Re: Doubt about formula transcription

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.