Re: /internet

[Sylvain Pion <Sylvain.Pion@sophia.inria.fr>]

On Wed, Dec 16, 1998 at 05:34:47PM -0700, Jeffrey A Law wrote:
> [...] Though
> I believe in the case reassociating a series of multiplies we are safe.
>
> I challenge anyone to come up with a case where a reassociation of
> a * b * c * d  produces different results than ((a * b) * c) * d.

If you want that, you'd better first _prove_ that it works in every case.
But you won't be able to do so because it's false.

It might be true when the following both conditions are met:
- no intermediate overflow/underflow appears (nor denormalized numbers).
- the rounding mode is set to nearest.

I'd be interested in reading the proof in this case (if it's true).

Case if you have an intermediate overflow is easy:
DBL_MAX * DLB_MAX * DBL_MIN  gives you either Inf or DBL_MAX.
Case when rounding is set to +Infinity:
0.1 * 0.1 * -1.0  doesn't give you the same result, try it.

-- 
Sylvain