Subject: SC22 N2879 - Vote Summary on CD 10967-2 - Elementary Numeric Functions

From: William Rinehuls <[email-masked]>
Date: Fri, 29 Jan 1999 18:52:36 -0500 (EST)

____________________ beginning of title page _________________________
ISO/IEC JTC 1/SC22
Programming languages, their environments and system software interfaces
Secretariat:  U.S.A.  (ANSI)

ISO/IEC JTC 1/SC22
N2879

TITLE:
Summary of Voting on CD Ballot for CD 10967-2: Information technology -
Language Independent Arithmetic - Part 2: Elementary Numeric Functions
(Third CD Ballot)

DATE ASSIGNED:
1999-01-29

SOURCE:
Secretariat, ISO/IEC JTC 1/SC22

BACKWARD POINTER:
N/A

DOCUMENT TYPE:
Summary of Voting

PROJECT NUMBER:
JTC 1.22.33

STATUS:
WG11 is requested to prepare a Disposition of Comments Report and make a
recommendation on the further processing of the CD.

ACTION IDENTIFIER:
FYI

DUE DATE:
N/A

DISTRIBUTION:
Text

CROSS REFERENCE:
SC22 N2824

DISTRIBUTION FORM:
Def

Address reply to:
ISO/IEC JTC 1/SC22 Secretariat
William C. Rinehuls
8457 Rushing Creek Court
Springfield, VA 22153 USA
Telephone:  +1 (703) 912-9680
Fax:  +1 (703) 912-2973
email:  [email-masked]

__________ end of title page; beginning of overall summary __________

                      SUMMARY OF VOTING ON

Letter Ballot Reference No:  SC22 N2824
Circulated by:               JTC 1/SC22
Circulation Date:            1998-10-12
Closing Date:                1999-01-26

TITLE:  CD Ballot for CD 10967-2: Information technology - Language
        Independent Arithmetic - Part 2: Elementary Numeric Functions
        (Third CD Ballot)

----------------------------------------------------------------------
The following responses have been received on the subject of approval:

"P" Members supporting approval
      without comments                    8

"P" Members supporting approval
      with comments                       1

"P" Members not supporting approval       4

"P" Members abstaining                    2

"P" Members not voting                    7

"O" Members supporting approval
      without comment                     1

"O" Members supporting approval
      with comments                       1

-------------------------------------------------------------------
Secretariat Action:

WG11 is requested to prepare a Disposition of Comments Report and make a
recommendation on the further processing of the CD.

The comment accompanying the abstention vote from Denmark was:  "Lack of
Danish expertise."

The comments accompanying the negative votes from France, Germany, Japan
and the United Kingdom are attached, along with the comments accompanying
the affirmative votes from Sweden and the United States of America.

______________ end of overall summary; beginning of detail summary _____

                 ISO/IEC JTC1/SC22  LETTER BALLOT SUMMARY

PROJECT NO:    JTC 1.22.33

SUBJECT:  CD Ballot for CD 10967-2: Information technology - Language
          Independent Arithmetic - Part 2: Elementary Numeric Functions
          (Third CD Ballot)

Reference Document No:  N2824           Ballot Document No:  N2824
Circulation Date:       1998-10-12      Closing Date:  1999-01-26
                                                              
Circulated To: SC22 P, O, L             Circulated By: Secretariat

                  SUMMARY OF VOTING AND COMMENTS RECEIVED

                     Approve  Disapprove  Abstain Comments   Not Voting
'P' Members

Australia               (X)      ( )       ( )       ( )       ( )
Austria                 ( )      ( )       ( )       ( )       (X)
Belgium                 ( )      ( )       ( )       ( )       (X)
Brazil                  (X)      ( )       ( )       ( )       ( )    
Canada                  ( )      ( )       (X)       ( )       ( )
China                   (X)      ( )       ( )       ( )       ( )
Czech Republic          ( )      ( )       ( )       ( )       (X)
Denmark                 ( )      ( )       (X)       (X)       ( )
Egypt                   ( )      ( )       ( )       ( )       (X)
Finland                 (X)      ( )       ( )       ( )       ( )
France                  ( )      (X)       ( )       (X)       ( )
Germany                 ( )      (X)       ( )       (X)       ( )
Ireland                 (X)      ( )       ( )       ( )       ( )
Japan                   ( )      (X)       ( )       (X)       ( )
Netherlands             (X)      ( )       ( )       ( )       ( )
Norway                  (X)      ( )       ( )       ( )       ( )
Romania                 ( )      ( )       ( )       ( )       (X)
Russian Federation      ( )      ( )       ( )       ( )       (X)
Slovenia                ( )      ( )       ( )       ( )       (X)
UK                      ( )      (X)       ( )       (X)       ( )
Ukraine                 (X)      ( )       ( )       ( )       ( )
USA                     (X)      ( )       ( )       (X)       ( )

'O' Members Voting

Korea Republic          (X)      ( )       ( )       ( )       ( )
Sweden                  (X)      ( )       ( )       (X)       ( )

___ end of detail summary; beginning of France comments ____________

TITLE: Ballot comments on document ISO/IEC JTC1/SC22N2824 : CD 10967-2: Information technology - Language Independent Arithmetic - Part 2: Elementary Numeric Functions (Third CD Ballot) 

SOURCE: AFNOR

France votes NO to document SC22/WG11 CD 10967-2. The vote will be
reversed if the following comments are satisfactorily resolved.

Comment 1. 
Committee Draft subsection: C.4
Category: Request for rewording (minor editorial)
Title: Separation of C binding from C++ binding

Rationale:

This proposed rewording is a consequence of comment 2.

Proposed change:

a) This subsection should read "C" (and not "C and C++")

b) For reasons exposed in comment 2, we proposed that the last
sentence (refering to C++) of the first paragraph of section C.4 be 
removed.

Comment 2. 
Committee Draft Section: C
Category: subsection that should be included (major editorial)
Title: Proposal for a C++ binding

Rationale:

C++ is a quite different language from C in its features, namely type
safety, name space management and overloading. Requiring C++ to have
the same binding is not necessary and unjustified. C++ has its own
mecanism to maintain (library functions) compatibility with C. 

Proposed change:

We feel that the following subsection should be included as C++
binding.

=================== cut here ======================
C.??? C++

The programming language C++ is defined by ISO/IEC 14882:1998,
Information Technology -- Programming Languages - C++.

An implementation should follow all the requirements of LIA-2 unless
otherwise specified by this language binding.

The operations or parameters marked "[dag]" are not part of the
language and should be provided by an implementation that wishes to
conform to the LIA-2 for that operation. For each of the marked items
a suggested identfier is provided.

LIA-2 recommands that all identifers suggested therein be defined in
the namespace std::math.

The C++ datatype "bool" corresponds to the LIA-1 datatype "Boolean".

Every implementation of C++ has integral datatypes "int", "long int",
"unsigned int" and "unsigned long int" which (can) conform to LIA-1.

C++ has three floating point datatypes that (can) conform to LIA-1:
"float", "double", "long double".

The additional integer operations are listed below along with the
syntax to invoke them:

minI(x, y)		min(x, y)
maxI(x, y)		max(x, y)
min_seqI(xs)		min_element(xs_start, xs_end)
max_seqI(xs)		max_element(xs_start, xs_end)

dimI(x, y)		positive_difference(x, y)		[dag]
sqrtI(x)		sqrt(x)					[dag]
powerI(x, y)		power(x, y)				[dag]

dividesI(x, y)		divides(x, y)				[dag]
evenI(x)		x % 2 == 0
oddI(x)			x % 2 != 0
gcdI(x, y)		gcd(x, y)				[dag]
lcmI(x, y)		lcm(x, y)				[dag]
gcd_seqI(xs)		gcd(xs_start, xs_end)			[dag]
lcm_seqI		lcm(xs_start, xs_end)			[dag]

add_wrapI(x, y)		add_wrap(x, y)				[dag]
add_ovI(x, y)		add_overflow(x, y)			[dag]
sub_wrapI(x, y)		sub_wrap(x, y)				[dag]
sub_ovI(x, y)		sub_overflow(x, y)			[dag]
mul_wrapI(x, y)		mul_wrap(x, y)				[dag]
mul_ovI(x, y)		mul_overflow(x, y)			[dag]

where x and y are expressions of type INT and where xs is expression of
type a sequence (list<INT>, deque<INT>, vector<INT>, valarray<INT>) or
INT[]. xs_start and xs_end are expressions denoting the beginning and one
past end iterators of xs.  

The additional non-transcendental floating point operations are listed
below, along with the syntax used to invoke them:

minF(x, y)		max(x, y)
maxF(x, y)		max(x, y)
min_seqF(xs)		min(xs_start, xs_end)
max_seqF(xs)		max(xs_start, xs_end)

floorF(x)		floor(x)
roundingF(x)		round(x)				[dag]
ceilingF(x)		ceil(x)

dimF(x, y)		positive_difference(x, y)		[dag]
add3F(x, y, z)		add(x, y, z)				[dag]
sumF(sx)		accumulate(xs_start, xs_end, 0.)
dprodF->F'(x, y)	???(x, y)				[dag]
mul_addF(x, y, z)	mul_add(x, y, z)			[dag]
iremF(x, y)		remainder(x, y)				[dag]
sqrtF(x)		sqrt(x)
rsqrtF(x)		reciprocal_sqrt(x)			[dag]

add_loF(x, y)		add_low(x, y)				[dag]
sub_loF(x, y)		sub_low(x, y)				[dag]
div_restF(x, y)		div_rest(x, y)				[dag]
sqrt_restF(x)		sqrt_rest(x)				[dag]

where x and y are expressions of type FLT and where xs is expression of
type a sequence (list<FLT>, deque<FLT>, vector<FLT>, valarray<FLT>) or
FLT[]. xs_start and xs_end are expressions denoting the beginning and
one past end iterators of xs. 

The parameters for operations for approximating real valued
transcendal functions can be accessed by the following syntax:

max_err_hypothF		err_hypothenuse<FLT>()			[dag]

max_err_expF		err_exp<FLT>()				[dag]
max_err_powerF(b, x)	err_power(b, x)				[dag]

max_err_sinhF(x)	err_sinh(x)				[dag]
max_err_tanhF(x)	err_tanh(x)				[dag]

big_radian_angleF(x)	err_radian_angle(x)			[dag]
max_err_sinF(x)		err_sin(x)				[dag]
max_err_tanF(x)		err_tan(x)				[dag]

big_angleF		big_angle<FLT>()			[dag]
max_err_sinuF(u)	err_sin_cycle(u)			[dag]
max_err_tanhF(u)	err_tan_cycle(u)			[dag]

where b, x and u are expressions of type FLT.

<< The rest of this subsection is identical to the corresponding part of
the subsection titled "Java". >>
=================== cut here ======================

Comment 3.
Committee Draft subsection: 1.1
Category: request for rewording (minor editorial)
Title: reference for bindings

Rationale:

This proposal is a logical consequence of comment 2.

Proposed change:

We propose that the paragraph 1.2p3 be rephrased as follow:

  ISO/IEC 10967-2 covers most numerical functions required by the ISO
  standards for Ada, Basic, C, C++, Fortran, Extented Pascal, ISLisp,
  and PL/I. In particular, specifications are provided for...

_____ end of France comments; beginning of Germany comments _________

German vote on ISO/IEC CD 10967-2:
Information technology - Language Independent Arithmetic -
Part 2: Elementary Numeric Functions

Reference No. ISO/IEC JTC1/SC22 N 2824

Germany votes: NO with comments

The document still contains many editorial and English language errors
such as incorrect usage of the singular or the plural, of technical 
or mathematical terms (e.g. monotonous instead of monotonic (function)),
typos and misprints as well as structural errors (e.g. chapter structure 
of sections 5.2.7 - 8 does not match Annex A where 5.2.7 - 10 appear).

Germany still believes that the problem of summation of many terms, 
especially of floating-point numbers or of simple products 
thereof (i.e. the dot product) is not addressed adequately and 
poses a fundamental problem in many numerical applications.
However, Germany has noticed improvements in this area and is willing 
to provide assistance in this matter.   

Also, some references are out of date, e.g. to the Fortran standard.
The new Fortran standard is Fortran 95, published in 1997.  It should be
cited throughout, and adjustments should be made in the text.

_____ end of Germany comments; beginning of Japan comments _________

CD Ballot (SC22 N2824, due 1999-01-26)

ISO/IEC 10967-2,
Information technology - Language independent arithmetic - Part 2:
Elementary numerical functions

Japan disapproves the draft for reasons shown below.

---------------------------------------------------------------------------

1. Error limit

The definition of conformity to this standard has been improved, but
there still remain some points to be revised.

We understand that the error limits of each function should be defined
by each implementation, not by binding standards.  This interpretation
is supported by the descriptions in Clause 8 and Annex B.  However, it
would also be possible to interpret that the error limits may be
defined by binding standards.

Error limits defined for Ada numeric functions are rather loose than
those defined in this standard.  This leads to an unfortunate
consequence that Ada implementations conforming to the Ada standard
does not necessarily conform to this standard.  We have heard that, in
order to escape from this situation, the binding standard for Ada can
itself define error limits larger than those defined in this standard.

We cannot deduce this explanation from the text of the standard.  If
this explanation is a right one, it should be explicitly mentioned in
the text.  In any case, it should be clearly defined whether a binding
standard can define error limits or not.

In A.2, it is suggested that a binding standard should define error
limits, but this can only be taken as informative.  The same thing
should be stated in the normative part of the standard.

In the fourth paragraph of Clause 2, the term "conflict between a
binding standard and this part of ISO/IEC 10967-2" appears.  It is not
clear what type of conflict is allowed.  We consider that some "upper
bound" of conflict is necessary, since without such upper bound, a
binding standard can define anything totally disregarding the
definitions in this standard.

2. Definition of F

The symbol F is used throughout the document to represent a "floating
point datatype".  There is some confusion on the usage of F:

 (a) In each function definition, F looks to represent a subset of R.
     A condition clause "if x in F" should read "if x is not a special
     value".  This standpoint is stated in the definition of
     "arithmetic datatype" (4.2).

 (b) In other places, F looks to represent the type which may contain
     special values.  See the second paragraph of 5.2.

Usage (a) is the fundamental one, and is the way adopted in LIA-1 and
the previous versions of LIA-2.  The document should clearly state
this standpoint and avoid any ambiguous usage of F.

We suggest possible improvement below, with <<addition>> and
<replacement> to the text.

== suggested changes in wording ==================================

4.1 Symbols

The following symbols are defined in ISO/IEC 10967-1:1994, and used
in this part <<for an integer type I and for a floating type F and F'>>.
  ...
The following symbols represent <<special>> values defined in IEC 559...
  ...
These <<special values>> are not part of the <<value>> set F, but if
iec_599F has the value true, <the floating point datatype corresponding
to F has these special values available in it>.

<<For an arithmetic datatype F conforming to ISO/IEC 10967-1:1994,
  the symbol F is also used to designate its value set that consists
  of only those values in R (for a floating point datatype) or in Z
  (for an integer datatype), specifically in specification of a function
  or operation for the datatype.>>

4.2 Definitions
  ...
arithmetic datatype: A datatype whose values are member of Z, R or C.
  ....
signature: A summary of information about an operation or function.
  ... The signature
    addI: IxI -> I U {integer_overflow}
  ....
<<Note:  I represents a value set of the target integer datatype which
  contains only those values in Z, i.e. I does not contain NaN and
  infinity values.>>

5.1 Additional basic integer operations
  ...
I is an integer datatype conforming to ISO/IEC 10967-1<<:1994>>.
Integer types conforming to ISO/IEC 10967-1<<:1994>> usually do not
<have> any NaN or infinity values, even though they may do so.
Therefore this clause has no specification for such values as arguments.
  ...
<<Note: When the datatype I includes such special values, each conforming
  implementation shall document specification for the cases when such
  special values appear as arguments. (see 8.)>>

5.2 Additional basic floating point operations
  ...
F is a floating point datatype conforming to ISO/IEC 10967<<:1994>>.
Floating point datatypes conforming to ISO/IEC 10967-1<<:1994>> usually
do <have> NaN and infinity values.  Therefore, in this clause
<each function or operation specification includes specifications
for the cases when such values appear as arguments>.

== end of suggested changes in wording ===========================

3. minor errors

We found many minor errors in the standard.  We judge that this CD
text is still immature, and should be improved before going to DIS
stage.

Foreword: According to the ISO home page, the full name of ISO is "the
International Organization for Standardization".  They do not use
British spelling for the name of the organization.

Foreword: The scope of SC22 should be written correctly.

1.1: The current wording "C/C++" implies that C and C++ are compatible
languages.  This is not true, and they should be written as "C, C++"".

1.1: An "and" should be added at the end of (e).

3.: The second word of the title should be written in lower case.

4.1: The operator "|" is not enumerated in the list of notations.

4.1: "it" should be changed to "is" in the following sentence.
"... difference of conventions it the arccot function.".

4.1: The period after "s2" should be changed to a comma, in "s1 and
then s2. Etc.".  "Etc" should be changed to "etc".

4.1: The current list of exceptional values is "integer_overflow,
floating_overflow, underflow, and undefined".  "overflow" should be
added to this list.  "overflow" is used, for example, in 5.4.5.

4.1: "an" should be changed to "a", in "an highly accurate result".

4.2, precision: "109671" should be changed to "10967-1".

5.1: We cannot understand why the word "additional" is used in the
title of this section.

5.1.1, Note 1: The conditions of two alternatives are the same.  In
what case should we use the first alternative, and in what case the
second alternative?

5.1.2, max_seqI: The definition is not complete.  What happens if n =
0 and -infinity is available?

5.1.2, min_seqI: The same as above (+infinity).

5.1.4, shift2I: We consider that "invalid" does not occur in this
function.

5.1.4: shift10I: The same as above.

5.1.8, gcdI: The definition is not complete.  What happens if n = 0
and +infinity is available?

5.1.9, add_ovI: We consider that the conditions I /= Z and I = Z are
not adequate.  Even if an implementation supports multiple precision
arithmetic, an integer type can never cover the whole set of
mathematical integers.  There might be an argument that an integer
datatype I can be any subset of Z conceptually.  But, then, what
happens if I consists of all the positive values of Z?

5.2.3, dimF: "invalid" should be added to the list of possible output
values.

5.2.3: The function rndF is used in the definition of dimF, but we
could not find its definition.

5.2.4, Note 3: "handed" should be changed to "handled".

5.2.4: "invalid" should be added to the list of possible output values
in the definitions of the following functions.  rounding_restF,
floor_restF, and ceiling_restF.

5.2.5, iremF: In the eighth alternative, "yis" should be changed to "y
is".

5.2.7: "invalid" should be added to the list of possible output values
in the definitions of the following functions.  add_loF, sub_loF,
mul_loF, add3_midF, and mul_add_midF.

5.2.7, add_loF and sub_loF: There are many question marks in the
definitions, which means that the definitions are not yet fixed.  The
third and the fourth alternatives of add_loF are not consistent with
those of sub_loF.  The symbol "u" appears freely, without definition.

5.2.7, mul_addF: We cannot understand why 0 is handled separately.

5.2.8, sum: We cannot understand why the sum is -0 when n = 0.  We
think that 0 is quite reasonable.

5.3.3.2, Note 1: There is no predicate verb in the last sentence,
which starts with "Something which ...".

5.3.3.2, expm1F: "underflow" is listed in the list of possible output
values, but underflow never occurs in this function.

5.3.3.3, powerF: 1^infinity is defined as invalid(1).  We think that 1
is quite reasonable in this case.

5.3.3.3, Note 2: Non-overflow conditions is written as "when x = 0 or
when x = 1".  This is not consistent with the style of Note 1, where
the same condition is written as "x in {0, 1}".

5.3.3.4, powerm1F: The result value of the third alternative is -0,
but this is not adequate.  There may be implementations not supporting
this value.  We understand that the result value in such cases should
be written as negF(0).  The same comment applies to 5.2.5, etc.

5.3.3.4, powerm1F: 1^infinity-1 is defined as invalid(0).  We think
that 0 is quite reasonable in this case.

5.3.3.8, Note: "requireing" should be changed to "requiring".

5.3.3.9, logbaseF: The definition seems to assume that if +infinity is
available, so is -infinity.  Does this assumption always hold?

5.3.3.9, logbaseF: We consider that the result should be "invalid"
when x = +infinity and y is in F, and when x = 1 and y = +infinity.

5.3.3.9, logbaseF: The intersection of the conditions of the 16th and
the 17th alternatives is not empty.

5.3.5: Something is wrong in the sentence "... for each the ... 
functions are ...".

5.3.6, Note: Since this Note gives a definition, it should not be a
Note, and should be moved to the main part of the text.  We could not
deduce the contents of this Note from other definitions in this
document.

5.3.6.2, sinF: The second axiom is not correct.  pi/4 should be
changed to pi/2.

5.3.6.2 -- 5.3.6.8, sinF -- cscF: "invalid" should be added to the
list of possible output values for these functions.

5.3.6.9 -- 5.3.6.15, arcsinF -- arccscF, We think that the range of
result values should be mentioned in the definitions of reverse
trigonometric functions.

5.3.6.11, Note 1: The word "section" is not adequate.  "clause" should
be used.

5.3.6.11, arcF: There are many question marks in the definition of
this function, which means that the definition is not yet fixed.

5.3.6.13, arcctgF: We do not know the mathematical meaning of this
function.  Is this function necessary?

5.3.7, Note 2: It says that the negative angular unit is not
considered.  This is not true.  In sinuF, for example, the negative
angular unit is explicitly considered.

5.3.7.5, tanuF: "-u/2" in the conditions of the first and the second
alternatives should be changed to "u/2".  When x approaches 180 degrees
from the second quadrant, tan(x) approaches to 0 from the negative
side.

5.3.9.1: The value "max_error_radF" is used, but we could not find its
definition.

5.4, Note 2: "10967does" should be changed to "10967 does".  A period
should be added after "etc".

5.4.1, Note 1: The first "are" in "both are I and I' are" should be
removed.

5.4.1 -- 5.4.6: There are many question marks in the definitions of
these functions, which means that the definitions are not yet fixed.

5.4.1 -- 5.4.6: The notion "sNaN without notification" seems strange.
Is it different from qNaN?

5.4.4, convert(nearest): "x" in the last alternative should be printed
in italic font.

5.4.5: "overflowif" should be changed to "overflow if".

5.4.5, resultD: We feel that the sentence "D is a fixed point type, it
cannot conform to LIA-1 ..." is somewhat strange as an English
sentence.

5.4.6, convert(nearest): The result value of the sixth and seventh
alternatives is "overflow".  We consider that this should be changed to
"floating_overflow".

5.5.2: An "and" is necessary in the first sentence.  It should be
inserted between "resultF(x, downF)" and "shall".

5.5.2: It is mandatory for an implementation to prepare a numeral for
positive infinity and NaNs.  We think that this rule is an
over-specification.  An implementation supporting these special values
but not providing numerals is a reasonable one.

6.: The usage of "so that" in the second line is not a recommended
one.  It should not be used in a negative statement.

6.: The last sentence in the second paragraph contains two "if"s.

7.: "10967and" should be changed to "10967 and".  "of clause 5" should
be changed to "in clause 5".

A.1: "Sufficient" should be changed to "sufficient".

A.4.1: "denormalized" should be changed to "denormalised".

The clause A.5.1.7 should be added.

The clauses A.5.2.8 and A.5.2.9 should be deleted.

The clause A.5.3.1.5 should be deleted.

A.5.3.1.5: "thought" should be changed to "though" in "thought they
are valid if the ...".  "the an approach" should be changed to "the
approach".  "if" should be changed to "is" in "approach to zero if
from ...".

The clause A.5.5 should be added.

______ end of Japan comments; beginning of Sweden comments _______

From:  Ann Flod ([email-masked])
Subject:  Ballot on SC 22 N 2824

Replacement of the Swedish vote on SC 22 N 2824 and FCD 10967-2.

Yes for approval with comments as below:

Minot comment:

1.  A consistent and practical choice must be made for the by the editor
7-marked specification lines.

2.  The bindings examples annex should be better completed for more of the
languages than just Ada.

Editorial comment:

Some lines go a bit far into the margin, and should be wrapped or
otherwise shortened.

____ end of Sweden comments; beginning of UK comments _______________

SC22 Letter Ballot N2824 - Approval Ballot for FCD 10967-2 Language
Independent Arithmetic - elementary Numeric Functions

UK votes NO with comments to CD 10967-2 (LIA-2).

STRATEGIC COMMENTS

1 Clause 5.4.6 includes questions to the reviewers concerning the
behaviour of convert(... , F to D, x) when x is a signalling NaN. It would
help reviewers to have a complete list of such questions, and the
arguments in favour of each possibility (it would also help the editor
because the questions are more likely to be answered).

2 A large part of this draft defines the values of the arithmetic
functions when one or more input arguments is an IEC559 continuation
value. This is neither desirable nor necessary. Part 1 of the standard
does not define the basic arithmetic operations under such circumstances,
and part 2 should not do so either. 

Does any programming language standard do so? Or is planning to do so? Or
has even considered doing so? If there is no candidate for usage of this
facility then it should be omitted.

TECHNICAL COMMENTS

1 Clause 4.1 defines three separate meanings for [ and ] (square
brackets): (i) designating a closed interval, (ii) to delimit a finite
sequence of values, (iii) a set of finite sequences.  Multiple meanings
for square brackets, or any other term/usage, may potentially lead to
errors in understanding by readers.  

NOTE 5 says 'it should be clear from context if [X] is a sequence of one
element ...'.  If the note can be rewritten to read truthfully 'It is
always obvious ...', then perhaps the multiple meanings can be justified,
but the UK cannot check this since the source was not available in
electronic form.

2 Annex B - Partial conformity belongs in clause 2, not as an informative
annex.

3 Clause 5.1.2 - We do not think that -infinity is ever available for an
integer type, but if it is, then the definitions leave max_seq and
min_seq undefined for the case when n=0 and -infinity is available.

4 Clause 5.1.5 - defines the result as 'round(sqrt(x))'. 'round' should
be replaced by a round function (in math font) which itself needs to be
defined as a new helper function in 5.1.1.

5 Clause 5.1 states ''Integer datatypes conforming to ISO/IEC 10967-1
usually do not contain any NaN or infinity values'. The integer datatypes
defined in ISO/IEC 10967-1 NEVER contain any NaN or infinity values.

6 Clause 5.3.7 Natural logarithm. The ln*(F) function is defined with a
Real -> Real signature. This should be Real -> Complex, i.e. R -> Z.
Should there be any special consideration when the input argument is a
denormalized floating point value?

EDITORIAL COMMENTS

1 The draft refers throughout to 'sinus hyperbolicus' rather than
'hyperbolic sine', and similarly with many other functions. This does not
appear to the UK to be common usage, nor consistent with LIA-1.

2 Clause 6, para 3 says 'An implementation shall suppress spurious
notifications'. What is a 'spurious notification'? The UK is sceptical
about the value of suppressing any notification.

3 Clause 6 includes 'NOTE'. It should be 'NOTES'.

4 Claus =e 6 includes a sentence 'The results of ... is ...' instead of
'The results of ... are ...'.

5 Clause 5.4.2 Note 2 Misprint 'ISO/IEC 10967does' 

6 Is it necessary for each annex to begin on an odd-numbered page, and
thus some blank pages? It was not necessary in 10967-1.

7 Clause 5.3.1.2 The sentence (Those extentions ... .) should be a note,
and 'extentions' should be 'extensions'.

8 Clause 5.1.3 What is a 'limited integer type'? Is this what 10967-1
defines as an integer type with bounded = true?

OTHER COMMENTS

1. When faced with a new draft standard, it is important that reviewers
are provided with a list of what has changed in order to simplify their
task.  No such list is provided with this draft. It is strongly
recommended that such a list is provided with the next versions, although
this need not be too detailed as long as it indicates the major areas of
change.  It is not necessarily appropriate, for example, to provide change
bars.

2. Many forms of review are only possible if the source is available, for
example, how is a particular word used throughout the standard, writing
programs to check completeness and consistency. The source has not been
published. It is strongly recommended that an electronic searchable
version is provided with the next (paper) version

_________ end of UK comments; beginning of USA comments _____________

The US National Body votes to Approve with comments ISO/IEC CD 10967-2,
Information Technology - Language Independent Arithmetic - Part 2:
Elementary Numeric Functions.  Please see comments listed below.

Global:

IEC 559 has been renumbered to IEC 60559.  The particular LIA-2
reference is page 3: 3. Normative References.

Change the notations for intervals which do not include the end point:
]x,z]  to  (x,z]
[x,z[  to  [x,z)
]x,z[  to  (x,z)
based upon CRC Standard Mathematical Tables.  The particular LIA-2
reference is page 4: 4.1 Symbols.

Replace "I not equal to Z" (shows up in 5.1.1 for wrapI(x) and elsewhere)
with "I is bounded".  Replace "I equal to Z" with "I is unbounded".

Consider changing conformance to allow some legacy languages such as FORTRAN
to comply to LIA-1 but not LIA-2, but to at least pass through the LIA-1
conformant data types when dealing with LIA-2 level interchange. This will
allow interoperation even when languages cannot be extended to conform to
LIA-2.

Specific pages:

Page 3: 2 Conformity: Note 2: Remove: ", which in turn includes
(explicitly or by reference) a binding for IEC 559 as well".
Reason: Our understanding of LIA-1 is that it does not require
conformance to IEC 559 (IEEE-754).

Page 8: 4.2 Definitions: Change: The number of digits in the fraction of a
floating point number to The number of base-r digits in the fraction f of
a floating point number of the form 0.f * r**e.

Page 9: Change subnormal to some other term as it conflicts with the
usage in IEEE-854.

Page 9: Move: "For some operations the exceptional value invalid is
produced only by input values of -0, +INF, -INF, or sNaN. For these
operations the signature does not contain invalid." from page 83
A.5.3.1	Specification format to page 9 5. Specifications for the
numerical functions.  It can be made into a Note.

Page 9: 5.1 Additional basic integer operations: Rewrite the sentence:
String formats for integer values usually do contain (signalling) NaNs,
however, when that string format is regarded as an (non-ISO/IEC 10967-1)
integer datatype.

It makes no sense and we do not understand the intent, so do not have a
suggested rewrite.  Also, we have yet to seen an integer sNaN, so we
disagree with the word "usually" here.

Page 10: 5.1.2 Integer maximum and minimum operations: Either add
definition for the case of max_seq: n == 0 and -INF is available or remove
"and -INF is available".

Either add definition for the case of min_seq: n == 0 and +INF is
available or remove "and -INF is available".

Page 10: 5.1.3 Integer positive difference (monus, diminish) operation:
Should the note mention the case of x = +INF and y = +INF?
Change "limited integer types" to "bounded integer types".

Page 10: 5.1.4 Integer power and arithmetic shift operations: Change
"invalid(1)" to 1.  Aside: Based upon other parts of LIA-2, it appears
that "(1)" is a continuation value (not a footnote).  But, where is that
convention defined?
Add the case: = 1 if x = 1
Add the case: = +1 if x = -1 and y is even
Add the case: = -1 if x = -1 and y is odd

Page 12: 5.1.8 Greatest common divisor and least common multiple
operations:
For the invalid case, change invalid to invalid(0) and remove: and +INF
is not available.
Change Note 1: "would be incorrect, since the greatest common divisor for
0 and 0 is infinity" to "was considered but rejected".
Reason:  INF | 0 means INF * n = 0 for some n.  But there is no n that
satisfies the requirement.  Hence, +INF is not the GCD of 0 and 0.  Also,
we believe that 0 <= GCD(x,y) <= min(abs(x),abs(y)).
In: gcd_seqI ([x1 ; ...; xn]), remove and +INF is not available.
Add a note to that entry: { 0 } = { x1 ; ...; xn } means all xi are 0.

Page 14: 5.2.1 The rounding and floating point result helper functions:
Change: "= 0 if x = 0" to "= x if x = 0".  Reason: To do the correct
action for -0 and IEEE-754.
Add a note to that section: If denormF is false, the distinction between the
ordering of rounding and underflow detection is not made.  That is, a
number x might be just under fminNF, so might round to fminNF in one
implementation and be flushed to zero (before rounding) in another.

Page 18: 5.2.5 Operation for remainder after division and round to
integer (IEEE remainder): Add the missing space in "yis" in: "if x is a
quiet NaN and yis not a signalling NaN".

Page 19: 5.2.7 Support operations for extended floating point precision:
add_lo: If x, y, and addF(x,y) are all in F then the specified result is
fine.  But, one or more of x, y, and addF(x,y) are not in F, then there
are two viewpoints: add_lo(x,y) is always zero (and there are no
exceptions), or add_lo(x,y) is the same as addF(x,y) with the same
exceptions.  Both viewpoints are acceptable.  Whichever you adopt, the
definitions need to be redone.  For example, the "underflow(0)?" entry
should be either "0" or "underflow(0)".  And the entry "0?" should be
either "0" or "floating_overflow(+/-INF)".
The same idea applies to sub_lo, mul_lo, div_rest, and sqrt_rest.

Page 20: Remove add3 as we see no need for it.

Page 21: Remove add3_mid as we see no need for it.

Page 22: Remove mul_add_midF as we see no need for it.  It can be
simulated with *, mul_lo, +, and add_lo.

Page 23: 5.2.8 Exact summation operation: Change result in:
= sNaN if x = +INF and y = -INF to be qNaN.
Change result in: = sNaN if x = -INF and y = + INF to be qNaN.

Page 25: 5.3.1.2 The trans result helper function:
= underflow(nearestF(x)) clause has two problems:
(nearestF (x) < 0 or x  0) seems wrong and we do not know what is should
be. It also seems that if nearestF(x) == x, e.g., x is exactly
representable as a denormal, there should not be an underflow.

Page 26: 5.3.2 Hypotenuse operation: Change the specification so that
hypot(+/-INF, qNaN) and hypot(qNaN, +/-INF) is +INF (not qNaN).  Reason: if
one of x or y is an infinity, then no matter what value the other
argument has, the result is +INF.

Pages 28-29: We disagree with many of the powerFF and powerFI subcases.  We
have complained before and been rejected, so we believe that it will do
no good to give the detailed rewrites, but we can provide them if you
would like them.

Page 42: 5.3.6 Operations for radian trigonometrics and inverse radian
trigonometrics: Change: "It [big_angle_r] shall have the following
default value" to "It shall have a default value at least as large as".
Reason: We know of implementations that use enough digits of pi for
argument reduction to correctly compute the trig functions for all
arguments.

Page 48: arcF: remove the "?inval?" items.

Page 48: arcF (we call it arctan2): We disagree with the +/-0, +/-0
subcases.  We have complained before and been rejected, so we believe
that it will do no good to give the detailed rewrites, but we can provide
them if you would like them.

Page 58: 5.3.7.11 Argument angular-unit arcus operation: Remove "?inval?"
items.

Pages 66-72: For all the 5.4.* functions: Add:
invalid if x is a quiet NaN and quiet NaN is not available in the
target type.
For all the 5.4.* functions: There are several cases to consider for
signaling NaNs.  It the type is changed (int - float, or float - int), or
if the precision is changed (I - I' or F - F'), that is, a conversion is
done, then signaling NaNs shall raise invalid and produce a qNaN as a
continuation value.  But, if the type and precison are the same, then it
is implementation defined if the copy operation leaves sNaN alone or
raises invalid and produces a qNaN as a continuation value.  Reason:
IEEE-754 allows the implementor to pick if copying sNaNs raises invalid or
not. IEEE-754 requires sNaNs to raise invalid on conversions.

[MAJOR] For roundingF, floorF, ceilingF, change integer_overflow to
integer_overflow or invalid (implementation defined).  Reason: There are
many hardware implementations of IEEE-754 that raise invalid for bad
conversions from floating-point to integer.

Page 68: 5.4.4 Floating point to floating point conversions: It appears
that LIA-2 is missing functions to meet IEEE-754 for directed rounding of
binary <-- decimal conversions, e.g., "input" and "output" of string
formats.  Each function for input or output is supposed to use the current
rounding direction.  This also applies to 5.4.5 and 5.4.6 functions.

Page 69: 5.4.5 Floating point to fixed point conversions:  Need to add a
definition or reference to LID.  Should "limited" be changed to "bounded"?

Page 73: 5.5.2 Numerals for floating point types: Change statically to
dynamically in: The rounding circumstance should be statically
determined, if other than the normal is at all available.
Check signalling versus signaling.  Both are used in LIA-2 (in particular on
page 74).
Expand note 2 in clause 7 to include COBOL, which is still the most widely
used programming language.  In particular, please add the following:
"function asin(x)     in COBOL".

Page 79: A.1.1 Specifications included in ISO/IEC 10967-2: Change
"intened" to "intended".

Page 82: A.5.2.7 Support operations for extended floating point
precision: 3rd paragraph: Add a missing 'by' to: the high parts are
calculated the corresponding floating point operations.

Page 93: Annex C: Example bindings for specific languages: Remove: In
turn, a complete binding for the ISO/IEC 10967-1 will include a binding
for IEC 559.

Page 99: C.2 Ada: Complete: Numerals for infinity...

Page 99: C.3 BASIC: Complete: The BASIC datatype ???? corresponds to the
LIA-1 datatype Boolean.

Page 103: C.4 C and C++: Add the reference number for C++ to the first
paragraph.

Page 104: Change: divides(x, y) to y % x == 0.

Page 104: Change: evenI(x) x % 2 = 0 to  evenI(x) x % 2 == 0.

Page 104: Change: min(x, y) to fmin(x, y).

Page 104: Change: max(x, y) to fmax(x, y).

Page 104: Change: ffloorf(x), ffloor(x), ffloorl(x) to floor(x).

Page 104: Change: ceiling(x) to ceil(x).

Page 104: Change: dim(x, y) to fdim(x,y).

Page 104: Change: ????(x, y) to dprod(x,y).

Page 104: Change: mul_add(x, y, z) to fma(x,y,z).

Page 104: Change: sqrtf(x), sqrt(x), sqrtl(x) to sqrt(x).

Page 105: Change: hypotenuse(x, y) to hypot(x,y).

Page 105: Change: power(b, y) to pow(b,y).

Page 105: Change: ln(x) to log(x).

Page 105: Change: ln1p(x) to log1p(x).

Page 105: Change: log(b, x) to logbase(b,x).

Page 105: Change: log1p(b, x) to logbase1p(b,x).

Page 107: Add to: convertI-I-(x): cast, e.g., (type of I-)x.

Page 107: Change: rounding(y) to (INT)round(y).

Page 107: Change: floor(y) to (INT)floor(y).

Page 107: Change: ceil(y) to (INT)ceil(y).

Page 107: Add to: cvtnearestF-D(y): sprintf().

Page 107: Add to: cvtnearestD-F(z): strtod(z,NULL).

Page 107: Either remove or replace the .... in: C provides non-negative
numerals .......  with for all its integer and floating point types.

Page 112: C.6 Java: Remove long double and change three to two.

Page 121: C.7 ISLisp and Common Lisp: Complete: The details are not
repeated here, see ....

Page 125: C.8 Modula 2: Complete: Modula-2 provides non-negative numerals
.......

Page 129: C.9 Pascal and Extended Pascal: Complete: Pascal provides
non-negative numerals .......

Page 131: Annex D Bibliography: Item [1]: Change 559 to 60559.  Add at
end: (previously designated IEC 559:1989).

Page 132: Add to item [27]: A corrected tenth edition has been published by
Dover Publications, New York.

_______________________ end of USA comments ________________________

________________________end of SC22 N2879 _________________________