Re: CRAY

"Dick Hendrickson" <dick.hendrickson@[EMAIL PROTECTED]
> wrote in message
news:F7nhk.130370$102.76643@[EMAIL PROTECTED]
> robin wrote:
> > "glen herrmannsfeldt" <gah@[EMAIL PROTECTED]
> wrote in message
> > news:P7ednZuBjMKrsRzVnZ2dnUVZ_gWdnZ2d@[EMAIL PROTECTED]
> >> robin wrote:
> >>
> >> (snip, someone wrote)
> >>
> >>>> When you multiply two 48 bit values (the Cray
> >>>> mantissa) you potentially get a 96 bit product.  The
> >>>> Cray hardware only computed about 60 bits in the product
> >>>> and added in a couple of "statistical" round to make up
> >>>> for the missing 30 or so bits.  This was then trimmed down
> >>>> to 48 bits.  It was accurate to 48 bits in the majority
> >>>> of cases.  I think it was always accurate to 46 or so
> >>>> bits.  Whether that is foolish or broken is a judgment
> >>>> call.
> >>> I'd call it broken.
> >>> Makes it difficult to get integer results.
> >>> Makes it difficult to get a double precision product.
> >> There are many algorithms where the result depends on the
> >> average precision of a large number of steps, and many of
> >> those were popular on Cray machines.
> >
> > Multiplication produces an exact result.  Always.
> > That exact result can be truncated or rounded when
> > the number of product bits exceed requirements.
> > It is unlike division, which may not produce an exact result.
> >
> >>  When the choice was
> >> to run the problem, or nothing at all, one took what was
> >> available.   The Cray-1 single precision was 64 bits with,
> >> I believe, 15 for exponent.  I believe double precision
> >> in software, probably to satisfy the Fortran standard.
> >
> > As I said, having a wrong result for single precision
> > makes it difficult to obtain double precision result.
> >
> >
> Difficult, but not particularly hard.

But it didn't use the single precision float multplier
as a starting point!!  Obviously too difficult,
which was my point!

>  The Cray double
> precision multiply (done in software) broke up the 96
> bit mantissas into four 24 bit integers, did all of the
> cross multiplies to produce a series of exact 48 bit
> intermediate values.  A few tedious adds, ****fts and
> masks produced a 96 bit result which was then combined
> with the separately computed exponent.  My recollection
> is that it took 10 or 20 times as long as a single
> precision multiply.