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