On 15.01.2015 12:22, Павел Кудан wrote:
But at any comparison mode arithmetic functions must return correct result.
This[1] article mentions the following: "There is, however, no consensus on interval division. In most expositions, interval division, X/Y , is only defined under the condition that 0 not be contained in Y." "Interval computation involving division has to be a compromise between information gain, computational efficiency, and program complexity." "For efficiency in computation, one may choose to represent sets of reals by a single closed interval. This can be simply achieved by replacing <a, b> / <c, d> by the least interval con- taining it. For the example above this would yield the inter- val <−∞, +∞>. Another choice would be to represent this quotient as a finite union of closed intervals, which would result in more information but also a greater cost in storage and processing for the operation. For the example above, this would yield <−∞, 0> ∪ <1, +∞>, which captures all infor- mation except for the openness of the right endpoint of the first interval." I'm not very familiar with interval arithmetics, but I do work with some algorithms where it could be useful and as such have been looking into it some. A policy for how to handle divisions seems like a good compromise if it's not too difficult to implement, ie current behavior vs throw in cases where the result should technically be a union of intervals. [1]: http://fab.cba.mit.edu/classes/S62.12/docs/Hickey_interval.pdf - Asbjørn