Re: CRAY

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.  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.

Dick hendrickson