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Dear colleagues, just before the discussion period for IEEE 1788 closes let me make a final remark. Interval arithmetic defined over the real and floating-point numbers leads to an exception-free calculus. I have said this repeatedly. But I feel it is not yet really understood. Developing interval arithmetic over the IEEE 754 numbers pulls all the IEEE 754 exceptions like -oo, +oo, NaN, +0, -0 into interval arithmetic where they do not occur and definitely are not needed. In IEEE 754 -oo and +oo are numbers. In interval arithmetic -oo and +oo are just used to describe unbounded sets of real numbers. But they are themselves not elements of these intervals. This is a subtle difference! Interval arithmetic is an arithmetic for connected sets of real numbers! If you take -oo and +oo as numbers, you have to study and provide operations like oo - oo, 0 times oo, oo/oo which in IEEE 754 are set to NaN. Then you have to define operations for NaNs and so on. All these operations do not occur in interval arithmetic if it is defined over the real and floating-point numbers. All this, of course, has to be proved. The proof can be found in my book Computer Arithmetic and Validity, in its second edition in sections 4.9 to 4.12, for instance. Let me still mention that the book was published before IEEE 1788 was founded. Best regards Ulrich -- Karlsruher Institut für Technologie (KIT) Institut für Angewandte und Numerische Mathematik D-76128 Karlsruhe, Germany Prof. Ulrich Kulisch KIT Distinguished Senior Fellow Telefon: +49 721 608-42680 Fax: +49 721 608-46679 E-Mail: ulrich.kulisch@xxxxxxx www.kit.edu www.math.kit.edu/ianm2/~kulisch/ KIT - Universität des Landes Baden-Württemberg und nationales Großforschungszentrum in der Helmholtz-Gesellschaft |