Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.lang.c++ > #69652

Re: two's complement idea

Show all headers | View raw

On 08/11/2019 11:01, Öö Tiib wrote:
> On Wednesday, 6 November 2019 22:50:30 UTC+2, David Brown  wrote:
>> 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.)
> 
> Is it all very similar to issue like where compiler uses 80 bit 
> long double (as best supported by hardware) to do mid-way
> double arithmetics and so the end result does not saturate into
> INF or -INF on that platform but it does on other that uses
> 64 bit double all the way.
> 

Yes - and that is a real mess for standardisation and repeatability.
It's okay if you are not bothered about the portability and
repeatability of your floating point calculations, and are happy to
accept that an unrelated change in one part of your program can lead to
different results somewhere else just because it changed when floating
point registers get moved out into the stack.  If that's fine, you can
use "-ffast-math" or equivalent switches and tell your compiler it is
free to make such code.  (Personally, I use "-ffast-math" in my own code
- but it is not something everyone wants.)

I do not want that situation in integer code.  I fully expect the
compiler to generate identical code - equally efficient, equal results,
equal levels of static checking - whether I break a calculation into
multiple statements or have it all as one expression.  I want to make
the decisions about the arrangements based on the clarity of the code,
not on where I want the compiler to optimise or where I want it to
insert hidden range checks.

I am much happier with the function of
"-fsanitize=signed-integer-overflow" here - it generates more checks,
less efficient code, but the functionality is clear and consistent.
I'll use that when I am happy to take the performance hit in the name of
debugging code.

> I feel dealing with such issue" to be *lot* easier than dealing
> with utter undefined behavior (that all such examples are by
> current scripture). For me every solution is better than
> undefined behavior.

The whole point is that you /don't/ hit undefined behaviour.  Any time
your code attempts to execute something with undefined behaviour, it is
a bug in your code.  Tools (like sanitizers) that help you find the
undefined behaviour are good.  Static analysis can help too.  Once you
have your code correct, you are not doing anything undefined, and there
is no need for run-time checks that can't ever be triggered.

To me, undefined behaviour is /better/ than the alternatives for most
purposes.  It helps me write better and more correct code, and as a
bonus it is more efficient.

Maybe this is something that stems from my programming education - I was
taught in terms of specifications.  Any function has a specification
that gives its pre-conditions and its post-conditions.  The function
will assume the pre-conditions are valid, and establish the
post-conditions.  If you don't ensure you satisfy the pre-conditions
before calling the function, you have no write to expect any know
behaviour at all from the function.  This principle is known popularly
as "garbage in, garbage out".  It has been understood since the birth of
the programmable computer:

"""
On two occasions I have been asked, 'Pray, Mr. Babbage, if you put into
the machine wrong figures, will the right answers come out?' I am not
able rightly to apprehend the kind of confusion of ideas that could
provoke such a question.
"""

If you want to say that some programmers don't know that integer
overflow is undefined behaviour, and think it wraps, then blame the way
C and C++ is taught and what the books say, and do something about that
- don't try to dumb down and water out the language.

> 
>> 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.
> 
> I have looked and measured its actual impact quite a lot. My
> thinking of it (is surely biased but it) revolves around handful of
> points.
> 
> 1) It is about default behavior, in most code its efficiency does
> not matter and for where it matters there indeed *must* be
> alternatives. 

C++ (and C) are often chosen because of their efficiency.  If you start
adding run-time tests everywhere, you lose that.  Why would you then use
C and C++ at all?  If you want extra safety and are willing to pay the
efficiency price, there are other languages to choose from - such as
Java or C#.  When you choose to program in C or C++, you are accepting a
responsibility to program carefully and correctly.  You are picking a
language that trusts the programmer.  Why would you then want the
language or compiler to tell you "I /know/ you claim to be a good
programmer who knows the language and codes carefully - but I don't
believe you, and I'm going to nanny you all the way" ?

And once you start saying "C++ programmers can't be trusted to write
expressions that don't overflow", where do you stop?  Can you trust them
to use pointers, or do you want run-time checks on all uses of pointers?
 Can you trust them to use arrays?  Function pointers?  Memory
allocation?  Multi-threading?  There are many, many causes of faults and
bugs in C++ programs that are going to turn up a lot more often than
integer overflows (at least in the 32-bit world - most calculations
don't come close to that limit).

> 
> 2) Efficiency of sub-steps of processing usually does matter
> where we intensively process lot of different data. With lot of data
> we do hit memory latency. Processing has been for decades so
> much cheaper that it can be worth to reduce memory latency
> problems by adding even more processing. For example 1:4
> uncompressing is faster than copy. 
> Note: it is ultra rare case where speed of memcpy is our actual
> bottleneck and not stupidity of copying same data over and 
> over too lot or even copying it at all. Same is with processing
> same thing pointlessly over and over.
> 
> 3) World evolves. The Swift, Rust, Go, and D communities
> already ask for hardware support for trapping integer
> conversions and trapping arithmetic. People like the languages.
> If hardware starts to support it better then C++ will seem
> backwards without convenient ways to use trapping integers
> in production code.

I have nothing against using trapping integer arithmetic in cases where
it is useful.  But it should only be as an active choice - either by
choosing special types in the code, or by enabling debug options in the
tools.

And hardware-assisted trapping cannot reach the efficiency of having
overflow as undefined behaviour, or even of wrapping, precisely for the
reasons I gave above about optimising "x + 1 - 1".

>  
> 4) Compilers will evolve. What happened to "register" or
> "inline"? Same can happen with usage of current "assume
> that it does not overflow" operations. Just make those not 
> default but performance optimizations like register and
> inline.   
> 
>>>>> 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!).
> 
> It is not that. We see wrapping and saturating is used rarely.

And thus it should be written explicitly, with types that have names.
Symbol combinations are easily mixed up and forgotten, especially if
they are rarely used.

One option - which could easily be implemented in C++ of today - would
be to write "x + wrapping + y" as a wrapping addition operator.

> Also wrapping is on half of cases used without need where
> it can confuse like "for (unsigned u = 10; u < 11; --u)".

That is an example of well-defined behaviour that is void of meaning.

> There will not be lot of mixed usages, just sometimes.    
> 
>> 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 saturating type perhaps has to be separate type indeed. It
> will have "magical" values and so needs separate protection.
> On rest of cases operators feel to be best. About too implicit
> conversions ... it is another source of hard-to-notice defects. 
> 

I would be careful about providing implicit conversions.

>> That also has the advantage that it can be done today, with current C++.
> 
> Life has shown that library features (or even worse "debugging tools")
> as opposed to language features will be adopted slowly by programmers
> and the compiler writers are even slower to start thinking in correct
> direction. 
> 

Life has shown that library features are precisely how C++ has evolved
in the last decade or two - language features have mostly been added in
order to make library features safer to use, easier to use, more
efficient, or easier to implement.  The next big leap for the C++
language - metaclasses - is precisely so that we can write libraries
that handle things that would previously need language changes.

Back to comp.lang.c++ | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

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

csiph-web