Date: Tuesday 05 Sep 2006 at 6:55 p.m. EDT (2006-09-05 22:55 GMT)
To: stds-754 <stds-754@xxxxxxxxxxxxxxxxx>,
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From: Michel Hack (1-914-784-7648) <hack@xxxxxxxxxxxxxx>
Subject: Clarifications for unqualified "number"
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(The following should be taken as an addition to my amendment proposing
that "floating-point number" be the universal inclusive term. If that
amended motion is defeated, it may still be useful as a starting point
for alternate replacements.)
The phrase "number of" (e.g. "number of digits") can be left alone.
From the following analysis it appears that we need a new glossary entry:
3.2.30bis Representable number: A floating-point number which
is not a NaN; a finite number
or Infinity.
Corrections to unqualified or misqualified uses of "number":
------------------------------------------------------------
3.2.15 line 1: number -> floating-point number
3.2.16 line 3: a number -> the entity
3.2.31 result: (usually representing a number) ->
(representing a floating-point number)
5.2, 1st bullet (describing triples): number -> finite number
5.3 in bullets: m is a number -> m is a finite number
c is a number -> c is a finite number
5.4 paragraph 2: Numbers -> Floating-point numbers
5.5 para 1 line 2: representable number -> finite number
(There are several instances of "number" in this paragraph,
but common English usage allows the omission of the qualifier
in subsequent instances.)
5.5 paragraph 5: Numbers -> Floating-point numbers
5.5 last para (after table 6), line -2:
valid numbers -> valid digit triplets
5.6 Table 7 title: representable number -> finite number
(For a moment I wondered whether "representable" was a synonym
for "finite", but in fact it is not; here it means "finite",
but for NextUp() it includes Infinities. Indeed, that should
go into the glossary -- but not all uses of "representable"
include infinity, so the corrections remain valid.)
6.2 para 1 line 1: number -> finite number
(Infinity is not subject to rounding, so "finite" is correct
here. Several uses of "representable number" in this section
do however include finite and infinite numbers (but not NaNs).
7.3.1 descriptions of minNum() and maxNum(), two instances:
the number if one operand is a number ->
the number if one operand is a representable number
7.3.2, para under quantize() bullet, line 1:
decimal operands x and y -> finite decimal numbers x and y
(This one is a bit awkward as there are two qualifications.
Note that Infinities and NaNs are described separately here.)
7.3.2, para under quantize() bullet, line 4: number -> finite number
7.5.1, para 1, line 3: numbers -> representable numbers
7.7.2 isCanonical(), line 1: number -> finite number
7.7.2 isCanonical(), line 3: numbers -> finite numbers
(Here floating-point numbers are explicitly broken up into
three subclasses, for clarity. It could simply say "if x
is a floating-point number that is canonical"...)
It might also be useful to refer to the glossary entry 3.2.4.
In fact, I think it should say "that has a canonical encoding"
instead of "that is canonical" --- mark this for Style Review.
7.10 d) 1) number -> representable number
7.10 d) 2) number -> representable number
7.11 para 1 line 1: numbers -> floating-point numbers
7.12 para 3 lines 2 and 3: numbers -> floating-point numbers
7.12 para 3 line4: the binary internal number ->
finite binary internal numbers
(This is a tough one. The first instance of "number" could have
been interpreted as applying to numeric components of the result
string, but that is actually false, as the exponent is supposed
to be given with decimal digits, and it is unclear what to do
about NaN payloads.)
7.12.1 para 1 line 3: numbers exactly -> finite numbers exactly
(A 2nd instance, "those numbers", inherits the qualifier implicitly.)
7.12.3 para 1 line 4: all decimal numbers -> all finite numbers
(I'm correcting my own correction, which had replaced "integers"
with "numbers", not thinking ahead.)
7.12.3 para 3: The context is numbers with a certain number of digits;
I don't believe this needs fixing.
7.12.3 next-to-last paragraph:
"The result format's values are the numbers representable
within that language specification."
numbers -> floating-point numbers
9.4 last sentence ("However nextAfter() ..."):
number x -> finite number x
9.5 last sentence ("However nextAfter() ..."):
number x -> finite number x
Annex C, para 1, line 2: exact number -> exact finite number
Annex D, para 3, line 1: precise number -> precise finite number
These are all instances I found in the Aug30 draft 1.1.8. Basically,
unqualified "number" becomes either "floating-point", "representable"
or "finite", as appropriate. This should remove ambiguities and also
provide the desired consistency.
(The analogy for qualified numbers including non-numbers still eludes
me. Can somebody help me out?)
Michel.
Sent: 2006-09-06 00:38:16 UTC