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Groups > comp.lang.c > #11342

Re: is the < operator transitive?

From James Kuyper <jameskuyper@verizon.net>
Newsgroups comp.lang.c
Subject Re: is the < operator transitive?
Date 2011-10-07 15:36 -0400
Organization A noiseless patient Spider
Message-ID <4E8F54C9.5080009@verizon.net> (permalink)
References <4e8f3298$0$23280$426a74cc@news.free.fr>

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On 10/07/2011 01:10 PM, Francois Grieu wrote:
> Is it certain that  ( a<b && b<c && !(a<c) )  is 0?

No.

> First assume that each of  a b c  is a constant
> per ISO/IEC 9899:1999 6.4.4 ?

None of the counterexamples  that I was able to come up with could be
demonstrated using constants, since C constants cannot be negative (-1
is a unary expression, not a constant), or have pointer type, be NaNs,
or have a trap representation.

> If not, what about a counterexample?

For pointer types the behavior is undefined unless all three pointers
point into or one past the end of the same array object.

Any relation involving a NaN is required to have a value of false.

    #include <math.h>

    double a = 1.0;
    double b = nan();
    double c = 2.0;

Another type of counter-example involves expressions where the usual
arithmetic conversions (6.3.1.8p1) result in the same variable being
converted to two different values in the two different places where it
occur in that expression:

   unsigned long a = 98765UL;
   int b = -12345;
   short c = 1;

The key here is that in a<b, unsigned long has greater rank than long.
As a result, the usual arithmetic conversions (6.3.1.8p1) call for b to
be converted to unsigned long, with the resulting value of
ULLONG_MAX-12344, which is guaranteed to be greater than 98765UL. The
same conversion occurs in a<c, but since c is positive, the conversion
doesn't change it's value. No such conversion occurs in b<c.

> How far can we extend (or shrink) the kind of things
> that  a b c  can be for this to hold?
>
> In particular, what about unitialized variable such as
> 
> int foo(void) {
>    {
>    unsigned a,b,c;
>    return a<b && b<c && !(a<c);

An uninitialized object may contain a trap representation. If that's the
case, attempting to read it will render the behavior undefined. When the
behavior is undefined, then anything is permitted by the standard. foo()
could return 1, or 0, or -3.5, or "You did it wrong". Your program could
also abort(), or get stuck in an infinite loop, or send hate mail to
your boss.

>    }
> 
> What if unsigned is changed to int? To double?

The behavior of foo() may be undefined when using any type which is
allowed to have a trap representation. The types which are not allowed
to trap include char, unsigned char, signed char, and the exact-width
types from <stdint.h>.

However, even if you use only those types for a, b, and c, the value you
get by reading an uninitialized variable is unspecified; it's not
required to be the same unspecified value each time you read it.
Therefore, foo() could still return either 0 or 1.

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Thread

is the < operator transitive? Francois Grieu <fgrieu@gmail.com> - 2011-10-07 19:10 +0200
  Re: is the < operator transitive? Robert Wessel <robertwessel2@yahoo.com> - 2011-10-07 13:44 -0500
  Re: is the < operator transitive? Edward Rutherford <edward.p.rutherford79@REMOVETHIS.gmail.com> - 2011-10-07 18:50 +0000
    Re: is the < operator transitive? Keith Thompson <kst-u@mib.org> - 2011-10-07 12:42 -0700
      Re: is the < operator transitive? Edward Rutherford <edward.p.rutherford79@REMOVETHIS.gmail.com> - 2011-10-07 20:23 +0000
        Re: is the < operator transitive? Patrick Scheible <kkt@zipcon.net> - 2011-10-07 14:29 -0700
        Re: is the < operator transitive? Keith Thompson <kst-u@mib.org> - 2011-10-07 16:49 -0700
          Re: is the < operator transitive? Patrick Scheible <kkt@zipcon.net> - 2011-10-07 19:19 -0700
        Re: is the < operator transitive? Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-10-08 09:57 -0400
    Re: is the < operator transitive? "BartC" <bc@freeuk.com> - 2011-10-08 13:17 +0100
      Re: is the < operator transitive? Harald van Dijk <truedfx@gmail.com> - 2011-10-08 06:06 -0700
        Re: is the < operator transitive? "BartC" <bc@freeuk.com> - 2011-10-08 14:48 +0100
          Re: is the < operator transitive? Harald van Dijk <truedfx@gmail.com> - 2011-10-08 07:18 -0700
          Re: is the < operator transitive? "BartC" <bc@freeuk.com> - 2011-10-08 15:19 +0100
  Re: is the < operator transitive? Edward Rutherford <edward.p.rutherford79@REMOVETHIS.gmail.com> - 2011-10-07 18:50 +0000
    Re: is the < operator transitive? jacob navia <jacob@spamsink.net> - 2011-10-07 21:23 +0200
      Re: is the < operator transitive? Edward Rutherford <edward.p.rutherford79@REMOVETHIS.gmail.com> - 2011-10-07 20:24 +0000
        Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-07 16:40 -0400
          Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-07 23:12 +0100
            Re: is the < operator transitive? Harald van Dijk <truedfx@gmail.com> - 2011-10-07 15:28 -0700
              Re: is the < operator transitive? Harald van Dijk <truedfx@gmail.com> - 2011-10-07 15:31 -0700
              Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-07 23:36 +0100
                Re: is the < operator transitive? Patrick Scheible <kkt@zipcon.net> - 2011-10-07 16:18 -0700
                Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-08 10:32 +0100
            Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-07 18:30 -0400
              Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-08 00:21 +0100
                Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-07 21:33 -0400
                Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-08 10:45 +0100
                Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-08 14:02 -0400
                Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-08 21:49 +0100
                Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-08 17:17 -0400
                Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-08 22:59 +0100
                Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-08 21:33 -0400
                Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-09 09:09 +0100
                Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-09 07:00 -0400
                Re: is the < operator transitive? "BartC" <bc@freeuk.com> - 2011-10-09 01:12 +0100
                Re: is the < operator transitive? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-10-09 08:55 +0100
            Re: is the < operator transitive? Robert Wessel <robertwessel2@yahoo.com> - 2011-10-07 18:16 -0500
              Re: is the < operator transitive? David Thompson <dave.thompson2@verizon.net> - 2011-10-18 02:03 -0400
                Re: is the < operator transitive? Robert Wessel <robertwessel2@yahoo.com> - 2011-10-20 18:03 -0500
        Re: is the < operator transitive? Keith Thompson <kst-u@mib.org> - 2011-10-07 16:50 -0700
    Re: is the < operator transitive? "io_x" <a@b.c.invalid> - 2011-10-09 11:00 +0200
      Re: is the < operator transitive? Willem <willem@toad.stack.nl> - 2011-10-09 09:42 +0000
        Re: is the < operator transitive? Ike Naar <ike@sverige.freeshell.org> - 2011-10-09 12:20 +0000
          Re: is the < operator transitive? Willem <willem@toad.stack.nl> - 2011-10-09 12:40 +0000
            Re: is the < operator transitive? Ike Naar <ike@sverige.freeshell.org> - 2011-10-09 12:54 +0000
              Re: is the < operator transitive? Willem <willem@toad.stack.nl> - 2011-10-09 13:04 +0000
            Re: is the < operator transitive? "BartC" <bc@freeuk.com> - 2011-10-09 15:34 +0100
              Re: is the < operator transitive? Willem <willem@toad.stack.nl> - 2011-10-09 15:08 +0000
            Re: is the < operator transitive? Robert Wessel <robertwessel2@yahoo.com> - 2011-10-09 12:14 -0500
  Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-07 15:36 -0400
    Re: is the < operator transitive? Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-10-07 20:00 -0400
      Re: is the < operator transitive? James Kuyper <jameskuyper@verizon.net> - 2011-10-07 21:38 -0400
      Re: is the < operator transitive? Francois Grieu <fgrieu@gmail.com> - 2011-10-09 21:40 +0200
        Re: is the < operator transitive? Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-10-09 16:34 -0400
          Re: is the < operator transitive? Francois Grieu <fgrieu@gmail.com> - 2011-10-11 14:08 +0200
          Re: is the < operator transitive? Tim Rentsch <txr@alumni.caltech.edu> - 2012-01-24 16:14 -0800

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