RE: Correction [P1788] Motion P-1788/M0000: Accept TheDocument -- Voting begins
June 2, 2014
In general, I vote For.
Many ma ny thanks to the editors, especially to John Pryce, and to
all the folks who nit-picked the text. It reads very well.
I have a few minor editorial suggestions, which will hopefully make
the text slightly easier to read for folks outside our standard
community (some of them are also related to the difference between
the British and US English).
p. iv, third bullet item: the word "algebraic" is used here -- and
in general in our community -- as indicating that we have a
composition of basic functions; in this sense, since, for example,
sin(x) is a basic function, this function is algebraic in this
sense. To a mathematicians, however, the notion of an algebraic
function has a different meaning: it is a function which is a
solution of a polynomial equation. From this viewpoint, a
polynomial or a square root are algebraic functions, while sin(x)
is not. I suggest deleting the word "algebraic" here, to avoid
confusion.
p. iv, section titled "The Fundamental Theorem", paragraph 1, last
line: we are so accustomed to the word "enclosure" but this word is
rarely used in mathematics outside our community, it may be
confusing without an explanation. Maybe explain instead of using
this word, e.g., "is guaranteed to produce a set that contains the
range of ..."
p. v, line 3: space missing before reference [9]
item (2), line 1: add "whether" after "check"; this may be British
English vs. US one :-), but I hope adding the word "whether" will
make it clearer
p. v, last paragraph, line 3: add a dash between IEEE and 754, as
is done in previous mentions of this standard
p. 1, first paragraph, last line: "owner" here is a slang word, may
be confusing with material ownership (like owners of copyright;
academic reviewers will be appalled that we consulted with owners
and not with developers). Maybe "developers"? "developers and
maintainers"?
p. 1, Section 1.2, last line: replace semicolon before "ability" by
a comma, since this is a continuation of a description of what is
lacking, not a new item
p. 2, Section 1.8, line 2: "von Neumann languages" is not a
frequently used term; computer science folks use "procedural
languages", maybe we should explain what it means; this is the
first time I hear this term, although Wikipedia proves that it is
legit: languages which are adjusted for von Neumann architecture
p. 4, Section 3.1, second paragraph, line 1: "after" is a confusing
Britishism; a US reader may mistakenly interpret this as "at a
later moment of time"; better something like "in accordance with"
paragraph 4, last line, and throughout the text: it is better to
repeat the paragraph sign (as it is done later in Section 3.2), or
write two paragraph signs followed by "8 and 9"; same comment: last
line of the last bullet item on p. 4
paragraph -2, last phrase, I would suggest adding "that" after
"implies" and placing a colon after "Note", to make it clearer to
US readers
p. 5, Section 3.2.2, first bullet item: "enquiry" is a British
spelling, may be unclear to many readers, US spelling is "inquiry"
p. 5, Section 3.3, centered description: since the words "Name of
... and version" are included in square brackets -- to indicate
that these words have to be replaces by the actual wording -- why
not add the same square brackets around the two other parts which
have to be replaced?
Section 3.4, (2)(d), line 2: this may be British vs. US, but I
suggest replacing "includes how" with "includes: How", to make it
clear that "includes" also covers the next question
general comment: to make it clearer, instead of "see paragraph
13.4?" which sounds like "shall we see this paragraph?" better
"text representations? (see paragraph 13.4). Same for all other
similarly formulated questions
(3) (k): also add paragraph sign before 13.3
p. 8, Section 4.2.13, line 2: replace "they" with "the types";
reason: "they" usually refers to the last mentioned, here last
mentioned are sets not types
p. 9, Section 4.2.30, this is explained later, but now it sounds as
if everywhere defined functions are now allowed; maybe something
like "functions (possibly partially defined)"
Section 4.2.40 and throughout the text: the notation R^0 is not
clear; in programming languages, we have indeed empty tuples, but
in mathematics, I am not even sure what it means, I do not remember
seeing it before, and I am still puzzled what is the precise
mathematical meaning of this is set theory; this needs to be
clarified. One possible clarification may come from the fact that
A^B in set theory also means the set of all the functions from B to
A. This is somewhat consistent with the usual Cartesian product
notation X^2 for the set of pairs, if we interpret 2 (as in
foundations of set theory) as the set consisting of two elements 0
and 1, then functions from {0,1} to X are simply pairs of elements
of X. From this viewpoint, 0 is an empty set. However, since 0 is
an empty set, X^0 makes no sense.
Maybe explicitly mention that by X^0, we will denote a 1-element
set consisting of a special object called an empty tuple.
p. 14, Section 6.3, pown() is mentioned but never explained, it is
only explained on p. 17, explain it here
p. 18 and throughout the text: to a mathematician, the notation
"dx" may be confusing, especially since in linearization-based
techniques, differentials are actually used; maybe Dx or d(x)? or
at least explain in a footnote that this is NOT a differential?
p. 21, Section 8.1, paragraph -4 (which is all in italics), line 2:
delete the word "result", it may be confusing since "result"
without qualifiers usually refers to the final outcome of the
computations, while here we talk about intermediate results
last paragraph of Section 8.2, Example, line 1: I suggest adding
"that" after "specify" -- or "the" before "execution" and "to"
after it, to make it clearer
p. 24, Section 9.4, second bullet, add paragraph sign before 12.11
p. 28, Section 10.2, line 2: Cartesian is usually capitalizes, see
Wikipedia
p. 29, Section 10.5, first paragraph, last line, add "operations"
after "these", to make the text easier to read
second paragraph, replace "any" (possibly meaning all?) with "a"
and add "programming" before "language", to make it clearer
Section 10.5.2: replace "value" with "values", otherwise it may be
confusingly implying that the two functions have the same value --
and then the reader will have to go back and re-read it after
seeing "respectively"
p. 30, last bullet of Section 10.5.5: delete comma after E. in E.g.
p. 31, Section 10.5.7, first paragraph, add ~ between "and" and
"y", to avoid "y" appearing as the only symbol on the second line
p. 31, Section 10.5.8, second paragraph, make [l,u]={... in double
dollar signs, to avoid it being split inside the set description
p. 37, Section 11.1: add paragraph signs before 11.3, 11.4, and
11.6
p. 46, Section 12.4, second bullet: "both" may be confusing, better
something like "all three zero values"
p. 47, Section 12.6.1, second paragraph, replace "one" with "an
implementation", for clarity; also, replace "in the next" with
"described in the next"
p. 50, Notes at the end of Section 12.10.1, last paragraph: "ulp"
is only defined later, so maybe place here a reference to the
corresponding paragraph 12.11.3
p. 51, Section 12.11.2 (a): instead of a somewhat confusing "-
sign", better "minus sign --", especially since that minus is in
different font from the actual minus later on the page; same with
(c)
p. 51, Section 12.11.4 (a) and (b): the description seems to be
indicate that there should be space after [ and space after ], but
no such space appears in the examples of p. 52, so maybe it is
better to delete these spaces, e.g, replace "[ empty ]" with
"[empty]", etc. ; same on p. 52, Section 12.11.5 (a)
p. 53, Section 12.11.6, paragraph -2, first line: add paragraph
sign before 13.2
p. 55, Section 12.12.7, second paragraph: what is former and what
is latter? I am confused
p. 56, first and second of last two bullets: why not replace "not
less" with a more widely used "greater than or equal to" and "not
greater than" with "less than or equal to"? Even LaTeX notations
are \ge and \le which indicates that these are indeed more widely
used
p. 57, Section 12.12.8: this is the only case when a minus-like
dash indicating different bullet items appears directly in front of
the formulas, making it somewhat confusing with minuses; maybe add
the words "the expression" between the bullet sign and the symbols?
or, in this particular case, make \item[$\bullet$] which will
replace the minus-like signs with actual bullet signs?
it may also be a good idea to add "of the function inf(x)" after
"value", to make it clearer
p. 60, Section 13.3, third line: replace dot before X with a
semicolon, and add "here" before X, since this is a continuation of
the previous phrase. Last line of this paragraph: add space before
Section 12.11.
p. 61, Section 13.4.1, line 2: the use of equality b = the radius
is unusual and may be confusing, why not something like "the radix
$b$, the number of digits in the significand (precision) $p$", etc.
last line: somewhat confusing: I suggest replacing "difference that
754" by "difference: 754" and then, on the next page, "expansion.
The" with "expansion, while the"
p. 63, Section 14.3, third paragraph: add paragraph sign before 6.5
p. 64, Section 14.4, third paragraph, line 2: there is an extra
closing parenthesis at the end of the triple
Note at the end: add "that" after "imply"; I do not know what is
"cohort information"
p. 65, Annex A, line 2: capitalize Clauses since they are numbered
here
p. 68, Section B.1, paragraph titled "Constant functions", line 3:
in the formula for the empty tuple, there should be space between
opening and closing parentheses (as later on in the same section)
p. 69, line 1: replace (32, 33) with a more traditional (32) and
(33)
same after formula (38): replace "(31, 32, 33)" with "(31), (32),
and (33)"
p. 72, Section C2.2, last paragraph: the word "any" may be
confusing, since "for any" is the same as "for all"; better "at
least one"
p. 73, Section C2.4.1, first bullet: need to mention that we
consider also partial functions; a mathematical function is usually
everywhere defined
p. 80, Section C3.7.1, first line: move the word "and" to the
previous line, there is space for it
p. 82, Section C4.4: add ~ between Level and 2 (making it Level~2),
to avoid moving 2 to the next line; same with Level 1 in the same
section
p. 83, Section 4.6: same comment about minus sign and [ empty ] as
for p. 51
p. 85, Section C4.7.5: same comment as for p. 57
also, in Section C4.7.6, the first line goes beyond the margin
p. 89, references:
Kulisch, either delete "vol. 33" or explain what series it is a
volume of, otherwise, it sounds like Vol. 33 of Kulisch's book
Moore's book: since everywhere else the city is not mentioned,
delete the city, keep only the publisher; maybe also add the 2009
second edition?
Nehmeir et al: looks like 7134 a volume of the journal, but it is
actually a volume of Springer Lecture Notes in Computer Science,
add this information
[13]: delete the ending "/main.html"; this was needed earlier when
the web was not yet stabilized and different systems used different
default endings; not it is not needed, the standard default ending
is index.html; I keep the identical file main.html because some
people still use the old URL :-(