Re: real.c fails floating-point tests

[Brad Lucier <lucier at math dot purdue dot edu>]

Re:

> > Previously the REAL_VALUE_TYPE could not contain auxiliary
> > information, because often it was actually just emulating a host computer
> > double.  If you have removed that restriction then you can put various
> > other items into the data structure and then it looks like it would be
> > simple to make the 160-bit precision follow some arithmetic rules that
> > are easier to analyze and test.
> 
> I definitely agree with this analysis. High precision is never an adequate
> susbtitute for well defined axiomatic properties when it comes to fpt.

"High precision" *is* an axiomatic property; and if the precision is high
enough then you get the right target answer, at least for large enough
intermediate precisions and round-to-nearest, as I pointed out in

http://gcc.gnu.org/ml/gcc/2002-10/msg01051.html

I think the categorization of goals and strategies in that e-mail is
useful; it seems that Steve wants to use Strategy 1 and Richard wants
to use Strategy 2; either can work with round-to-nearest, which I
called Goal A.  If we ever want to implement directed rounding in real.c,
then only Steve's strategy (Strategy 1) will work.

Brad