Re: Doubt about formula transcription

robin wrote:
> robert.corbett@[EMAIL PROTECTED]
 wrote in message
> <7395644e-71a3-41c6-9b76-d65f7e86226e@[EMAIL PROTECTED]
>...
>> On Jun 27, 9:01 pm, "robin" <robi...@[EMAIL PROTECTED]
> wrote:
>>> "glen herrmannsfeldt" <g...@[EMAIL PROTECTED]
> wrote in message
>>>
>>> news:9NidnaRYwaLYNGbanZ2dnUVZ_o3inZ2d@[EMAIL PROTECTED]
>>>
>>>> Constant folding yes, but commutativity and associativity
>>>> are different.   (Especially on Cray machines where
>>>> A*B wasn't always equal to B*A, as stories go.)
>>> And why would they be different?
>> The Cray-1 series did not compute all of the trailing bits of
>> a floating-point product.  On the first Cray-1's, the bits
>> chosen were not symmetric and so the multiplication was not
>> commutative.  On the Cray-1s and later machines, the bits chosen
>> were commutative.  The advantages of not computing some of the
>> product bits were that the machine was cheaper to build (though
>> hardly cheap) and the multiplication instruction was faster.
> 
> 
> Any fool can build hardware that omits some of the product bits
> and say it's faster.
> 
> Were these different bits visible in the same precision as
> the operands, or were they the extended bits?
> (i.e., if the operands were n bits, were the upper n bits of the product
> correct, or were they the lower n bits that were incorrect?)
> 
> If the upper n bits of product were incorrect, you'd have to say that
the
> multiplier was broken.
> 
> 
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.  Would you describe a problem that you think is
interesting and significant that requires 48 bit accuracy
and fails if some products are off a bit or two.

Dick Hendrickson