From: cilibrar@... (Rudi Cilibrasi)
Date: 2003-04-19T23:57:34+09:00
Subject: Re: Roundoff problem with Float and Marshal

I followed up with Guy on this, and it seems that my original test
script (on a single machine) passes fine on a Sun, which means that 
the patch is working for big-endian and little-endian seperately.  
Apparently sometimes it makes a mistake when comparing big-endian and
little-endian results.   I wonder, however, what causes it?  I can 
imagine one possibilities:

1) Math.exp, or some simpler floating-point operation, is behaving
differently on the two platforms, but only by a small amount.  In
other words, the "true" value of many operations is somewhere inbetween
two different actually representable doubles, and the FPU has to
arbitrarily decide which one to choose.  I believe the IEEE754 standard
specifies a tolerance that allows several different answers to be
compliant, so long as the results of the operations are reasonably close
to the correct value.

I am wondering if there is any general way to fix this?  I tend to think
this is beyond the scope of Ruby; we cannot guarantee that floating-point
programs running on different architectures that are started with the
same state will continue to evolve in the same way, because there is
always the chance for different round-off choices.  I think it is ok
if we can simply guarantee that moving a floating-point number across
the network or through a file will not change its value so long as the
architecture remains consistent, and also that the value will not change
much if the architecture changes.  I believe this is still the behavior
that is observed with this patch.

Rudi