Unum II announcement

[John L Gustafson via Digitalmars-d]

On Wednesday, 24 February 2016 at 21:14:46 UTC, Ola Fosheim 
Grøstad wrote:
> On Wednesday, 24 February 2016 at 20:59:20 UTC, Timon Gehr 
> wrote:
>> Unums represent either single numbers or entire segments and 
>> those segments are not closed under the arithmetic operations, 
>> so without a efficient representation for sets, Unums are not 
>> useful as a more rigorous replacement for floating point 
>> numbers.
>
> I don't know if Unums are more useful than interval 
> arithmetics, but without the 2008 edition of IEEE754 you cannot 
> even represent interval arithmetics using floats AFAIK!
>
> The basic idea for Unums seems that you get an estimate of the 
> bounds and then recompute using higher precision or better 
> algorithm when necessary. With regular floats you just get a 
> noisy value and you need much more heavy machinery to know 
> whether you need to recompute using a better algorithm/higher 
> precision.

Not quite. What you describe is a very old idea. When unums lose 
accuracy, they become multiple unums in a row, or in a 
multidimensional volume (uboxes). The next calculation starts not 
from the "interval" described by the largest and smallest unum, 
but from each unum in the set; the results are then combined as a 
set union, which leads to bounds that grow linearly instead of 
exponentially.