu> - 2026-08-13 12:59 -0400
Re: why is there not a ipow version of pow? antispam@fricas.org (Waldek Hebisch) - 2026-08-12 20:23 +0000
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-11 18:19 +0000
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 20:21 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-11 21:10 +0000
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-12 00:42 +0300
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 06:41 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-12 14:19 +0000
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 16:56 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-12 15:32 +0000
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-12 22:05 +0300
Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-12 19:09 -0400
Re: why is there not a ipow version of pow? Michael S <already5chosen@yahoo.com> - 2026-08-11 21:58 +0300
Re: why is there not a ipow version of pow? Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-08-11 21:44 -0700
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 15:45 +0100
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 16:56 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:23 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:24 +0200
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 16:23 +0100
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:26 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 17:54 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 18:40 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 08:49 +0200
Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-12 09:11 -0400
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 16:05 +0200
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-12 12:40 -0700
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-13 15:46 +0200
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-13 14:28 -0700
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-11 16:20 -0700
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 18:43 +0100
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 19:56 +0200
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 20:41 +0100
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 06:42 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-12 10:23 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 20:24 +0200
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 20:27 +0100
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 06:45 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:16 +0200
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-16 07:33 -0700
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-16 17:12 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-16 17:51 +0200
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-16 18:35 +0200
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-16 18:41 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-16 21:30 +0200
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-16 23:41 +0100
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-17 08:56 +0200
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-17 03:32 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-17 08:59 +0200
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-17 11:08 +0200
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-17 03:48 -0700
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-17 04:25 -0700
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-17 13:44 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-17 14:26 +0000
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-17 16:58 +0200
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-17 16:49 -0700
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-17 10:22 -0700
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-17 19:49 +0200
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-17 20:00 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-17 20:37 +0200
Re: why is there not a ipow version of pow? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-08-18 18:18 -0700
Re: why is there not a ipow version of pow? cross@spitfire.i.gajendra.net (Dan Cross) - 2026-08-18 20:26 +0000
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 15:17 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 15:28 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 16:43 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-11 16:47 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-11 17:24 +0200
Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-11 09:36 -0400
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 16:42 -0500
Re: why is there not a ipow version of pow? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2026-08-11 19:15 +0200
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 16:41 -0500
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 16:49 -0500
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-11 23:28 +0100
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 17:51 -0500
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-11 15:33 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-11 17:49 -0500
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-11 16:19 -0700
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-12 00:32 -0500
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 14:08 +0200
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-12 18:40 +0200
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-14 02:50 +0000
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-12 04:26 +0000
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-12 01:37 -0500
Re: why is there not a ipow version of pow? Paul <nospam@needed.invalid> - 2026-08-13 00:12 -0400
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-14 11:22 +0800
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 01:00 -0500
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-14 14:47 +0800
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 13:54 -0500
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-16 22:49 +0000
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 14:56 -0500
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-17 23:53 +0000
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 19:59 -0500
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-18 02:47 +0000
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-17 15:17 -0500
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:03 -0700
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-15 03:51 +0800
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 12:52 -0700
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-15 04:01 +0800
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 13:27 -0700
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 13:29 -0700
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-15 04:49 +0800
Re: why is there not a ipow version of pow? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-08-14 20:32 -0700
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-12 11:28 +0100
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-12 23:52 +0000
Re: why is there not a ipow version of pow? bart <bc@freeuk.com> - 2026-08-13 01:30 +0100
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-13 02:24 +0000
Re: why is there not a ipow version of pow? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-08-12 21:13 -0700
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-13 14:33 +0000
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-13 16:45 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-13 14:55 +0000
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-13 18:10 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-13 16:16 +0000
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-13 16:21 +0000
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-17 06:37 +0000
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-17 21:37 +0800
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-13 17:19 +0200
Re: why is there not a ipow version of pow? scott@slp53.sl.home (Scott Lurndal) - 2026-08-13 16:09 +0000
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-13 18:52 +0200
Re: why is there not a ipow version of pow? antispam@fricas.org (Waldek Hebisch) - 2026-08-18 16:33 +0000
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-13 17:19 +0800
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-13 19:07 -0500
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-14 10:58 +0800
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-14 01:14 -0500
Re: why is there not a ipow version of pow? Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-08-17 06:40 +0000
Re: why is there not a ipow version of pow? Johann 'Myrkraverk' Oskarsson <johann@myrkraverk.invalid> - 2026-08-17 21:40 +0800
Re: why is there not a ipow version of pow? Lynn McGuire <lynnmcguire5@gmail.com> - 2026-08-18 00:42 -0500
Re: why is there not a ipow version of pow? Bonita Montero <Bonita.Montero@gmail.com> - 2026-08-18 09:34 +0200
Re: why is there not a ipow version of pow? David Brown <david.brown@hesbynett.no> - 2026-08-18 11:32 +0200
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2026-08-12 03:58 -0700 |
| Message-ID | <115hjka$o7k2$1@kst.eternal-september.org> |
| In reply to | #401061 |
David Brown <david.brown@hesbynett.no> writes:
[...]
> And I thought it is entirely obvious that when you are actually
> implementing a floating point power function on a binary computer
> using floating point formats specified in binary, it is most efficient
> to use base 2 for the log and anti-log. If you had a floating point
> format that used base 10, you'd probably want to use base 10 for the
> log and anti-log.
Is it obvious? It had never occurred to me.
log and exp are certainly more mathematically straightforward in
base e than in other bases. Of course floating-point is typically
binary, but I didn't know that would imply that log(x) base 2 is
easier to compute that log(x) base e. I've always assumed that
base e is more efficient than other bases.
Also, I vaguely recall that though x**y is mathematically equivalent
to exp(y * log(x)), that's not the most efficient and/or accurate
way to compute it.
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2026-08-12 13:31 +0200 |
| Message-ID | <115hlii$nov9$1@dont-email.me> |
| In reply to | #401066 |
On 12/08/2026 12:58, Keith Thompson wrote: > David Brown <david.brown@hesbynett.no> writes: > [...] >> And I thought it is entirely obvious that when you are actually >> implementing a floating point power function on a binary computer >> using floating point formats specified in binary, it is most efficient >> to use base 2 for the log and anti-log. If you had a floating point >> format that used base 10, you'd probably want to use base 10 for the >> log and anti-log. > > Is it obvious? It had never occurred to me. > > log and exp are certainly more mathematically straightforward in > base e than in other bases. Of course floating-point is typically > binary, but I didn't know that would imply that log(x) base 2 is > easier to compute that log(x) base e. I've always assumed that > base e is more efficient than other bases. Maybe I have been too quick to jump to conclusions. I have not done much work with implementing such floating point functions - when I have implementing things like trig functions it is because I needed a very different balance of speed and precision than standard library functions, and where I have a clear knowledge of the range needed. There's a lot of detail in making a good "pow" function that I don't know. However, when dealing with logs and anti-logs of floating point numbers, you are going to use base 2 for at least part of the job. Your float f is already in the form m * (2 ** p), so log_n(f) will be log_n(m) + log_n(2 ** p), the later part being p * log_n(2). If you can keep that part as the simple integer "p" for the rest of your calculations - using base n = 2 for that part at least, then you would probably want to do that. Similarly, anti-logs of integer parts are easiest in base 2 and turn into an addition or subtraction on the exponent part of the floating point format. In general, I don't think logs or exponents are likely to be much difference to calculate in different bases. Clearly base "e" is nicer mathematically, but I expect you'd be doing numerical calculations using range reductions, then approximation polynomials, and different bases just mean different factors in the polynomials. The biggest factor, I expect, is how this all fits with instruction sets on the target processor. I've been thinking in terms of doing it all in software - particular instructions might make a big change to the best tactics. > > Also, I vaguely recall that though x**y is mathematically equivalent > to exp(y * log(x)), that's not the most efficient and/or accurate > way to compute it. > Certainly there are complications involved to keep the accuracy. You would not want to use this expression as-is. At the very least, I would expect you would handle the mantissa and exponent of the float separately.
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| From | Michael S <already5chosen@yahoo.com> |
|---|---|
| Date | 2026-08-12 22:43 +0300 |
| Message-ID | <20260812224333.000065c4@yahoo.com> |
| In reply to | #401066 |
On Wed, 12 Aug 2026 03:58:16 -0700 Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: > David Brown <david.brown@hesbynett.no> writes: > [...] > > And I thought it is entirely obvious that when you are actually > > implementing a floating point power function on a binary computer > > using floating point formats specified in binary, it is most > > efficient to use base 2 for the log and anti-log. If you had a > > floating point format that used base 10, you'd probably want to use > > base 10 for the log and anti-log. > > Is it obvious? It had never occurred to me. > > log and exp are certainly more mathematically straightforward in > base e than in other bases. Only near x=1 for log(x) and near x=0 for exp(x). > Of course floating-point is typically > binary, but I didn't know that would imply that log(x) base 2 is > easier to compute that log(x) base e. I've always assumed that > base e is more efficient than other bases. You are mostly wrong. David is mostly correct. > > Also, I vaguely recall that though x**y is mathematically equivalent > to exp(y * log(x)), that's not the most efficient and/or accurate > way to compute it. > Apart from corner cases, it is the most efficient. And I am pretty sure that it's sufficiently accurate for most uses, including you typical C library. I did no deep numeric analysis, but my intuition suggest that as long as underlaying primitives, i.e. log2 and 2**x, are well implemented, i.e. their maximal error is under 0.6 ULP, then the worst case error of combined calculation should be below 2.5 ULP and most likely even lower than that. Which is good enough. For more than 50% of inputs you will end within 1 ULP. Of course, you don't do it stupidly. You start by splitting a with frexp() and splitting b to integer and fractional, probably with fractional in range [-0.5:0.5]. Then you take away trivial parts, i.e integer power of two. But then you come to the main part and this part is as David suggested.
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2026-08-12 13:44 -0700 |
| Message-ID | <115im0c$136js$1@kst.eternal-september.org> |
| In reply to | #401079 |
Michael S <already5chosen@yahoo.com> writes:
> On Wed, 12 Aug 2026 03:58:16 -0700
> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:
>> David Brown <david.brown@hesbynett.no> writes:
>> [...]
>> > And I thought it is entirely obvious that when you are actually
>> > implementing a floating point power function on a binary computer
>> > using floating point formats specified in binary, it is most
>> > efficient to use base 2 for the log and anti-log. If you had a
>> > floating point format that used base 10, you'd probably want to use
>> > base 10 for the log and anti-log.
>>
>> Is it obvious? It had never occurred to me.
>>
>> log and exp are certainly more mathematically straightforward in
>> base e than in other bases.
>
> Only near x=1 for log(x) and near x=0 for exp(x).
Can you explain what you mean by that?
Mathematically, exp(x) (base e) is described by the Taylor series.
In clumsy ASCII notation, it's:
1 + x + x**2/2! + x**3/3! + x**4/4! + ...
b**x, were b is a base other than e (often 2 or 10) is
exp(x * log(base)), where exp() and log() are base e. In other
words, exp and log for bases other than e are most straightforwardly
defined on top of exp and log for base e.
That's what I meant by "more mathematically straightforward".
If you say there are computational reasons why exp2 and log2 are
advantageous when using binary floating-point, I can believe that.
I just don't understand the reasons (and to be honest, I'm not sure
I'd understand an explanation without more effort than I'm willing
to expend, unless somebody wants to pay me to work on this stuff).
>> Of course floating-point is typically
>> binary, but I didn't know that would imply that log(x) base 2 is
>> easier to compute that log(x) base e. I've always assumed that
>> base e is more efficient than other bases.
>
> You are mostly wrong. David is mostly correct.
Quite possibly.
>> Also, I vaguely recall that though x**y is mathematically equivalent
>> to exp(y * log(x)), that's not the most efficient and/or accurate
>> way to compute it.
>
> Apart from corner cases, it is the most efficient.
> And I am pretty sure that it's sufficiently accurate for most uses,
> including you typical C library. I did no deep numeric analysis, but my
> intuition suggest that as long as underlaying primitives, i.e. log2 and
> 2**x, are well implemented, i.e. their maximal error is under 0.6 ULP,
2**x is provided in <math.h> as exp2(), since C99.
> then the worst case error of combined calculation should be below 2.5
> ULP and most likely even lower than that. Which is good enough.
> For more than 50% of inputs you will end within 1 ULP.
>
> Of course, you don't do it stupidly. You start by splitting a with
> frexp() and splitting b to integer and fractional, probably with
> fractional in range [-0.5:0.5]. Then you take away trivial parts, i.e
> integer power of two. But then you come to the main part and this part
> is as David suggested.
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */
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| From | Michael S <already5chosen@yahoo.com> |
|---|---|
| Date | 2026-08-13 00:24 +0300 |
| Message-ID | <20260813002409.00003f1d@yahoo.com> |
| In reply to | #401084 |
On Wed, 12 Aug 2026 13:44:50 -0700 Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: > Michael S <already5chosen@yahoo.com> writes: > > On Wed, 12 Aug 2026 03:58:16 -0700 > > Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: > >> David Brown <david.brown@hesbynett.no> writes: > >> [...] > >> > And I thought it is entirely obvious that when you are actually > >> > implementing a floating point power function on a binary computer > >> > using floating point formats specified in binary, it is most > >> > efficient to use base 2 for the log and anti-log. If you had a > >> > floating point format that used base 10, you'd probably want to > >> > use base 10 for the log and anti-log. > >> > >> Is it obvious? It had never occurred to me. > >> > >> log and exp are certainly more mathematically straightforward in > >> base e than in other bases. > > > > Only near x=1 for log(x) and near x=0 for exp(x). > > Can you explain what you mean by that? > > Mathematically, exp(x) (base e) is described by the Taylor series. > In clumsy ASCII notation, it's: > > 1 + x + x**2/2! + x**3/3! + x**4/4! + ... > > b**x, were b is a base other than e (often 2 or 10) is > exp(x * log(base)), where exp() and log() are base e. In other > words, exp and log for bases other than e are most straightforwardly > defined on top of exp and log for base e. > > That's what I meant by "more mathematically straightforward". > > If you say there are computational reasons why exp2 and log2 are > advantageous when using binary floating-point, I can believe that. > I just don't understand the reasons (and to be honest, I'm not sure > I'd understand an explanation without more effort than I'm willing > to expend, unless somebody wants to pay me to work on this stuff). > It's late here and I want to sleep, so very briefly: The best computational way to calculate a**x for constant a on relatively big interval of x, like [0:1] or [-0.5:0.5] is not through evaluation of polynomial of very high degree, but by splitting interval into sub ranges and calculating y = Yi * a**(x-Xi) where Yi is tabulated and may be Xi tabulated too, or may be Xi just regularly spaced. For double precision and for speed/space/precision requirements of C math library you will probably want many dozen of intervals, or low hundreds. That allows much lower degree of poly for a**(x-Xi). And to lower degree even further you use Chebyshev series or may be even series derived by Remez exchange algorithm rather than Taylor series. It means that even for a=e the second coefficient is not 1 and likely the 1st coefficient is also not 1. So, a=e has no advantage vs a=2. Of course, in this part of calculation a=2 also holds no advantages vs any other base, but it has advantages in other parts of of solution. Different but ideologically similar reasoning applies to natural log vs log2.
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-12 16:49 -0500 |
| Message-ID | <115ippl$15jbt$1@dont-email.me> |
| In reply to | #401085 |
On 8/12/2026 4:24 PM, Michael S wrote: > On Wed, 12 Aug 2026 13:44:50 -0700 > Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: > >> Michael S <already5chosen@yahoo.com> writes: >>> On Wed, 12 Aug 2026 03:58:16 -0700 >>> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: >>>> David Brown <david.brown@hesbynett.no> writes: >>>> [...] >>>>> And I thought it is entirely obvious that when you are actually >>>>> implementing a floating point power function on a binary computer >>>>> using floating point formats specified in binary, it is most >>>>> efficient to use base 2 for the log and anti-log. If you had a >>>>> floating point format that used base 10, you'd probably want to >>>>> use base 10 for the log and anti-log. >>>> >>>> Is it obvious? It had never occurred to me. >>>> >>>> log and exp are certainly more mathematically straightforward in >>>> base e than in other bases. >>> >>> Only near x=1 for log(x) and near x=0 for exp(x). >> >> Can you explain what you mean by that? >> >> Mathematically, exp(x) (base e) is described by the Taylor series. >> In clumsy ASCII notation, it's: >> >> 1 + x + x**2/2! + x**3/3! + x**4/4! + ... >> >> b**x, were b is a base other than e (often 2 or 10) is >> exp(x * log(base)), where exp() and log() are base e. In other >> words, exp and log for bases other than e are most straightforwardly >> defined on top of exp and log for base e. >> >> That's what I meant by "more mathematically straightforward". >> >> If you say there are computational reasons why exp2 and log2 are >> advantageous when using binary floating-point, I can believe that. >> I just don't understand the reasons (and to be honest, I'm not sure >> I'd understand an explanation without more effort than I'm willing >> to expend, unless somebody wants to pay me to work on this stuff). >> > > It's late here and I want to sleep, so very briefly: > The best computational way to calculate a**x for constant a on > relatively big interval of x, like [0:1] or [-0.5:0.5] is not through > evaluation of polynomial of very high degree, but by splitting > interval into sub ranges and calculating y = Yi * a**(x-Xi) where > Yi is tabulated and may be Xi tabulated too, or may be Xi just regularly > spaced. For double precision and for speed/space/precision requirements > of C math library you will probably want many dozen of intervals, or > low hundreds. That allows much lower degree of poly for a**(x-Xi). > And to lower degree even further you use Chebyshev series or may be > even series derived by Remez exchange algorithm rather than Taylor > series. It means that even for a=e the second coefficient is not 1 and > likely the 1st coefficient is also not 1. So, a=e has no advantage vs > a=2. Of course, in this part of calculation a=2 also holds no > advantages vs any other base, but it has advantages in other parts of > of solution. > Different but ideologically similar reasoning applies to natural > log vs log2. I have found over the years that 200 points seems to be best when performing a numerical integration of a curve. For me, 200 points is the point where diminishing returns has set in. Of course, YMMV. Lynn
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2026-08-13 08:38 +0200 |
| Message-ID | <115jopi$1dak6$1@dont-email.me> |
| In reply to | #401086 |
On 12/08/2026 23:49, Lynn McGuire wrote: > On 8/12/2026 4:24 PM, Michael S wrote: >> On Wed, 12 Aug 2026 13:44:50 -0700 >> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: >> >>> Michael S <already5chosen@yahoo.com> writes: >>>> On Wed, 12 Aug 2026 03:58:16 -0700 >>>> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote: >>>>> David Brown <david.brown@hesbynett.no> writes: >>>>> [...] >>>>>> And I thought it is entirely obvious that when you are actually >>>>>> implementing a floating point power function on a binary computer >>>>>> using floating point formats specified in binary, it is most >>>>>> efficient to use base 2 for the log and anti-log. If you had a >>>>>> floating point format that used base 10, you'd probably want to >>>>>> use base 10 for the log and anti-log. >>>>> >>>>> Is it obvious? It had never occurred to me. >>>>> >>>>> log and exp are certainly more mathematically straightforward in >>>>> base e than in other bases. >>>> >>>> Only near x=1 for log(x) and near x=0 for exp(x). >>> >>> Can you explain what you mean by that? >>> >>> Mathematically, exp(x) (base e) is described by the Taylor series. >>> In clumsy ASCII notation, it's: >>> >>> 1 + x + x**2/2! + x**3/3! + x**4/4! + ... >>> >>> b**x, were b is a base other than e (often 2 or 10) is >>> exp(x * log(base)), where exp() and log() are base e. In other >>> words, exp and log for bases other than e are most straightforwardly >>> defined on top of exp and log for base e. >>> >>> That's what I meant by "more mathematically straightforward". >>> >>> If you say there are computational reasons why exp2 and log2 are >>> advantageous when using binary floating-point, I can believe that. >>> I just don't understand the reasons (and to be honest, I'm not sure >>> I'd understand an explanation without more effort than I'm willing >>> to expend, unless somebody wants to pay me to work on this stuff). >>> >> >> It's late here and I want to sleep, so very briefly: >> The best computational way to calculate a**x for constant a on >> relatively big interval of x, like [0:1] or [-0.5:0.5] is not through >> evaluation of polynomial of very high degree, but by splitting >> interval into sub ranges and calculating y = Yi * a**(x-Xi) where >> Yi is tabulated and may be Xi tabulated too, or may be Xi just regularly >> spaced. For double precision and for speed/space/precision requirements >> of C math library you will probably want many dozen of intervals, or >> low hundreds. That allows much lower degree of poly for a**(x-Xi). >> And to lower degree even further you use Chebyshev series or may be >> even series derived by Remez exchange algorithm rather than Taylor >> series. It means that even for a=e the second coefficient is not 1 and >> likely the 1st coefficient is also not 1. So, a=e has no advantage vs >> a=2. Of course, in this part of calculation a=2 also holds no >> advantages vs any other base, but it has advantages in other parts of >> of solution. >> Different but ideologically similar reasoning applies to natural >> log vs log2. > > I have found over the years that 200 points seems to be best when > performing a numerical integration of a curve. For me, 200 points is > the point where diminishing returns has set in. Of course, YMMV. > Your mileage may very much vary. The best number of points depends on many factors, such as the type of curve (how "wiggly" it is, whether it has additional characteristics like monoticity that you can use, etc.), whether you are using linearly separated points or free points, how your interpolation works, what characteristics you need for the generated results, your required precision, etc. Characteristics of the target architecture can influence the best choice of points - bigger tables may let you use simpler calculations, but calculations may be cheaper than more complicated table lookup schemes. There is no single guideline for the number of points in such tables that can be useful in any general sense. I don't quite understand the use of the table Michael is describing here, but it does not at all surprise me that practical implementations of "pow" (and no doubt many other irrational functions) combine range-splitting and tables so that the polynomial approximations are efficient. My own understanding here is probably on a similar level to Keith's - I know the theoretical maths (Taylor series and all), know the difference between the theoretical infinite precision infinite series and limited precision numerical analysis, know about error analysis, basis polynomials like Chebyshev, etc. But I also know there's a lot of detail that I would have to learn or look up, that real-world speed can have surprising differences from what you expect, that people have figured out smart tricks to get good results faster, and that you need a great deal of experience working on this kind of code to write it well. I don't have that experience or practical knowledge - I have to trust those that do (like Michael). For my own uses, I typically need things like sin functions for motor control and other such applications. Tables of perhaps 16 or 32 evenly spaced points, with cubic interpolation, are often fine to get the accuracy I need in a few clock cycles on a microcontroller. (I don't think I have ever needed a floating point "pow" on a microcontroller.)
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| From | scott@slp53.sl.home (Scott Lurndal) |
|---|---|
| Date | 2026-08-13 14:36 +0000 |
| Subject | Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) |
| Message-ID | <dEkfS.12442$A5U.4318@fx02.iad> |
| In reply to | #401104 |
Janis Papanagnou <janis_papanagnou+ng@hotmail.com> writes: >On 2026-08-13 08:38, David Brown wrote: > >(And speedy BCD-shifts. - Which reminds me the discussion here about >binary shifts in the float representation of 'pow' when using binary >exp/log representations for optimization purposes.) One of the nice features of the B3500 BCD architecture was the speed of multiplication and division by powers of 10 by simply adjusting the boundaries of a move digits instruction.
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2026-08-13 17:07 +0200 |
| Subject | Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) |
| Message-ID | <115kmiv$1mcf7$1@dont-email.me> |
| In reply to | #401104 |
On 13/08/2026 14:45, Janis Papanagnou wrote: > One "hammer" (a small CORDIC table) for a whole class of functions; > amazing. > I agree - the CORDIC concept is very cool. The same structure can be used for trig functions, hyperbolic functions, converting between Cartesian and radial forms, multiplication, division, and a few other things - all with very simple operations. It is, however, slower and more complex than tables and interpolation for the things I needed, and slower for calculating high-accuracy transcendental functions on "big" processors than alternatives. > Janis > > PS: I'm astonished that Google has all that information - after all > that pocket calculator things are just legacy stuff. (Around 1980, > without the Web (or search engines), it had been really a hard job > to find and identify all that information.) > Some people get really "nerdy" about calculators. (I spent a good proportion of my spare cash on a programmable Casio fx-3600P in my youth, and wrote all sorts of programs despite its 36 byte program memory. It is still in my desk drawer, and still works.) It is amazing how much detailed information people have published about various calculators. Google's search has got very good about summarising information from web pages, and helpfully gives links to the references it uses. But it's the work done by calculator fans (as well as people writing articles and Wikipedia pages about Cordic) that is astonishing to me, rather than how well Google finds the information.
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| From | Janis Papanagnou <janis_papanagnou+ng@hotmail.com> |
|---|---|
| Date | 2026-08-13 19:07 +0200 |
| Subject | Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) |
| Message-ID | <115ktla$183lr$2@dont-email.me> |
| In reply to | #401113 |
On 2026-08-13 17:07, David Brown wrote: > > [...] But it's the work done by calculator fans (as well as people > writing articles and Wikipedia pages about Cordic) that is astonishing > to me, rather than how well Google finds the information. Well, sure; honor to whom it deserves! (Thanks for catching and correcting my sloppiness.) Janis
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| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Date | 2026-08-13 22:24 +0200 |
| Subject | Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) |
| Message-ID | <115l953$1vk09$1@dont-email.me> |
| In reply to | #401123 |
On 13/08/2026 19:07, Janis Papanagnou wrote: > On 2026-08-13 17:07, David Brown wrote: >> >> [...] But it's the work done by calculator fans (as well as people >> writing articles and Wikipedia pages about Cordic) that is astonishing >> to me, rather than how well Google finds the information. > > Well, sure; honor to whom it deserves! > > (Thanks for catching and correcting my sloppiness.) > I didn't see any sloppiness on your part. Even though it was mainly from Google, based on other people's work, it was still a post with interesting history. And I suppose Google deserves some credit for making a pretty good search engine!
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-08-13 16:36 -0700 |
| Subject | Re: Calculation of sine with tables (was Re: why is there not a ipow version of pow?) |
| Message-ID | <gl-dnW_WQv1ByeP3nZ2dnZfqnPednZ2d@giganews.com> |
| In reply to | #401124 |
On 08/13/2026 01:24 PM, David Brown wrote: > On 13/08/2026 19:07, Janis Papanagnou wrote: >> On 2026-08-13 17:07, David Brown wrote: >>> >>> [...] But it's the work done by calculator fans (as well as people >>> writing articles and Wikipedia pages about Cordic) that is >>> astonishing to me, rather than how well Google finds the information. >> >> Well, sure; honor to whom it deserves! >> >> (Thanks for catching and correcting my sloppiness.) >> > > I didn't see any sloppiness on your part. Even though it was mainly > from Google, based on other people's work, it was still a post with > interesting history. > > And I suppose Google deserves some credit for making a pretty good > search engine! > Google, Bing, Altavista, Webcrawler, all ate by the big fish, fronting the same "search and hide and huff and stuff" engine, "Google" deserves some debit. It's called a monopoly there are laws against it for the common good and in the interests of free-market capitalism. Of course the Internet is pretty great. Data centers should pay excise for juice, and bot-chat-farms should pay excise for RAM. I'm surprised nobody's mentioned Kuratsaba (sp.) et alia, the usual account of trading multiplies for additions to compute multiplication.
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-13 18:59 -0500 |
| Message-ID | <115llou$23b6g$1@dont-email.me> |
| In reply to | #401104 |
On 8/13/2026 1:38 AM, David Brown wrote:
> On 12/08/2026 23:49, Lynn McGuire wrote:
>> On 8/12/2026 4:24 PM, Michael S wrote:
>>> On Wed, 12 Aug 2026 13:44:50 -0700
>>> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:
>>>
>>>> Michael S <already5chosen@yahoo.com> writes:
>>>>> On Wed, 12 Aug 2026 03:58:16 -0700
>>>>> Keith Thompson <Keith.S.Thompson+u@gmail.com> wrote:
>>>>>> David Brown <david.brown@hesbynett.no> writes:
>>>>>> [...]
>>>>>>> And I thought it is entirely obvious that when you are actually
>>>>>>> implementing a floating point power function on a binary computer
>>>>>>> using floating point formats specified in binary, it is most
>>>>>>> efficient to use base 2 for the log and anti-log. If you had a
>>>>>>> floating point format that used base 10, you'd probably want to
>>>>>>> use base 10 for the log and anti-log.
>>>>>>
>>>>>> Is it obvious? It had never occurred to me.
>>>>>>
>>>>>> log and exp are certainly more mathematically straightforward in
>>>>>> base e than in other bases.
>>>>>
>>>>> Only near x=1 for log(x) and near x=0 for exp(x).
>>>>
>>>> Can you explain what you mean by that?
>>>>
>>>> Mathematically, exp(x) (base e) is described by the Taylor series.
>>>> In clumsy ASCII notation, it's:
>>>>
>>>> 1 + x + x**2/2! + x**3/3! + x**4/4! + ...
>>>>
>>>> b**x, were b is a base other than e (often 2 or 10) is
>>>> exp(x * log(base)), where exp() and log() are base e. In other
>>>> words, exp and log for bases other than e are most straightforwardly
>>>> defined on top of exp and log for base e.
>>>>
>>>> That's what I meant by "more mathematically straightforward".
>>>>
>>>> If you say there are computational reasons why exp2 and log2 are
>>>> advantageous when using binary floating-point, I can believe that.
>>>> I just don't understand the reasons (and to be honest, I'm not sure
>>>> I'd understand an explanation without more effort than I'm willing
>>>> to expend, unless somebody wants to pay me to work on this stuff).
>>>>
>>>
>>> It's late here and I want to sleep, so very briefly:
>>> The best computational way to calculate a**x for constant a on
>>> relatively big interval of x, like [0:1] or [-0.5:0.5] is not through
>>> evaluation of polynomial of very high degree, but by splitting
>>> interval into sub ranges and calculating y = Yi * a**(x-Xi) where
>>> Yi is tabulated and may be Xi tabulated too, or may be Xi just regularly
>>> spaced. For double precision and for speed/space/precision requirements
>>> of C math library you will probably want many dozen of intervals, or
>>> low hundreds. That allows much lower degree of poly for a**(x-Xi).
>>> And to lower degree even further you use Chebyshev series or may be
>>> even series derived by Remez exchange algorithm rather than Taylor
>>> series. It means that even for a=e the second coefficient is not 1 and
>>> likely the 1st coefficient is also not 1. So, a=e has no advantage vs
>>> a=2. Of course, in this part of calculation a=2 also holds no
>>> advantages vs any other base, but it has advantages in other parts of
>>> of solution.
>>> Different but ideologically similar reasoning applies to natural
>>> log vs log2.
>>
>> I have found over the years that 200 points seems to be best when
>> performing a numerical integration of a curve. For me, 200 points is
>> the point where diminishing returns has set in. Of course, YMMV.
>>
>
> Your mileage may very much vary. The best number of points depends on
> many factors, such as the type of curve (how "wiggly" it is, whether it
> has additional characteristics like monoticity that you can use, etc.),
> whether you are using linearly separated points or free points, how your
> interpolation works, what characteristics you need for the generated
> results, your required precision, etc. Characteristics of the target
> architecture can influence the best choice of points - bigger tables may
> let you use simpler calculations, but calculations may be cheaper than
> more complicated table lookup schemes. There is no single guideline for
> the number of points in such tables that can be useful in any general
> sense.
>
> I don't quite understand the use of the table Michael is describing
> here, but it does not at all surprise me that practical implementations
> of "pow" (and no doubt many other irrational functions) combine range-
> splitting and tables so that the polynomial approximations are efficient.
>
> My own understanding here is probably on a similar level to Keith's - I
> know the theoretical maths (Taylor series and all), know the difference
> between the theoretical infinite precision infinite series and limited
> precision numerical analysis, know about error analysis, basis
> polynomials like Chebyshev, etc. But I also know there's a lot of
> detail that I would have to learn or look up, that real-world speed can
> have surprising differences from what you expect, that people have
> figured out smart tricks to get good results faster, and that you need a
> great deal of experience working on this kind of code to write it well.
> I don't have that experience or practical knowledge - I have to trust
> those that do (like Michael).
>
>
> For my own uses, I typically need things like sin functions for motor
> control and other such applications. Tables of perhaps 16 or 32 evenly
> spaced points, with cubic interpolation, are often fine to get the
> accuracy I need in a few clock cycles on a microcontroller. (I don't
> think I have ever needed a floating point "pow" on a microcontroller.)
Mine is coming from a chemical process simulator where chemicals are
moving between the four phases of matter that we support: vapor,
hydrocarbon liquid, aqueous liquid, and solids, based on temperature and
pressure. The tables are incredibly non-linear.
This is my people and I:
https://www.winsim.com/
Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-13 18:51 -0700 |
| Message-ID | <115lsa8$25dmf$2@dont-email.me> |
| In reply to | #401133 |
On 8/13/2026 4:59 PM, Lynn McGuire wrote: [...] > Mine is coming from a chemical process simulator where chemicals are > moving between the four phases of matter that we support: vapor, > hydrocarbon liquid, aqueous liquid, and solids, based on temperature and > pressure. The tables are incredibly non-linear. > > This is my people and I: > https://www.winsim.com/ Notice any fractal growth in there?
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 00:58 -0500 |
| Message-ID | <115maqt$295ib$1@dont-email.me> |
| In reply to | #401136 |
On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: > On 8/13/2026 4:59 PM, Lynn McGuire wrote: > [...] >> Mine is coming from a chemical process simulator where chemicals are >> moving between the four phases of matter that we support: vapor, >> hydrocarbon liquid, aqueous liquid, and solids, based on temperature >> and pressure. The tables are incredibly non-linear. >> >> This is my people and I: >> https://www.winsim.com/ > > Notice any fractal growth in there? We don't do that. Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 12:08 -0700 |
| Message-ID | <115np2q$2pjt6$1@dont-email.me> |
| In reply to | #401147 |
On 8/13/2026 10:58 PM, Lynn McGuire wrote: > On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >> [...] >>> Mine is coming from a chemical process simulator where chemicals are >>> moving between the four phases of matter that we support: vapor, >>> hydrocarbon liquid, aqueous liquid, and solids, based on temperature >>> and pressure. The tables are incredibly non-linear. >>> >>> This is my people and I: >>> https://www.winsim.com/ >> >> Notice any fractal growth in there? > > We don't do that. Let me clarify... Do you make renders of a simulation? If so, do some of them look fractal?
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 15:48 -0500 |
| Message-ID | <115nuvq$2rkd3$1@dont-email.me> |
| In reply to | #401167 |
On 8/14/2026 2:08 PM, Chris M. Thomasson wrote:
> On 8/13/2026 10:58 PM, Lynn McGuire wrote:
>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote:
>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote:
>>> [...]
>>>> Mine is coming from a chemical process simulator where chemicals are
>>>> moving between the four phases of matter that we support: vapor,
>>>> hydrocarbon liquid, aqueous liquid, and solids, based on temperature
>>>> and pressure. The tables are incredibly non-linear.
>>>>
>>>> This is my people and I:
>>>> https://www.winsim.com/
>>>
>>> Notice any fractal growth in there?
>>
>> We don't do that.
> Let me clarify... Do you make renders of a simulation? If so, do some of
> them look fractal?
In short, no. We have a diagrammatic user interface that allows our
users to build a diagram of a chemical process flow diagram such as a
refinery, a natural gas plan, a pipeline with compressor stations, or a
chemical plant.
https://www.winsim.com/screenshots.html
And we have a calculation engine that takes a textual version of that
diagram and solves it thermodynamically. If, it can be solved as not
all chemical processes can be solved due to constraints or violation of
the laws of thermodynamics.
Thanks,
Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 13:51 -0700 |
| Message-ID | <115nv50$2rkpr$1@dont-email.me> |
| In reply to | #401181 |
On 8/14/2026 1:48 PM, Lynn McGuire wrote: > On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>> [...] >>>>> Mine is coming from a chemical process simulator where chemicals >>>>> are moving between the four phases of matter that we support: >>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>> temperature and pressure. The tables are incredibly non-linear. >>>>> >>>>> This is my people and I: >>>>> https://www.winsim.com/ >>>> >>>> Notice any fractal growth in there? >>> >>> We don't do that. >> Let me clarify... Do you make renders of a simulation? If so, do some >> of them look fractal? > > In short, no. We have a diagrammatic user interface that allows our > users to build a diagram of a chemical process flow diagram such as a > refinery, a natural gas plan, a pipeline with compressor stations, or a > chemical plant. > https://www.winsim.com/screenshots.html > > And we have a calculation engine that takes a textual version of that > diagram and solves it thermodynamically. If, it can be solved as not > all chemical processes can be solved due to constraints or violation of > the laws of thermodynamics. Ahhhh! So, you are not making any animations of the processes. Okay. But you have the data to do so... Fwiw, I bet you already have the data to make one of my 2d examples here: https://youtu.be/YS-tyDJVy4M
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| From | Lynn McGuire <lynnmcguire5@gmail.com> |
|---|---|
| Date | 2026-08-14 16:40 -0500 |
| Message-ID | <115o20c$2sj52$1@dont-email.me> |
| In reply to | #401183 |
On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: > On 8/14/2026 1:48 PM, Lynn McGuire wrote: >> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>> [...] >>>>>> Mine is coming from a chemical process simulator where chemicals >>>>>> are moving between the four phases of matter that we support: >>>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>>> temperature and pressure. The tables are incredibly non-linear. >>>>>> >>>>>> This is my people and I: >>>>>> https://www.winsim.com/ >>>>> >>>>> Notice any fractal growth in there? >>>> >>>> We don't do that. >>> Let me clarify... Do you make renders of a simulation? If so, do some >>> of them look fractal? >> >> In short, no. We have a diagrammatic user interface that allows our >> users to build a diagram of a chemical process flow diagram such as a >> refinery, a natural gas plan, a pipeline with compressor stations, or >> a chemical plant. >> https://www.winsim.com/screenshots.html >> >> And we have a calculation engine that takes a textual version of that >> diagram and solves it thermodynamically. If, it can be solved as not >> all chemical processes can be solved due to constraints or violation >> of the laws of thermodynamics. > Ahhhh! So, you are not making any animations of the processes. Okay. But > you have the data to do so... > > Fwiw, I bet you already have the data to make one of my 2d examples here: > > https://youtu.be/YS-tyDJVy4M Actually, I do make an animation of the process simulation diagram (PSD). If the users run a dynamic (time sensitive) version of the simulation, the user can roll through their displayed results on the various sheets of the PSD using their time breaks. Lynn
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2026-08-14 19:24 -0700 |
| Message-ID | <115oiku$314lo$1@dont-email.me> |
| In reply to | #401189 |
On 8/14/2026 2:40 PM, Lynn McGuire wrote: > On 8/14/2026 3:51 PM, Chris M. Thomasson wrote: >> On 8/14/2026 1:48 PM, Lynn McGuire wrote: >>> On 8/14/2026 2:08 PM, Chris M. Thomasson wrote: >>>> On 8/13/2026 10:58 PM, Lynn McGuire wrote: >>>>> On 8/13/2026 8:51 PM, Chris M. Thomasson wrote: >>>>>> On 8/13/2026 4:59 PM, Lynn McGuire wrote: >>>>>> [...] >>>>>>> Mine is coming from a chemical process simulator where chemicals >>>>>>> are moving between the four phases of matter that we support: >>>>>>> vapor, hydrocarbon liquid, aqueous liquid, and solids, based on >>>>>>> temperature and pressure. The tables are incredibly non-linear. >>>>>>> >>>>>>> This is my people and I: >>>>>>> https://www.winsim.com/ >>>>>> >>>>>> Notice any fractal growth in there? >>>>> >>>>> We don't do that. >>>> Let me clarify... Do you make renders of a simulation? If so, do >>>> some of them look fractal? >>> >>> In short, no. We have a diagrammatic user interface that allows our >>> users to build a diagram of a chemical process flow diagram such as a >>> refinery, a natural gas plan, a pipeline with compressor stations, or >>> a chemical plant. >>> https://www.winsim.com/screenshots.html >>> >>> And we have a calculation engine that takes a textual version of that >>> diagram and solves it thermodynamically. If, it can be solved as not >>> all chemical processes can be solved due to constraints or violation >>> of the laws of thermodynamics. >> Ahhhh! So, you are not making any animations of the processes. Okay. >> But you have the data to do so... >> >> Fwiw, I bet you already have the data to make one of my 2d examples here: >> >> https://youtu.be/YS-tyDJVy4M > > Actually, I do make an animation of the process simulation diagram > (PSD). Can you give me a link to some screenshots so I can get on the same page? Thanks. Are you almost done with your Fortran port? > If the users run a dynamic (time sensitive) version of the > simulation, the user can roll through their displayed results on the > various sheets of the PSD using their time breaks. Cool. Fwiw, check this shit out: https://youtu.be/poXeq5V0dso A simulation for the field of one of my circle intersection fractals.
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