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Vincent On 4 Jan 2012, at 13:08, Vincent Lefevre wrote: > Sorry, I'm quite late in the discussion... > On 2011-12-14 15:37:26 -0800, Dan Zuras Intervals wrote: >> If our compiler people do not object, I think this is an >> excellent idea. The use of "type" as an abstraction & >> "format" as the layout in memory is more in keeping with >> the colloquial use of these words. Therefore, more clear >> to our users. > > Well, in languages, the "type" notion carries more than an abstraction > and even the layout in memory. For instance, in C, you have two > different types "int" and "long", and they are different even if > they have the same properties (same width and so on). > > One needs to be very careful here. For instance, what if you have > an interval encoded by (inf,sup) and another one (-inf,sup), with > the same abstraction (Level 3 is also the same). Would you consider > that since the abstraction is the same, their type (in P1788) is > also the same? If yes, would you allow operations between them? Late, but well asked. I have tried to address this in the Level 2 text. Here is the current, pretty rough, version. IGNORE everything from 6.7 onward. The key subclauses for the question you ask are 6.1 to 6.3. See especially the Example in 6.3.1. My answer to your (inf,sup) question is that they would normally be different types. A silly addendum to this is: However, a weird implementation could treat them as the same type T. It would have to have some way to know which mode of storage was being used for each particular datum. Then the Level 3 pairs of, say binary64, numbers (2,3) and (-2,3) could both represent the Level 2 datum "[2,3] of type T" and would therefore be regarded as the same datum at Level 2, see end of 6.1 para 3. This might conceivably make sense if you had a 200-processor machine where (inf,sup) was more efficient on 100 of the processors, and (-inf,sup) was more efficient the other 100, and the compiler inserts code to flip the relevant sign bit whenever it sees a datum is flying from one kind of processor to the other...?? Vincent, you are just the person whom I should like to pick holes in my presentation. I look forward to your doing so. Regards John
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