J3/05-153 Date: 4 Feb 2005 To: J3 From: John Reid Subject: Interpretation request re SPACING and RRSPACING NUMBER: F03/00xx TITLE: Denormal inputs to SPACING and RRSPACING KEYWORDS: denormal, intrinsic, SPACING, RRSPACING DEFECT TYPE: Erratum STATUS: J3 consideration in progress QUESTION: What results do SPACING and RRSPACING return if the value of X lies outside the model of 13.4, in particular if it is denormal? In the definition of EXPONENT, the words 'of the model representation for the value of X' appear; but in the definition of SPACING and RRSPACING, the words are 'for the model representation of X'. Was this difference intended? Is the intention to indicate that for SPACING and RRSPACING, the model is that of all reals with the same kind type parameter value as X? In the IEEE model, the spacing between any two adjacent denorms is equal to the smallest denorm. Is it intended that this value be returned by SPACING? ANSWER: The informal description refers to 'model numbers near the argument value', but the text does not reflect this. Edits are provided to correct this. Yes, the difference was intended. In both models, the lower bound on the exponent has a profound effect on the spacing of tiny values, so it is important that it be taken into account. It was intended to refer to the model for all the reals with the same kind type parameter value as X. Here is it the model of 13.4 that is involved, as the words in 13.4 make clear. If the argument value is a positive denorm, the model numbers near it are TINY(X) and 0. Their spacing is TINY(X). Edits are provided to make this intention clear. EDITS: Page and line numbers refer to J3/04-007. [347:22] Subclause 13.7.100, Result Value, line 2. Replace "the model representation of X." by "the value nearest to X in the model for real values whose kind type parameter is that of X; if there are two such values, the value of greater absolute value is taken." [353:9] Subclause 13.7.113, Result Value, line 2. Replace "the model representation of X." by "the value nearest to X in the model for real values whose kind type parameter is that of X; if there are two such values, the value of greater absolute value is taken." SUBMITTED BY: John Reid HISTORY: J3/05-153 at J3 meeting 171