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Groups > comp.lang.c++ > #69709

Re: two's complement idea

From Paavo Helde <myfirstname@osa.pri.ee>
Newsgroups comp.lang.c++
Subject Re: two's complement idea
Date 2019-11-11 12:08 +0200
Organization A noiseless patient Spider
Message-ID <qqbbvo$fce$1@dont-email.me> (permalink)
References (6 earlier) <qps668$s0h$1@news.albasani.net> <qpsjg8$srn$1@dont-email.me> <86lfspcekw.fsf@linuxsc.com> <qq96vl$7iq$1@dont-email.me> <qq9jbb$gap$1@gioia.aioe.org>

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On 10.11.2019 20:02, Manfred wrote:
> The main difference between the hardware and the language is that 1) the
> former can count on accessory entities that are not part of a variable
> (the flags register) and 2) it does not have to fit within the semantics
> of a type system, so that it is OK for WORD op WORD to yield DWORD
>
> If you go into the specifics, you may see that:
> 1) flags information would need to be handled by the compiler, with the
> possible result of littering the generated code with branches for every
> integer expression.

Yes, that's correct.

> 2) Having an arithmetic operator (multiplication) yield a different type
> than the operands would pose significant complications to the language -
> if you really want this, try mimicking that with some C++ wrapper
> classes and operators thereof, and see where you go.
> The solution, when the full range is needed, is to tell the compiler
> that this is what you want by casting the /operands/.
> In this way the compiler can deliver the result you want (while
> optimizing away the extra space for the operands themselves).

Note that when the operands are cast to suitable larger types, then 
overflow cannot happen, so for this usage case the overflow behavior 
does not need to be defined.

>
>>
>> The problem with C is that they decided the best way to deal with this
>> is just to ignore the overflow flag and the upper half of the
>> multiplication result. Not sure about PDP-11 itself, but they had to
>> think about other hardware too, and at some point they decided that
>> the best way to deal with the problem was just to ignore all the extra
>> information the current or future CPU-s might provide
>
> See above.
> Moreover, given the impact of the choice, and its business consequences,
> it is hard to believe that this was just sloppiness.

Of course not. The decision to produce fastest code was a deliberate 
choice made by smart people, as you said. Any kind of overflow checking 
would have slowed the code down at least twice, which would have been of 
course disastrous for a language meant as "better assembler".

With the specified wrapping behavior for unsigneds the story is 
different however. They defined the unsigned overflow as wrapping 
because they could, not because of some deeper considerations. Would the 
existing hardware have provided some other behavior (like saturating) at 
zero cost, I'm sure they would have standardized that behavior instead.

Note that they did not just copy the hardware behavior. The common 
hardware itself does not have wrapping behavior, rather it produces the 
correct result with carry/overflow flags and extended registers. One 
only gets wrapping behavior by deliberately ignoring the correct result.

In a similar token, they did not define the behavior for signed overflow 
because they couldn't. More specifically, the zero cost behavior was 
different on different hardware, and they could not find enough 
justification for any kind of non-zero cost overflow behavior.

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Thread

two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-04 20:48 +0100
  Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-04 21:19 +0100
    Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-04 14:39 -0800
      Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-05 10:31 +0100
        Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-05 11:23 +0100
          Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-05 15:43 +0100
            Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-05 16:58 +0100
              Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-05 21:45 +0200
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 13:33 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 13:51 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-06 14:37 +0100
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 15:38 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 15:53 +0100
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-11-06 10:06 -0500
                Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2019-11-06 17:00 +0100
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 17:47 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 17:54 +0100
                Re: two's complement idea Bo Persson <bo@bo-persson.se> - 2019-11-06 20:00 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 20:13 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-06 20:44 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-06 20:36 +0100
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 22:54 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-07 00:52 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-06 17:54 +0200
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 18:15 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 18:33 +0100
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-06 10:55 -0800
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 20:15 +0100
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 20:53 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-06 22:25 +0200
                Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-06 23:05 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-07 10:23 +0200
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-06 22:20 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-06 22:12 +0200
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-11-09 06:24 -0800
                Re: two's complement idea Siri Cruise <chine.bleu@yahoo.com> - 2019-11-09 07:14 -0700
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-10 11:52 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-10 16:31 +0200
                Re: two's complement idea Manfred <noname@invalid.add> - 2019-11-10 19:02 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-11 12:08 +0200
                Re: two's complement idea scott@slp53.sl.home (Scott Lurndal) - 2019-11-11 13:59 +0000
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2019-11-11 17:09 +0200
                Re: two's complement idea Richard Damon <Richard@Damon-Family.org> - 2019-11-18 07:40 -0500
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-11-28 12:27 -0800
                Re: two's complement idea cdalten@gmail.com - 2020-01-24 05:39 -0800
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-01-24 17:53 +0200
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-24 17:31 +0000
              Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-05 21:48 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 07:08 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-06 09:30 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-06 09:57 +0100
        Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-05 09:02 -0800
          Re: two's complement idea scott@slp53.sl.home (Scott Lurndal) - 2019-11-05 17:15 +0000
            Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-05 10:19 -0800
          Re: two's complement idea Manfred <noname@invalid.add> - 2019-11-05 19:31 +0100
            Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-05 11:55 -0800
              Re: two's complement idea Manfred <noname@add.invalid> - 2019-11-05 22:48 +0100
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-05 15:49 -0800
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-11-09 06:13 -0800
                Re: two's complement idea Manfred <noname@invalid.add> - 2019-11-10 18:37 +0100
            Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-05 23:14 +0100
          Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-05 23:00 +0100
            Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-06 05:26 -0800
              Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-06 21:50 +0100
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-08 02:01 -0800
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-08 14:03 +0100
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-08 12:08 -0800
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-10 13:17 +0100
                Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2019-11-10 14:37 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-10 17:08 +0100
                Re: two's complement idea Manfred <noname@invalid.add> - 2019-11-10 18:34 +0100
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2019-11-11 07:48 +1300
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-10 21:31 +0100
  Re: two's complement idea Bo Persson <bo@bo-persson.se> - 2019-11-04 23:55 +0100
    Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-05 10:32 +0100
  Re: two's complement idea Siri Cruise <chine.bleu@yahoo.com> - 2019-11-04 19:55 -0700
    Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2019-11-05 05:52 +0100
      Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2019-11-05 18:17 +1300
      Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-11-09 05:55 -0800
        Re: two's complement idea Siri Cruise <chine.bleu@yahoo.com> - 2019-11-09 06:33 -0700
          Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-09 07:46 -0800
        Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-09 06:46 -0800
          Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-11-28 12:19 -0800
            Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2019-11-29 00:14 +0100
              Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-29 09:15 +0100
                Re: two's complement idea Bo Persson <bo@bo-persson.se> - 2019-11-29 10:58 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2019-11-29 12:49 +0100
              Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-12-07 07:53 -0800
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-12-07 08:22 -0800
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-10 20:44 -0800
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-10 23:44 -0800
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-14 07:08 -0800
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-14 08:42 -0800
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-21 02:09 -0800
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2020-01-21 05:14 -0800
                Re: two's complement idea Daniel <danielaparker@gmail.com> - 2020-01-21 13:08 -0800
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2020-01-22 00:07 -0500
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-21 23:21 -0800
                Re: two's complement idea Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-01-22 01:51 -0800
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-22 11:28 +0100
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2020-01-22 11:52 +0100
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-22 04:47 -0800
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-04-02 07:19 -0700
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2020-04-02 08:07 -0700
                Re: two's complement idea boltar@nowhere.org - 2020-01-21 16:44 +0000
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-21 20:01 +0000
                Re: two's complement idea boltar@nowhere.org - 2020-01-22 11:26 +0000
                Re: two's complement idea Christian Gollwitzer <auriocus@gmx.de> - 2020-01-22 20:04 +0100
                Re: two's complement idea Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-01-22 11:30 -0800
                Re: two's complement idea Chris Vine <chris@cvine--nospam--.freeserve.co.uk> - 2020-01-22 19:57 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-23 10:03 +1300
                Re: two's complement idea boltar@nowhere.org - 2020-01-23 09:24 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-24 07:29 +1300
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-23 10:03 +1300
                Re: two's complement idea "Fred. Zwarts" <F.Zwarts@KVI.nl> - 2020-01-23 10:09 +0100
                Re: two's complement idea boltar@nowhere.org - 2020-01-23 09:29 +0000
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-24 01:08 +0000
                Re: two's complement idea boltar@nowhere.org - 2020-01-24 12:27 +0000
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-24 01:06 +0000
                Re: two's complement idea Bo Persson <bo@bo-persson.se> - 2020-01-24 10:07 +0100
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-01-24 11:36 +0200
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-24 17:34 -0800
                Re: two's complement idea Siri Cruise <chine.bleu@yahoo.com> - 2020-01-24 17:57 -0800
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-24 12:19 +0000
                Re: two's complement idea Bo Persson <bo@bo-persson.se> - 2020-01-24 14:19 +0100
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-24 14:11 +0000
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-24 17:26 +0000
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-24 17:35 +0000
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-01-24 22:27 +0200
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2020-01-24 23:21 -0500
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-25 11:06 +1300
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-24 22:12 +0000
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2020-01-24 23:24 -0500
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-25 09:04 +0000
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-25 04:15 -0800
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-25 19:55 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-25 00:05 +0100
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-25 01:19 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-25 19:50 +1300
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-25 11:57 +0000
                Re: two's complement idea Chris Vine <chris@cvine--nospam--.freeserve.co.uk> - 2020-01-25 13:42 +0000
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-25 14:58 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-26 07:58 +1300
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-25 20:34 +0100
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-25 12:41 -0800
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-01-26 16:08 +0200
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-27 02:20 -0800
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-01-27 15:03 +0200
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-02-15 06:44 -0800
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-03-06 10:18 +0200
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-04-02 07:05 -0700
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-04-02 20:03 +0300
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-04-04 12:37 -0700
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-26 07:45 +1300
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-25 19:56 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-26 09:49 +1300
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-25 21:33 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-26 11:00 +1300
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-25 22:23 +0000
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-26 11:46 +1300
                Re: two's complement idea Paavo Helde <myfirstname@osa.pri.ee> - 2020-01-26 10:55 +0200
                Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2020-01-26 03:47 -0800
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-27 01:28 -0800
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-25 22:22 +0000
                Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2020-01-25 18:24 -0500
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-26 12:54 +0100
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-26 12:44 +0000
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-26 14:58 +0100
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-26 14:53 +0000
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-26 19:10 +0100
                Re: two's complement idea Robert Wessel <robertwessel2@yahoo.com> - 2020-01-26 13:20 -0600
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-26 20:51 +0000
                Re: two's complement idea Robert Wessel <robertwessel2@yahoo.com> - 2020-01-26 21:02 -0600
                Re: two's complement idea Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-01-26 19:06 -0800
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-27 18:50 +0000
                Re: two's complement idea Robert Wessel <robertwessel2@yahoo.com> - 2020-01-27 14:18 -0600
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-27 22:13 +0100
                Re: two's complement idea Bart <bc@freeuk.com> - 2020-01-27 21:38 +0000
                Re: two's complement idea Robert Wessel <robertwessel2@yahoo.com> - 2020-01-27 19:37 -0600
                Re: two's complement idea Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-01-27 19:15 -0800
                Re: two's complement idea "Fred. Zwarts" <F.Zwarts@KVI.nl> - 2020-01-28 11:45 +0100
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-27 16:31 +1300
                Re: two's complement idea Manfred <noname@add.invalid> - 2020-01-26 18:50 +0100
                Re: two's complement idea Jorgen Grahn <grahn+nntp@snipabacken.se> - 2020-01-26 18:57 +0000
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-26 20:46 +0100
                Re: two's complement idea Robert Wessel <robertwessel2@yahoo.com> - 2020-01-26 13:14 -0600
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-26 22:15 +0100
                Re: two's complement idea Robert Wessel <robertwessel2@yahoo.com> - 2020-01-27 21:06 -0600
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-28 13:08 +0100
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-27 01:50 -0800
                Re: two's complement idea Ian Collins <ian-news@hotmail.com> - 2020-01-27 08:21 +1300
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-25 20:14 +0100
                Re: two's complement idea David Brown <david.brown@hesbynett.no> - 2020-01-25 20:12 +0100
                Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-27 07:48 -0800
                Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2020-02-18 18:46 +0100
        Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-09 17:03 +0100
    Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-05 06:56 +0100
      Re: two's complement idea Christian Gollwitzer <auriocus@gmx.de> - 2019-11-05 08:24 +0100
        Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2019-11-05 08:35 +0100
        Re: two's complement idea Öö Tiib <ootiib@hot.ee> - 2019-11-04 23:36 -0800
          Re: two's complement idea James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-11-05 09:19 -0500
  Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2020-01-22 08:32 +0100
    Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2020-01-22 09:23 +0100
      Re: two's complement idea Bonita Montero <Bonita.Montero@gmail.com> - 2020-01-22 14:20 +0100
        Re: two's complement idea Chris Vine <chris@cvine--nospam--.freeserve.co.uk> - 2020-01-22 13:37 +0000
      Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-01-27 01:17 -0800
        Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2020-01-27 12:35 +0100
          Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-02-15 05:56 -0800
            Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2020-02-16 09:17 +0100
              Re: two's complement idea Richard Damon <Richard@Damon-Family.org> - 2020-02-21 19:35 -0500
                Re: two's complement idea "Alf P. Steinbach" <alf.p.steinbach+usenet@gmail.com> - 2020-02-22 07:01 +0100
              Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-02-24 08:22 -0800
      Re: two's complement idea cross@spitfire.i.gajendra.net (Dan Cross) - 2020-02-24 03:12 +0000
        Re: two's complement idea cdalten@gmail.com - 2020-02-24 05:53 -0800
        Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-02-25 07:56 -0800
          Re: two's complement idea cross@spitfire.i.gajendra.net (Dan Cross) - 2020-02-25 22:00 +0000
            Re: two's complement idea Tim Rentsch <tr.17687@z991.linuxsc.com> - 2020-02-25 16:14 -0800
              Re: two's complement idea cdalten@gmail.com - 2020-02-25 18:18 -0800
              Re: two's complement idea cross@spitfire.i.gajendra.net (Dan Cross) - 2020-02-26 02:22 +0000

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