the "set paradigm" is harmful
Baker Kearfott wrote:
> I see several possibilities of accommodating midpoint-radius
> representations in the standard. One might be to simply
> specify two representations for intervals, and specify
> conversion between the two. (That might be the simplest way.)
> ...
> There is another representation of intervals in use to
> avoid having to change the rounding mode: ?-inf,supÙ.
> However, we may be able to accommodate that representation
> within the ?inf,supÙ representation by "as if" wording.
There is a big difference between the two uses of "representation".
InfSup and MidRad have different arithmetic properties and do not
cover the same set of floating-point numbers even when the same
precision (and radix) is used for all four components. The two
forms of InfSup (one with inverted sign for Inf) are completely
equivalent however. In 754-2008 there are two different decimal
encodings, with different implementation properties, but they are
completely equivalent in terms of the finite set of represented
floating-point values, as well as all arithmetic properties.
Chenyi Hu wrote:
> An interval can be represented in two ways in the IEEE-1788 standard.
No, it can't, because of the distinction I pointed out above. What is
possible is to define TWO KINDS of interval, each with its own rules,
and with defined conversions between them.
Whether we want to go down this road is a different issue, and is
certainly worthy of a motion.
Michel.
Sent: 2009-02-10 16:05:27 UTC