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Vincent Lefevre wrote:
On 2010-10-14 17:43:19 +0200, Arnold Neumaier wrote:For me, the criterion distinguishing between good and bad representations is whether they can represent highly asymmetric intervals such as [1,1e6] or [-1,inf] without much overestimation.Why? If one uses valid mode, an implementation could still return the same result for f([-1,inf]) and f(Entire). So, requiring [-1,inf] to be representable exactly would be useless.
Of course, one can implement all operations to give the result Entire. Then requiring any interval besides Entire to be representable exactly would be useless.But I assumed that a reasonable standard would impose at least some sensible requirements on accuracy.
In particular, one can and should require that all arithmetic operations +-*/ preserve the sign of the optimal result. If this is not guaranteed by an implementation, I'd consider it useless as a general interval representation, and hence for stand-alone use.