quad precision question

[nealgacray.com]

> I guess I should have phrased my question better.  I know why the 
> RS6000 and SGI numbers are different from HP and Sun.  I wanted to
> know why the RS6000 and SGI numbers are different from each other.
> 
> >               radix digits minexponent maxexponent
> >
> > RS6000          2    106        -968        1024
> > SGI             2    107        -915        1023
> 
> Thanks.
> 
> --Stu Anderson
> _______________________________________________________________
> stu.andersonaboeing.com -- Mathematics and Computing Technology
> http://www.rt.cs.boeing.com/MEA/comp_math/sla/
> http://www.halcyon.com/stuander/
> Who speaks for Boeing?  Not me! 


I was involved in selecting the SGI model when I was with SGI.  
Here is my recollection.

IBM and SGI are very similar.  I do not know IBM's fine points.

The first choice was the choice of 107 bits accuracy
over IBM's 106.  The SGI arithmetic is indeed capable of
107 bits as is IBM's.  I *speculate* on this below.

The second choice was to have 2**maxexponent greater than
any representable finite number or (1-2**-radix)**maxexponent
not representable.

It was based on fine points about the standard's model.
The reason that 1023 was chosen, rather than 1024 was that
there is a hole at the upper end of the range, since the 
number (1-2**-radix)*2**1024 is not representable, though
SGI keeps (effectively) 107 bits of accuracy.  The hole is 
because the representation rule says that all numbers x are
represented as two 64 bit doubles, x1 and x2.  x1+x2 must not
round to Infinity when added.  

If you allow |x2| >= 2**-54 when |x1| is (1-2**-53)*2**1024 then
you can represent (1-2**-106)*2**1024, but not (1-2**-107)*2**1024.
There would be a performance penalty on SGI for this.  It also 
implies 106 bit accuracy for the interval [(1-2**-53)*2**1024, Inf). 
Perhaps this is why IBM made their choice.

Neal
---------
Neal Gaarder - Mathematics Libraries, Cray Inc.
nealgacray.com
Not speaking for Cray, Inc.