Re: Radians Or Degrees?

From	Michael S <already5chosen@yahoo.com>
Newsgroups	comp.lang.c, comp.arch
Subject	Re: Radians Or Degrees?
Date	2024-03-20 18:21 +0200
Organization	A noiseless patient Spider
Message-ID	<20240320182147.000067e1@yahoo.com> (permalink)
References	(12 earlier) <ur9qtp$fnm9$1@dont-email.me> <20240314112655.000011f8@yahoo.com> <jwv1q87l5ou.fsf-monnier+comp.arch@gnu.org> <9a5b9a6a445bd41ff75a93b589982970@www.novabbs.org> <jwv8r2djafq.fsf-monnier+comp.arch@gnu.org>

Cross-posted to 2 groups.

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On Wed, 20 Mar 2024 09:54:36 -0400
Stefan Monnier <monnier@iro.umontreal.ca> wrote:

> >>>> There are groups who have shown that exactly rounded
> >>>> trancendental functions are in fact achievable with maybe 3X
> >>>> reduced performance.  
> >> That much?  I had the impression it was significantly cheaper.  
> > The J. M. Muller book indicates about 2× to 2.5×  
> 
> The [Rlibm](https://people.cs.rutgers.edu/~sn349/rlibm/) project
> claims to get much better performance (basically, in the same
> ballpark as not-correctly-rounded implementations).
> 

I had only read the 1st page.
It sounds like they are not particularly interested in IEEE binary64
which appears to be the major point of interest of math libs of
conventional languages.

> [ Their key insight is the idea that to get correct rounding, you
>   shouldn't try to compute the best approximation of the exact result
>   and then round, but you should instead try to compute any
>   approximation whose rounding gives the correct result.  ]
> 
> My impression was that their performance was good enough that the case
> for not-correctly-rounded implementations becomes very weak.
>

It all depend of what you compare against.
For scalar call for majority of transcendental functions on IEEE-754
list, it's probably very easy to get correctly rounded binary32 results
in approximately the same time as results calculated with max. err of,
say, 0.75 ULP. Especially so if target machine has fast binary64
arithmetic.
But in practice when we use lower (than binary64) precision we often
care about vector performance rather than scalar.
I.e. we care little about speed of sinf(), but want ippsTone_32f() as
fast as possible. In case you wonder, this function is part Intel
Performance Primitives and it is FAST. Writing correctly rounded
function that approaches the speed of this *almost* correctly
rounded routine (I think, for sane input ranges it's better than
0.55 ULP) would not be easy at all!

> >> I don't know what are/were the motivations for the people working
> >> on exact transcendentals, but they have applications unrelated to
> >> the fact that they're "better": the main benefit (from this here
> >> PL guy) is that it gives them a reliable, reproducible semantics.
> >> Bit-for-bit reproducibility makes several things much easier.  
> >
> > Consider moving an application which uses libm from machine to
> > machine. When libm is correctly rounded, there is no issue at all;
> > not so other- wise.  
> 
> Exactly!
> [ Or should I say "Correctly rounded!"?  ]
> 
> 
>         Stefan

You like this proposal because you are implementer of the language/lib.
It makes your regression tests easier. And it's good challenge.
I don't like it because I am primarily user of the language/lib. My
floating-point tests have zero chance of repeatability of this sort for
a thousand of other reasons. 
I don't want to pay for correct rounding of transcendental functions.
Neither in speed and especially nor in tables footprint. Not even a
little. Because for me there are no advantages.
Now, there are things that I am ready to pay for. E.g. preservation of
mathematical properties of original exact function. I.e. if original is
monotonic on certain interval then I do want at least weak monotonicity
of approximation. If original is even (or odd) I want the same for
approximation. If original never exceed 1, I want the same
for approximation. Etc... But correct rounding is not on the list.

Thread

Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-21 22:35 +0000
  Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-21 17:55 -0500
    Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-22 01:59 +0200
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 01:55 +0000
        Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 19:14 +0000
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:48 +0000
            Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 20:16 +0000
              Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 21:04 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-22 23:39 +0200
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 21:47 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-22 22:57 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 00:13 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:49 -0800
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:59 -0800
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 02:42 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-23 12:28 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:42 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-24 12:40 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 22:52 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-24 19:26 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-25 06:30 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-22 21:58 -0700
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 02:28 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-23 11:10 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-14 11:26 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:34 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 19:48 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 12:16 +0100
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-03-14 20:30 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:12 -0700
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 22:19 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:21 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:22 -0700
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 13:49 +0200
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 11:23 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 14:15 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:23 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-16 16:59 +0100
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 13:59 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:13 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-16 13:23 -0700
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 14:16 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:26 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:30 -0700
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 15:48 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 13:41 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 21:49 -0700
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:16 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 19:08 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 17:22 +0000
                Re: Radians Or Degrees? scott@slp53.sl.home (Scott Lurndal) - 2024-03-16 18:32 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 20:49 +0200
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 16:19 -0700
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 00:00 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 18:38 -0700
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 01:57 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 19:57 -0700
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-03-17 13:10 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:06 +0200
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:34 +0200
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 10:59 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 14:15 +0200
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 15:13 -0700
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-18 15:18 -0400
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-18 22:19 +0000
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 09:54 -0400
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-20 18:21 +0200
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 12:59 -0400
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:40 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:52 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 14:51 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-21 16:37 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-23 09:11 +0100
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-03-20 17:02 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:47 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:33 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 00:03 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:26 +0000
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 16:34 -0400
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:38 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-23 14:32 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 20:02 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 20:38 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 22:29 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:39 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 04:03 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 04:47 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 05:27 +0000
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 05:48 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 05:38 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 06:13 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:15 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 23:20 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:39 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-23 23:16 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 23:44 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-24 01:15 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 01:19 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-24 01:27 +0000
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 01:42 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-25 00:18 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-25 12:57 +0200
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 02:21 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 02:49 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 03:07 +0000
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 03:12 +0000
                Re: Radians Or Degrees? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-02-23 18:49 -0800
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-23 23:30 +0000
                Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-24 02:25 -0500
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 21:21 +0000
                Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-24 17:32 -0500
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 22:50 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-25 16:19 +0100
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-25 18:11 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-23 11:01 +0100
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 22:09 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 22:30 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-23 00:56 +0200
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 23:03 +0000
  Re: Radians Or Degrees? fir <fir@grunge.pl> - 2024-02-22 00:15 +0100
    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 01:55 +0000
      Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 09:32 +0100
        Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 09:38 +0000
          Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 11:04 +0100
      Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-22 14:28 +0000
        Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 16:26 +0100
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:45 +0000
          Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-22 21:30 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:11 +0100
        GGs [was Radians Or Degrees?] Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-23 13:57 +0000
          Re: GGs [was Radians Or Degrees?] "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-23 11:15 -0800
            Re: GGs [was Radians Or Degrees?] Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-23 19:26 +0000
  Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 07:17 +0000
    Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-22 16:49 +0000
  Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 09:06 +0100
  Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-22 08:27 +0000
    Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 11:09 +0100
      Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 13:48 +0000
      Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-22 15:29 +0000
        Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 20:02 +0100
          Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-23 02:15 +0000
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 02:24 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:16 +0100
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:39 +0000
        Re: Radians Or Degrees? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2024-02-22 21:25 +0100
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 20:58 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:33 +0100
              Re: Radians Or Degrees? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2024-02-23 12:53 +0100
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 20:23 +0000
        Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-25 11:19 +0000
          Re: Radians Or Degrees? Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-25 13:08 +0000
            Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-25 22:21 +0000
              Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-25 22:29 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:29 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-26 13:44 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 23:15 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-26 16:02 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-27 00:55 +0000
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-27 09:53 +0100
              Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-25 14:43 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:32 +0000
              Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-02-25 23:09 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:32 +0000
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-02-26 23:01 +0000
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-27 09:59 +0100
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:44 +0000

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