Groups > comp.lang.java.programmer > #6313

Re: Arithmetic overflow checking

From	gordonb.3urm7@burditt.org (Gordon Burditt)
Subject	Re: Arithmetic overflow checking
Newsgroups	comp.lang.java.programmer, comp.lang.c
References	(6 earlier) <3797038f-22d1-40b2-8c12-60db5a0976b8@t5g2000yqj.googlegroups.com> <chine.bleu-F754B3.02470710072011@news.eternal-september.org> <289ad570-65fc-49d8-9cc8-1f15d13ff3e3@gv8g2000vbb.googlegroups.com> <_bednSTX_oyqDbvTnZ2dnUVZ7radnZ2d@brightview.co.uk> <65991dc2-9acf-4867-b54a-8569b9683320@l37g2000yqd.googlegroups.com>
Message-ID	<JLWdnVqh_ZZrobrTnZ2dnUVZ_gSdnZ2d@posted.internetamerica> (permalink)
Date	2011-07-20 15:39 -0500

Cross-posted to 2 groups.

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>> Some software relies on overflows NOT triggering
>> anything - encryption software, for example.
>>
>> I think an interrupt every time THAT overflows
>> would have performance implications ;-)

I think there would be more than performance implications:  there
isn't any easy way, and certainly not portable way, to tell
specifically where the overflow happened so it can be ignored.
Aborting the program certainly will have (infinite) performance
implications.

> In C and other languages integer values are used for two
> things:
> 
>  1. Integer arithmetic ( + - * / )
>  2. Bit manipulation (shifts, masks, logical and, logical or)

Bit manipulation may include integer arithmetic also:  consider
checksums.  You can't tell the difference between (1) and (2)
by looking at the machine instructions.

> Bit manipulation works best without overflow detection.
> Your example of encryption software is IMHO a bit
> manipulation. I am interested in integer arithmetic with
> overflow checking.

It is often not possible to tell the difference between intended
bit manipulation and intended integer arithmetic.  (x*2) is sometimes
written as (x << 1), and under some circumstances *needs* an overflow
check.  One good indication that bit manipulation is intended seems
to be the use of an unsigned type in C.

> The programmer should decide, if he wants overflow checking.
> E.g. with a compiler switch, different types or pragmas.

A compiler switch alone would seem to be usually too coarse-grained.
I prefer a special operator/function which evaluates its arguments
with or without overflow checking.  E.g. 
	nooverflowcheck(checksum += buffer[i]);
although this has problems when there are function calls in the
expression.  I prefer that *both* nooverflowcheck() and overflowcheck()
exist, to override more global defaults of pragmas and compiler
options.

I can also see the possibility of an expression which needs over
a dozen pragmas in it.  Pragma may also be too coarse-grained
in some situations.

> In C unsigned integer types are defined to have no overflow
> checking, while signed integer types have an undefined
> behavior, when an overflow occurs. Gcc and clang have the
> flag -ftrapv, which checks the signed operations +, +, *, /
> and % for overflow.

GCC omits mention that -ftrapv checks signed / or % operations.
Does it really check that?  No mention is made of checking on unary
minus.  Also blatantly missing is any check on overflow during
conversions such as long to short or int to char.  Also, as others
have brought up, recent GCC versions break -ftrapv completely.

> Existing code should continue to work in the way it was
> defined (no overflow checking or undefined behavior), but
> the programmer should have the possibility to use overflow
> checking. 

>The CPUs and the compilers should be changed to
> allow cheap overflow checking (with zero cost when no
> overflow happens). 

I don't believe this (zero cost on no overflow) is possible.
Conventional wisdom says that conditional branches are
oh-so-horribly-expensive on modern CPUs.  I expect that conditional
traps are approximately equally expensive.  I expect a cost in the
pipeline even for a predicted-trap-not-taken actual trap-not-taken
overflow check, even if it's just failure to pipeline one more
instruction.

Also, you need a way to distinguish between overflow-trapping and
non-overflow-trapping instructions.  That seems to have several
possibilities:

(1) Use a check/don't check bit in the instruction.  Since
instruction-set designers try to use most of the bit combinations
effectively, this means pushing other instructions into a longer
format or out of the instruction set entirely.  Some code is going
to get longer.  Here you're hiding the cost in the instruction set
design.

(2) Use a status bit to control checking.  This implies that the
compiler has to insert instructions to turn the bit on and off, and
there's a need for saving and restoring the state of that bit.
Those instructions take memory and have a cost, even if it's the
opportunity cost of not being able to pipeline another instruction.

If there's a spare bit in an existing status register, this might
not require additional instructions in the instruction set, making
use of existing instructions to set and clear bits in the status
register, and save and restore it.  Existing interrupt handler
code may not need to be changed.

(3) Explicitly check for overflow.  This could be ftrapv, or a
conditional branch or call to a routine that raises a signal.  Note
that the conditional branch method loses information on exactly
where the overflow happened.  These instructions take memory and
time.


>This can IMHO only be done when an
> overflow raises an exception (or a signal in a language
> which does not support exceptions). An approach with an
> overflow flag will probably not allow zero overhead when
> no overflow occurs.

I'm not sure I believe in "zero overhead overflow checking".

> A new language (or a language variant) has other
> possibilities, since there is no backward compatibility.
> For my own language I want to use overflow checking.
> I use C as implementation language for interpreter and
> runtime library and as backend for the compiler. A such
> I only can support what C, the C compiler, the OS and
> the hardware allows me to do.

I think using longjmp out of a signal handler, currently undefined
behavior, could be made defined with restrictions for the overflow
signal.

> If languages like C, C++ and Java start to consider
> overflow checking as important, the CPU designers and
> compiler writers will be motivated to support it.
> 
>  Correct results are the most important thing you want
>  from an computer.

This depends on the application.  Rolling over and dying is
not always acceptable, *especially* in certain safety-critical
applications like flight control.  "scramming" a nuclear reactor
to shut it down is acceptable, but shutting down the cooling
system is not.  Shutting down an ISP's primary nameserver because
one query overflowed a statistics counter, or even something
important to the query, is not acceptable (but failing a single
query is).

> Sometimes errors are accepted, just to get maximum
> performance. Some people accept errors, because they want
> no exception. But this are corner cases, which should
> be handled as special.
 
>  Correct results (with overflow checking) should be
>  the normal case and everything else should be handled
>  as special case (e.g. a pragma to ignore overflow).

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Thread

Arithmetic overflow checking rop rop <rop049@gmail.com> - 2011-07-06 08:35 -0700
  Re: Arithmetic overflow checking markspace <-@.> - 2011-07-06 09:42 -0700
    Re: Arithmetic overflow checking stefan@nyniva.se - 2011-07-06 11:30 -0700
      Re: Arithmetic overflow checking markspace <-@.> - 2011-07-06 11:36 -0700
      Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-18 23:06 -0400
  Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-06 10:16 -0700
    Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-07 02:26 -0400
      Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-18 23:07 -0400
    Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-07 07:11 -0700
      Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-07 10:02 -0700
        Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-07 17:51 -0700
          Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-07 20:04 -0700
            Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-07 20:29 -0700
            Re: Arithmetic overflow checking rop rop <rop049@gmail.com> - 2011-07-08 15:52 -0700
              Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-18 23:12 -0400
            Re: Arithmetic overflow checking Tom Anderson <twic@urchin.earth.li> - 2011-07-09 10:31 +0100
              Re: Arithmetic overflow checking rop rop <rop049@gmail.com> - 2011-07-09 02:58 -0700
                Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-09 08:53 -0400
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-09 07:46 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-18 23:17 -0400
                Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-18 23:22 -0700
            Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-10 01:47 -0700
              Re: Arithmetic overflow checking China Blue Dolls <chine.bleu@yahoo.com> - 2011-07-10 02:47 -0700
                Re: Arithmetic overflow checking pete <pfiland@mindspring.com> - 2011-07-10 06:04 -0400
                Re: Arithmetic overflow checking China Blue Dolls <chine.bleu@yahoo.com> - 2011-07-10 03:29 -0700
                Re: Arithmetic overflow checking Phil Carmody <thefatphil_demunged@yahoo.co.uk> - 2011-07-10 20:52 +0300
                Re: Arithmetic overflow checking pete <pfiland@mindspring.com> - 2011-07-10 23:29 -0400
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-10 04:44 -0700
                Re: Arithmetic overflow checking "BartC" <bc@freeuk.com> - 2011-07-12 11:33 +0100
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 04:17 -0700
                Re: Arithmetic overflow checking "BartC" <bc@freeuk.com> - 2011-07-12 12:33 +0100
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 05:24 -0700
                Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-12 21:45 -0400
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-12 05:25 -0700
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 10:21 -0700
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 23:54 -0700
                Re: Arithmetic overflow checking "BartC" <bc@freeuk.com> - 2011-07-12 19:14 +0100
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-13 00:20 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-12 09:26 -0700
                Re: Arithmetic overflow checking Joe Pfeiffer <pfeiffer@cs.nmsu.edu> - 2011-07-12 10:52 -0600
                Re: Arithmetic overflow checking Keith Thompson <kst-u@mib.org> - 2011-07-12 10:48 -0700
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-12 16:54 +0000
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-12 11:35 -0700
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 10:13 -0700
                Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-12 21:53 -0400
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-14 23:41 -0500
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-15 10:56 -0700
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-15 21:27 -0500
                Re: Arithmetic overflow checking bugbear <bugbear@trim_papermule.co.uk_trim> - 2011-07-20 09:22 +0100
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-20 10:51 -0700
                Re: Arithmetic overflow checking gordonb.3urm7@burditt.org (Gordon Burditt) - 2011-07-20 15:39 -0500
                Re: Arithmetic overflow checking "BartC" <bc@freeuk.com> - 2011-07-21 12:12 +0100
                Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-10 09:28 -0400
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-10 06:52 -0700
                Re: Arithmetic overflow checking Keith Thompson <kst-u@mib.org> - 2011-07-10 14:47 -0700
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-14 23:07 -0500
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-10 12:25 -0400
              Re: Arithmetic overflow checking Robert Wessel <robertwessel2@yahoo.com> - 2011-07-10 10:47 -0500
              Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 07:58 -0700
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-11 10:48 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 14:40 -0700
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-11 14:54 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 15:55 -0700
                Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-11 21:51 -0400
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 21:31 -0700
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-11 23:16 -0700
                Re: Arithmetic overflow checking James Kuyper <jameskuyper@verizon.net> - 2011-07-12 06:28 -0400
                Re: Arithmetic overflow checking David Thompson <dave.thompson2@verizon.net> - 2011-07-24 22:13 -0400
                Re: Arithmetic overflow checking Lew Pitcher <lpitcher@teksavvy.com> - 2011-07-25 10:24 -0400
              Re: Arithmetic overflow checking "io_x" <a@b.c.invalid> - 2011-07-12 09:05 +0200
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 02:22 -0700
                Re: Arithmetic overflow checking "io_x" <a@b.c.invalid> - 2011-07-12 11:34 +0200
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-12 03:04 -0700
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-12 03:33 -0700
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-12 08:29 -0400
                Re: Arithmetic overflow checking "io_x" <a@b.c.invalid> - 2011-07-12 13:18 +0200
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-12 11:39 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-12 12:38 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-12 13:20 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-12 13:23 -0700
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-12 21:08 +0000
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-12 14:48 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-12 15:24 -0700
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-12 16:09 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-13 10:38 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-13 11:00 -0700
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-13 12:16 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-13 13:10 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-13 13:21 -0700
                Re: Arithmetic overflow checking Keith Thompson <kst-u@mib.org> - 2011-07-13 13:41 -0700
                Re: Arithmetic overflow checking Robert Wessel <robertwessel2@yahoo.com> - 2011-07-14 21:10 -0500
                Re: Arithmetic overflow checking "io_x" <a@b.c.invalid> - 2011-07-15 11:57 +0200
                Re: Arithmetic overflow checking Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-07-15 04:36 -0700
                Re: Arithmetic overflow checking tm <thomas.mertes@gmx.at> - 2011-07-13 00:52 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-13 07:45 -0700
          Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-08 00:30 -0400
            Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-08 01:29 -0700
              Re: Arithmetic overflow checking markspace <-@.> - 2011-07-08 07:38 -0700
                Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-08 20:40 -0400
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-08 18:17 -0700
                Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-08 19:49 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-08 22:26 -0700
                Re: Arithmetic overflow checking Peter Duniho <NpOeStPeAdM@NnOwSlPiAnMk.com> - 2011-07-08 17:42 -0700
            Re: Arithmetic overflow checking Tom Anderson <twic@urchin.earth.li> - 2011-07-09 10:21 +0100
            Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-10 10:53 -0400
              Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-10 18:07 +0000
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-10 11:29 -0700
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-10 19:22 +0000
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:40 -0400
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 23:06 +0000
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 19:38 -0400
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-22 00:27 -0400
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-22 13:00 +0000
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-10 17:17 -0700
          Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-08 10:23 -0700
            Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-08 19:30 -0400
              Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 08:04 -0700
            Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:43 -0400
          Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-15 00:28 -0500
      Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-18 23:09 -0400
    Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-15 00:14 -0500
      Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-15 07:00 -0700
        Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-15 08:09 -0700
          Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 22:07 -0400
        Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-15 23:29 -0500
          Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-15 22:26 -0700
            Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-16 00:32 -0500
              Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-16 11:00 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-16 11:15 -0700
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-16 15:41 -0500
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-16 23:18 +0000
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-17 00:30 -0500
          Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-16 08:39 -0400
            Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-16 10:33 -0700
              Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-16 15:51 -0500
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-17 08:46 -0700
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-18 07:03 -0500
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-18 06:21 -0700
            Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-16 15:43 -0500
              Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-17 09:50 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-17 08:15 -0700
                Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-18 01:12 -0400
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:50 -0400
                Re: Arithmetic overflow checking "MikeP" <mp011011@some.org> - 2011-07-18 06:56 -0500
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-18 19:26 -0400
              Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-18 15:03 -0700
            Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 22:16 -0400
              Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-20 22:25 -0400
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-21 08:50 -0400
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-21 07:37 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:52 -0400
              Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 12:19 +0000
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:54 -0400
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-21 14:46 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 18:10 -0400
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 23:22 +0000
                Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-21 21:47 -0400
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-23 10:15 -0400
          Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-16 10:46 -0700
            Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-16 11:13 -0700
          Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 22:09 -0400
            Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-20 21:01 -0700
            Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-21 07:05 -0300
              Re: Arithmetic overflow checking supercalifragilisticexpialadiamaticonormalizeringelimatisticantations <supercalifragilisticexpialadiamaticonormalizeringelimatisticantations@averylongandannoyingdomainname.com> - 2011-07-21 06:28 -0400
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-21 12:32 +0000
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:58 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-21 15:58 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 19:14 -0400
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-22 13:07 +0000
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-22 17:33 +0000
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-22 13:36 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-22 23:16 +0000
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-22 16:50 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-23 20:09 +0000
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 08:56 -0700
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-23 09:37 -0700
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-23 11:23 -0400
                Re: Arithmetic overflow checking supercalifragilisticexpialadiamaticonormalizeringelimatisticantations <supercalifragilisticexpialadiamaticonormalizeringelimatisticantations@averylongandannoyingdomainname.com> - 2011-07-23 12:04 -0400
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-23 14:45 -0400
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-23 11:51 -0700
                Re: Arithmetic overflow checking supercalifragilisticexpialadiamaticonormalizeringelimatisticantations <supercalifragilisticexpialadiamaticonormalizeringelimatisticantations@averylongandannoyingdomainname.com> - 2011-07-23 22:39 -0400
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-25 10:20 -0700
                Re: Arithmetic overflow checking supercalifragilisticexpialadiamaticonormalizeringelimatisticantations <supercalifragilisticexpialadiamaticonormalizeringelimatisticantations@averylongandannoyingdomainname.com> - 2011-07-25 13:29 -0400
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-25 13:35 -0400
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-23 09:39 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-23 21:09 +0000
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-23 21:24 +0000
              Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:57 -0400
          Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 22:12 -0400
        Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-21 06:41 -0300
          Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 16:38 -0400
  Re: Arithmetic overflow checking Wanja Gayk <brixomatic@yahoo.com> - 2011-07-06 22:28 +0200
    Re: Arithmetic overflow checking Wanja Gayk <brixomatic@yahoo.com> - 2011-07-06 22:30 +0200
    Re: Arithmetic overflow checking Tom Anderson <twic@urchin.earth.li> - 2011-07-06 22:32 +0100
      Re: Arithmetic overflow checking rop rop <rop049@gmail.com> - 2011-07-07 00:30 -0700
        Re: Arithmetic overflow checking Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-07-07 07:54 -0400
          Re: Arithmetic overflow checking rop rop <rop049@gmail.com> - 2011-07-07 05:36 -0700
          Re: Arithmetic overflow checking Daniele Futtorovic <da.futt.news@laposte-dot-net.invalid> - 2011-07-07 19:11 +0200
        Re: Arithmetic overflow checking Tom Anderson <twic@urchin.earth.li> - 2011-07-07 14:21 +0100
      Re: Arithmetic overflow checking Stanimir Stamenkov <s7an10@netscape.net> - 2011-07-09 16:34 +0300
  Re: Arithmetic overflow checking Roedy Green <see_website@mindprod.com.invalid> - 2011-07-06 22:41 -0700
    Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-07 14:34 -0700
      Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-07 14:53 -0700
        Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-07 17:12 -0700
          Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-07 17:29 -0700
            Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-08 10:27 -0700
              Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-08 13:15 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-19 20:54 -0400
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-19 18:07 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-19 21:31 -0400
                Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-20 07:36 -0300
                Re: Arithmetic overflow checking RedGrittyBrick <RedGrittyBrick@spamweary.invalid> - 2011-07-20 11:58 +0100
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-20 09:51 -0700
                Re: Arithmetic overflow checking RedGrittyBrick <RedGrittyBrick@spamweary.invalid> - 2011-07-21 12:11 +0100
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 12:43 +0000
                Re: Arithmetic overflow checking Tom McGlynn <taqmcglynn@googlemail.com> - 2011-07-21 07:15 -0700
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-21 07:35 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-21 15:38 +0000
                Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-21 09:03 -0700
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-21 12:00 -0700
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-22 17:16 +0000
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-23 11:28 -0400
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-23 21:03 +0000
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-23 22:55 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 09:16 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-24 10:40 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 10:54 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-24 11:09 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 12:53 -0700
                Re: Arithmetic overflow checking markspace <-@.> - 2011-07-24 15:15 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-24 15:41 -0700
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-25 03:21 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-25 00:56 -0700
                Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-25 07:03 -0300
                Re: Arithmetic overflow checking Thomas Richter <thor@math.tu-berlin.de> - 2011-07-26 09:43 +0200
                Re: Arithmetic overflow checking Andreas Leitgeb <avl@gamma.logic.tuwien.ac.at> - 2011-07-25 11:06 +0000
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-25 11:12 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-25 09:09 -0700
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-25 09:30 -0700
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-25 13:33 -0400
                Re: Arithmetic overflow checking "John B. Matthews" <nospam@nospam.invalid> - 2011-07-26 03:04 -0400
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-26 03:28 -0400
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-26 04:53 -0400
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-26 11:35 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-26 10:48 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 17:00 -0400
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 19:50 -0400
                Re: Arithmetic overflow checking Arved Sandstrom <asandstrom3minus1@eastlink.ca> - 2011-07-20 23:21 -0300
                Re: Arithmetic overflow checking Martin Gregorie <martin@address-in-sig.invalid> - 2011-07-21 12:52 +0000
                Re: Arithmetic overflow checking Henderson <h1@g1.f1> - 2011-07-21 15:58 -0400
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-21 17:06 -0400
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-20 14:35 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 18:22 -0400
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-21 14:54 -0700
            Re: Arithmetic overflow checking rop rop <rop049@gmail.com> - 2011-07-08 15:34 -0700
              Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 08:09 -0700
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-11 10:30 -0700
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-11 14:43 -0700
                Re: Arithmetic overflow checking Joshua Cranmer <Pidgeot18@verizon.invalid> - 2011-07-11 14:49 -0700
                Re: Arithmetic overflow checking Daniele Futtorovic <da.futt.news@laposte-dot-net.invalid> - 2011-07-17 17:14 +0200
                Re: Arithmetic overflow checking David Lamb <dalamb@cs.queensu.ca> - 2011-07-18 19:28 -0400
                Re: Arithmetic overflow checking Patricia Shanahan <pats@acm.org> - 2011-07-18 16:36 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-19 21:33 -0400
              Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-19 20:56 -0400
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-20 14:36 -0700
                Re: Arithmetic overflow checking Arne Vajhøj <arne@vajhoej.dk> - 2011-07-20 18:24 -0400
                Re: Arithmetic overflow checking Gene Wirchenko <genew@ocis.net> - 2011-07-21 14:55 -0700
  Re: Arithmetic overflow checking Roedy Green <see_website@mindprod.com.invalid> - 2011-07-06 22:43 -0700
  Re: Arithmetic overflow checking Jukka Lahtinen <jtfjdehf@hotmail.com.invalid> - 2011-07-07 14:56 +0300
  Re: Arithmetic overflow checking "Nasser M. Abbasi" <nma@12000.org> - 2011-07-08 21:27 -0700
    Re: Arithmetic overflow checking "Nasser M. Abbasi" <nma@12000.org> - 2011-07-08 21:57 -0700
    Re: Arithmetic overflow checking lewbloch <lewbloch@gmail.com> - 2011-07-09 12:16 -0700

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