Comparisons of incompatible types

[John Nagle]

On 12/7/2010 3:59 PM, Mark Wooding wrote:
>> Exactly one of
>> >
>> >  	a>  b
>> >  	a = b
>> >  	a<  b
>> >
>> >  is true, or an type exception must be raised.
> This will get the numerical people screaming.  Non-signalling NaNs are
> useful, and they don't obey these axioms.

    As a sometime numerical person, I've been screaming at this from
the other side.   The problem with comparing non-signalling NaNs is that
eventually, the program has to make a control flow decision, and it
may not make it correctly.

    I used to do dynamic simulation engines for animation.  I was
probably the first person to get ragdoll physics to work right,
back in 1996-1997.  In hard collisions, the program would get
floating point overflows, and I had to abort the interation, back
up, cut the time step down, and go forward again, until the time
step was small enough to allow stable integration.  This was
under Windows on x86, where it's possible, in a Windows-dependent
way, to catch signalling NaNs and turn the hardware exception into
a C++ exception.  If the computation just plowed ahead with
non-signalling NaNs, with a check at the end, it could go wrong
and produce bad results, because incorrect branches would be taken
and the final bogus results might not contain NaNs.

    I personally think that comparing NaN with numbers or other
NaNs should raise an exception.  There's no valid result for
such comparisons.

				John Nagle