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Radians Or Degrees?

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  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

Page 6 of 9 — ← Prev page 1 2 3 4 5 [6] 7 8 9  Next page →

#382987

Kaz Kylheku <433-929-6894@kylheku.com> writes:

> On 2024-02-24, Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:
>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>
>>> On Sat, 24 Feb 2024 01:15:58 +0000, Ben Bacarisse wrote:
>>>
>>>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>>> 
>>>>> I thought they were the same thing: extra numbers inserted in the gap
>>>>> between the normalized number closest to zero on each side, to allow
>>>>> for gradual underflow.
>>>> 
>>>> Those are subnormal.  They are smaller (in magnitude) than the smallest
>>>> normal.  Denormals are simply representations with leading zeros.  IEEE
>>>> FP's implicit leading 1 means these (denormals that are not subnormal)
>>>> can't exist in that representation.
>>>
>>> So in IEEE754, they are the same thing.
>>
>> No.  I am pretty sure you understand what's been said so you must be
>> arguing for the sake of it.
>
> I have only bicycles in my garage, so in my garage, "bicycles" and
> "vehicles" are the same thing, not just the same set.

I'm not sure what your point is.  LD'O wanted to know why "they" brought
in the more specific term:

  "Why did they bring in the term “subnormal”, anyway? What was wrong
  with “denormalized”?"

I just suggested they "they" might have chosen to use the more specific
term "bicycles" for the vehicles in you garage because it's more
precise.  Are you disagreeing or using mockery to support that rather
obvious idea?

-- 
Ben.

[toc] | [prev] | [next] | [standalone]

#383002

On Sun, 25 Feb 2024 00:18:33 +0000
Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:

> Kaz Kylheku <433-929-6894@kylheku.com> writes:
> 
> > On 2024-02-24, Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:  
> >> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> >>  
> >>> On Sat, 24 Feb 2024 01:15:58 +0000, Ben Bacarisse wrote:
> >>>  
> >>>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> >>>>   
> >>>>> I thought they were the same thing: extra numbers inserted in
> >>>>> the gap between the normalized number closest to zero on each
> >>>>> side, to allow for gradual underflow.  
> >>>> 
> >>>> Those are subnormal.  They are smaller (in magnitude) than the
> >>>> smallest normal.  Denormals are simply representations with
> >>>> leading zeros.  IEEE FP's implicit leading 1 means these
> >>>> (denormals that are not subnormal) can't exist in that
> >>>> representation.  
> >>>
> >>> So in IEEE754, they are the same thing.  
> >>
> >> No.  I am pretty sure you understand what's been said so you must
> >> be arguing for the sake of it.  
> >
> > I have only bicycles in my garage, so in my garage, "bicycles" and
> > "vehicles" are the same thing, not just the same set.  
> 
> I'm not sure what your point is.  LD'O wanted to know why "they"
> brought in the more specific term:
> 
>   "Why did they bring in the term “subnormal”, anyway? What was wrong
>   with “denormalized”?"
> 
> I just suggested they "they" might have chosen to use the more
> specific term "bicycles" for the vehicles in you garage because it's
> more precise.  Are you disagreeing or using mockery to support that
> rather obvious idea?
> 

[toc] | [prev] | [next] | [standalone]

#382960

On Sat, 24 Feb 2024 01:27:28 +0000, Ben Bacarisse wrote:

> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
> 
>> On Sat, 24 Feb 2024 01:15:58 +0000, Ben Bacarisse wrote:
>>
>>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>> 
>>>> I thought they were the same thing: extra numbers inserted in the gap
>>>> between the normalized number closest to zero on each side, to allow
>>>> for gradual underflow.
>>> 
>>> Those are subnormal.  They are smaller (in magnitude) than the
>>> smallest normal.  Denormals are simply representations with leading
>>> zeros.  IEEE FP's implicit leading 1 means these (denormals that are
>>> not subnormal) can't exist in that representation.
>>
>> So in IEEE754, they are the same thing.
> 
> No.  I am pretty sure you understand what's been said so you must be
> arguing for the sake of it.

So, give me an example, in IEEE754, of something that is one but not the 
other.

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#382962

On Sat, 24 Feb 2024 02:21:57 +0000, Lawrence D'Oliveiro wrote:

> On Sat, 24 Feb 2024 01:27:28 +0000, Ben Bacarisse wrote:
> 
>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>> 
>>> On Sat, 24 Feb 2024 01:15:58 +0000, Ben Bacarisse wrote:
>>>
>>>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>>> 
>>>>> I thought they were the same thing: extra numbers inserted in the
>>>>> gap between the normalized number closest to zero on each side, to
>>>>> allow for gradual underflow.
>>>> 
>>>> Those are subnormal.  They are smaller (in magnitude) than the
>>>> smallest normal.  Denormals are simply representations with leading
>>>> zeros.  IEEE FP's implicit leading 1 means these (denormals that are
>>>> not subnormal) can't exist in that representation.
>>>
>>> So in IEEE754, they are the same thing.
>> 
>> No.  I am pretty sure you understand what's been said so you must be
>> arguing for the sake of it.
> 
> So, give me an example, in IEEE754, of something that is one but not the
> other.

Well, that's a conundrum.  One cannot give you an example as IEEE 754
does not describe unnormal numbers.

See https://en.wikipedia.org/wiki/Subnormal_number

PS: Yes, I know that page does not tell you what unnormal means.

-- 
steve

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#382963

On Sat, 24 Feb 2024 02:49:29 -0000 (UTC), Steven G. Kargl wrote:

> On Sat, 24 Feb 2024 02:21:57 +0000, Lawrence D'Oliveiro wrote:
> 
>> So, give me an example, in IEEE754, of something that is one but not
>> the other.
> 
> Well, that's a conundrum.  One cannot give you an example as IEEE 754
> does not describe unnormal numbers.

No, it’s not a conundrum. It’s just a confirmation of my point that, in 
IEEE754, you don’t need two words because there is only the single 
concept.

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#382964

On 2024-02-24, Lawrence D'Oliveiro <ldo@nz.invalid> wrote:
> On Sat, 24 Feb 2024 02:49:29 -0000 (UTC), Steven G. Kargl wrote:
>
>> On Sat, 24 Feb 2024 02:21:57 +0000, Lawrence D'Oliveiro wrote:
>> 
>>> So, give me an example, in IEEE754, of something that is one but not
>>> the other.
>> 
>> Well, that's a conundrum.  One cannot give you an example as IEEE 754
>> does not describe unnormal numbers.
>
> No, it’s not a conundrum.

Well, it's a subnundrum, which in your case is the same thing
as a denundrum.

-- 
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @Kazinator@mstdn.ca

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#382961

Ben Bacarisse <ben.usenet@bsb.me.uk> writes:

> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>
>> On Fri, 23 Feb 2024 23:16:32 +0000, Ben Bacarisse wrote:
>>
>>> Lawrence D'Oliveiro <ldo@nz.invalid> writes:
>>>
>>>> On Fri, 23 Feb 2024 20:38:59 -0000 (UTC), Steven G. Kargl wrote:
>>>>
>>>>> Note 2: subnormal values ...
>>>>
>>>> Why did they bring in the term "subnormal", anyway?  What was wrong with
>>>> "denormalized"?
>>>
>>> Greater clarity maybe?  After all, the two terms do mean different
>>> things.  In IEEE FP only subnormals can exist, but it surely helps to be
>>> able to talk about the difference.
>>
>> I thought they were the same thing:  extra numbers inserted in the gap
>> between the normalized number closest to zero on each side, to allow for
>> gradual underflow.
>
> Those are subnormal.  They are smaller (in magnitude) than the smallest
> normal.  Denormals are simply representations with leading zeros.  IEEE
> FP's implicit leading 1 means these (denormals that are not subnormal)
> can't exist in that representation.

There is some terminology confusion here.  Depending on what
source is consulted, the term "denormal" has different meanings.
On Wikipedia, for example, "denormal numbers" redirects to
"subnormal number".  Apparently the IEEE floating point standard
uses the term differently.  Other sources are not consistent.

Note that the ISO C standard uses and defines the terms "subnormal
floating-point numbers" and "unnormalized floating-point numbers",
as disjoint sets, distinct from normalized floating-point numbers
(which the ISO C standard also defines).  I expect it would help
the conversation to use these three terms (normalized, subnormal,
and unnormalized) and no others, since "denormal" or "denormalized"
seems to mean different things depending on which source is used.

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#382954

On 2024-02-23, Lawrence D'Oliveiro <ldo@nz.invalid> wrote:
> On Fri, 23 Feb 2024 20:38:59 -0000 (UTC), Steven G. Kargl wrote:
>
>> Note 2: subnormal values ...
>
> Why did they bring in the term “subnormal”, anyway? What was wrong with 
> “denormalized”?

subnormals are subset of denormals. In IEEE 754, the only denormals
are subnormals. This is because values that are outside of the subnormal
range have the implicit 1 in the mantissa.

Suppose you have a binary floating-point representation in which the 1
in the mantissa must be explicit, e.g.

                 101
  1.10100101 x 10

Then you can have denormals regardless of the exponent value.

E.g. the above normal number can also be expressed this way:

                  110 <-- incremented
  0.110100101 x 10

  ^
  |
  mantissa shifted right, bringing in a zero on the left

This denormal isn't subnormal, though; the subnormals are those
denormals which have a magnitude smaller than the smallest normal
magnitude. Those are the helpful/necessary ones which fill the gap
between zero and the smallest normals.

IEEE numbers don't have a zero on the left; the highest bit of the
mantissa is not represented and is assumed to be 1. As a special hack,
this implicit 1 assumption is lifted for the subnormals. This behavior
is turned on when the exponent value is the smallest possible one.

-- 
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @Kazinator@mstdn.ca

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#382971

On 2/23/24 17:39, Lawrence D'Oliveiro wrote:
> On Fri, 23 Feb 2024 20:38:59 -0000 (UTC), Steven G. Kargl wrote:
> 
>> Note 2: subnormal values ...
> 
> Why did they bring in the term “subnormal”, anyway? What was wrong with 
> “denormalized”?

The same thing that's wrong with calling a horse a quadruped. It's
technically correct, but in a context where it could only be a horse,
the term "quadruped" is unnecessarily vague. Denormal numbers that are
not subnormal are called unnormal, and are part of IEEE Decimal Floating
Point. Decimal floating point types have been an optional feature of C
since 2020.
The C standard never uses the term denormal, but it does use unnormal.
The only thing it does with the term is define it, and allow for the
presence of such numbers - but nothing that it says about normal or
subnormal numbers (which is quite a lot) applies to unnormal numbers,
and that is a deliberate feature of the standard.

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#382976

On Sat, 24 Feb 2024 02:25:51 -0500, James Kuyper wrote:

> Denormal numbers that are not subnormal are called unnormal, and are
> part of IEEE Decimal Floating Point.

Interesting, because when I brought up decimal floats in this thread, I 
was accused, by Michael S <already5chosen@yahoo.com>, of “trolling”, on 
the grounds that “nobody uses DFP for science or engineering”.

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#382979

On 2/24/24 16:21, Lawrence D'Oliveiro wrote:
> On Sat, 24 Feb 2024 02:25:51 -0500, James Kuyper wrote:
> 
>> Denormal numbers that are not subnormal are called unnormal, and are
>> part of IEEE Decimal Floating Point.
> 
> Interesting, because when I brought up decimal floats in this thread, I 
> was accused, by Michael S <already5chosen@yahoo.com>, of “trolling”, on 
> the grounds that “nobody uses DFP for science or engineering”.

Yes, that makes sense. Precisely because DFP is not likely to be used
for this kind of application, it's inappropriate to talk about denormal
number, because outside of DFP, you're unlikely to run into any denormal
numbers that aren't also subnormal.

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#382980

On Sat, 24 Feb 2024 17:32:47 -0500, James Kuyper wrote:

> Precisely because DFP is not likely to be used for this kind of
> application ...

But remember why the IEEE decided to formulate a standard for numerics in 
the first place: it’s because your typical (non-computer) engineer is just 
as naïve about numerical techniques as anybody else. IEEE754 was designed 
to reduce many of the unpleasant surprises that bedevilled computer 
arithmetic back in the day (Prof William “Mr IEEE754” Kahan’s foreword to 
Apple’s Standard Numerics manual, from back in 1987, still makes 
entertaining reading today). But as you know, binary arithmetic still has 
its share of nonintuitive results. So it only seems logical to go to 
decimal arithmetic, as the next step.

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#383006

Steven G. Kargl wrote:
> Fortunately, for 32-bit single precision floating point, one can
> exhaustively test single-argument functions.  For the SW implementation
> on FreeBSD, exhaustive testing shows
> 
> % tlibm sinpi -fPED -x 0 -X 0x1p23 -s 0
> Interval tested for sinpif: [0,8.38861e+06]
> 1000000 calls, 0.015453 secs, 0.01545 usecs/call
>         ulp <= 0.5:  99.842% 1253631604 |  99.842% 1253631604
> 0.5 <  ulp <  0.6:  0.158% 1989420 | 100.000% 1255621024
> Max ulp: 0.583666 at 6.07950642e-05

That seems worse than it should be, I would expect better results than 
the 0.5009 quoted for regular sin() below, and still with the same or 
better performance. The only obvious explanation would be that sin(x) 
over +/- 45 degrees would have a first Taylor term of 1.0*x, and you 
could probably force the first Cheby term to be the same, so by adding 
that as the last stage you get improved precision for free?

> 
> % tlibm sin -fPED -x 0 -X 0x1p23 -s 0
> Interval tested for sinf: [0,8.38861e+06]
> 1000000 calls, 0.019520 secs, 0.01952 usecs/call
>         ulp <= 0.5:  99.995% 1249842491 |  99.995% 1249842491
> 0.5 <  ulp <  0.6:  0.005%   60102 | 100.000% 1249902593
> Max ulp: 0.500900 at 3.68277281e+05
> 
> The speed test is for 1M values evenly distributed over
> the interval.  The difference in speed for sinpi vs sin
> is due to the argument reduction.
> 
> Note 1: libm built with clang/llvm with only -O2 on a
> AMD Phenom II X2 560 Processor (3300.14-MHz K8-class CPU).
> 
> Note 2: subnormal values for x are test not included in
> the count as subnormal are tested with a different approach.
> 

sin(x) for Subnormal x seems like it should be trivial: If you just 
return x the maximum error of a Taylor series with two terms
  (x - x^3/3!)
would be that second term which is by definition zero since x is already 
subnormal, right?

If you want to perform well on a platform where subnormal ops traps to a 
much slower hardware or software path, then it might make sense to start 
by checking for |x| < 2^-340 or so?

Terje
-- 
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"

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#383012

Terje Mathisen wrote:

> 

> sin(x) for Subnormal x seems like it should be trivial: If you just 
> return x the maximum error of a Taylor series with two terms
>   (x - x^3/3!)
> would be that second term which is by definition zero since x is already 
> subnormal, right?

The 2 term polynomial begins to be accurate when |x| < ~2^-19 which is far
bigger than 2^-1023. (2^-19)^3 is 2^-57 which has few digits in the resulting
fraction 2^-19; certainly no 3rd term is required.

> If you want to perform well on a platform where subnormal ops traps to a 
> much slower hardware or software path, then it might make sense to start 
> by checking for |x| < 2^-340 or so?

Many subnormal operands yield constant results or themselves::

cos(sn) = 1.0
sin(sn) = sn
tan(sn) = sn


> Terje

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#382937

Michael S wrote:
> On Thu, 22 Feb 2024 21:04:52 -0000 (UTC)
> Lawrence D'Oliveiro <ldo@nz.invalid> wrote:
>>
>> π radians = half a circle. Are there any other examples of the
>> usefulness of half-circles as an angle unit? As opposed to the dozens
>> or hundreds of examples of the usefulness of radians as an angle unit?
> 
> In digital signal processing circle-based units are pretty much always
> more natural than radians.
> For specific case of 1/2 circle, I can't see where it can be used
> directly.
>  From algorithmic perspective, full circle looks like the most obvious
> choice.
>  From [binary floating point] numerical properties perspective, 1/8th of
> the circle (==pi/4 radians = 45 degrees) is probably the best option
> for a library routine, because for sin() its derivative at 0 is closest
> to 1 among all powers of two which means that loss of precision
> near 0 is very similar for input and for output. But this advantage
> does not sound like particularly big deal.

ieee754 defines sinpi() and siblings, but imho it really doesn't matter 
if you use circles, half-circles (i.e. sinpi) or some other binary 
fraction of a circle: Argument reduction for huge inputs are just as 
easy, you might just have to multiply by the corresponding power of two 
(i.e. adjust the exponent) before extracting the fractional term.

For sinpi(x) I could do it like this:

  if (abs(x) >= two_to_52nd_power) error("Zero significant bits.");
  ix = int(x);
  x_reduced = x - (double) (ix & ~1);
  if (x_reduced < 0.0) x_reduced += 2.0;

but it is probably better to return a value in the [-1.0 .. 1.0> range?

Terje

-- 
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"

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#382922

On Thu, 22 Feb 2024 21:04:52 +0000, Lawrence D'Oliveiro wrote:

> On Thu, 22 Feb 2024 20:16:25 -0000 (UTC), Steven G. Kargl wrote:
> 
>> Apparently, you missed the part about argument reduction.  For sinpi(x),
>> it is fairly easy to reduce x = n + r with n an integer and r in [0,1). 
>> For the extended interval, x in [0,2^23], there are roughly 2^23 values
>> with r = 0.5; and thus, sinpi(x) = 1 exactly.  There are no such values
>> for sin(x), and argument reduction for sin(x) is much more involved.
> 
> You are working with approximations anyway. That those approximations 
> happen to exactly equal some random value seems irrelevant.
> 

These aren't some random values for individuals dealing
with wave propagation and resonances phenomena.  Here's 
a better example for you, cospi(1234.5) = 0, exactly.  The
two closest single precision floating numbers that bracket
this zero are
cos(0x1.e4c96ap+11) =  1.94140221e-03f
cos(0x1.e4c97ap+11) = -1.17215250e-05f

-- 
steve

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#382923

On Thu, 22 Feb 2024 22:09:36 -0000 (UTC), Steven G. Kargl wrote:

> On Thu, 22 Feb 2024 21:04:52 +0000, Lawrence D'Oliveiro wrote:
> 
>> You are working with approximations anyway. That those approximations
>> happen to exactly equal some random value seems irrelevant.
>> 
> These aren't some random values for individuals dealing with wave
> propagation and resonances phenomena.  Here's a better example for you,
> cospi(1234.5) = 0, exactly.  The two closest single precision floating
> numbers that bracket this zero are cos(0x1.e4c96ap+11) = 
> 1.94140221e-03f cos(0x1.e4c97ap+11) = -1.17215250e-05f

Is that in binary or decimal? Remember that IEEE754 has the option for 
both.

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#382924

On Thu, 22 Feb 2024 22:30:19 -0000 (UTC)
Lawrence D'Oliveiro <ldo@nz.invalid> wrote:

> On Thu, 22 Feb 2024 22:09:36 -0000 (UTC), Steven G. Kargl wrote:
> 
> > On Thu, 22 Feb 2024 21:04:52 +0000, Lawrence D'Oliveiro wrote:
> >   
> >> You are working with approximations anyway. That those
> >> approximations happen to exactly equal some random value seems
> >> irrelevant. 
> > These aren't some random values for individuals dealing with wave
> > propagation and resonances phenomena.  Here's a better example for
> > you, cospi(1234.5) = 0, exactly.  The two closest single precision
> > floating numbers that bracket this zero are cos(0x1.e4c96ap+11) = 
> > 1.94140221e-03f cos(0x1.e4c97ap+11) = -1.17215250e-05f  
> 
> Is that in binary or decimal? Remember that IEEE754 has the option
> for both.

IIRC, IEEE-754 has no option for *single precision* decimal FP.

Besides, I hope that you were trolling, you should know very well
that nobody uses DFP for science or engineering.

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#382926

On Fri, 23 Feb 2024 00:56:02 +0200, Michael S wrote:

> Besides, I hope that you were trolling, you should know very well that
> nobody uses DFP for science or engineering.

You forget that the last “E” in “IEEE” stands for “engineering”.

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#382890

Lawrence D'Oliveiro wrote:
> What units should be used for angles in trig functions?
>
> Radians are the most natural unit for most trig calculations, and that’s
> what the library routines in C and many other languages use. However,
> degrees are a more natural unit for humans to input, and to get results
> in.
>
> Thus, other languages, but not (yet?) C, provide conversion functions. For
> example, Python has math.radians() for converting degrees to radians, and
> math.degrees() for going the other way. Java has something similar.
>
> But I think providing conversion functions is an unnecessarily clumsy way
> of doing it, because for every alternative angle unit, you need two
> functions.
>
> Better to provide just a single conversion factor. E.g.
>
>     DEG = π / 180
>
> Now it is easy enough to input angles to a calculation in degrees, e.g.
>
>      sin(45 * DEG)
>
> And getting outputs in degrees is equally easy, e.g.
>
>      atan2(Y, X) / DEG
>
> Sometimes it is convenient to work in terms of whole circles (360°):
>
>      CIRCLE = 2 * π
>
> Thus the examples become:
>
>      sin(CIRCLE / 8)
>
> and
>
>      atan2(Y, X) / CIRCLE
>
> Anybody remember “gradians”?
>
>      GRAD = π / 200
>
> And of course, for completeness, we can have a factor for explicitly
> specifying that you are working radians:
>
>      RAD = 1.0
>

long time i think it should be measured in what you call here circle,
it is rather in "1" not in "360" nor "2PI" ..in my coding hovevver i use
degree360 = 2*PI/360.0

this what you call circle imo wpuld be better and i doubt in a reason to
use PI in mathematics yet defien it as 3.14 instead of 6.28 here if this 
value is really needed

also on assembly level i would like if fsin arguments woyld be not on 
radians but in "1.0" floats

if someone knows the reason why "6.28" radians are expected to better 
than "1.0" 'circkles' in both mathemathics and assembly tell me
- as i dont know the reason

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