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Groups > comp.lang.c++ > #69613

Re: two's complement idea

From David Brown <david.brown@hesbynett.no>
Newsgroups comp.lang.c++
Subject Re: two's complement idea
Date 2019-11-06 21:50 +0100
Organization A noiseless patient Spider
Message-ID <qpvbmb$qkk$1@dont-email.me> (permalink)
References (2 earlier) <fb41f203-289c-40f5-b667-3866bcf4d351@googlegroups.com> <qprfhd$2r5$1@dont-email.me> <f79803ae-7c19-41d3-8f0c-e8dab4b29bca@googlegroups.com> <qpsrd4$tr3$1@dont-email.me> <d1487f24-9fad-4a77-8b11-9266200e733d@googlegroups.com>

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On 06/11/2019 14:26, Öö Tiib wrote:
> On Wednesday, 6 November 2019 00:00:16 UTC+2, David Brown  wrote:
>> On 05/11/2019 18:02, Öö Tiib wrote:
>>
>>> * trap (overflow that signals or throws) helps to find programming
>>>      errors most reliably and quickly
>>
>> Agreed (where "trap" could mean any kind of notification, exception,
>> error log, etc.).  But this is something you might only want during
>> debugging - it is of significant efficiency cost.
> 
> Indeed, majority of programming errors should be found during
> debugging.
> 
>>> I myself would like most current operators to trap on overflow
>>> (by raising SIGFPE or throwing std::overflow_error) both for
>>> signed and unsigned.
>>
>> I like that in debugging or finding problems - with tools like
>> sanitizers.  But I would not want that in normal code.  With this kind
>> of semantics, the compiler can't even simplify "x + 1 - 1" to "x".
> 
> It may be can or may be can not that depends on wording.
> I have not really thought it thru how to word the semantics
> precisely. The major purpose is to get errors when program
> is actually storing value into type where it does not fit (IOW
> really overflows).

It is possible to consider intermediary results as "infinite precision", 
which would give you that optimisation.  But how would you treat:

	x = x + 1;
	x = x - 1;

Would that cause a trap if x started at 0x3ffffff (assuming 32-bit int)? 
  What if "x" is held in a register rather than stored in memory?  There 
are lots of possible inconsistencies here.  (If it is any guide, gcc 
with "-ftrapv" optimises the two statements into "x".  With 
"-fsanitize=signed-integer-overflow", the single expression "x + 1 - 1" 
is simplified to "x", but the two statements lead to checks.)

Actually, it is worth looking at some gcc (or clang) generated code with 
-ftrapv and -fsanitize=signed-integer-overflow, perhaps with 
<https://gotbolt.org>, to see just host costly trapping semantics can 
be.  They are very far from negligible.

> 
> Analogical argument is that automatic storage overflow may
> not be trapped in principle since that would disallow optimizing
> recursions (that exhaust stack) into loops (that don't exhaust
> stack). The rules can be still likely worded in a way that
> implementation is allowed not to trap when it manages to get
> the job done without exhausting automatic storage somehow.
> 
>> I  much prefer to be able to write code in whatever way is simplest,
>> clearest or most maintainable for /me/, knowing that the compiler will
>> turn it into the most efficient results.  I intentionally use an
>> optimising compiler for C and C++ programming - when efficiency doesn't
>> matter, I'll program in Python where integers grow to avoid overflow.
> 
> I do almost same but I think of some of it slightly differently.
> Exact formula in programming is unfortunately more important
> than its clarity and intuitivity for reader.
> 
> For example we need to calculate average of two values of A and B.
> Mathematically there are lot of ways to calculate it and what is
> most intuitive may depend on meaning of A and B. Like:
> 1) (A + B) / 2
> 2) A / 2 + B / 2
> 3) A + (B - A) / 2
> 4) B + (A - B) / 2
> etc.
> But in software these can be very different expressions because
> these have different potential overflows and/or losses of
> accuracy. Until something helps to reduce that issue it is
> all about exactly that formula and period.

Yes.  It is up to the programmer to ensure the expression is written in 
a way that does not overflow or lose accuracy (at least, not more than 
you are willing to lose).  It is up to the compiler to pick the most 
efficient way to get the results requested from that expression, 
according to the rules of the language (and compiler flags) that 
determine the semantics of the expression.

> 
> As of efficiency It is anyway often uncertain until it is
> shown where the bottlenecks are. Also it can be often only
> shown by profiling products with realistic worst case loads
> of data and then it is usually small subset of code that can
> change overall efficiency.
> 
> Python I use less not because of its bad performance but
> because I have failed to use it scalably. Lot of of lIttle script
> programs is great, but when any of those starts to grow bigger
> then my productivity with those drops. For C++ same feels like
> nonsensically unimportant size. Somehow in C++ I have
> learned to separate different concerns and to abstract details
> away but not in Python.

That's fine.  Different languages have their advantages and 
disadvantages - and programmer preference is very subjective.

> 
>>> For wrap, snap and "compiler may assume that the operation
>>> does not overflow" cases I would like new operators.
>>>
>>
>> I suggested new types for the different behaviour, but of course it is
>> the operations that have the behaviour, not the types.  However, I can't
>> see a convenient way to specify overflow behaviour on operations - using
>> types is the best balance between flexibility and legible code.
> 
> I mean totally new "advanced" operators like  (A +% B) or (C +^ D).
> Yes there will be precedence (and may be associativity etc.)
> to define but it is business as usual and not some show-stopper
> issue. In some languages (like Swift) it is done and it seems to
> work fine.
> 

Ah, okay.  I think there is a big risk of confusion here, and for people 
to forget which operators do what.  (There is also the risk of 
accidentally writing smilies in your code!).

I am happier with the type-based solution, and simply refusing to 
compile combinations of types that don't make sense (like adding a 
wrapping type and a saturation type).  Undefined or unspecified 
behaviour types can be silently promoted to other more defined behaviour 
as needed.

That also has the advantage that it can be done today, with current C++.

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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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