Re: The current proposal

[Paul Langevin <kkwweett@xxxxxxxxxx>]

>
> ----- Original Message ----- From: "Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>
> To: <stds-1788@xxxxxxxxxxxxxxxxx>
> Cc: "Kearfott Ralph B" <rbk5287@xxxxxxxxxxxxx>
> Sent: Monday, February 23, 2009 9:34 AM
> Subject: Re: The current proposal
>
>
> >I think the point Siegfreid makes is that the "ideal" mathematical
> >properties of the interval arithmetic should drive the implementation, not
> >the other way around.
> >
>

I agree.
Here is another example suggesting intervals of the form [a,b]  should be treated differerently when sign(a) and sign(b) are different or when they're equal.

Let x in [a,b], y in [c,d]. The product xy can be expected in [min ((ac)+,(ad)-,(bc)-,(bd)+), max ((ac)+,(ad)-,(bc)-,(bd)+)] where z+ = max (0,z) and z-=min (0,z)
The sum, as you mentionned, can be expected in [a+c, b+d].

When the signs of some boundaries are not equal, the product ceased to be distributive over the sum. For instance, let x in [-3, 2], y in [1, 6] and z in [-5, -4],

x (y + z) should be expected in [-3, 2] ( [1-5, 6-4]) = [-3,2] [-4,2] = [-8, 12] whereas
xy + xz should be expected in [-18, 12] + [-10,15] = [-28, 27]

On the other hand, when 0 is on the same side for a,b,c,d,e and f, no matter what form we take the result is the same. For instance, let u in [2, 3], v in [1,6] and w in [4,5]
u (v + w) and uv + uw  should both be expected in [10,33].

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