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From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
To: std-interval@compgeom.poly.edu
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Subject: [std-interval] Current draft of the proposal for std::interval
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Dear subscribers,

First, a bit of history. We (Herv=E9 Br=F6nnimann, Guillaume Melquiond, and
Sylvain Pion) have written a C++ library for interval arithmetic that is
part of the Boost project. This work gave us a better understanding on
how to provide interval arithmetic in C++. So we submitted a proposal
for adding this arithmetic to the C++ Standard Library. We had decided
that the template classes would be simple, and in particular that they
would not be policy-based, contrarily to the Boost library.

This proposal was presented during the Fall'05 meeting of the C++
standardization committee. It was rather well received, but developers
of implementations of the STL were concerned whether there was or not a
sufficient user demand for interval arithmetic.

Anyway, we have decided to submit a revised version of the proposal to
the Spring'06 meeting. Since the first release of our proposal, a lot of
comments have been sent to us and we have tried to take them into
account. This is a draft of our revised proposal. Please note that
interval comparisons have been temporarily left aside from this draft
because we have yet to converge on a syntax.

Among these comments, a major concern was the kind of interval
arithmetic. The current proposal implements an arithmetic that is usable
for doing forward evaluation on the set of real numbers. Some would like
the computations to be on the set of extended real numbers: it would for
example allow <0,inf> * <1,inf> =3D <-inf,inf>. Some would like the
computations to have backward propagation properties: <0,0> / <0,0> =3D
<-inf,inf>. Some would like both forward and backward semantics in order
to do global optimization. And so on.

As long as intervals have finite bounds and do not contain zero, all
these semantics are equivalent. But in presence of infinities and zeroes
(that is as soon as there is an underflow or an overflow on the
floating-point bounds), these various arithmetics produce incompatible
results. And they all have their own use cases. As a consequence, this
is the main point left unsolved.

We are interested in your comments on this draft.

Best regards,

Herv=E9, Guillaume, and Sylvain


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From hbr@poly.edu Fri Feb 24 15:01:59 2006
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From: =?ISO-8859-1?Q?Herv=E9_Br=F6nnimann?= <hbr@poly.edu>
Subject: Re: [std-interval] Current draft of the proposal for std::interval
Date: Fri, 24 Feb 2006 15:56:05 -0500
To: For discussions concerning the C++ standardization of intervals
	<std-interval@compgeom.poly.edu>
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Peux tu stp repondre a ton courrier et donner un pdf au lieu d'un  
ps.gz?  C'est plus portable...
Merci.
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu


On Feb 24, 2006, at 12:34 PM, Guillaume Melquiond wrote:

> Dear subscribers,
>
> First, a bit of history. We (Hervé Brönnimann, Guillaume Melquiond,  
> and
> Sylvain Pion) have written a C++ library for interval arithmetic  
> that is
> part of the Boost project. This work gave us a better understanding on
> how to provide interval arithmetic in C++. So we submitted a proposal
> for adding this arithmetic to the C++ Standard Library. We had decided
> that the template classes would be simple, and in particular that they
> would not be policy-based, contrarily to the Boost library.
>
> This proposal was presented during the Fall'05 meeting of the C++
> standardization committee. It was rather well received, but developers
> of implementations of the STL were concerned whether there was or  
> not a
> sufficient user demand for interval arithmetic.
>
> Anyway, we have decided to submit a revised version of the proposal to
> the Spring'06 meeting. Since the first release of our proposal, a  
> lot of
> comments have been sent to us and we have tried to take them into
> account. This is a draft of our revised proposal. Please note that
> interval comparisons have been temporarily left aside from this draft
> because we have yet to converge on a syntax.
>
> Among these comments, a major concern was the kind of interval
> arithmetic. The current proposal implements an arithmetic that is  
> usable
> for doing forward evaluation on the set of real numbers. Some would  
> like
> the computations to be on the set of extended real numbers: it  
> would for
> example allow <0,inf> * <1,inf> = <-inf,inf>. Some would like the
> computations to have backward propagation properties: <0,0> / <0,0> =
> <-inf,inf>. Some would like both forward and backward semantics in  
> order
> to do global optimization. And so on.
>
> As long as intervals have finite bounds and do not contain zero, all
> these semantics are equivalent. But in presence of infinities and  
> zeroes
> (that is as soon as there is an underflow or an overflow on the
> floating-point bounds), these various arithmetics produce incompatible
> results. And they all have their own use cases. As a consequence, this
> is the main point left unsolved.
>
> We are interested in your comments on this draft.
>
> Best regards,
>
> Hervé, Guillaume, and Sylvain
>
> <interval.ps.gz>
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval


From guillaume.melquiond@ens-lyon.fr Sat Feb 25 05:34:22 2006
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Subject: Re: [std-interval] Current draft of the proposal for std::interval
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
To: std-interval@compgeom.poly.edu
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Le vendredi 24 février 2006 à 18:34 +0100, Guillaume Melquiond a écrit :
> This is a draft of our revised proposal.

Here is a PDF version of the draft.

Best regards,

Guillaume

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From hbr@poly.edu Fri Mar  3 12:14:05 2006
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Dear std-interval list subscriber:

At the Mont-Tremblant meeting, it was suggested that we (the  
submitters of the std::interval<T> proposal) evaluate the impact of  
having IA provided by the C++ standard.  To this end, we have set up  
a web questionnaire.  We would be grateful if you could

1.  Fill in the questionnaire yourself.

2. Send this email to any party (esp. users of IA in goverment lab,  
industrial or commercial settings) whom you know is interested in IA,  
and ask them to support our efforts by filling in the questionnaire.

We have tried to keep this questionnaire short, while maximizing the  
opportunity to give feedback on several aspects of the proposal.  I  
would hope it is possible to answer it in less than 10 minutes,  
perhaps 15 if giving more elaborate answers towards the end (feedback  
on pros/cons of IA in C++ standard).

We thank you for you support,
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu



From Stephen.Clamage@Sun.COM Fri Mar  3 12:42:27 2006
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Date: Fri, 03 Mar 2006 10:38:37 -0800
From: Steve Clamage <Stephen.Clamage@Sun.COM>
Subject: Re: [std-interval] Please reply to
	http://compgeom.poly.edu/std-interval/questionnaire.html
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 <std-interval@compgeom.poly.edu>
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... and where is the questionnaire?

---
Steve Clamage, stephen.clamage@sun.com

Hervé Brönnimann wrote:

> Dear std-interval list subscriber:
> 
> At the Mont-Tremblant meeting, it was suggested that we (the  submitters 
> of the std::interval<T> proposal) evaluate the impact of  having IA 
> provided by the C++ standard.  To this end, we have set up  a web 
> questionnaire.  We would be grateful if you could
> 
> 1.  Fill in the questionnaire yourself.
> 
> 2. Send this email to any party (esp. users of IA in goverment lab,  
> industrial or commercial settings) whom you know is interested in IA,  
> and ask them to support our efforts by filling in the questionnaire.
> 
> We have tried to keep this questionnaire short, while maximizing the  
> opportunity to give feedback on several aspects of the proposal.  I  
> would hope it is possible to answer it in less than 10 minutes,  perhaps 
> 15 if giving more elaborate answers towards the end (feedback  on 
> pros/cons of IA in C++ standard).
> 
> We thank you for you support,
> -- 
> Hervé Brönnimann
> CIS, Polytechnic University
> hbr@poly.edu
> 
> 
> 
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval


From hbr@poly.edu Fri Mar  3 13:17:04 2006
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Subject: Re: [std-interval] Please reply to
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Date: Fri, 3 Mar 2006 14:13:32 -0500
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	<std-interval@compgeom.poly.edu>
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Sorry, it's in the subject line, but you're right that it should also  
be clearly mentioned in the text...

http://compgeom.poly.edu/std-interval/questionnaire.html

--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu


On Mar 3, 2006, at 1:38 PM, Steve Clamage wrote:

> ... and where is the questionnaire?
>
> ---
> Steve Clamage, stephen.clamage@sun.com
>
> Hervé Brönnimann wrote:
>
>> Dear std-interval list subscriber:
>> At the Mont-Tremblant meeting, it was suggested that we (the   
>> submitters of the std::interval<T> proposal) evaluate the impact  
>> of  having IA provided by the C++ standard.  To this end, we have  
>> set up  a web questionnaire.  We would be grateful if you could
>> 1.  Fill in the questionnaire yourself.
>> 2. Send this email to any party (esp. users of IA in goverment  
>> lab,  industrial or commercial settings) whom you know is  
>> interested in IA,  and ask them to support our efforts by filling  
>> in the questionnaire.
>> We have tried to keep this questionnaire short, while maximizing  
>> the  opportunity to give feedback on several aspects of the  
>> proposal.  I  would hope it is possible to answer it in less than  
>> 10 minutes,  perhaps 15 if giving more elaborate answers towards  
>> the end (feedback  on pros/cons of IA in C++ standard).
>> We thank you for you support,
>> -- 
>> Hervé Brönnimann
>> CIS, Polytechnic University
>> hbr@poly.edu
>> _______________________________________________
>> Std-interval mailing list
>> Std-interval@compgeom.poly.edu
>> http://compgeom.poly.edu/mailman/listinfo/std-interval
>
>
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval
>


From hbr@poly.edu Fri Mar  3 13:18:53 2006
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Subject: Re: [std-interval] Please reply to
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Date: Fri, 3 Mar 2006 14:15:23 -0500
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	<std-interval@compgeom.poly.edu>
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If this wasn't clear from the subject line, I apologize. In any case,  
let me make it even clearer: the questionnaire is available at

    http://compgeom.poly.edu/std-interval/questionnaire.html

Thanks,
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu



From eliasen@mindspring.com Fri Mar  3 14:34:28 2006
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   I would suggest that the buttons at the bottom of the form be
re-ordered to have "submit" first and "clear" second to follow more
common interface conventions.  I didn't quite click "clear," but my
finger was a millimeter away.... :)  Otherwise, looks like a useful and
well-considered survey.

   FYI, I'm a developer who has developed my own Interval Arithmetic
library for my programming language "Frink" (implemented in Java).  See
http://futureboy.us/frinkdocs/ for more information about the language.

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
From hbr@poly.edu Fri Mar  3 14:45:51 2006
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Thanks for sharing the feedback. I'm not an interface designer :-)
Done.
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu


On Mar 3, 2006, at 3:31 PM, Alan Eliasen wrote:
>    I would suggest that the buttons at the bottom of the form be
> re-ordered to have "submit" first and "clear" second to follow more
> common interface conventions.  I didn't quite click "clear," but my
> finger was a millimeter away.... :)  Otherwise, looks like a useful  
> and
> well-considered survey.
>
>    FYI, I'm a developer who has developed my own Interval Arithmetic
> library for my programming language "Frink" (implemented in Java).   
> See
> http://futureboy.us/frinkdocs/ for more information about the  
> language.
>
> -- 
>   Alan Eliasen                 |  "When trouble is solved before it
>   eliasen@mindspring.com       |    forms, who calls that clever?"
>   http://futureboy.us/         |              --Sun Tzu
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval
>


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Overall, I thought the proposal well written.  I do have some
comments.

(A date would have helped in identifying the document, even if you do
not yet have a document number.)

============

Should std::valarray<interval> be allowed?

   Note that Sun's interval library includes specializations for
   valarray over intervals.  This specialization improves performance
   over the simple approach.

Should intervals be passed by value or by reference?

   I strongly prefer the pass-by-value approach over the legacy
   pass-by-reference approach of std::complex.  The choice has
   implications beyond the efficiency of the interval operations
   because users will tend to copy the style of the standard.  This
   pass-by-reference style leads to inefficiency and incorrectness.

   "Changing [interval parameters from pass-by-reference] to pass by
   value would only penalize the other ABIs."

   What evidence do you have to support this claim?  In fact, for most
   ABIs, the performance of intervals pass-by-value will be faster
   than pass-by-reference.  On those ABIs where performance by-value
   is lower, it will be only marginally lower. (For example, on x86
   pass-by-value pushes two words to the stack; pass-by-reference
   varies from pushing one word to writing two words and pushing one.)
   On the other hand, ABIs that support "small structs passed in
   registers", the difference is signficant, often avoiding memory
   entirely.

   "Note that this point is moot when functions are inline, which is
   expected to be the case most of the time."

   This statement is entirely untrue for the simple implementations.

   Pass-by-reference inhibits optimization.  The problem is that
   pass-by-reference introduces potential aliases between parameters.
   The compiler must load/store intervals to memory at many
   intermediate stages of computation to avoid incorrect results.  In
   contrast, value parameters cannot be aliased, and hence may be
   retained in registers.

   The aliasing problem is particularly severe because programmers
   often write programs as though it did not exist.  That is, they
   write functions that fail when parameters are in fact aliased.
   For example, the typical code for complex::operator*= is:

      real = real*rhs.real - imag*rhs.imag;
      imag = imag*rhs.real + real*rhs.imag;

   and it fails under pass-by-reference for the expression c*=c.
   Workarounds to this problem genrally involve retaining an extra copy
   of something, which ends up being very similar to pass-by-value.

   Now, imagine all that code where the programmer did not account for
   aliasing in user-written functions.  Now imagine all that code just
   naturally corrected with pass-by-value.

   This issue is very important.

26.6 Interval Numbers

   Paragraph 2 has a stale reference to interval<bool>.

   Paragraph 2 also says "instantiating the template interval for any
   type other than ... is unspecified".  By omitting the generic
   template definition, and defining only the specializations, the user
   cannot instantiate interval over any other type and the unspecified
   behavior is gone.  Is there any particular reason to provide the
   generic template definition?  If not, I suggest you remove it.
   Section 26.6.2 would go away.

26.6.1 Header <interval> synopsis // values:

   Several of the free functions seem more natural to me as member
   functions.  They are inf, sup, midpoint, and width.

26.6.1 Header <interval> synopsis // algebraic operators:

   Why is square a "value", but sqrt is a "algebraic operator"?

26.6.1 Header <interval> synopsis // set operations:

   These operations seem much more natural to me as member functions.
   Consider:

      if ( contains( a, b ) )

   versus

      if ( a.contains(b) )

   or more signficiantly

      a = intersect( hull( a, b ), c );

   versus

      a = a.hull(b).intersect(c);

   As with the values functions, we need to balance the expectations of
   the users.  I speak of my expectations as a C++ expert, not of the
   expectations of an interval expert.  It may well be that changing
   would be worse than not.

26.6.11 interval static value operations

   Based on the example in VI.1, you also need

      interval<T> interval<T>::epsilon()
         { return interval( -std::numeric_limits<T>::min(), 
                             std::numeric_limits<T>::min() ); }

   And based on the example in VI.2, you also need

      interval<T> interval<T>::min()
         { return interval( std::numeric_limits<T>::min(), 
                            std::numeric_limits<T>::min() ); }

   which results in

      assign_box( r, -std::interval<T>::min() );

============

  Lawrence Crowl             650-786-6146   Sun Microsystems, Inc.
                   Lawrence.Crowl@Sun.com   16 Network Circle, UMPK16-303
           http://www.Crowl.org/Lawrence/   Menlo Park, California, 94025

From george.corliss@marquette.edu Sun Mar  5 15:58:58 2006
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Guillaume, Hervé, Sylvain,

Is there, or is there a plan for, a suite a program to check compliance with
the proposed C++ interval standard?

It would seem that such a suite might serve several functions:

1.  Writing careful test cases might uncover weaknesses in the proposal.

2.  If the proposal and the test suite agree, reading the code in the test
suite may help some people understand what is the intent of the standard.
If so, the intent of the standard might benefit from clarification.

3.  One way to produce multiple reference implementations of the standard
quickly is to write wrappers for existing packages so that they can support
standard-compliant programs with zero modification to existing packages.
One would like to check the resulting wrapper plus underlying package for
compliance with the standard.


If there is no plan for a compliance checker, I'd volunteer to work on one.
Volunteers to work with me are MOST welcome.

I have a framework I used to check arithmetic operations and elementary
functions in COSY and INTLAB.  That framework is not in C++, and it is
rather awkward, depending on Maple for after-the-fact result checking, but
it IS a starting point.  I'd guess that authors of existing packages may
have test suites that could be modified to the proposed standard without TOO
much work?

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu



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Le dimanche 05 mars 2006 à 15:56 -0600, George Corliss a écrit :
> Guillaume, Hervé, Sylvain,
> 
> Is there, or is there a plan for, a suite a program to check compliance with
> the proposed C++ interval standard?

None that I know of.

> It would seem that such a suite might serve several functions:
> 
> 1.  Writing careful test cases might uncover weaknesses in the proposal.
> 
> 2.  If the proposal and the test suite agree, reading the code in the test
> suite may help some people understand what is the intent of the standard.
> If so, the intent of the standard might benefit from clarification.
> 
> 3.  One way to produce multiple reference implementations of the standard
> quickly is to write wrappers for existing packages so that they can support
> standard-compliant programs with zero modification to existing packages.
> One would like to check the resulting wrapper plus underlying package for
> compliance with the standard.

This third point seems interesting to me the other way around too. Such
a suite would indeed provide a tool for testing a common subset of any
existing interval package. The only work would be in writing a (cheap)
wrapper. This would be great.

Best regards,

Guillaume

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From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
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Subject: [std-interval] Re: winter 2006 draft for standard C++ intervals
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Thanks a lot for your comments.

Le jeudi 02 mars 2006 à 17:09 -0800, Lawrence.Crowl@sun.com a écrit :

> Should intervals be passed by value or by reference?
> 
>    I strongly prefer the pass-by-value approach over the legacy
>    pass-by-reference approach of std::complex.  The choice has
>    implications beyond the efficiency of the interval operations
>    because users will tend to copy the style of the standard.  This
>    pass-by-reference style leads to inefficiency and incorrectness.
> 
>    "Changing [interval parameters from pass-by-reference] to pass by
>    value would only penalize the other ABIs."
> 
>    What evidence do you have to support this claim?

I didn't write this sentence (or at least I don't think so), so I can't
tell what its author meant. But as I understand it, it just means that
an ABI that prefers pass-by-value will not be more penalized than it
already is with std::complex (since both types have the same memory
layout and std::complex is passed by reference), while an ABI that
prefers pass-by-reference will be more penalized than it is with
std::complex when passing by value.

>    "Note that this point is moot when functions are inline, which is
>    expected to be the case most of the time."
> 
>    This statement is entirely untrue for the simple implementations.

By the time interval arithmetic is in the Standard (if it ever is), I
expect the compilers to be able to make this statement holds true, since
inlining is such a strong requirement in C++. But I am perhaps giving
too much credit to compiler writers.

>    This issue is very important.

Agreed. In my opinion, the interval class should indicate (by a typedef
member for example) which parameter-passing convention it uses, so that
it can be left undecided in the Standard. As a consequence, an
implementation would always be optimal yet standardized. No architecture
would be penalized by the passing conventions of its ABI. But I fear
this additional layer of complexity would raise the bar even higher in
order for the proposal to be accepted.

I know some other C++ specialists are subscribed to this mailing-list.
So I would be happy to hear their opinions on a Standard-compliant
parameter-passing convention the interval class should use.

> 26.6 Interval Numbers
> 
>    Paragraph 2 has a stale reference to interval<bool>.

I did some wild cutting in our draft, in order to get this version out
and the ball rolling. So I am not surprised I missed some references to
interval<bool> :-).

> 26.6.1 Header <interval> synopsis // values:
> 
>    Several of the free functions seem more natural to me as member
>    functions.  They are inf, sup, midpoint, and width.

There is an inconvenience with such member functions: you can't use them
in template algorithms that expects a "UnaryFunction" argument. This is
one of the concepts of the STL and the C++ language cannot use member
functions in these places unfortunately. By providing these functions as
free functions, the user can for example type

  std::transform(vec1.begin(), vec1.end(), vec2.begin(), midpoint);

in order to compute the vector of midpoints of a vector of intervals.

> 26.6.1 Header <interval> synopsis // set operations:
> 
>    These operations seem much more natural to me as member functions.
>    Consider:
> 
>       if ( contains( a, b ) )
> 
>    versus
> 
>       if ( a.contains(b) )

Agreed, the member function syntax is nicer. But for the same reason as
before, this prevents "contains" from being directly used with
algorithms that expect "BinaryFunction" or "BinaryPredicate" arguments.

>    or more signficiantly
> 
>       a = intersect( hull( a, b ), c );
> 
>    versus
> 
>       a = a.hull(b).intersect(c);

On the previous examples, I agree that the member function syntax looked
nicer and more natural. But on this example I disagree. Such a syntax is
tied to a different semantic in my opinion. If I read "a.hull(b)", I
expect the interval stored in "a" to be modified by adding "b". The
syntax is too close from "a += b" to have the semantic of "a + b".

> 26.6.11 interval static value operations
> 
>    Based on the example in VI.1, you also need
> 
>       interval<T> interval<T>::epsilon()
>          { return interval( -std::numeric_limits<T>::min(), 
>                              std::numeric_limits<T>::min() ); }

I suppose this one could be mathematically defined as the tightest
representable interval such that it contains zero yet zero is not a
bound. Is epsilon a suitable name?

>    And based on the example in VI.2, you also need
> 
>       interval<T> interval<T>::min()
>          { return interval( std::numeric_limits<T>::min(), 
>                             std::numeric_limits<T>::min() ); }

I cannot find a concise mathematical definition for this interval. Are
there practical uses for it?

On this subject, are there other interval constants that people feel
useful?

Best regards,

Guillaume


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FYI:

Wednesday, March 29, Sun Microsystems
Ned Nedialkov and I (George Corliss)  with quite a few Sun people.
Here is my visit report:


C++ compiler developers:
Steve Clamage <Stephen.Clamage@Sun.com>
Lawrence Crowl <Lawrence.Crowl@Sun.com>

Steve and Lawrence are both members of the C++ Committee (J16),
representing Sun. Steve is the chair of J16.  It was Lawrence
who wrote the comment to the this group in early March about
passing by value.

The discussion was quite wide ranging, but here are some points.

The standards committee is also considering user-defined literals.
If they adopt something there, we can probably use whatever is
adopted for our problems of literals in an interval context.

Sun has an open source release of its interval elementary functions,
so the barrier to entry is low.  That means we CAN require math.h
functions be provided in an interval standard.

Lawrence feels strongly that the standard should be to pass by
value.  Intervals are small data structures; by value allows them
to be passed in registers for speed.  That is how the current Sun
C++ compiler works.  There is no reason to follow the C++ complex
standard.  The library is often taken as an example by coders, and
there is no good reason to follow the tradition of C from 20 years
ago that structures should be passed by reference.

Infinities, etc.  Define mathematically what you must contain, and
permit as much implementation creativity as you can.

At this point, correctness is MUCH more important than speed.  When
people start demanding intervals be fast, we'll know we've won.
Having tests in each operation is not a problem.

Uninitialized.  The convention in C/C++ is to initialize to zero,
but we agree that is not correct for intervals.  Whole is probably
the best we can do.  Aside: The next day, we visited Berkeley and
talked with Jim Demmel and Bill Kahan.  Among other things, Kahan
wants user-defined data types to be tagged.  If we have the
Kahan-suggested tag, we can tag intervals as Uninitialized.

The 1999 C standard provides for access to IEEE hardware.  The
next version of the C++ standard will also address features new
in the 1999 C standard to be included in C++.

The current C++ standard does not discuss or acknowledge threads.
They are working on the next revision of the standard, which will
have something to say about threads in the language proper and in
the standard library.  Probably the interval standard should say,
"Intervals will be implemented in a thread-safe manner."

What it really takes to sell intervals to the standard committee
is evidence of users, together with broad agreement from the
domain experts.  I'll contact Siegfried to see what he knows about
numbers of users of his packages.  At some point, an open letter
to the standards committee with 100 signatures from the interval
community would help.

A freely available reference implementation is necessary.

Evidence of widespread teaching of intervals will help.



IEEE 754R
David Hough <David.Hough@Sun.com>

IEEE 754R is nearly over.  It is likely to include
   Decimal formats for floating point
       (Should C++ IA standard permit decimal intervals?)
   Quad precision
       (Should C++ IA standard quad intervals?)
   Fused Multiply and Add
       (I assume with directed rounding?
        Great for interval linear algebra, too)
   min/max
       (I wonder how they handle NaN, infinity, etc.)
   expression evaluation
       (Don't remember what that means)

As far as David is concerned, ISVs (Independent Software Vendors)
drive the market.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


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George,
Very interesting indeed. I added a few comments
Juergen

George Corliss schrieb:
> FYI:
> 
> Wednesday, March 29, Sun Microsystems
> Ned Nedialkov and I (George Corliss)  with quite a few Sun people.
> Here is my visit report:
> 
> 
> C++ compiler developers:
> Steve Clamage <Stephen.Clamage@Sun.com>
> Lawrence Crowl <Lawrence.Crowl@Sun.com>
> 
> Steve and Lawrence are both members of the C++ Committee (J16),
> representing Sun. Steve is the chair of J16.  It was Lawrence
> who wrote the comment to the this group in early March about
> passing by value.
> 
> The discussion was quite wide ranging, but here are some points.
> 
> The standards committee is also considering user-defined literals.
> If they adopt something there, we can probably use whatever is
> adopted for our problems of literals in an interval context.
> 
> Sun has an open source release of its interval elementary functions,
> so the barrier to entry is low.  That means we CAN require math.h
> functions be provided in an interval standard.

We SHOULD do this, but perhaps not with last bit accuracy.
filib provides another open source implementation with guaranteed bounds
> 
> Lawrence feels strongly that the standard should be to pass by
> value.  Intervals are small data structures; by value allows them
> to be passed in registers for speed.  That is how the current Sun
> C++ compiler works.  There is no reason to follow the C++ complex
> standard.  The library is often taken as an example by coders, and
> there is no good reason to follow the tradition of C from 20 years
> ago that structures should be passed by reference.

I fully agree
> 
> I
> IEEE 754R
> David Hough <David.Hough@Sun.com>
> 
> IEEE 754R is nearly over.  It is likely to include
>    Decimal formats for floating point
>        (Should C++ IA standard permit decimal intervals?)
>  
   Quad precision
>        (Should C++ IA standard quad intervals?)
basic arithmetic operations should work via template instantiation.
of course that does not hold for elementary functions
>    Fused Multiply and Add
>        (I assume with directed rounding?
>         Great for interval linear algebra, too)
>    min/max
>        (I wonder how they handle NaN, infinity, etc.)
>    expression evaluation
>        (Don't remember what that means)

perhaps the distinction of interval constants and variables with some 
possible preprocessing, such that x-x = 0 ??

> Dr. George F. Corliss
> Electrical and Computer Engineering
> Marquette University
> PO Box 1881 
> 1515 W. Wisconsin Ave.
> Milwaukee WI 53201-1881 USA
> 414-288-6599; Fax: 288-5579; Dept. 288-6280
> Office: Haggerty Engineering 296
> George.Corliss@Marquette.edu
> 
> 
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval
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George Corliss wrote:
> FYI:
> 
> Wednesday, March 29, Sun Microsystems
> Ned Nedialkov and I (George Corliss)  with quite a few Sun people.
> Here is my visit report:

Thanks for the report.

> C++ compiler developers:
> Steve Clamage <Stephen.Clamage@Sun.com>
> Lawrence Crowl <Lawrence.Crowl@Sun.com>
> 
> Steve and Lawrence are both members of the C++ Committee (J16),
> representing Sun. Steve is the chair of J16.  It was Lawrence
> who wrote the comment to the this group in early March about
> passing by value.

Note that I am attending the ISO C++ meeting this week in Berlin,
so I will have the opportunity to present the status (briefly, as
I don't think we are ready to show a concrete update adressing all
the comments), and discuss with Lawrence and Steve.

> The discussion was quite wide ranging, but here are some points.
> 
> The standards committee is also considering user-defined literals.
> If they adopt something there, we can probably use whatever is
> adopted for our problems of literals in an interval context.
> 
> Sun has an open source release of its interval elementary functions,
> so the barrier to entry is low.  That means we CAN require math.h
> functions be provided in an interval standard.

There are also other open source implementations available.
However, at the presentation in Mont-Tremblant, the committee was
a bit reluctant to add more "complicated numeric functions" to
the standard, because there was other proposals with such a common
theme.  So the question might boild down to whether we prefer to
have nothing or an incomplete library.

I however agree that this would make the proposal attractive to more
users, and that the more complete implementation based on existing
codes is probably not that hard.

> Lawrence feels strongly that the standard should be to pass by
> value.  Intervals are small data structures; by value allows them
> to be passed in registers for speed.  That is how the current Sun
> C++ compiler works.  There is no reason to follow the C++ complex
> standard.  The library is often taken as an example by coders, and
> there is no good reason to follow the tradition of C from 20 years
> ago that structures should be passed by reference.

I don't have any strong opinion on this.
I only did a very local experiment on some code of mine on x86, and
changing to pass-by-value slowed the code down a bit.
I am ready to follow any recommendation from the commitee on this.
I tend to think that there should be a general policy for the standard
library, otherwise I fear that the library might become inconsistent
in that respect.


> Infinities, etc.  Define mathematically what you must contain, and
> permit as much implementation creativity as you can.
> 
> At this point, correctness is MUCH more important than speed.  When
> people start demanding intervals be fast, we'll know we've won.
> Having tests in each operation is not a problem.

Well, if we're arguing that passsing-by-value is fundamentally important
for speed, and that adding a few more tests is not because speed is less
important... ;)

It's important to get the semantics that most people want first,
I agree.

> Uninitialized.  The convention in C/C++ is to initialize to zero,
> but we agree that is not correct for intervals.  Whole is probably
> the best we can do.

I'm not convinced.  Initilization to [0,0] seems nice to me for
intervals because of homogeneity reasons with floating-point.
I could even imagine that the empty interval would make as much
sense as whole.

What makes you think that [0,0] is "not correct", and why 'whole'
would be better than 'empty' ?

 >  Aside: The next day, we visited Berkeley and
> talked with Jim Demmel and Bill Kahan.  Among other things, Kahan
> wants user-defined data types to be tagged.  If we have the
> Kahan-suggested tag, we can tag intervals as Uninitialized.

Could you elaborate on this tag ?  What would it do ?
Would this be a run-time feature of the objects telling if
they are initialized or not ?  Can't this be left to some
"debug mode" ?

> The 1999 C standard provides for access to IEEE hardware.  The
> next version of the C++ standard will also address features new
> in the 1999 C standard to be included in C++.
> 
> The current C++ standard does not discuss or acknowledge threads.
> They are working on the next revision of the standard, which will
> have something to say about threads in the language proper and in
> the standard library.  Probably the interval standard should say,
> "Intervals will be implemented in a thread-safe manner."

I guess this will have to be true for the whole standard library,
or almost all, so I don't think we should worry specifically about
this at the interval level, other than stating this requirement.

> What it really takes to sell intervals to the standard committee
> is evidence of users, together with broad agreement from the
> domain experts.  I'll contact Siegfried to see what he knows about
> numbers of users of his packages.  At some point, an open letter
> to the standards committee with 100 signatures from the interval
> community would help.

The web-survey we are conducting has already been able to collect
some informations for this purpose.  I hope Herve will be able to
produce a summary soon.

> A freely available reference implementation is necessary.

We have already a preliminary one, but it should be improved
and updated.  We (Herve, Guillaume and myself) are lacking time
for this, so we should organize a bit more with other volunteers.

> Evidence of widespread teaching of intervals will help.

> 
> 
> IEEE 754R
> David Hough <David.Hough@Sun.com>
> 
> IEEE 754R is nearly over.  It is likely to include
>    Decimal formats for floating point
>        (Should C++ IA standard permit decimal intervals?)

We have explicitly asked this question (at the Mont-Tremblant meeting)
to the IBM representant supporting the decimal floating-point proposal.
He agreed that, at least currently, there is no need for this
compatibility as the corresponding user communities targetted are
a priori separate.

>    Quad precision
>        (Should C++ IA standard quad intervals?)

I would say that it depends if quads appear in the C++ language
(or is this supposed to be the already existing "long double" ?).
But if they appear, probably support for interval<quads> should
be added, yes.

>    Fused Multiply and Add
>        (I assume with directed rounding?
>         Great for interval linear algebra, too)

I guess it also depends if there appears a function for doing fma
on floating-point types in C++, in which case a natural overload
for intervals would be nice and natural.

>    min/max
>        (I wonder how they handle NaN, infinity, etc.)
>    expression evaluation
>        (Don't remember what that means)
> 
> As far as David is concerned, ISVs (Independent Software Vendors)
> drive the market.

More generally, since IEEE754R will most probably be released before
C++0x, it would be nice if C++0x would take it into account.

-- 
Sylvain
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Sylvain Pion <Sylvain.Pion@sophia.inria.fr> writes:
 >Well, if we're arguing that passsing-by-value is fundamentally important
 >for speed, and that adding a few more tests is not because speed is less
 >important... ;)

Pass-by-value is also a correctness issue.

 >> Uninitialized.  The convention in C/C++ is to initialize to zero,
 >> but we agree that is not correct for intervals.  Whole is probably
 >> the best we can do.
 >
 >I'm not convinced.  Initilization to [0,0] seems nice to me for
 >intervals because of homogeneity reasons with floating-point.
 >I could even imagine that the empty interval would make as much
 >sense as whole.
 >
 >What makes you think that [0,0] is "not correct", and why 'whole'
 >would be better than 'empty' ?

Note that on modern systems, initialization to [0,0] is more efficient.

 >>    Quad precision
 >>        (Should C++ IA standard quad intervals?)
 >
 >I would say that it depends if quads appear in the C++ language
 >(or is this supposed to be the already existing "long double" ?).
 >But if they appear, probably support for interval<quads> should
 >be added, yes.

The meaning of long double is implementation-dependent.  On Solaris
SPARC, it is 128 bits.  On Solaris x86, it is 80 bits.

 >More generally, since IEEE754R will most probably be released before
 >C++0x, it would be nice if C++0x would take it into account.

An explicit mention of IEEE754R in the C++ standard will require a
paper.

  Lawrence Crowl             650-786-6146   Sun Microsystems, Inc.
                   Lawrence.Crowl@Sun.com   16 Network Circle, UMPK16-303
           http://www.Crowl.org/Lawrence/   Menlo Park, California, 94025
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Subject: Re: [std-interval] C++ interval std
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Sylvain Pion wrote:
>> Steve and Lawrence are both members of the C++ Committee (J16),
>> representing Sun. Steve is the chair of J16.  It was Lawrence
>> who wrote the comment to the this group in early March about
>> passing by value.
> 
> Note that I am attending the ISO C++ meeting this week in Berlin,
> so I will have the opportunity to present the status (briefly, as
> I don't think we are ready to show a concrete update adressing all
> the comments), and discuss with Lawrence and Steve.
Understood.  I hope that as soon as you have an updated draft of the
proposal, you'll let us all know.

>> Sun has an open source release of its interval elementary functions,
>> so the barrier to entry is low.  That means we CAN require math.h
>> functions be provided in an interval standard.
> 
> There are also other open source implementations available.
> However, at the presentation in Mont-Tremblant, the committee was
> a bit reluctant to add more "complicated numeric functions" to
> the standard, because there was other proposals with such a common
> theme.  So the question might boild down to whether we prefer to
> have nothing or an incomplete library.
> 
> I however agree that this would make the proposal attractive to more
> users, and that the more complete implementation based on existing
> codes is probably not that hard.
Since there are AT LEAST two implementations of elementary functions
available, I favor asking that they be included in the standard, unless the
committee balks.

>> Infinities, etc.  Define mathematically what you must contain, and
>> permit as much implementation creativity as you can.
>> 
>> At this point, correctness is MUCH more important than speed.  When
>> people start demanding intervals be fast, we'll know we've won.
>> Having tests in each operation is not a problem.
> 
> Well, if we're arguing that passsing-by-value is fundamentally important
> for speed, and that adding a few more tests is not because speed is less
> important... ;)
> 
> It's important to get the semantics that most people want first,
> I agree.
Pass by value vs. pass by reference is an issue of speed and flexibility, as
I understand it.  There is no question of tightness.

Several of the possible choices about infinities, for example, give
enclosures in a wider set of cases, at the expense of additional tests.
There, I argue that we MUST get enclosures (I hear no opposition to that),
we SHOULD get them in as wide a set of circumstances as possible
(alternative being some form of "I can't," such as an exception or some form
of NaN), and we should get as tight as we can (but that's a Quality of
Implementation issue.

>> Uninitialized.  The convention in C/C++ is to initialize to zero,
>> but we agree that is not correct for intervals.  Whole is probably
>> the best we can do.
> 
> I'm not convinced.  Initilization to [0,0] seems nice to me for
> intervals because of homogeneity reasons with floating-point.
> I could even imagine that the empty interval would make as much
> sense as whole.
> 
> What makes you think that [0,0] is "not correct", and why 'whole'
> would be better than 'empty' ?
I agree that initialization of uninitialized intervals to [0,0] is easy, and
it is consistent with floating-point practice.  My reservation is that it
can lead to violations of containment.

The issue is not with "our" code.  It is with users' code.  Floating-point
arithmetic makes no promises of accuracy.  Intervals promise a guaranteed
enclosure.  If a user mis-uses our tools and gets a violation of
containment, WE will be blamed, not the programmer who forgot to initialize
all variables.  I want to make it as difficult as possible for even
incorrect code to lie.

Simple example:
   interval Pi;
   cout << "Pi is enclosed by " << Pi;

The result violates containment if the default initializer is either [0, 0]
or Empty.  It is truthful if the initializer is Whole.

Of course, no one would do that on purpose, but programmers DO sometimes use
variables they have not initialized.

One easy-to-imagine case might define a variable by a complicated set of
nested cases/ifs.  The programmer thinks all possible cases are covered, but
misses one case.  In that case, the variable is not given a value, but the
following code uses it, unaware that it might not have been assigned a valid
value.

Asserting that a set is empty is perhaps the strongest assertion one can
make about a set.  Asserting that it is contained in the universal set is
the weakest assertion one can make.  That is why I argue for Whole.

I'd like to have some special "undefined" value that would propagate like a
NaN, but that is too much to ask for.  Whole does not lie.

A Tag (see below) could be used for exactly that purpose.

>>  Aside: The next day, we visited Berkeley and
>> talked with Jim Demmel and Bill Kahan.  Among other things, Kahan
>> wants user-defined data types to be tagged.  If we have the
>> Kahan-suggested tag, we can tag intervals as Uninitialized.
> 
> Could you elaborate on this tag ?  What would it do ?
> Would this be a run-time feature of the objects telling if
> they are initialized or not ?  Can't this be left to some
> "debug mode" ?
Let me explain Kahan's reasoning, as well as I am able.

The request is that a tag be permitted by the standard.  As I understand it,
what would be required is to remove the phrase that an interval is
represented by two values.  The down side, of course, is that it is harder
to know how much memory an interval may require.

If we are permitted a tag, the tag can be used in MANY different ways within
an implementation.  The tag could be an attribute, or it could be a pointer
to a complicated internal data structure of properties of the interval.  The
most extreme case I can think of is that the tag might point to the Abstract
Syntax Tree that generated the interval, allowing run-time symbolic
processing.

In most implementations I can imagine, the tag could be used for
"uninitialized," "exterior interval," various flavors of NaN, precision in a
multiple precision implementation, and the like.  If we want a (center,
radius) implementation, a tag could distinguish semi-infinite intervals, or
it could distinguish [lo, hi] from (center, radius) intervals.

The proposed standard is 1-D, where boxes and ellipses are the same (finite)
sets, but if we want to build higher-dimensional Interval, we might consider
subclasses Box and Ellipse, although polymorphism handles that without
explicit tags.  Hmmmm.  That suggests that C++ run-time types form a sort of
tag.

>> The 1999 C standard provides for access to IEEE hardware.  The
>> next version of the C++ standard will also address features new
>> in the 1999 C standard to be included in C++.
>> 
>> The current C++ standard does not discuss or acknowledge threads.
>> They are working on the next revision of the standard, which will
>> have something to say about threads in the language proper and in
>> the standard library.  Probably the interval standard should say,
>> "Intervals will be implemented in a thread-safe manner."
> 
> I guess this will have to be true for the whole standard library,
> or almost all, so I don't think we should worry specifically about
> this at the interval level, other than stating this requirement.
Agreed.

>> IEEE 754R
>> David Hough <David.Hough@Sun.com>
>> 
>> IEEE 754R is nearly over.  It is likely to include
>>    Decimal formats for floating point
>>        (Should C++ IA standard permit decimal intervals?)
> 
> We have explicitly asked this question (at the Mont-Tremblant meeting)
> to the IBM representant supporting the decimal floating-point proposal.
> He agreed that, at least currently, there is no need for this
> compatibility as the corresponding user communities targeted are
> a priori separate.
As I read it, there is nothing to prevent someone from offering additional
base types, including decimal or multiple precision?  Technically, they
would not be standard-conforming, but they could conform to the spirit.

>>    Fused Multiply and Add
>>        (I assume with directed rounding?
>>         Great for interval linear algebra, too)
> 
> I guess it also depends if there appears a function for doing fma
> on floating-point types in C++, in which case a natural overload
> for intervals would be nice and natural.
The benefit to intervals is clearer at the vector level, which the proposed
standard does not consider.  My observation is that a dot product is easier,
tighter, or faster with a directed rounding FMA.

>>    min/max
>>        (I wonder how they handle NaN, infinity, etc.)
>>    expression evaluation
>>        (Don't remember what that means)
>> 
>> As far as David is concerned, ISVs (Independent Software Vendors)
>> drive the market.
> 
> More generally, since IEEE754R will most probably be released before
> C++0x, it would be nice if C++0x would take it into account.
Yes, probably.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


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Subject: Re: [std-interval] C++ interval std 
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Lawrence Crowl writes:
>> Well, if we're arguing that passsing-by-value is fundamentally important
>> for speed, and that adding a few more tests is not because speed is less
>> important... ;)
> Pass-by-value is also a correctness issue.
Opps.  I missed that point.

>>> Uninitialized.  The convention in C/C++ is to initialize to zero,
>>> but we agree that is not correct for intervals.  Whole is probably
>>> the best we can do.
>> 
>> I'm not convinced.  Initilization to [0,0] seems nice to me for
>> intervals because of homogeneity reasons with floating-point.
>> I could even imagine that the empty interval would make as much
>> sense as whole.
>> 
>> What makes you think that [0,0] is "not correct", and why 'whole'
>> would be better than 'empty' ?
> 
> Note that on modern systems, initialization to [0,0] is more efficient.
That may be, but I maintain Whole is most faithful to "Thou shalt not lie."

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


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George Corliss wrote:
>> Lawrence feels strongly that the standard should be to pass by
>> value.  Intervals are small data structures; by value allows them
>> to be passed in registers for speed.  That is how the current Sun
>> C++ compiler works.  There is no reason to follow the C++ complex
>> standard.  The library is often taken as an example by coders, and
>> there is no good reason to follow the tradition of C from 20 years
>> ago that structures should be passed by reference.

Sylvain Pion wrote:
> I don't have any strong opinion on this.
> I only did a very local experiment on some code of mine on x86, and
> changing to pass-by-value slowed the code down a bit.

   I was curious to see about the speed difference between passing by
value and passing by reference, because passing by value always has been
slower and always *has* to be slower because it (unnecessarily) creates
a copy of the object when passed in.  I tried three ways on x86_64, gcc
3.4.4, linux:

No optimization:
addByValue:     2230000 ticks
addByRef:       1850000 ticks
addByConstRef:  1880000 ticks

-O:
addByValue:     870000 ticks
addByRef:       550000 ticks
addByConstRef:  510000 ticks

-O2:
addByValue:     720000 ticks
addByRef:       410000 ticks
addByConstRef:  440000 ticks

-O3:
addByValue:     1110000 ticks
addByRef:       600000 ticks
addByConstRef:  610000 ticks

   There's a bit of noise in the numbers, but passing by value is always
significantly slower.  These tests were run repeatedly and the
proportions are always the same.  -O3 is actually consistently slower,
which shouldn't surprise anyone who has worked with performance tuning
in gcc.  It usually is.

   Also ran on x86 Windows.  Pattern was the same.  With -O2, passing by
value took about 2.6 times as long!

   I didn't test passing by pointer, but I can.

   Passing in unmodifiable objects as constant references when
appropriate both obviates the need for copying and gives explicit
const-correctness from the start.  We don't have to worry about
dereferencing pointers or memory ownership issues.  It's indeed the
pattern followed by most modern libraries.

   To the caller of the functions, it just looks like an ordinary
pass-by-value, but is faster, and allows the compiler to catch a lot of
types of problems.

   I recommend that for long-term performance and const-correctness,
that objects be passed as constant references when possible.

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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Alan Eliasen wrote, On 04/05/06 15:20:
> George Corliss wrote:
>>>Lawrence feels strongly that the standard should be to pass by
>>>value.  Intervals are small data structures; by value allows them
>>>to be passed in registers for speed.
[...]
>    I was curious to see about the speed difference between passing by
> value and passing by reference, because passing by value always has been
> slower and always *has* to be slower because it (unnecessarily) creates
> a copy of the object when passed in.  I tried three ways on x86_64, gcc
> 3.4.4, linux:
[...]
>    To the caller of the functions, it just looks like an ordinary
> pass-by-value, but is faster, and allows the compiler to catch a lot of
> types of problems.
> 
>    I recommend that for long-term performance and const-correctness,
> that objects be passed as constant references when possible.

This experiment is extremely platform specific, as you probably are
aware.  Most platforms in use today other than x86 will be the other way
around (add-by-value will be faster than add-by-const-ref).
(Was this 64-bit code?  I thought x86_64 would be faster with
pass-by-value since I got the impression the ABI passed parameters in
registers)

With inlining then they should be identical (perhaps you could re-run
your experiment with inlining to verify this?).

Surely it is possible to permit the implementer to choose the parameter
passing convention, between pass-by-value and pass-by-const-ref?  It
should have no visible impact on the programmer which is used.

e.g., within interval<T>:
typedef interval<T> param_type;
or
typedef const interval<T>& param_type;

cheers,
/lib
-- 
/lib BillClarke PostdoctoralFellow CompSci ANU cs.anu.edu.au/CC-NUMA
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 -------------- Original message ----------------------
From: std-interval-request@compgeom.poly.edu
> Send Std-interval mailing list submissions to
> 	std-interval@compgeom.poly.edu
----------------------------------------------------------------------
> 
> Message: 1
> Date: Mon, 03 Apr 2006 20:13:45 -0500
> From: George Corliss <George.Corliss@marquette.edu>
> Subject: [std-interval] C++ interval std
> To: <std-interval@compgeom.poly.edu>
> Message-ID: <C0573279.37DC%George.Corliss@Marquette.edu>
> Content-Type: text/plain;	charset="US-ASCII"
> 

[snip]

> Lawrence feels strongly that the standard should be to pass by
> value.  Intervals are small data structures;

That perspective causes problems, just as it did for complex.  Intervals should be considered atomic types whose internal structure is opaque.  We don't consider fp types as structures even though they consist of three distinct fields (and in fact are treated as separate fields in software implementations of the run-time library).

> by value allows them
> to be passed in registers for speed.  That is how the current Sun
> C++ compiler works.  There is no reason to follow the C++ complex
> standard.  The library is often taken as an example by coders, and
> there is no good reason to follow the tradition of C from 20 years
> ago that structures should be passed by reference.

There may or may not be a good reason for it.  On FPUs with weak connections to the CPU, such as x87, passing by value is strongly preferred.  Yet on FPUs with strong connections to the main CPU passing by reference might be much more efficient.

If the standard syntax is pass by value then a compiler that prefered pass by reference would be free to do so internally (assuming appropriate referential safe guards).

> Uninitialized.  The convention in C/C++ is to initialize to zero,

Not quite.  The default initialization convention in C depends on the lifetime of the object.  Dynamic objects (typically stack and heap) are not initialized at all by default.  Static objects are initialized to zero, but that is not a special property of numerics.  All static objects lacking an initialization expression get a default expression of zero.

Intervals should work the same way.  Anything with an init expression gets it.  Anything without one gets default initialized.  Statics get zero and dynamics don't get touched (c.f. core constants).  Only the latter is a concern, and then only during development/debug.

Typical C programmer rant:  If I _wanted_ it initialized I would have done it _myself_ -- don't slow me down without my permission.

On platforms with NaN support uninitialized FP objects that will be initialized without the programmer's explicit permission should get a characteristic NaN.  On platforms without NaN support they should get HUGE_VAL because that is the standard diagnostic value.

So the default constructor should either use NaN, which would then be an empty interval or HUGE_VAL, which would match the existing standard for "something to think about here".

> but we agree that is not correct for intervals.  Whole is probably
> the best we can do.

Yuck.  Empty is clearly superior to whole in that it has less chance of accidentally producing apparently sensible results.  And for production an uninitialized interval should not be initialized.  After all,  C++ lacks basis support for array initialization so any default initialization effort, like touching every value in a big array, is just wasted time.

>  Aside: The next day, we visited Berkeley and
> talked with Jim Demmel and Bill Kahan.  Among other things, Kahan
> wants user-defined data types to be tagged.  If we have the
> Kahan-suggested tag, we can tag intervals as Uninitialized.

How will uninit tags be handled when they meet other values?  Will they have precedence as NaNs do?  If so then external tags are unnecessarily duplicative of internal values such as a characteristic NaN.

> 
> The 1999 C standard provides for access to IEEE hardware.  The
> next version of the C++ standard will also address features new
> in the 1999 C standard to be included in C++.
> 
> The current C++ standard does not discuss or acknowledge threads.
> They are working on the next revision of the standard, which will
> have something to say about threads in the language proper and in
> the standard library.  Probably the interval standard should say,
> "Intervals will be implemented in a thread-safe manner."

That is a tall order.  Intervals should be thread safe when the underlying language is thread-safe.  Consider errno and matherr() for intervals.

> IEEE 754R is nearly over.  It is likely to include
>    Decimal formats for floating point
>        (Should C++ IA standard permit decimal intervals?)

Of course.  For every floating point type we need a corresponding interval type.  The radix is irrelevant.

>    Quad precision
>        (Should C++ IA standard quad intervals?)

Of course.  For every floating point type we need a corresponding interval type.  The mantissa width is irrelevant.

>    Fused Multiply and Add
>        (I assume with directed rounding?
>         Great for interval linear algebra, too)
>    min/max
>        (I wonder how they handle NaN, infinity, etc.)

In the proposal only NaNs are special.  In min() NaNs are greater than all numbers. In max() NaNs are lesser than all numbers.

>    expression evaluation
>        (Don't remember what that means)

Mainly control over the width or temporaries used during calculation (implict promotion to double or extended double causes problems such as multiple rounding and can be orders of magnitude slower if the wider types are not supported in hardware).

This is a complex area.  There are other aspects under consideration such as programmer control of order of evaluation and programmer permission for various optimization transforms.

_____________________________________________
> > Std-interval mailing list
> > Std-interval@compgeom.poly.edu
> > http://compgeom.poly.edu/mailman/listinfo/std-interval
> 
> ------------------------------
> Message: 3
> Date: Tue, 04 Apr 2006 11:11:58 +0200
> From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <4432385E.4050805@sophia.inria.fr>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed

> George Corliss wrote:
> > Lawrence feels strongly that the standard should be to pass by value.  Intervals are small data structures; by value allows them to be passed in registers for speed.  That is how the current Sun C++ compiler works.  There is no reason to follow the C++ complex standard.  The library is often taken as an example by coders, and there is no good reason to follow the tradition of C from 20 years ago that structures should be passed by reference.
 
> I don't have any strong opinion on this. I only did a very local experiment on some code of mine on x86, and changing to pass-by-value slowed the code down a bit.

Some compilers give the programmer little control over parameter passing.  Others give a great deal of control, including offering both stack and register passing for atomic types, putting small structs in registers, and even hybrids with part in registers and part on the stack.

This matters because the implementor _must_ have the freedom to optimize parameter passing.  So the standard should be as quiet as possible on the issue.  The _syntax_ should be by-value because that imposes the least (i.e., no actual) constraints.  But the code generated could be either at the discretion of the implementor.

The best approach is probably a second set of types that are specifically used for argument passing.  Portable code often uses this approach.  It allows an implementor to alter the parameter passing convention on a platform-by-platform basis.

So non-inline interval functions would take arguments of type IntervalArg<double> from which the function could obtain the actual argument.

> > Uninitialized.  The convention in C/C++ is to initialize to zero,
> > but we agree that is not correct for intervals.  Whole is probably
> > the best we can do.
> 
> I'm not convinced.  Initilization to [0,0] seems nice to me for
> intervals because of homogeneity reasons with floating-point.

But it's not homogeneous except in the case of static variables.  The default constructor simply needs an _isBSS() predicate or something similar to determine whether to initialize the value to binary zero, which might or might not be tge numeric value [0,0], or to leave the value uninitialized.

> I could even imagine that the empty interval would make as much sense as whole.

More IMHO.

>  >  Aside: The next day, we visited Berkeley and
> > talked with Jim Demmel and Bill Kahan.  Among other things, Kahan
> > wants user-defined data types to be tagged.  If we have the
> > Kahan-suggested tag, we can tag intervals as Uninitialized.
> 
> Could you elaborate on this tag ?  What would it do ?
> Would this be a run-time feature of the objects telling if
> they are initialized or not ?  Can't this be left to some
> "debug mode" ?

The concept includes things like the openness of the ends of the intervals and the possiblity of including dependency info (or links) to enable run-time narrowing of exaggerated interval widths caused by inconsistent expression evaluation (commony called multiple dependency).  It also includes the possiblity of representing the full set of function results rather than only the results of domain-filtered parameters.

> > IEEE 754R is nearly over.  It is likely to include
> >    Decimal formats for floating point
> >        (Should C++ IA standard permit decimal intervals?)
> 
> We have explicitly asked this question (at the Mont-Tremblant meeting)
> to the IBM representant supporting the decimal floating-point proposal.
> He agreed that, at least currently, there is no need for this
> compatibility as the corresponding user communities targetted are
> a priori separate.

If you adopt this reasoning then there should be no interval standard.  Consider that a standard based upon the above rationale would maintain and/or increase that division within the user community.  I consider that to be a Bad Thing(tm).

> >    Fused Multiply and Add
> >        (I assume with directed rounding?
> >         Great for interval linear algebra, too)
> 
> I guess it also depends if there appears a function for doing fma
> on floating-point types in C++, in which case a natural overload
> for intervals would be nice and natural.

This is an iceberg issue.  It is not only the existence of an explicit fma function that is at issue.  The hidden part of this issue is that the compiler may transform ordinary algebraic expressions into fma instructions rather than just add & mul instructions.  If the code generation works for fp types but not for interval types then users will not want to use intervals.

The hidden part of this issue is not a library issue, but a compiler/code generator issue.  If fma support makes it into the language (which is mostly an issue of how to tell the compiler when it is forbidden to generate the fma instruction) then inline and template implementations of intervals will need to be written so they work no matter how the controls are set.  That can be fairly subtle due to the fact that the effect of outward rounding on an fma instruction is sometimes murky.

> ------------------------------
> 
> Message: 4
> Date: Tue, 04 Apr 2006 03:33:53 -0700
> From: Lawrence.Crowl@Sun.com
> Subject: Re: [std-interval] C++ interval std 
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <200604041033.k34AXrbd008489@philmont.sfbay.sun.com>
> 
> Sylvain Pion <Sylvain.Pion@sophia.inria.fr> writes:
>  >Well, if we're arguing that passsing-by-value is fundamentally important
>  >for speed, and that adding a few more tests is not because speed is less
>  >important... ;)
> 
> Pass-by-value is also a correctness issue.

How so?

> 
>  >> Uninitialized.  The convention in C/C++ is to initialize to zero,
>  >> but we agree that is not correct for intervals.  Whole is probably
>  >> the best we can do.
>  >
>  >I'm not convinced.  Initilization to [0,0] seems nice to me for
>  >intervals because of homogeneity reasons with floating-point.
>  >I could even imagine that the empty interval would make as much
>  >sense as whole.
>  >
>  >What makes you think that [0,0] is "not correct", and why 'whole'
>  >would be better than 'empty' ?
> 
> Note that on modern systems, initialization to [0,0] is more efficient.

Please state the reasoning behind the above statement.

> 
>  >>    Quad precision
>  >>        (Should C++ IA standard quad intervals?)
>  >
>  >I would say that it depends if quads appear in the C++ language
>  >(or is this supposed to be the already existing "long double" ?).
>  >But if they appear, probably support for interval<quads> should
>  >be added, yes.
> 
> The meaning of long double is implementation-dependent.  On Solaris
> SPARC, it is 128 bits.  On Solaris x86, it is 80 bits.

And some compilers accept the syntax of long double but don't implement it (long double becomes a synonym for double).

===================
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Bill Clarke wrote:
> 
> Surely it is possible to permit the implementer to choose the parameter
> passing convention, between pass-by-value and pass-by-const-ref?  It
> should have no visible impact on the programmer which is used.

The standard can state, for example, that that whether a parameter is passed by 
value or by reference is implementation-defined, meaning that an implementation 
can choose either and must document the choice. Or it could say that the choice 
is unspecified, meaning that the implementation does not need to document what 
it does, and does not need to be consistent.

The choice can have an effect on programmers, however, since the types of the 
functions
   interval foo(interval);
   interval foo(const interval&);
are different.

1. If you create a function pointer interval(*)(interval), it cannot be used to 
hold the address of "interval foo(const interval&)". I don't know of a 
convenient way to deal with this problem, where you need to modify your code 
based on details of a predefined type.

2. The result of typeid(foo) is different in the two cases, which can affect the 
operation of a program.
     interval bar(const interval&);
     if( typeid(foo) == typeid(bar) ) ...

That said, it is already the case that member functions of classes in the 
standard library are explicitly allowed to vary from the exemplars listed in the 
standard. But the implementation is required to accept code that is valid for 
the exemplars.

Example: An implementation can add a default parameter to a class member 
function. If the standard says this:
      class Foo {
      public:
            fun(int);
      };
An implemtation can have this:
     class Foo {
     public:
           fun(int, int=0);
     };
According to the standard, the following is valid:
     Foo f;
     f.fun(3);
and indeed that code compiles with the modified implementation.

Similarly, code that can call one of the versions of the interval function foo 
above can also call the other version.

My point is that allowing freedom of implementation is not without consequences 
for C++ programmers, but there is already some precedent for that freedom of 
implementation. We need to be aware of the potential problems for programmers, 
and make a considered choice.

---
Steve Clamage, stephen.clamage@sun.com

From Sylvain.Pion@sophia.inria.fr Wed Apr  5 04:25:05 2006
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[ Let me create separate threads of discussion on each point. ]


Summary of the arguments on this issue:

1- pass by value can be faster or slower than pass by reference
    depending on the processor/ABI.
2- pass by value can be faster due to removal of aliasing issues.
3- pass by value is safer in general as a programming idiom
    (an example is operator*= which may need tweaking to protect
     itself multipliying by *this)
4- pass by reference is consistent with std::complex
5- having it specified is useful when taking addresses of functions.


Possible solutions, assuming we want a uniform treatment for all
functions on intervals:

1- enforce pass-by-value
2- enforce pass-by-ref
3- leave freedom for the implementation to choose
4- leave freedom for the implementation and have it provide
    a standard specified way to obtain this information.


Now, I assume that users want the best performance on all
compilers/processors, so I don't like 1 nor 2.
I also do not see a large need for manipulating function
pointers for the intervals, I never needed that personnaly
at least (speak up if you think it is an important use case).
If there is indeed no large need for these, and given that it
is always possible (though painful) to write function wrappers
to get function pointers, then I would prefer 3 to 4.  I think
the complexity of implementing 4 is not worth it.  Moreover,
specifying 4- can be proposed later as an addition (e.g. in
the more general context of the whole standard library).


So, as for the proper text in the proposal, let me propose:
- to have the text of the function prototypes use pass-by-value,
   as it fulfills the "advocate safer programming style" argument
   of Lawrence, and it is also shorter.
- a note at the beginning mentionning that the implementation
   is free to use pass-by-reference.


Does this seem reasonnable ?

-- 
Sylvain
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Bill Clarke wrote:
> This experiment is extremely platform specific, as you probably are
> aware.  Most platforms in use today other than x86 will be the other way
> around (add-by-value will be faster than add-by-const-ref).

   How can that assertion possibly be made?  As you know, if a parameter
is passed by value, then the copy constructor is automatically called
for each object (e.g. twice for an add operator) on function entry, and
then the destructor is called (twice) on function exit.  The passed-in
objects should not be modified in the interim.  So pass-by-value
*always* has completely unnecessary overhead.  There is absolutely no
reason to copy and subsequently destroy the objects being passed in.
Passing by constant reference will *always* be faster in this respect,
as the copy constructors and destructors will never be called.

   The architecture doesn't matter.  Say, for an addition operator, if
you pass by value, you're *always* incurring the additional overhead of
two unnecessary object copies and two unnecessary object destructions.
There is simply no advantage to pass-by-value over
pass-by-constant-reference in any way.  Your compiler might be smart
enough to optimize out the copies and destructions, but pass-by-value
should *never* be faster with a reasonable compiler.

   Why would one ever want the compiler to potentially call copy
constructors and destructors when we *know* they're a total waste of
cycles?  We can simply prevent that inefficiency in advance for all
compilers.

> (Was this 64-bit code?  I thought x86_64 would be faster with
> pass-by-value since I got the impression the ABI passed parameters in
> registers)

   As I mentioned in my original message, I did the test with both
x86_64 code and x86.  The x86_64 code was 64-bit code, and those were
the numbers cited.  The difference in performance, as I noted, was even
greater on the x86.  (Pass-by-value was about 1.7 times slower on
x86_64, about 2.6 times slower on x86.)  Registers don't enter into the
picture.  Pass-by-constant-reference arguments can be passed in
registers too, of course.

   The difference is that pass-by-value is likely to perform unnecessary
copy constructors and unnecessary destructions.  There is simply no
advantage to this, when we can be smart and tell even the dumbest
compilers that these copying and destroying operations should never even
be attempted.  Silly, useless performance problems (e.g. unnecessary
copy constructor calls) will be avoided in advance.  That's a good thing.

> With inlining then they should be identical (perhaps you could re-run
> your experiment with inlining to verify this?).

   The constructor was inlined.  I fail to see how inlining could ever
make pass-by-value faster, as it always has unnecessary overhead.  A
smart compiler could make it *as* fast as pass-by-constant-reference,
but I can't see how it could ever make it faster.  Specifying
pass-by-constant-reference would simply eliminate a source of
inefficiency with broken compilers.

> Surely it is possible to permit the implementer to choose the parameter
> passing convention, between pass-by-value and pass-by-const-ref?  It
> should have no visible impact on the programmer which is used.

   I agree that it should have no visible impact on the library user.
But there is really no reason to *not* use pass-by-constant-reference.
 Even if you are doing lazy operations and need to modify some part of
the passed-in object, you can always use the "mutable" keyword.

   In short, if you can find a compiler that does pass-by-value faster
than pass-by-constant-ref, I'll show you a broken compiler.

   Specifying pass-by-constant-reference also allows the compiler to
detect and prevent accidental modification of the objects being passed
in, or erroneous programmer attempts to modify a passed-in object (which
is probably never what you want to do, and should always fail.)

   Const-correctness is also a desirable goal, in my opinion.  It
becomes prohibitive and breaks code to add const-correctness late in the
game, which is why we should get it right the first time.

   If you're interested, you can dowload the really simple test programs
here and run them on your own computer:

   http://futureboy.us/temp/Interval.h
   http://futureboy.us/temp/Interval.cc

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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first.i.last@comcast.net wrote:
>>but we agree that is not correct for intervals.  Whole is probably
>>the best we can do.
> 
> Yuck.  Empty is clearly superior to whole in that it has less 
> chance of accidentally producing apparently sensible results.
> And for production an uninitialized interval should not be
> initialized.  After all,  C++ lacks basis support for array
> initialization so any default initialization effort, like touching
> every value in a big array, is just wasted time.

   I think that there should *never* be a zero-arg default constructor
for intervals.  All constructors should have at least one argument to
force the programmer to declare their intent.  There's no point to a
zero-argument constructor, because allowing such gives the programmer
*lots* of ways to mess up and use uninitialized objects.  If you want to
use an interval, you should provide reasonable arguments to it in a
constructor.  That way, you *never* get an Interval object that hasn't
been initialized to a known value.  A huge class of errors is eliminated
at compile-time!

   In my interval implementations in Java, there's no way to construct
an interval without specifying its values.  There's no reason to allow a
"default" interval.  I believe in constructing APIs that eliminate
sources of expected programmer error at compile-time.  This is an
obvious case.

   There is simply no reason to allow a "default" interval initialized
to a value that we *know* isn't right for anything.  We can prevent this
mess at compile time, and should.

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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Le mercredi 05 avril 2006 à 05:13 -0600, Alan Eliasen a écrit :

>    I think that there should *never* be a zero-arg default constructor
> for intervals.  All constructors should have at least one argument to
> force the programmer to declare their intent.

This is too strong a requirement. Forbidding arrays of intervals is a
sure way of alienating any C++ user. You need a default constructor if
you don't want the users to go to great and error-prone lengths to
create arrays (or any higher-level containers).

Best regards,

Guillaume

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Alan Eliasen wrote:
> Bill Clarke wrote:
> 
>>This experiment is extremely platform specific, as you probably are
>>aware.  Most platforms in use today other than x86 will be the other way
>>around (add-by-value will be faster than add-by-const-ref).
> 
> 
>    How can that assertion possibly be made?  As you know, if a parameter
> is passed by value, then the copy constructor is automatically called
> for each object (e.g. twice for an add operator) on function entry, and
> then the destructor is called (twice) on function exit.

A simple object like complex or interval should have no user-defined copy 
constructor or destructor. That is, the default copy constructor generated by 
the compiler does the right thing and does not need to be user-defined. The 
destructor has nothing to do, and so should not be user-defined. In that case, 
pass-by-value can be optimized into register passing with no additional copying.

It is possible to construct a test case where pass-by-value gives worse 
performance than pass-by-reference, and your example does indeed run faster with 
pass-by-reference using Sun compilers at low optimization.

At high optimization, the compiler eliminated the loops and all but one call to 
"add", which it inlined. I played with the test case for a short time, but was 
unable to defeat the optimizer with minor changes.

I will need a little time to construct a test case that forces the compiler to 
retain the loops and call the add functions. I'm at the C++ Committee meeting 
right now, and don't have much time to work on this test.

---
Steve Clamage, stephen.clamage@sun.com

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Subject: Re: [std-interval] C++ interval std
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
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Le mercredi 05 avril 2006 à 04:52 -0600, Alan Eliasen a écrit :
> Bill Clarke wrote:
> > This experiment is extremely platform specific, as you probably are
> > aware.  Most platforms in use today other than x86 will be the other way
> > around (add-by-value will be faster than add-by-const-ref).
> 
>    How can that assertion possibly be made?  As you know, if a parameter
> is passed by value, then the copy constructor is automatically called
> for each object (e.g. twice for an add operator) on function entry, and
> then the destructor is called (twice) on function exit.  The passed-in
> objects should not be modified in the interim.  So pass-by-value
> *always* has completely unnecessary overhead.  There is absolutely no
> reason to copy and subsequently destroy the objects being passed in.
> Passing by constant reference will *always* be faster in this respect,
> as the copy constructors and destructors will never be called.

Please note that our proposed interval type is meant to be a POD (plain
old data) type and as such has no copy constructor nor destructor. As a
consequence, on some architectures and with non-broken compilers, they
will behave no differently than if the function arguments were simply
integers; except that the register will probably be bigger, or two
registers will be used. When this happens, passing by value will be
faster than passing by const-reference. Indeed there is no architecture
such that foo(int) is slower than bar(int const &).

Best regards,

Guillaume

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Subject: Re: [std-interval] passing by value vs reference
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
To: std-interval@compgeom.poly.edu
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Le mercredi 05 avril 2006 à 11:32 +0200, Sylvain Pion a écrit :

> 3- leave freedom for the implementation to choose
> 4- leave freedom for the implementation and have it provide
>     a standard specified way to obtain this information.

> I would prefer 3 to 4.  I think
> the complexity of implementing 4 is not worth it.

I don't see any additional complexity in 4 with respect to 3. As already
mentioned by Bill Clarke, you could simply have a typedef member in
interval<T> to express the calling convention of the functions of the
interval library: typedef interval<T> const &param_type;

This requires all the functions of the library to use the same calling
convention. But I don't think it is too strong a requirement since there
is no function that uses more than two interval arguments.

Best regards,

Guillaume

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Subject: Re: [std-interval] C++ interval std 
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Alan Eliasen <eliasen@mindspring.com> writes:
 >   I was curious to see about the speed difference between passing by
 >value and passing by reference, because passing by value always has been
 >slower and always *has* to be slower because it (unnecessarily) creates
 >a copy of the object when passed in.

It does not unnecessarily create an object.  In particular, when the
parameter to a function is the result of an expression, the const ref
approach requires allocating a temporary and passing its address.  In
contrast, pass-by-value can put the result of the expression directly
into the parameter register; no copies are required.

Pass-by-reference aften introduces additional copies because the
programmer must copy the parameter into a local variable in order to
avoid aliases between parameters.

 >I tried three ways on x86_64, gcc 3.4.4, linux:

I would need the benchmark source in order to evaluate it and to
execute it on other systems.

In developing the SPARC V9 ABI, I showed a 7x performance advantage for
pass-by-value over pass-by-reference when computing Mandelbrot with
complex numbers.

 >   Passing in unmodifiable objects as constant references when
 >appropriate both obviates the need for copying and gives explicit
 >const-correctness from the start.  We don't have to worry about
 >dereferencing pointers or memory ownership issues.  It's indeed the
 >pattern followed by most modern libraries.

You are assuming that "const" means "unmodifiable".  It does not.  It
means that non-mutuable fields may not change when accessed through the
const-qualified name.  The object may still change via access through
non-const-qualified names.  The distinction between a value and a
reference is critical here, because the former is unaliased and the
latter is potentially aliased.  This aliasing can also have substantial
effect on the ability of the compiler to apply global optimizations.

 >   To the caller of the functions, it just looks like an ordinary
 >pass-by-value, but is faster, and allows the compiler to catch a lot of
 >types of problems.

But it doesn't look the same, because of the aliasing issue.  With
reference parameters, the function must make an explicit declaration
about its behavior in the presence of aliasing.

 >   I recommend that for long-term performance and const-correctness,
 >that objects be passed as constant references when possible.

Would you recommend that ints be passed by const reference?

  Lawrence Crowl             650-786-6146   Sun Microsystems, Inc.
                   Lawrence.Crowl@Sun.com   16 Network Circle, UMPK16-303
           http://www.Crowl.org/Lawrence/   Menlo Park, California, 94025
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first.i.last@comcast.net writes:
 >> Lawrence feels strongly that the standard should be to pass by
 >> value.  Intervals are small data structures;
 >
 >That perspective causes problems, just as it did for complex.
 >Intervals should be considered atomic types whose internal structure
 >is opaque.  We don't consider fp types as structures even though they
 >consist of three distinct fields (and in fact are t reated as separate
 >fields in software implementations of the run-time library).

The issue was the mechanism for passing the representation, not the
logical opacity of the type.

 >> by value allows them
 >> to be passed in registers for speed.  That is how the current Sun
 >> C++ compiler works.  There is no reason to follow the C++ complex
 >> standard.  The library is often taken as an example by coders, and
 >> there is no good reason to follow the tradition of C from 20 years
 >> ago that structures should be passed by reference.
 >
 >There may or may not be a good reason for it.  On FPUs with weak
 >connections to the CPU, such as x87, passing by value is strongly
 >preferred.  Yet on FPUs with strong connections to the main CPU
 >passing by reference might be much more efficient.

I don't follow the reasoning here.

 >If the standard syntax is pass by value then a compiler that prefered
 >pass by reference would be free to do so internally (assuming
 >appropriate referential safe guards).

SPARC V7 (32-bit) does in fact do this.  SPARC V9 (64-bit) does so
for large structs, but passes in registers for small structs.

 >> Uninitialized.  The convention in C/C++ is to initialize to zero,
 >
 >Not quite.  The default initialization convention in C depends on the
 >lifetime of the object.  Dynamic objects (typically stack and heap)
 >are not initialized at all by default.  Static objects are initialized
 >to zero, but that is not a special property of numerics.  All static
 >objects lacking an initialization expression get a default expression
 >of zero.

Correct.

 >> The current C++ standard does not discuss or acknowledge threads.
 >> They are working on the next revision of the standard, which will
 >> have something to say about threads in the language proper and in
 >> the standard library.  Probably the interval standard should say,
 >> "Intervals will be implemented in a thread-safe manner."
 >
 >That is a tall order.  Intervals should be thread safe when the
 >underlying language is thread-safe.  Consider errno and matherr() for
 >intervals.

More specifically, two threads should be able to operate on their
disjoint data without worry of interference.  Shared variables may need
synchronization.

 >Some compilers give the programmer little control over parameter
 >passing.  Others give a great deal of control, including offering both
 >stack and register passing for atomic types, putting small structs in
 >registers, and even hybrids with part in registers and part on the
 >stack.

Yes, though the controls are of dubious value.

 >This matters because the implementor _must_ have the freedom to
 >optimize parameter passing.  So the standard should be as quiet as
 >possible on the issue.  The _syntax_ should be by-value because that
 >imposes the least (i.e., no actual) constraints.  But the code
 >generated could be either at the discretion of the implementor.

Agreed.

 >The best approach is probably a second set of types that are
 >specifically used for argument passing.  Portable code often uses this
 >approach.  It allows an implementor to alter the parameter passing
 >convention on a platform-by-platform basis.  So non-inline interval
 >functions would take arguments of type IntervalArg<double> from which
 >the function could obtain the actual argument.

As Steve Clamage pointed out, you have interference when function
pointers are involved if you delay the parameter types.

 >> Pass-by-value is also a correctness issue.
 >
 >How so?

Because users will copy the style of interval function declarations.
If that style includes reference paramters, the programmers will litter
their programs with unintended aliases.  These aliases are the source
of bugs.

 >> Note that on modern systems, initialization to [0,0] is more efficient.
 >
 >Please state the reasoning behind the above statement.

Variables of static extent (globals, function-local static, static member)
can be allocated in a "fill with zeros" section if and only if their
initial representation consists of all zero.  This implies a [0,0] interval
with modern floating-point representations.  The same issue arises with
dynamically allocated code, though only on systems that first ensure
that they clear the memory.

 >> The meaning of long double is implementation-dependent.  On Solaris
 >> SPARC, it is 128 bits.  On Solaris x86, it is 80 bits.
 >
 >And some compilers accept the syntax of long double but don't
 >implement it (long double becomes a synonym for double).

This behavior falls under "quality of implementation". :-)

  Lawrence Crowl             650-786-6146   Sun Microsystems, Inc.
                   Lawrence.Crowl@Sun.com   16 Network Circle, UMPK16-303
           http://www.Crowl.org/Lawrence/   Menlo Park, California, 94025
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Steve Clamage <Stephen.Clamage@Sun.COM> writes:

| Alan Eliasen wrote:
| > Bill Clarke wrote:
| >
| >>This experiment is extremely platform specific, as you probably are
| >>aware.  Most platforms in use today other than x86 will be the other way
| >>around (add-by-value will be faster than add-by-const-ref).
| >    How can that assertion possibly be made?  As you know, if a
| > parameter
| > is passed by value, then the copy constructor is automatically called
| > for each object (e.g. twice for an add operator) on function entry, and
| > then the destructor is called (twice) on function exit.
| 
| A simple object like complex or interval should have no user-defined
| copy constructor or destructor. That is, the default copy constructor
| generated by the compiler does the right thing and does not need to be
| user-defined. The destructor has nothing to do, and so should not be
| user-defined. In that case, pass-by-value can be optimized into
| register passing with no additional copying.

I do agree with Steve.

-- Gaby
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Guillaume Melquiond wrote:
> Le mercredi 05 avril 2006 à 11:32 +0200, Sylvain Pion a écrit :
> 
> 
>>3- leave freedom for the implementation to choose
>>4- leave freedom for the implementation and have it provide
>>    a standard specified way to obtain this information.
> 
> 
>>I would prefer 3 to 4.  I think
>>the complexity of implementing 4 is not worth it.
> 
> 
> I don't see any additional complexity in 4 with respect to 3. As already
> mentioned by Bill Clarke, you could simply have a typedef member in
> interval<T> to express the calling convention of the functions of the
> interval library: typedef interval<T> const &param_type;
> 
> This requires all the functions of the library to use the same calling
> convention. But I don't think it is too strong a requirement since there
> is no function that uses more than two interval arguments.

I meant complexity for the proposal.  I think this issue has the
potential to raise questions I would prefer to avoid discussing
if possible, like:
- should this be a mecanism applicable to the whole std library
   types instead?
- should it be fine grained for each argument of each function?
- is such a type-based mecanism enough for all users needs
   (or is a macro necessary for example)?
   For example: how would a user defined template function on
   intervals be defined to play nicely with this implementation
   "preference":
     template < typename T >
     void f(std::interval<T>::param_type i)
   does not work.

So, let's first hear if there is a need for such a mechanism at all,
or if the "unspecified" approach, 3, is good enough.

-- 
Sylvain
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Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr> writes:

| Le mercredi 05 avril 2006 à 05:13 -0600, Alan Eliasen a écrit :
| 
| >    I think that there should *never* be a zero-arg default constructor
| > for intervals.  All constructors should have at least one argument to
| > force the programmer to declare their intent.
| 
| This is too strong a requirement. Forbidding arrays of intervals is a
| sure way of alienating any C++ user.

Indeed, that is an excellent observation.  It is good to take into
account experience of interval libraries in other languages; we must
however not forget ways C++ is natively used.

-- Gaby

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Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr> writes:

| Le mercredi 05 avril 2006 à 11:32 +0200, Sylvain Pion a écrit :
| 
| > 3- leave freedom for the implementation to choose
| > 4- leave freedom for the implementation and have it provide
| >     a standard specified way to obtain this information.
| 
| > I would prefer 3 to 4.  I think
| > the complexity of implementing 4 is not worth it.
| 
| I don't see any additional complexity in 4 with respect to 3. As already
| mentioned by Bill Clarke, you could simply have a typedef member in
| interval<T> to express the calling convention of the functions of the
| interval library: typedef interval<T> const &param_type;

If done that way, in the typical cases, the "T" would then appear in
non-deducible context. 

-- Gaby

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Le mercredi 05 avril 2006 à 15:37 +0200, Gabriel Dos Reis a écrit :

> | > I would prefer 3 to 4.  I think
> | > the complexity of implementing 4 is not worth it.
> | 
> | I don't see any additional complexity in 4 with respect to 3. As already
> | mentioned by Bill Clarke, you could simply have a typedef member in
> | interval<T> to express the calling convention of the functions of the
> | interval library: typedef interval<T> const &param_type;
> 
> If done that way, in the typical cases, the "T" would then appear in
> non-deducible context. 

Right. This occurred to me when reading Sylvain's reply. However,
although typical, it seems to me this only applies to cases outside the
interval library. Indeed, the functions of the library do not have to
use param_type, since they already know their own calling convention,
and hence T is deducible there. So the issue only applies to
user-defined template functions that would try to benefit from using the
same calling convention.

Anyway, do you know of a way to avoid this issue?
(Please do not suggest macros :-)

Best regards,

Guillaume


From Sylvain.Pion@sophia.inria.fr Wed Apr  5 08:56:16 2006
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Guillaume Melquiond wrote:
> Le mercredi 05 avril 2006 à 15:37 +0200, Gabriel Dos Reis a écrit :
> 
> 
>>| > I would prefer 3 to 4.  I think
>>| > the complexity of implementing 4 is not worth it.
>>| 
>>| I don't see any additional complexity in 4 with respect to 3. As already
>>| mentioned by Bill Clarke, you could simply have a typedef member in
>>| interval<T> to express the calling convention of the functions of the
>>| interval library: typedef interval<T> const &param_type;
>>
>>If done that way, in the typical cases, the "T" would then appear in
>>non-deducible context. 
> 
> 
> Right. This occurred to me when reading Sylvain's reply. However,
> although typical, it seems to me this only applies to cases outside the
> interval library. Indeed, the functions of the library do not have to
> use param_type, since they already know their own calling convention,
> and hence T is deducible there. So the issue only applies to
> user-defined template functions that would try to benefit from using the
> same calling convention.
> 
> Anyway, do you know of a way to avoid this issue?
> (Please do not suggest macros :-)

"friend injection" I guess can be used for that, but then it
competes with macros in terms of code cleanliness.

-- 
Sylvain
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Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr> writes:

[...]

| Anyway, do you know of a way to avoid this issue?
| (Please do not suggest macros :-)

I happen to have the luck to seat in front of Sylvain at this moment
so we had a brief discussion.

While I do agree with Lawrence and Steve, I think Sylvain has a point
about the performance on some x86-based systems there is a performance
problem.  I'm afraid I do not have a clean solution at the moment.
Even template aliases don't help here.

-- Gaby
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Sylvain Pion wrote:

>
> So, as for the proper text in the proposal, let me propose:
> - to have the text of the function prototypes use pass-by-value,
>   as it fulfills the "advocate safer programming style" argument
>   of Lawrence, and it is also shorter.
> - a note at the beginning mentionning that the implementation
>   is free to use pass-by-reference.
>
FWIW, I agree with this for the reasons Sylvain gave (comparing the 
other choices).
The note should say pass-by-const-reference though.

Regarding the pass by-value vs by-const-reference discussion, it is 
important to consider that the fields of this POD are floating point types.
A compiler will use a register to pass the address of the interval in 
the pass-by-const-reference case, but that's the wrong register...
When the interval fields are actually used inside the called function, 
they will have to be loaded in the FPU registers.

The most efficient scenario occurs when the compiler elides the 
copy-constructor and the calling function had already the fields of the 
interval arguments (typically 2) already loaded in FPU registers. In 
that case, there is no argument passing at all.

In my experience, this sort of optimization is common when the argument 
is passed-by-value (yes, it is common); yet I've never seen it in a 
pass-by-const-reference case.

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com




From Sylvain.Pion@sophia.inria.fr Wed Apr  5 09:55:18 2006
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Here is the summary of the various options I saw:

1- no default constructor at all
2- [0,0]
3- empty
4- whole
5- uninitialized tag
6- see below (something a la "singular iterator")


1- does not seem reasonnable for the array argument.
2-,3-,4- seem not clearly distinguisable from each other.
5- may cause additional run-time overhead which I'm not
ready to pay.  However, let me suggest that this goes
in some "debug mode".

Let me propose 6-:

We can do something similar to the "singular values"
of standard iterators.  That is, the default constructed
value is considered "uninitialized", and the standard would
only allow assignment on such an uninitialized value.
Only assignment from a non-uninitialized interval makes
it non-uninitialized.  And all other operations on
uninitialized intervals have undefined behavior (which
means everything can happen including WWIII).

This way, we can simply use the default compiler-generated
default constructor, no particular value is specified.
This is optimal for efficiency.
And, a "debug mode" is allowed to store an "uninitialized tag"
in the intervals to abort in case of operations using such
uninitialized intervals.
Note that some STLs ship with a debug mode which adds some
validity checks to iterators and other classes.
This "debug mode" would not be specified by the C++ standard,
but allowed thanks to defining "uninitialized" and undefined
behavior.  It then becomes a QoI issue.


Would such a solution answer the requests for more "safety",
and keep others happy ?

-- 
Sylvain
From guillaume.melquiond@ens-lyon.fr Wed Apr  5 10:18:37 2006
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Subject: Re: [std-interval] passing by value vs reference
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
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Le mercredi 05 avril 2006 à 11:39 -0300, Fernando Cacciola a écrit :

> Regarding the pass by-value vs by-const-reference discussion, it is 
> important to consider that the fields of this POD are floating point types.
> A compiler will use a register to pass the address of the interval in 
> the pass-by-const-reference case, but that's the wrong register...
> When the interval fields are actually used inside the called function, 
> they will have to be loaded in the FPU registers.
> 
> The most efficient scenario occurs when the compiler elides the 
> copy-constructor and the calling function had already the fields of the 
> interval arguments (typically 2) already loaded in FPU registers. In 
> that case, there is no argument passing at all.

This is not completely true: except for trivial cases, there is argument
passing even when registers are used.

Consider the following example with a, b, c, and d four intervals. I
will assume that the multiplications are not inlined (otherwise there
would be no difference between pass-by-reference and pass-by-value with
any sane compiler). Let us call r0:r1 the registers used to return an
interval, and a0:a1 and a2:a3 the registers used to pass first and
second interval arguments.

e = (a * b) * (c * d)

First (the expression is symmetric, so order of evaluation does not
matter), a * b is computed and the result is stored in r0:r1. It cannot
stay there, since r0:r1 will also be used to get the result of c * d. It
cannot be directly moved to a0:a1, since a0:a1 will be used to store c.
So it is moved to another register pair d0:d1. Then, the product c * d
can be computed and its value is moved from r0:r1 to a2:a3. Finally the
content of d0:d1 is moved to a0:a1 and the last multiplication can be
launched.

So there is argument passing and its cost is far from negligible: the
content of six registers has to be moved around just to get the
arguments of the last multiplication in the right places. Moreover,
registers like d0:d1 are probably either caller-save or callee-save. So
somebody somewhere may have to save and restore their values on the
stack. And so on.

But I agree that this whole register mess is still cheaper than any
stack usage caused by passing-by-reference on processors that are not
register-starved.

Best regards,

Guillaume

From fernando_cacciola@datafull.com Wed Apr  5 11:46:24 2006
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Guillaume Melquiond wrote:

>Le mercredi 05 avril 2006 à 11:39 -0300, Fernando Cacciola a écrit :
>
>  
>
>>Regarding the pass by-value vs by-const-reference discussion, it is 
>>important to consider that the fields of this POD are floating point types.
>>A compiler will use a register to pass the address of the interval in 
>>the pass-by-const-reference case, but that's the wrong register...
>>When the interval fields are actually used inside the called function, 
>>they will have to be loaded in the FPU registers.
>>
>>The most efficient scenario occurs when the compiler elides the 
>>copy-constructor and the calling function had already the fields of the 
>>interval arguments (typically 2) already loaded in FPU registers. In 
>>that case, there is no argument passing at all.
>>    
>>
>
>This is not completely true: except for trivial cases, there is argument
>passing even when registers are used.
>
>Consider the following example with a, b, c, and d four intervals. I
>will assume that the multiplications are not inlined (otherwise there
>would be no difference between pass-by-reference and pass-by-value with
>any sane compiler). Let us call r0:r1 the registers used to return an
>interval, and a0:a1 and a2:a3 the registers used to pass first and
>second interval arguments.
>
>e = (a * b) * (c * d)
>
>  
>
If  the FPU registers are stacked, like in the x86 family, it wouldn't 
be too uncommon, IMHO, for a compiler to do:

( a * b )

values stacked in st0,st1,st2,st3 in the FPU
result stored in st0,st1, and the FPU stack pointer moved to st2

( c * d )

values stacked in st2,st3,st4,st5 in the FPU
result stored in st2,st3, and the FPU stack pointer moved to st4

[( a * b )] * [( c * d )]

values for the subexpressions ALREADY stored in st0,st1,st2 and st3
final result stored in st0,st1


That is, stacked FPU registers allows the compiler to allocate the 
function frames (which is the problem in your example) without using the 
external memory-based stack or rearranging the registers manually.

Anyway, I was just pointing out the fact that pass-by-value allows reuse 
of FP registers (in non-inlined cases, of course, which is the point).
That's a fundamental source of FP optimizations even if it is only 
applicable to a fraction of the entire argument set.
Just consider that, for example, in the x86 architecture, storing a 
value back into memory may involve rounding besides the actual copy. 
Keeping values in the registers is more significant with floating-points 
than it is with integrals.

Best

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com


--------------090509050105000404080501
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<body bgcolor="#ffffff" text="#000000">
Guillaume Melquiond wrote:
<blockquote cite="mid1144250793.1575.90.camel@localhost" type="cite">
  <pre wrap="">Le mercredi 05 avril 2006 &agrave; 11:39 -0300, Fernando Cacciola a &eacute;crit :

  </pre>
  <blockquote type="cite">
    <pre wrap="">Regarding the pass by-value vs by-const-reference discussion, it is 
important to consider that the fields of this POD are floating point types.
A compiler will use a register to pass the address of the interval in 
the pass-by-const-reference case, but that's the wrong register...
When the interval fields are actually used inside the called function, 
they will have to be loaded in the FPU registers.

The most efficient scenario occurs when the compiler elides the 
copy-constructor and the calling function had already the fields of the 
interval arguments (typically 2) already loaded in FPU registers. In 
that case, there is no argument passing at all.
    </pre>
  </blockquote>
  <pre wrap=""><!---->
This is not completely true: except for trivial cases, there is argument
passing even when registers are used.

Consider the following example with a, b, c, and d four intervals. I
will assume that the multiplications are not inlined (otherwise there
would be no difference between pass-by-reference and pass-by-value with
any sane compiler). Let us call r0:r1 the registers used to return an
interval, and a0:a1 and a2:a3 the registers used to pass first and
second interval arguments.

e = (a * b) * (c * d)

  </pre>
</blockquote>
If&nbsp; the FPU registers are stacked, like in the x86 family, it wouldn't
be too uncommon, IMHO, for a compiler to do:<br>
<br>
( a * b )<br>
<br>
values stacked in st0,st1,st2,st3 in the FPU<br>
result stored in st0,st1, and the FPU stack pointer moved to st2<br>
<br>
( c * d )<br>
<br>
values stacked in st2,st3,st4,st5 in the FPU<br>
result stored in st2,st3, and the FPU stack pointer moved to st4<br>
<br>
[( a * b )] * [( c * d )]<br>
<br>
values for the subexpressions ALREADY stored in st0,st1,st2 and st3<br>
final result stored in st0,st1<br>
<br>
<br>
That is, stacked FPU registers allows the compiler to allocate the
function frames (which is the problem in your example) without using
the external memory-based stack or rearranging the registers manually. <br>
<br>
Anyway, I was just pointing out the fact that pass-by-value allows
reuse of FP registers (in non-inlined cases, of course, which is the
point). <br>
That's a fundamental source of FP optimizations even if it is only
applicable to a fraction of the entire argument set.<br>
Just consider that, for example, in the x86 architecture, storing a
value back into memory may involve rounding besides the actual copy.
Keeping values in the registers is more significant with
floating-points than it is with integrals.<br>
<br>
Best<br>
<br>
Fernando Cacciola<br>
SciSoft<br>
<a class="moz-txt-link-freetext" href="http://fcacciola.50webs.com">http://fcacciola.50webs.com</a><br>
<br>
</body>
</html>

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There's an attribution missing in the original.

> Message: 1
> Date: Tue, 04 Apr 2006 20:57:00 -0500
> From: George Corliss <George.Corliss@marquette.edu>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <C0588E1C.38EC%George.Corliss@Marquette.edu>
> Content-Type: text/plain;	charset="US-ASCII"
> 
> Sylvain Pion wrote:

> >> Uninitialized.  The convention in C/C++ is to initialize to zero,
> >> but we agree that is not correct for intervals.  Whole is probably
> >> the best we can do.
> > 
> > I'm not convinced.  Initilization to [0,0] seems nice to me for
> > intervals because of homogeneity reasons with floating-point.
> > I could even imagine that the empty interval would make as much
> > sense as whole.
> > 
> > What makes you think that [0,0] is "not correct", and why 'whole'
> > would be better than 'empty' ?
> I agree that initialization of uninitialized intervals to [0,0] is easy, and
> it is consistent with floating-point practice.

Not always true.   For dynamic creation on the stack or heap there is no such promise.  For static initialization the promise is _not_ initialization to the value zero, but to the bitpattern all bits off, which may or may not produce a value of zero..

>  My reservation is that it can lead to violations of containment.
> 
> The issue is not with "our" code.  It is with users' code.  Floating-point
> arithmetic makes no promises of accuracy.  Intervals promise a guaranteed
> enclosure.  If a user mis-uses our tools and gets a violation of
> containment, WE will be blamed, not the programmer who forgot to initialize
> all variables.  I want to make it as difficult as possible for even
> incorrect code to lie.
> 
> Simple example:
>    interval Pi;
>    cout << "Pi is enclosed by " << Pi;
> 
> The result violates containment if the default initializer is either [0, 0]
> or Empty.  It is truthful if the initializer is Whole.

I find that to be just as misleading.  The problem is that the variable is named in a misleading manner.  If you use a more descriptive name you will not be mislead:

    interval Uninitialized;
    cout << "Pi is enclosed by " <<Uninitialized";

This puts the problem out of the domain of the standard and squarely on the back of the quality of the implementation of the application software.

For a case where the whole number line is a lie consider:

    cout << "e^(i*pi) is enclosed by " << whole();
> 
> Of course, no one would do that on purpose, but programmers DO sometimes use
> variables they have not initialized.

That's not the problem of the standard.  When there is a choice between minimizing user errors at the cost of hiding some of them versus indicating user errors at the cost of convenience, the choice should always be the latter because the former is unacceptable.

> 
> One easy-to-imagine case might define a variable by a complicated set of
> nested cases/ifs.  The programmer thinks all possible cases are covered, but
> misses one case.  In that case, the variable is not given a value, but the
> following code uses it, unaware that it might not have been assigned a valid
> value.

That is not something you fix by providing an initialization that is magically correct in all cases.  That is something you fix by creating an unambiguous indication that a variable has been used without being initialized.  Note that there have been software tools to do this for a long time.  In fact many compilers now perform this check automatically.  It is not always possible to detect at compile time, so a run-time flag/state/value is called for.

There is a strong concensus within the software engineering community that what used to be known as defensive programming hides errors.  The modern practice is to prefer exaggerations of errors over exaggerations of correctness.

Taken to the limit (reductio) the standard would have to forbid this
    interval target = 0;
    memset( &target, 0 );


> 
> Asserting that a set is empty is perhaps the strongest assertion one can
> make about a set.  Asserting that it is contained in the universal set is
> the weakest assertion one can make.  That is why I argue for Whole.

Whole is not the universal set.  Whole asserts that the value is a number.  But an uninitialized variable does not contain a number.

> 
> I'd like to have some special "undefined" value that would propagate like a
> NaN, but that is too much to ask for.

Why is it too much?  On IEEE platforms NaN is easily available.  And the standard already has a definition of a special (bad) numeric value for other platforms.  The proposal should at least include the provisions parallel to those already supported by the standard.

>  Whole does not lie.

There are cases where it does lie.  And in the cases where it does not lie it certainly hides software defects.

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

> Message: 4
> Date: Wed, 05 Apr 2006 05:13:15 -0600
> From: Alan Eliasen <eliasen@mindspring.com>
> Subject: Re: [std-interval] Re: Std-interval Digest, Vol 3, Issue 1
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
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> 
> first.i.last@comcast.net wrote:
> >>but we agree that is not correct for intervals.  Whole is probably
> >>the best we can do.
> > 
> > Yuck.  Empty is clearly superior to whole in that it has less 
> > chance of accidentally producing apparently sensible results.
> > And for production an uninitialized interval should not be
> > initialized.  After all,  C++ lacks basis support for array
> > initialization so any default initialization effort, like touching
> > every value in a big array, is just wasted time.
> 
>    I think that there should *never* be a zero-arg default constructor
> for intervals.  All constructors should have at least one argument to
> force the programmer to declare their intent.  There's no point to a
> zero-argument constructor, because allowing such gives the programmer
> *lots* of ways to mess up and use uninitialized objects.  If you want to
> use an interval, you should provide reasonable arguments to it in a
> constructor.  That way, you *never* get an Interval object that hasn't
> been initialized to a known value.  A huge class of errors is eliminated
> at compile-time!
> 
>    In my interval implementations in Java, there's no way to construct
> an interval without specifying its values.  There's no reason to allow a
> "default" interval.  I believe in constructing APIs that eliminate
> sources of expected programmer error at compile-time.  This is an
> obvious case.
> 
>    There is simply no reason to allow a "default" interval initialized
> to a value that we *know* isn't right for anything.  We can prevent this
> mess at compile time, and should.

The reaction of a practicing software engineer to the above suggestion is to get out his garlic and silver crucifix and back away slowly sreaming CHANGE IN SCOPE!

Is the goal to incrementally add intervals to C++ as a kind of monotonic action or is there a willingness to force changes in the basic architecture of the language?

1. Some standard containers require default ctors.
2. Dynamic arrays (but not static arrays) require default ctors.
3. We should not make correctness promises for intervals that exceed the promises that:
    a. we can keep
           Uninitialized intervals would still exist because the user can:
                      interval * p = (interval *) malloc(100);
    b. already exist the language for similar types
           No matter what the standard says users are going to treat intervals as alternative
           forms of floating point.  So we should minimize the variations with existing C++
           numeric practice in both positive and negative directions.

The best way to get this issue into the standard is to propose that the standard recommend but not require a diagnostic.

=============================================

-- Lee Winter

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> ----------------------------------------------------------------------
> Message: 1
> Date: Tue, 04 Apr 2006 20:57:00 -0500
> From: George Corliss <George.Corliss@marquette.edu>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <C0588E1C.38EC%George.Corliss@Marquette.edu>
> Content-Type: text/plain;	charset="US-ASCII"
> 
> Sylvain Pion wrote:

> >>  Aside: The next day, we visited Berkeley and
> >> talked with Jim Demmel and Bill Kahan.  Among other things, Kahan
> >> wants user-defined data types to be tagged.  If we have the
> >> Kahan-suggested tag, we can tag intervals as Uninitialized.
> > 
> > Could you elaborate on this tag ?  What would it do ?
> > Would this be a run-time feature of the objects telling if
> > they are initialized or not ?  Can't this be left to some
> > "debug mode" ?
> Let me explain Kahan's reasoning, as well as I am able.
> 
> The request is that a tag be permitted by the standard.  As I understand it,
> what would be required is to remove the phrase that an interval is
> represented by two values.  The down side, of course, is that it is harder
> to know how much memory an interval may require.

That's what sizeof() is for.  Users who "know" the sizes of types are  sources of errors.  Let's not encourage them.

> 
> If we are permitted a tag, the tag can be used in MANY different ways within
> an implementation.  The tag could be an attribute, or it could be a pointer
> to a complicated internal data structure of properties of the interval.  The
> most extreme case I can think of is that the tag might point to the Abstract
> Syntax Tree that generated the interval, allowing run-time symbolic
> processing.
> 
> In most implementations I can imagine, the tag could be used for
> "uninitialized," "exterior interval," various flavors of NaN, precision in a
> multiple precision implementation, and the like.  If we want a (center,
> radius) implementation, a tag could distinguish semi-infinite intervals, or
> it could distinguish [lo, hi] from (center, radius) intervals.

Logically a tag is just a container for properties.  The existence of tags in the proposal might lead to questions about how they will be used and a demand for standardized properties.  That demand should be refused as premature.  The issue is not standardizing the properties but allowing implementors to create them directly rather than as shadow variables with the associated extremely high performance costs.

==================

-- Lee Winter

From fernando_cacciola@datafull.com Wed Apr  5 13:24:23 2006
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Sylvain Pion wrote:
> Here is the summary of the various options I saw:
>
> 1- no default constructor at all
> 2- [0,0]
> 3- empty
> 4- whole
> 5- uninitialized tag
> 6- see below (something a la "singular iterator")
>
> ...
>
> Let me propose 6-:
>
> We can do something similar to the "singular values"
> of standard iterators.  That is, the default constructed
> value is considered "uninitialized", and the standard would
> only allow assignment on such an uninitialized value.
> Only assignment from a non-uninitialized interval makes
> it non-uninitialized.  And all other operations on
> uninitialized intervals have undefined behavior (which
> means everything can happen including WWIII).
>
> This way, we can simply use the default compiler-generated
> default constructor.

I like this.
It allows the implementation to deal with uninitialization in the best 
possible way given its particular target.

I wonder if, for all the other operations, unspecified behaviour isn't 
better than undefined behaviour?
An implementation will have to define this one way or another I think.

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com/



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Steve Clamage wrote:


>> Bill Clarke wrote:
>>
>>> This experiment is extremely platform specific, as you probably are
>>> aware.  Most platforms in use today other than x86 will be the other way
>>> around (add-by-value will be faster than add-by-const-ref).

Alan Eliasen wrote:
>>    How can that assertion possibly be made?  As you know, if a parameter
>> is passed by value, then the copy constructor is automatically called
>> for each object (e.g. twice for an add operator) on function entry, and
>> then the destructor is called (twice) on function exit.
> 

Steve Clamage wrote:
> A simple object like complex or interval should have no user-defined
> copy constructor or destructor. That is, the default copy constructor
> generated by the compiler does the right thing and does not need to be
> user-defined. The destructor has nothing to do, and so should not be
> user-defined. In that case, pass-by-value can be optimized into register
> passing with no additional copying.

   You still agree, though, that even if the implementation doesn't do
memory allocation in the constructor, the compiler will still generate a
copy constructor and a destructor, (perhaps pretty simple and efficient)
and these will get normally get called in a pass-by-value.  Again, a
very smart compiler can optimize these away if it realizes that the copy
is unnecessary, but by simply specifying call-by-constant-reference, we
don't have to hope that the compiler is very smart.  We simply eliminate
even the possibility of calling the copy constructor and destructor.

> It is possible to construct a test case where pass-by-value gives worse
> performance than pass-by-reference, and your example does indeed run
> faster with pass-by-reference using Sun compilers at low optimization.

   As noted, it should always be the case that pass-by-value is at least
as slow as pass-by-constant-reference because of the overhead of calling
the copy constructors and destructors, which are almost always
unnecessary and can be trivially eliminated by specifying the calling
convention.  If it's ever faster, I'd argue that it's because the
compiler missed obvious optimizations for pass-by-constant-reference, or
is allocating registers badly.

> At high optimization, the compiler eliminated the loops and all but one
> call to "add", which it inlined. I played with the test case for a short
> time, but was unable to defeat the optimizer with minor changes.

   Heh!  That's a smart compiler!  I had considered adding some
randomization to the values to eliminate this possibility, but the
timing values would have likely been swamped by the random number generator.

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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Guillaume Melquiond wrote:
> Please note that our proposed interval type is meant to be a POD (plain
> old data) type and as such has no copy constructor nor destructor. As a
> consequence, on some architectures and with non-broken compilers, they
> will behave no differently than if the function arguments were simply
> integers; except that the register will probably be bigger, or two
> registers will be used. When this happens, passing by value will be
> faster than passing by const-reference. Indeed there is no architecture
> such that foo(int) is slower than bar(int const &).

   As a "primitive" type, int is a different case than an object,
though.  Please note that calling foo(Interval a) normally requires a
call to a copy constructor and a call to the destructor if Interval is a
class.  This (probably unnecessary) call to the copy constructor and
destructor is always eliminated when calling foo(const Interval&).

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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> Alan Eliasen <eliasen@mindspring.com> writes:
>  >   I was curious to see about the speed difference between passing by
>  >value and passing by reference, because passing by value always has been
>  >slower and always *has* to be slower because it (unnecessarily) creates
>  >a copy of the object when passed in.

Lawrence.Crowl@sun.com wrote:
> It does not unnecessarily create an object.  In particular, when the
> parameter to a function is the result of an expression, the const ref
> approach requires allocating a temporary and passing its address.  In
> contrast, pass-by-value can put the result of the expression directly
> into the parameter register; no copies are required.

   This is totally implementation-dependent in the compiler.  Of course,
a smart compiler could put the result of pass-by-constant reference into
a register too.  It may already be in a register.

   It could be argued that pass-by-value *always* creates temporaries
because of calls to the copy constructor for each argument passed in to
a function or method.  As I noted before, a smart compiler can optimize
this away, but these copy constructor calls are almost always unnecessary.

>  >I tried three ways on x86_64, gcc 3.4.4, linux:
> 
> I would need the benchmark source in order to evaluate it and to
> execute it on other systems.

   That was posted last night.  My benchmark was very simple indeed, and
you may choose to write your own.

> In developing the SPARC V9 ABI, I showed a 7x performance advantage for
> pass-by-value over pass-by-reference when computing Mandelbrot with
> complex numbers.

   That's an impressive difference!  I'd like to see that benchmark
source too and test it on other compilers.

>  >   Passing in unmodifiable objects as constant references when
>  >appropriate both obviates the need for copying and gives explicit
>  >const-correctness from the start.  We don't have to worry about
>  >dereferencing pointers or memory ownership issues.  It's indeed the
>  >pattern followed by most modern libraries.
> 
> You are assuming that "const" means "unmodifiable".

   No, of course I'm not.

> It does not.  It
> means that non-mutuable fields may not change when accessed through the
> const-qualified name.  The object may still change via access through
> non-const-qualified names.  The distinction between a value and a
> reference is critical here, because the former is unaliased and the
> latter is potentially aliased.  This aliasing can also have substantial
> effect on the ability of the compiler to apply global optimizations.

   I can see the point that aliasing could be an issue if functions are
modifying the objects passed in.  That would seem to me to be very bad
programming practice, (one in which explicitly declaring const-ness
would help the compiler point these out.)

   If the issue is complete safety against bad programmers, then we
should do pass-by-value everywhere and copy the object every time it's
used.  It'd be safer.

   However, my entire point earlier was to argue against the statements
made that pass-by-value would or should be faster.  My benchmarks showed
that in the most common compilers used in the world, on the most common
hardware architectures, that pass-by-value indeed wasn't faster, but
rather significantly slower at all optimization levels.  I'd be
interested to see a platform where the reverse was true.

>  >   I recommend that for long-term performance and const-correctness,
>  >that objects be passed as constant references when possible.
> 
> Would you recommend that ints be passed by const reference?

   Of course not.  That's why I said "objects", meaning instantiations
of classes.  ints don't incur copy constructors and destructors like
objects do when passed as function arguments.  To save time, let's
assume that any other rookie mistakes that you might want to try to
ascribe to me in an effort to make me look foolish will also be answered
the same way.  :)

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
From eliasen@mindspring.com Wed Apr  5 14:41:24 2006
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Guillaume Melquiond wrote:
> Le mercredi 05 avril 2006 à 05:13 -0600, Alan Eliasen a écrit :

>>   I think that there should *never* be a zero-arg default constructor
>>for intervals.  All constructors should have at least one argument to
>>force the programmer to declare their intent. 

> This is too strong a requirement. Forbidding arrays of intervals is a
> sure way of alienating any C++ user. You need a default constructor if
> you don't want the users to go to great and error-prone lengths to
> create arrays (or any higher-level containers).

   Okay, I concede this point, although it is dangerous.

   I would then consider the previous proposal that an interval is
initialized to an "uninitialized" value which causes errors or
propagates itself like NaN if used in a calculation.

   As you may know, there's more than one type of NaN.  There are
"quiet" and "signaling" NaNs.  Quiet NaNs just quietly propagate
themselves in floating-point calculations, like additions or multiplies,
and you'll generally notice them later, but this is incredibly dangerous
if you use them in a boolean expression like:

   if (NaN < 3)
      ...

   or

   if (NaN == NaN)        // (always returns false!)

   Which *doesn't* give you a way of knowing if your calculations were
"poisoned" by this meaningless comparison.

   On the other hand, if you use "signaling" NaNs, attempts at
performing the above comparisons would produce a floating-point error.

   As a result, in a former product, we chose to have switchable NaN
behavior.  In a developer/debug environment, we used signaling NaNs to
find errors of this sort immediately.  We may consider switchable
similar behavior for the Interval standard.  Using an "uninitialized"
interval in a calculation could produce an immediate error or exception.
  This behavior could also be switched off (but I can't think of a good
reason why except it could be faster as a check for uninitialized could
be eliminated.)  I haven't seen nor produced a concrete proposal for
this, but I think it should be considered strongly.

   In fact, the Interval specification could use the above behavior and
initialize itself to NaN (quiet or signaling) to prevent use of
uninitialized Intervals.

   As noted before, simply "poisoning" the results by propagating
uninitialized values isn't enough.  We have to have some way of
indicating errors in boolean comparisons.  What's our proposed policy on
exceptions?

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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Alan Eliasen <eliasen@mindspring.com> writes:

| Steve Clamage wrote:
| 
| 
| >> Bill Clarke wrote:
| >>
| >>> This experiment is extremely platform specific, as you probably are
| >>> aware.  Most platforms in use today other than x86 will be the other way
| >>> around (add-by-value will be faster than add-by-const-ref).
| 
| Alan Eliasen wrote:
| >>    How can that assertion possibly be made?  As you know, if a parameter
| >> is passed by value, then the copy constructor is automatically called
| >> for each object (e.g. twice for an add operator) on function entry, and
| >> then the destructor is called (twice) on function exit.
| > 
| 
| Steve Clamage wrote:
| > A simple object like complex or interval should have no user-defined
| > copy constructor or destructor. That is, the default copy constructor
| > generated by the compiler does the right thing and does not need to be
| > user-defined. The destructor has nothing to do, and so should not be
| > user-defined. In that case, pass-by-value can be optimized into register
| > passing with no additional copying.
| 
|    You still agree, though, that even if the implementation doesn't do
| memory allocation in the constructor, the compiler will still generate a
| copy constructor and a destructor, (perhaps pretty simple and efficient)
| and these will get normally get called in a pass-by-value.  Again, a
| very smart compiler can optimize these away if it realizes that the copy
| is unnecessary, but by simply specifying call-by-constant-reference, we
| don't have to hope that the compiler is very smart.  We simply eliminate
| even the possibility of calling the copy constructor and destructor.

Steve and Lawrence have been working on C++ and C++ compilers, long
long before I even knew the language existed -- let alone, started
working on C++ libraries and compilers.  Their inputs in that area
should not be taken lightly.
I know of no existing production C++ compilers that run trivial
destructors, or that do not implement trivial copy-constructor
appropriately (given ABI requirements) at usual optimization level.
If you find one, I would encourage you to report it to your vendor.
TC++PL3 has guidance, I believe, on exactly this point.  

You're right that we don't have to hope the compiler is very smart:
The compilers are already doing it; so that is a non-issue.

When you make your proposal to the committee, do expect that 
making pass-by-const-ref where it should have been pass-by-value (as
suggested by Lawrence and Steve) be a contentious point to resolve.

-- Gaby
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Alan Eliasen <eliasen@mindspring.com> writes:

| Guillaume Melquiond wrote:
| > Please note that our proposed interval type is meant to be a POD (plain
| > old data) type and as such has no copy constructor nor destructor. As a
| > consequence, on some architectures and with non-broken compilers, they
| > will behave no differently than if the function arguments were simply
| > integers; except that the register will probably be bigger, or two
| > registers will be used. When this happens, passing by value will be
| > faster than passing by const-reference. Indeed there is no architecture
| > such that foo(int) is slower than bar(int const &).
| 
|    As a "primitive" type, int is a different case than an object,
| though.  Please note that calling foo(Interval a) normally requires a
| call to a copy constructor and a call to the destructor if Interval is a
| class.

That is an abstract requirement -- remember the "as if rule".
In the real practice, I have not see any modern production C++
compiler run trivial destructor or trivial copy-constructor for POD,
i.e., they don't do anything beyond what they would have done for C
struct. 

People seem to focuse on what it costs to copy data in function call;
I would suggest that the focus should be what it costs to access data
when inside the called function.

-- Gaby
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 -------------- Original message ----------------------
From: std-interval-request@compgeom.poly.edu
> Send Std-interval mailing list submissions to
> 	std-interval@compgeom.poly.edu
> 
> ------------------------------
> Message: 3
> Date: Tue, 04 Apr 2006 23:20:27 -0600
> From: Alan Eliasen <eliasen@mindspring.com>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <4433539B.5000604@mindspring.com>
> Content-Type: text/plain; charset=us-ascii
> 
> 
> George Corliss wrote:
> >> Lawrence feels strongly that the standard should be to pass by
> >> value.  Intervals are small data structures; by value allows them
> >> to be passed in registers for speed.  That is how the current Sun
> >> C++ compiler works.  There is no reason to follow the C++ complex
> >> standard.  The library is often taken as an example by coders, and
> >> there is no good reason to follow the tradition of C from 20 years
> >> ago that structures should be passed by reference.
> 
> Sylvain Pion wrote:
> > I don't have any strong opinion on this.
> > I only did a very local experiment on some code of mine on x86, and
> > changing to pass-by-value slowed the code down a bit.
> 
>    I was curious to see about the speed difference between passing by
> value and passing by reference, because passing by value always has been
> slower and always *has* to be slower because it (unnecessarily) creates
> a copy of the object when passed in.

No it does not have to be slower.  First, the pass-by-value copies created by 
the constructor can be optimized away in some cases, especially when inlining is 
active.  Second, on primitive architectures such as x86 pass by reference is 
much worse because the compiler cannot create the address of a value in the FPU.  
So it has to copy the values back to the CPU and write them to memory (always a 
BadThing(tm)) typically on the stack.  The region around the top-of-stack 
usually has good cache response so a cache miss will be rare.  But writing a 
value to memory is still expensive.  Then the addrss is passed to the receiving 
routine which copies the values back into the FPU to operate upon them.  
Efficient this is not.

Compare that sequence with the worst case pass-by-value which takes two FPU 
instructions to duplicate a value on the FPU stack.  Those instructions are 
extremely common, and thus heavily optimized.  On the more deeply pipelined FPUs 
with register renaming the copy might take zero time.  If the values are not 
modified the copies might be eliminated completely (by a post-optimizer) even if 
the copy constructor is called and generates the copy instructions.

Optimizing floating point is a treacherous area even within the implementation 
variations of a single generation of a single architecture.  It will never make 
it into the standard because the Committee will almost certainly object to 
mandates that restrict implementor's freedom to implement.

>  I tried three ways on x86_64, gcc

[omitted]

In general these kinds of tests are not useful because they are not reliable 
guidelines.  They rely upon the competence of the compiler which can only be 
determined by inspecting the code generated.

>    There's a bit of noise in the numbers, but passing by value is always 
significantly slower.

On that machine with that compiler.  Others mileage will _certainly_ vary.

>    Also ran on x86 Windows.  Pattern was the same.  With -O2, passing by
> value took about 2.6 times as long!

See what turning off optimizations can do to you?  If you inspect the generated 
code you are going to find lots of silly register transfers.

> 
>    I didn't test passing by pointer, but I can.
> 
>    Passing in unmodifiable objects as constant references when
> appropriate both obviates the need for copying and gives explicit
> const-correctness from the start.  We don't have to worry about
> dereferencing pointers or memory ownership issues.  It's indeed the
> pattern followed by most modern libraries.

Over specification is always a mistake unless the target platform is very 
narrowly defined.  See some of Bernstein's work on optimization wherein the 
comments in the C code are actually the assembly instructions he expects to 
generate on a specific platform.

> ------------------------------
> 
> Message: 4
> Date: Wed, 05 Apr 2006 16:27:51 +1000
> From: Bill Clarke <llib@computer.org>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <44336367.9060400@computer.org>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Alan Eliasen wrote, On 04/05/06 15:20:
> > George Corliss wrote:
> >>>Lawrence feels strongly that the standard should be to pass by
> >>>value.  Intervals are small data structures; by value allows them
> >>>to be passed in registers for speed.
> [...]
> >    I was curious to see about the speed difference between passing by
> > value and passing by reference, because passing by value always has been
> > slower and always *has* to be slower because it (unnecessarily) creates
> > a copy of the object when passed in.  I tried three ways on x86_64, gcc
> > 3.4.4, linux:
> [...]
> >    To the caller of the functions, it just looks like an ordinary
> > pass-by-value, but is faster, and allows the compiler to catch a lot of
> > types of problems.
> > 
> >    I recommend that for long-term performance and const-correctness,
> > that objects be passed as constant references when possible.
> 
> This experiment is extremely platform specific, as you probably are
> aware.  Most platforms in use today other than x86 will be the other way
> around (add-by-value will be faster than add-by-const-ref).
> (Was this 64-bit code?  I thought x86_64 would be faster with
> pass-by-value since I got the impression the ABI passed parameters in
> registers)

Long doubles won't fit.  And typical argument passing occurs int he CPU 
registers rather than on the FPU stack.

> 
> With inlining then they should be identical (perhaps you could re-run
> your experiment with inlining to verify this?).
> 
> Surely it is possible to permit the implementer to choose the parameter
> passing convention, between pass-by-value and pass-by-const-ref?  It
> should have no visible impact on the programmer which is used.

Exactly.

----------------------------------------------------------------------
> 
> Message: 1
> Date: Wed, 05 Apr 2006 01:02:40 -0700
> From: Steve Clamage <Stephen.Clamage@Sun.COM>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <443379A0.7010800@sun.com>
> Content-Type: text/plain; charset=us-ascii; format=flowed
> 
> Bill Clarke wrote:
> > 
> > Surely it is possible to permit the implementer to choose the parameter
> > passing convention, between pass-by-value and pass-by-const-ref?  It
> > should have no visible impact on the programmer which is used.
> 
> The standard can state, for example, that that whether a parameter is passed 
by 
> value or by reference is implementation-defined, meaning that an 
implementation 
> can choose either and must document the choice. Or it could say that the 
choice 
> is unspecified, meaning that the implementation does not need to document what 
> it does, and does not need to be consistent.
> 
> The choice can have an effect on programmers, however, since the types of the 
> functions
>    interval foo(interval);
>    interval foo(const interval&);
> are different.

This is not an appropriate example.  The counter is as follows:

----- platform1.h, value -----
    typedef  IntervalArg  Interval;

----- platform2.h, ref2const -----
    typedef  IntervalArg  Interval const &;

----- Interval.h, agnostic -----
    interval atan2( IntervalArg Y, IntervalArg X );

----- User.cpp, agnostic -----
    void slope( IntervalArg height, IntervalArg width )
    {
        return atan2( height, width );
    }

This approach gives user code the portability benefit of the argument type with 
no user-level platform dependency.

> 
> 1. If you create a function pointer interval(*)(interval), it cannot be used 
to 
> hold the address of "interval foo(const interval&)". I don't know of a 
> convenient way to deal with this problem, where you need to modify your code 
> based on details of a predefined type.

You don't need to modify code that uses an abstract argument type.  It is rare 
that it matters, but it can for templates, type_info, RTTI, and other 
type-sensitive constructs.  But that can be solved by giving IntervalArg a 
static member such as shown below:

----- platform2.h, ref2const -----
    class IntervalArg {
        interval const & ref_to_const;
        static int /* can't be bool */ const by_value = false;
    };

> 
> 2. The result of typeid(foo) is different in the two cases, which can affect 
the 
> operation of a program.
>      interval bar(const interval&);
>      if( typeid(foo) == typeid(bar) ) ...
> 
> That said, it is already the case that member functions of classes in the 
> standard library are explicitly allowed to vary from the exemplars listed in 
the 
> standard. But the implementation is required to accept code that is valid for 
> the exemplars.

So we provide an exemplar that is abstract and maximize the freedom of the 
implementors.  Note that the definition of IntervalArg might vary based on the 
compile-time switches provided to the translator.

> 
> Example: An implementation can add a default parameter to a class member 
> function. If the standard says this:
>       class Foo {
>       public:
>             fun(int);
>       };
> An implemtation can have this:
>      class Foo {
>      public:
>            fun(int, int=0);
>      };
> According to the standard, the following is valid:
>      Foo f;
>      f.fun(3);
> and indeed that code compiles with the modified implementation.
> 
> Similarly, code that can call one of the versions of the interval function foo 
> above can also call the other version.
> 
> My point is that allowing freedom of implementation is not without 
consequences 
> for C++ programmers, but there is already some precedent for that freedom of 
> implementation. We need to be aware of the potential problems for programmers, 
> and make a considered choice.

Let's not make a choice.  The one of the very worst problems in software 
engineering is premature optimization.  A choice now would be an instance os 
that haste.  Think of parameter typing as subject to delayed evaluation.  It 
should be delayed until the very last moment possible because that is the point 
in time at which the most information is avalable upon which to make a good 
decision.  Up until that point in time we hide the indecision behind an abstract 
type.

> ------------------------------
> 
> Message: 2
> Date: Wed, 05 Apr 2006 11:32:52 +0200
> From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
> Subject: [std-interval] passing by value vs reference
> To: std-interval@compgeom.poly.edu
> Message-ID: <44338EC4.4020106@sophia.inria.fr>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> [ Let me create separate threads of discussion on each point. ]
> 
> 
> Summary of the arguments on this issue:
> 
> 1- pass by value can be faster or slower than pass by reference
>     depending on the processor/ABI.
> 2- pass by value can be faster due to removal of aliasing issues.
> 3- pass by value is safer in general as a programming idiom
>     (an example is operator*= which may need tweaking to protect
>      itself multipliying by *this)

I question this assertion (re safety, I understand op= quite well), but I doubt 
this issue will be decisive, so let's not pursue it until necessary.

> 4- pass by reference is consistent with std::complex

That is not a particularly attractive property.

> 5- having it specified is useful when taking addresses of functions.

That is false.  And having it specified is not neutral either.  It is a 
detriment -- it tends to embed platform degisn decision in user code, which is 
always a Bad Thing(tm).

> 
> 
> Possible solutions, assuming we want a uniform treatment for all
> functions on intervals:
> 
> 1- enforce pass-by-value
> 2- enforce pass-by-ref
> 3- leave freedom for the implementation to choose
> 4- leave freedom for the implementation and have it provide
>     a standard specified way to obtain this information.

5. Provide an abstraction that masks the issue from users so that only those 
concerned with the issue need deal with it, i.e., implementors.

> 
> 
> Now, I assume that users want the best performance on all
> compilers/processors, so I don't like 1 nor 2.
> I also do not see a large need for manipulating function
> pointers for the intervals, I never needed that personnaly
> at least (speak up if you think it is an important use case).
> If there is indeed no large need for these, and given that it
> is always possible (though painful) to write function wrappers
> to get function pointers, then I would prefer 3 to 4.  I think
> the complexity of implementing 4 is not worth it.  Moreover,
> specifying 4- can be proposed later as an addition (e.g. in
> the more general context of the whole standard library).

I agree but for different reasons.  There should be nothing in the standard that 
is no required by standardization.  If explicit manipulation of parameter types 
is perceived to be necessary (it is not so perceived by me), then an explicit 
type is called for.
But there is no showing that such explicit manipulation of parameter types is 
actually called for.  So the standard should use call-by-value syntax and allow 
call-by-ref2const semantics.

> 
> 
> So, as for the proper text in the proposal, let me propose:
> - to have the text of the function prototypes use pass-by-value,
>    as it fulfills the "advocate safer programming style" argument
>    of Lawrence, and it is also shorter.
> - a note at the beginning mentionning that the implementation
>    is free to use pass-by-reference.
> 
> 
> Does this seem reasonnable ?

Yes, but the proposal will need a rationale note explaining that implementors 
are explicitly permitted to vary the parameter handling as necessary to improve 
their quality of implementation.

> ------------------------------
> 
> Message: 3
> Date: Wed, 05 Apr 2006 04:52:50 -0600
> From: Alan Eliasen <eliasen@mindspring.com>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <4433A182.7060405@mindspring.com>
> Content-Type: text/plain; charset=us-ascii
> 
> Bill Clarke wrote:
> > This experiment is extremely platform specific, as you probably are
> > aware.  Most platforms in use today other than x86 will be the other way
> > around (add-by-value will be faster than add-by-const-ref).
> 
>    How can that assertion possibly be made?  As you know, if a parameter
> is passed by value, then the copy constructor is automatically called
> for each object (e.g. twice for an add operator) on function entry, and
> then the destructor is called (twice) on function exit.

Those function calls can be eliminated as unnecessary or optimized away after 
gode generation.  In many cases they will disappear when debugging is turned off 
and full optimization is turned on.

>  The passed-in
> objects should not be modified in the interim.  So pass-by-value
> *always* has completely unnecessary overhead.  There is absolutely no
> reason to copy and subsequently destroy the objects being passed in.
> Passing by constant reference will *always* be faster in this respect,
> as the copy constructors and destructors will never be called.

On some architectures/compilers this is true.  On others it is never true.

> 
>    The architecture doesn't matter.

Sure it does.  If there are no addresses for the memory holds operands for 
arithmetic instructions then mandating the creation of an address triggers huge 
overhead.  Suhc is life on platforms descended from calculator/watch chips.

>  Say, for an addition operator, if
> you pass by value, you're *always* incurring the additional overhead of
> two unnecessary object copies and two unnecessary object destructions.
> There is simply no advantage to pass-by-value over
> pass-by-constant-reference in any way.

On some popular architecture there is a huge advantage in avoiding the defects 
in the architecture.  Not all computer as carefully designed as a PDP-11.  There 
is a strong case for that claim that the most popular architecture wasn't really 
designed -- it "jest growd lak 'at".

>  Your compiler might be smart
> enough to optimize out the copies and destructions, but pass-by-value
> should *never* be faster with a reasonable compiler.

Our definitions of "reasonable" certainly differ.

> 
>    Why would one ever want the compiler to potentially call copy
> constructors and destructors when we *know* they're a total waste of
> cycles?  We can simply prevent that inefficiency in advance for all
> compilers.

Premature optimization cannot be justified no matter how good the underlying 
intentions are.

> 
> > (Was this 64-bit code?  I thought x86_64 would be faster with
> > pass-by-value since I got the impression the ABI passed parameters in
> > registers)
> 
>    As I mentioned in my original message, I did the test with both
> x86_64 code and x86.  The x86_64 code was 64-bit code, and those were
> the numbers cited.

But did you inspect the generated code?

> The difference in performance, as I noted, was even
> greater on the x86.  (Pass-by-value was about 1.7 times slower on
> x86_64, about 2.6 times slower on x86.)  Registers don't enter into the
> picture.

I don't understand that statement.  It is quite contrary to my experience.

>  Pass-by-constant-reference arguments can be passed in
> registers too, of course.
> 
>    The difference is that pass-by-value is likely to perform unnecessary
> copy constructors and unnecessary destructions.  There is simply no
> advantage to this, when we can be smart and tell even the dumbest
> compilers that these copying and destroying operations should never even
> be attempted.  Silly, useless performance problems (e.g. unnecessary
> copy constructor calls) will be avoided in advance.  That's a good thing.

That's what code optimizers are for.  These days they are quite smart about 
fixing the kind of simple inefficiencies you have mentioned.

> 
> > With inlining then they should be identical (perhaps you could re-run
> > your experiment with inlining to verify this?).
> 
>    The constructor was inlined.  I fail to see how inlining could ever
> make pass-by-value faster, as it always has unnecessary overhead.  A
> smart compiler could make it *as* fast as pass-by-constant-reference,
> but I can't see how it could ever make it faster.

Then try the experiment and see what happens to the inlined code sequence.  It 
can be quite a bit smaller/faster than an outlined function.

>  Specifying
> pass-by-constant-reference would simply eliminate a source of
> inefficiency with broken compilers.
> 
> > Surely it is possible to permit the implementer to choose the parameter
> > passing convention, between pass-by-value and pass-by-const-ref?  It
> > should have no visible impact on the programmer which is used.
> 
>    I agree that it should have no visible impact on the library user.
> But there is really no reason to *not* use pass-by-constant-reference.

If the argument for pass-by reference is so compelling than we should trust the 
implementors to be so compelled.  Otherwise the proposal should mandate either 
LSB-first or MSB-first memory layouts.  Anyone up for a food fight?  ;-) 

>  Even if you are doing lazy operations and need to modify some part of
> the passed-in object, you can always use the "mutable" keyword.
> 
>    In short, if you can find a compiler that does pass-by-value faster
> than pass-by-constant-ref, I'll show you a broken compiler.
> 
>    Specifying pass-by-constant-reference also allows the compiler to
> detect and prevent accidental modification of the objects being passed
> in, or erroneous programmer attempts to modify a passed-in object (which
> is probably never what you want to do, and should always fail.)
> 
>    Const-correctness is also a desirable goal, in my opinion.  It
> becomes prohibitive and breaks code to add const-correctness late in the
> game, which is why we should get it right the first time.

Const correctness should be a requirement.  But that does not have any effect 
upon calling conventions because both conventions can be const-correct.

> ------------------------------
> 
> Message: 6
> Date: Wed, 05 Apr 2006 04:51:32 -0700
> From: Steve Clamage <Stephen.Clamage@Sun.COM>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <4433AF44.8020308@sun.com>
> Content-Type: text/plain; charset=us-ascii; format=flowed
> 
> Alan Eliasen wrote:
> > Bill Clarke wrote:
> > 
> >>This experiment is extremely platform specific, as you probably are
> >>aware.  Most platforms in use today other than x86 will be the other way
> >>around (add-by-value will be faster than add-by-const-ref).
> > 
> > 
> >    How can that assertion possibly be made?  As you know, if a parameter
> > is passed by value, then the copy constructor is automatically called
> > for each object (e.g. twice for an add operator) on function entry, and
> > then the destructor is called (twice) on function exit.
> 
> A simple object like complex or interval should have no user-defined copy 
> constructor or destructor.

A desirable property, but unnecessarily restrictive.  In particular interval 
objects with explicit properties might not be PODs.  Histories of dependencies 
and restartable evaluations require pointers.  Pointer members will require an 
intelligent copy ctor and a deep dtor (modulo reference counting).

> That is, the default copy constructor generated by 
> the compiler does the right thing and does not need to be user-defined. The 
> destructor has nothing to do, and so should not be user-defined. In that case, 
> pass-by-value can be optimized into register passing with no additional 
copying.

That makes sense for PODs.  But any non-trivial imeplentations will not be able 
to use POD representations without fantastically high performance cost.

> ------------------------------
> 
> Message: 7
> Date: Wed, 05 Apr 2006 13:55:35 +0200
> From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Subject: Re: [std-interval] C++ interval std
> To: std-interval@compgeom.poly.edu
> Message-ID: <1144238135.1575.25.camel@localhost>
> Content-Type: text/plain; charset=ISO-8859-1
> 
> Le mercredi 05 avril 2006 à 04:52 -0600, Alan Eliasen a écrit :
> > Bill Clarke wrote:
> > > This experiment is extremely platform specific, as you probably are
> > > aware.  Most platforms in use today other than x86 will be the other way
> > > around (add-by-value will be faster than add-by-const-ref).
> > 
> >    How can that assertion possibly be made?  As you know, if a parameter
> > is passed by value, then the copy constructor is automatically called
> > for each object (e.g. twice for an add operator) on function entry, and
> > then the destructor is called (twice) on function exit.  The passed-in
> > objects should not be modified in the interim.  So pass-by-value
> > *always* has completely unnecessary overhead.  There is absolutely no
> > reason to copy and subsequently destroy the objects being passed in.
> > Passing by constant reference will *always* be faster in this respect,
> > as the copy constructors and destructors will never be called.
> 
> Please note that our proposed interval type is meant to be a POD (plain
> old data) type and as such has no copy constructor nor destructor.

Is it your plan that the proposal include the POD-only requirement?  I would 
suggest that it is an obvious possibility that yeilds good performence 
improvements, but how important is it to get fat intervals quickly?

I would must prefer not to see such a requirement in the standard.

> As a
> consequence, on some architectures and with non-broken compilers, they
> will behave no differently than if the function arguments were simply
> integers; except that the register will probably be bigger, or two
> registers will be used. When this happens, passing by value will be
> faster than passing by const-reference. Indeed there is no architecture
> such that foo(int) is slower than bar(int const &).

Of course there is.  When addresses are narrow (fit in a register) and ints are 
wide (don't fit in a register).  64-bit code on 32-bit hardware.  32-bit code on 
16-bit hardware.  16-bit code on 8-bit hardware.  I've even worked on a 
bit-slice machine with 20-bit ints and 16-bit addresses.

----------------------------------------------------------------------
> 
> Message: 1
> Date: Wed, 05 Apr 2006 14:05:54 +0200
> From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Subject: Re: [std-interval] passing by value vs reference
> To: std-interval@compgeom.poly.edu
> Message-ID: <1144238754.1575.37.camel@localhost>
> Content-Type: text/plain; charset=ISO-8859-1
> 
> Le mercredi 05 avril 2006 à 11:32 +0200, Sylvain Pion a écrit :
> 
> > 3- leave freedom for the implementation to choose
> > 4- leave freedom for the implementation and have it provide
> >     a standard specified way to obtain this information.
> 
> > I would prefer 3 to 4.  I think
> > the complexity of implementing 4 is not worth it.
> 
> I don't see any additional complexity in 4 with respect to 3. As already
> mentioned by Bill Clarke, you could simply have a typedef member in
> interval<T> to express the calling convention of the functions of the
> interval library: typedef interval<T> const &param_type;
> 
> This requires all the functions of the library to use the same calling
> convention.

How do you derive this requirement?  I don't see it.

> ------------------------------
> 
> Message: 2
> Date: Wed, 05 Apr 2006 05:24:54 -0700
> From: Lawrence.Crowl@Sun.com
> Subject: Re: [std-interval] C++ interval std 
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <200604051224.k35COsbd029560@philmont.sfbay.sun.com>
> 
> Alan Eliasen <eliasen@mindspring.com> writes:
>  >   I was curious to see about the speed difference between passing by
>  >value and passing by reference, because passing by value always has been
>  >slower and always *has* to be slower because it (unnecessarily) creates
>  >a copy of the object when passed in.
> 
> It does not unnecessarily create an object.  In particular, when the
> parameter to a function is the result of an expression, the const ref
> approach requires allocating a temporary and passing its address.  In
> contrast, pass-by-value can put the result of the expression directly
> into the parameter register; no copies are required.
> 
> Pass-by-reference aften introduces additional copies because the
> programmer must copy the parameter into a local variable in order to
> avoid aliases between parameters.
> 
>  >I tried three ways on x86_64, gcc 3.4.4, linux:
> 
> I would need the benchmark source in order to evaluate it and to
> execute it on other systems.
> 
> In developing the SPARC V9 ABI, I showed a 7x performance advantage for
> pass-by-value over pass-by-reference when computing Mandelbrot with
> complex numbers.

This is easily understandable for narrow function interfaces.  When the register 
set gets.  But the C99 suite of functions have up four fp arguments.  For quads 
it would be 128*2*4 = 1024 bits.  That's a lot of registers even at 64 bits 
each.  And even more of a concern on some of the crippled architectures still in 
use.

> 
>  >   Passing in unmodifiable objects as constant references when
>  >appropriate both obviates the need for copying and gives explicit
>  >const-correctness from the start.  We don't have to worry about
>  >dereferencing pointers or memory ownership issues.  It's indeed the
>  >pattern followed by most modern libraries.
> 
> You are assuming that "const" means "unmodifiable".  It does not.  It
> means that non-mutuable fields may not change when accessed through the
> const-qualified name.  The object may still change via access through
> non-const-qualified names.  The distinction between a value and a
> reference is critical here, because the former is unaliased and the
> latter is potentially aliased.  This aliasing can also have substantial
> effect on the ability of the compiler to apply global optimizations.
> 
>  >   To the caller of the functions, it just looks like an ordinary
>  >pass-by-value, but is faster, and allows the compiler to catch a lot of
>  >types of problems.
> 
> But it doesn't look the same, because of the aliasing issue.  With
> reference parameters, the function must make an explicit declaration
> about its behavior in the presence of aliasing.

That is an aspect of the language rather than the implementation.  Are we 
setting out to fix the aliasing problem WRT intervals?  It would be a huge 
change in scope.

> 
>  >   I recommend that for long-term performance and const-correctness,
>  >that objects be passed as constant references when possible.
> 
> Would you recommend that ints be passed by const reference?

Rarely.  But I would resist the argument that it is never necessary.
> ------------------------------
> 
> Message: 3
> Date: Wed, 05 Apr 2006 05:49:41 -0700
> From: Lawrence.Crowl@Sun.com
> Subject: Re: [std-interval] Re: C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <200604051249.k35Cnfbd008613@philmont.sfbay.sun.com>
> 
> first.i.last@comcast.net writes:
>  >> Lawrence feels strongly that the standard should be to pass by
>  >> value.  Intervals are small data structures;
>  >
>  >That perspective causes problems, just as it did for complex.
>  >Intervals should be considered atomic types whose internal structure
>  >is opaque.  We don't consider fp types as structures even though they
>  >consist of three distinct fields (and in fact are t reated as separate
>  >fields in software implementations of the run-time library).
> 
> The issue was the mechanism for passing the representation, not the
> logical opacity of the type.

The issue is the atomicity of the type.  Atomicity often implies effective 
opacity.  Opacity always implies atomicity.

In a few years we will expect to see hardware supporting native intervals types 
(the design papers have been around for decades).  At that point intervals are 
no longer "small data structures" as you described them.  They are native types.  
As soon as there are two dissimilar hardware implementations in existence all 
arguments about the internals of the representation leave the standard.

FP layouts are famous for being diverse.  There is almost every possible byte 
ordering available for 32-bit values.  We should not expect that historical 
trend to vanish even though it would make everyone's life easier.

So we should not predicate premature design decision on the current state of the 
art when we plan to drive a vigorous change process.

> 
>  >> by value allows them
>  >> to be passed in registers for speed.  That is how the current Sun
>  >> C++ compiler works.  There is no reason to follow the C++ complex
>  >> standard.  The library is often taken as an example by coders, and
>  >> there is no good reason to follow the tradition of C from 20 years
>  >> ago that structures should be passed by reference.
>  >
>  >There may or may not be a good reason for it.  On FPUs with weak
>  >connections to the CPU, such as x87, passing by value is strongly
>  >preferred.  Yet on FPUs with strong connections to the main CPU
>  >passing by reference might be much more efficient.
> 
> I don't follow the reasoning here.

To create a reference on weakly connected systems one must copy from the FPU to 
addressable memory, create the address in the CPU, pass the address to the 
recipient function and then copy the values from memory back into the FPU.

On strongly connected systems where there is one stack containing intergers, fp 
values, and addresses one simply passes the address of the fp values without 
moving them.

The effect of aliasing is irrelevant because we should be most concered with the 
passage of parameters during expression evaluation where there are cannot be 
aliases because there are no references or pointers to temporary objects.

> 
>  >If the standard syntax is pass by value then a compiler that prefered
>  >pass by reference would be free to do so internally (assuming
>  >appropriate referential safe guards).
> 
> SPARC V7 (32-bit) does in fact do this.  SPARC V9 (64-bit) does so
> for large structs, but passes in registers for small structs.

I'm certain Sun is not alone in that.  Watcom C/C++ provides explicit control 
over the passing conventions right down to individual function prototypes.

>  >> Pass-by-value is also a correctness issue.
>  >
>  >How so?
> 
> Because users will copy the style of interval function declarations.
> If that style includes reference paramters, the programmers will litter
> their programs with unintended aliases.  These aliases are the source of bugs.

OK, we appear to be agreed that the _syntax_ of parameter passing should not 
contain explicit references.  But implicit references, i.e., the semantics of 
parameter passing, whether via an explicit abstract type for interval parameters 
or by hidden manpilation by the compiler, are not affected by this issue.

> ------------------------------
> 
> Message: 7
> Date: 05 Apr 2006 15:37:20 +0200
> From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> Subject: Re: [std-interval] passing by value vs reference
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <m3d5fwcfe7.fsf@uniton.integrable-solutions.net>
> Content-Type: text/plain; charset=iso-8859-1
> 
> Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr> writes:
> 
> | Le mercredi 05 avril 2006 à 11:32 +0200, Sylvain Pion a écrit :
> | 
> | > 3- leave freedom for the implementation to choose
> | > 4- leave freedom for the implementation and have it provide
> | >     a standard specified way to obtain this information.
> | 
> | > I would prefer 3 to 4.  I think
> | > the complexity of implementing 4 is not worth it.
> | 
> | I don't see any additional complexity in 4 with respect to 3. As already
> | mentioned by Bill Clarke, you could simply have a typedef member in
> | interval<T> to express the calling convention of the functions of the
> | interval library: typedef interval<T> const &param_type;
> 
> If done that way, in the typical cases, the "T" would then appear in
> non-deducible context. 

It need not be a dependent type.  It could easily by a parallel set of 
templates.

========================

-- Lee Winter

P.S.  Does anyone know how I can get out of digest mode?
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Alan Eliasen <eliasen@mindspring.com> writes:

>    I can see the point that aliasing could be an issue if functions are
> modifying the objects passed in.  That would seem to me to be very bad
> programming practice, (one in which explicitly declaring const-ness
> would help the compiler point these out.)

That is not the kind of aliasing that causes the problem.  The problem stems from the fact that call-by-reference provides a way to access a variable that does not prevent other access.  THus the modification would not occur in the function receiving the parameter (the callee), but in another function called by the callee, which other function had access to the objected referred to by the paremeter.  It's effectively a minor fomr of volatility which defeats powerful optimization.

Truly volatile objects can change state at any point in time.  Potentially aliased objects, whether actually aliased or not, can logically change state any time a non-transparent function is called.

This is a classic complaint about C from FORTRAN users.

-- Lee Winter
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first.i.last@comcast.net writes:

[...]

| > Message: 6
| > Date: Wed, 05 Apr 2006 04:51:32 -0700
| > From: Steve Clamage <Stephen.Clamage@Sun.COM>
| > Subject: Re: [std-interval] C++ interval std
| > To: For discussions concerning the C++ standardization of intervals
| > 	<std-interval@compgeom.poly.edu>
| > Message-ID: <4433AF44.8020308@sun.com>
| > Content-Type: text/plain; charset=us-ascii; format=flowed
| > 
| > Alan Eliasen wrote:
| > > Bill Clarke wrote:
| > > 
| > >>This experiment is extremely platform specific, as you probably are
| > >>aware.  Most platforms in use today other than x86 will be the other way
| > >>around (add-by-value will be faster than add-by-const-ref).
| > > 
| > > 
| > >    How can that assertion possibly be made?  As you know, if a parameter
| > > is passed by value, then the copy constructor is automatically called
| > > for each object (e.g. twice for an add operator) on function entry, and
| > > then the destructor is called (twice) on function exit.
| > 
| > A simple object like complex or interval should have no user-defined copy 
| > constructor or destructor.
| 
| A desirable property, but unnecessarily restrictive.  In particular interval 
| objects with explicit properties might not be PODs.  

There are many PODs that do not have, nor need, a user-written copy
constructor and destructor.  If the mental model of interval is that
it is just a couple of floating point numbers, then Steve is
exactly right.  Are you operating under the assumption that an
interval is NOT essentially a couple of numbers?  If yes, please be
more specific.

[...]

| > Please note that our proposed interval type is meant to be a POD (plain
| > old data) type and as such has no copy constructor nor destructor.
| 
| Is it your plan that the proposal include the POD-only requirement?  I would 
| suggest that it is an obvious possibility that yeilds good performence 
| improvements, but how important is it to get fat intervals quickly?
| 
| I would must prefer not to see such a requirement in the standard.

The proposal would need to be precise about whether internal<T> is a
POD or not; that is unavoidable.

[...]

| > Message: 3
| > Date: Wed, 05 Apr 2006 05:49:41 -0700
| > From: Lawrence.Crowl@Sun.com
| > Subject: Re: [std-interval] Re: C++ interval std
| > To: For discussions concerning the C++ standardization of intervals
| > 	<std-interval@compgeom.poly.edu>
| > Message-ID: <200604051249.k35Cnfbd008613@philmont.sfbay.sun.com>
| > 
| > first.i.last@comcast.net writes:
| >  >> Lawrence feels strongly that the standard should be to pass by
| >  >> value.  Intervals are small data structures;
| >  >
| >  >That perspective causes problems, just as it did for complex.
| >  >Intervals should be considered atomic types whose internal structure
| >  >is opaque.  We don't consider fp types as structures even though they
| >  >consist of three distinct fields (and in fact are t reated as separate
| >  >fields in software implementations of the run-time library).
| > 
| > The issue was the mechanism for passing the representation, not the
| > logical opacity of the type.
| 
| The issue is the atomicity of the type.  Atomicity often implies effective 
| opacity.  Opacity always implies atomicity.

Yet, at the end of the day the proposal needs to spell out the
mechanism for passing the representation.  At the moment, I don't see
how the committee would buy a proposal that is very vague about such
issue.  Past experience with vagueness in that area has been a fertile
source of programmer confusion, and defect reports (that the committee
had to deal with).

[...]

| > Message: 7
| > Date: 05 Apr 2006 15:37:20 +0200
| > From: Gabriel Dos Reis <gdr@integrable-solutions.net>
| > Subject: Re: [std-interval] passing by value vs reference
| > To: For discussions concerning the C++ standardization of intervals
| > 	<std-interval@compgeom.poly.edu>
| > Message-ID: <m3d5fwcfe7.fsf@uniton.integrable-solutions.net>
| > Content-Type: text/plain; charset=iso-8859-1
| > 
| > Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr> writes:
| > 
| > | Le mercredi 05 avril 2006 à 11:32 +0200, Sylvain Pion a écrit :
| > | 
| > | > 3- leave freedom for the implementation to choose
| > | > 4- leave freedom for the implementation and have it provide
| > | >     a standard specified way to obtain this information.
| > | 
| > | > I would prefer 3 to 4.  I think
| > | > the complexity of implementing 4 is not worth it.
| > | 
| > | I don't see any additional complexity in 4 with respect to 3. As already
| > | mentioned by Bill Clarke, you could simply have a typedef member in
| > | interval<T> to express the calling convention of the functions of the
| > | interval library: typedef interval<T> const &param_type;
| > 
| > If done that way, in the typical cases, the "T" would then appear in
| > non-deducible context. 
| 
| It need not be a dependent type.  It could easily by a parallel set of 
| templates.

More specifically?


[ As I mentioned earlier, I'm not sure template aliases help in this
case. ]

-- Gaby

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To get out of digest mode, go to
  http://compgeom.poly.edu/mailman/listinfo/std-interval
and search "edit options" at the very bottom of the page.

Le mercredi 05 avril 2006 à 21:48 +0000, first.i.last@comcast.net a
écrit :
 
> > Please note that our proposed interval type is meant to be a POD (plain
> > old data) type and as such has no copy constructor nor destructor.
> 
> Is it your plan that the proposal include the POD-only requirement?  I would 
> suggest that it is an obvious possibility that yeilds good performence 
> improvements, but how important is it to get fat intervals quickly?
> 
> I would must prefer not to see such a requirement in the standard.

If an implementation follows the specification of our proposal, then the
resulting type is necessarily a POD. The interface has been specially
designed so that it happens. With respect to the scope of our proposal,
I don't see the point of adding a non-POD field to the interval class
(what would it contain?) or of saying that the copy constructor and the
destructor have side effects (what would they do?). Maybe we missed
something in writing the proposal, but at least our toy implementation
was clearly a POD.

> > As a
> > consequence, on some architectures and with non-broken compilers, they
> > will behave no differently than if the function arguments were simply
> > integers; except that the register will probably be bigger, or two
> > registers will be used. When this happens, passing by value will be
> > faster than passing by const-reference. Indeed there is no architecture
> > such that foo(int) is slower than bar(int const &).
> 
> Of course there is.  When addresses are narrow (fit in a register) and ints are 
> wide (don't fit in a register).  64-bit code on 32-bit hardware.  32-bit code on 
> 16-bit hardware.  16-bit code on 8-bit hardware.  I've even worked on a 
> bit-slice machine with 20-bit ints and 16-bit addresses.

It is not enough to consider only the part where the caller writes the
arguments. You are missing the part where the callee reads the
arguments. This requires an indirection when passing an argument by
reference. Let us consider a non-trivial example like the successor
function:

  int foo(int a)        { return a + 1; }
  int bar(int const &a) { return a + 1; }

So I state it again, slightly modified: there is no architecture such
that foo(int) is slower than bar(int const &) if the functions use the
integer argument.

> > I don't see any additional complexity in 4 with respect to 3. As already
> > mentioned by Bill Clarke, you could simply have a typedef member in
> > interval<T> to express the calling convention of the functions of the
> > interval library: typedef interval<T> const &param_type;
> > 
> > This requires all the functions of the library to use the same calling
> > convention.
> 
> How do you derive this requirement?  I don't see it.

If you have two functions with different calling conventions:

  interval foo(interval, interval);
  interval bar(interval const &, interval const &);

then one of them is obviously not of the type

  interval binary_function(param_type, param_type);

Best regards,

Guillaume


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Le mercredi 05 avril 2006 à 13:55 -0300, Fernando Cacciola a écrit :

> If  the FPU registers are stacked, like in the x86 family, it wouldn't
> be too uncommon, IMHO, for a compiler to do:

[...]

As a matter of fact, it would be really uncommon. For example, x86 ABIs
require the FPU stack to be empty (except maybe for arguments) at the
beginning of every functions. Otherwise the functions would cause FPU
stack overflows since they would have very little or no space left to do
their computations. Thanks to the empty stack, the compiler knows that
it can use eight FPU registers without crashing the whole process. So
for the particular example of (a*b)*(c*d), there is no way for a
compiler to avoid temporarily storing the result of a*b on the memory
stack.

> That is, stacked FPU registers allows the compiler to allocate the
> function frames (which is the problem in your example) without using
> the external memory-based stack or rearranging the registers
> manually. 

As a side note on this topic, stacked FPU registers seemed like a good
idea thirty years ago. But now that the technology has evolved and has
gone past GHz speeds, this good idea has become a nightmare for
processor designers. Translating stack positions to standard bank
positions incur a huge latency in decoding FPU instructions in the
processor. This translation work is better done once and for all at
compilation time. I would be really surprised if a modern processor
(that is not plagued by backward compatibility concerns) implements
stacked FPU registers.

Best regards,

Guillaume


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Subject: Re: [std-interval] C++ interval std
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Le mercredi 05 avril 2006 à 12:53 -0600, Alan Eliasen a écrit :

> > Please note that our proposed interval type is meant to be a POD (plain
> > old data) type and as such has no copy constructor nor destructor. As a
> > consequence, on some architectures and with non-broken compilers, they
> > will behave no differently than if the function arguments were simply
> > integers; except that the register will probably be bigger, or two
> > registers will be used. When this happens, passing by value will be
> > faster than passing by const-reference. Indeed there is no architecture
> > such that foo(int) is slower than bar(int const &).
> 
>    As a "primitive" type, int is a different case than an object,
> though.

Int is indeed different from a non-POD type, but not that different from
a POD type; this is why I chose int as an example. As any other class, a
POD type has a copy constructor and a destructor for the sake of
language uniformity, but a compiler should _never_ call them. As a
matter of fact, it should not even generate them. And this is not a
matter of optimizing or not: this is explicitly the point of a POD type.
So even when all the optimizations are disabled, a real compiler will
not call a destructor on a POD object.

Best regards,

Guillaume

From Stephen.Clamage@Sun.COM Thu Apr  6 02:23:18 2006
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Date: Thu, 06 Apr 2006 00:31:20 -0700
From: Steve Clamage <Stephen.Clamage@Sun.COM>
Subject: Re: [std-interval] C++ interval std
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Alan Eliasen wrote:
> Steve Clamage wrote:
> 
> 
> 
>>>Bill Clarke wrote:
>>>
>>>
>>>>This experiment is extremely platform specific, as you probably are
>>>>aware.  Most platforms in use today other than x86 will be the other way
>>>>around (add-by-value will be faster than add-by-const-ref).
> 
> 
> Alan Eliasen wrote:
> 
>>>   How can that assertion possibly be made?  As you know, if a parameter
>>>is passed by value, then the copy constructor is automatically called
>>>for each object (e.g. twice for an add operator) on function entry, and
>>>then the destructor is called (twice) on function exit.
>>
> 
> Steve Clamage wrote:
> 
>>A simple object like complex or interval should have no user-defined
>>copy constructor or destructor. That is, the default copy constructor
>>generated by the compiler does the right thing and does not need to be
>>user-defined. The destructor has nothing to do, and so should not be
>>user-defined. In that case, pass-by-value can be optimized into register
>>passing with no additional copying.
> 
> 
>    You still agree, though, that even if the implementation doesn't do
> memory allocation in the constructor, the compiler will still generate a
> copy constructor and a destructor, (perhaps pretty simple and efficient)
> and these will get normally get called in a pass-by-value.  Again, a
> very smart compiler can optimize these away if it realizes that the copy
> is unnecessary, but by simply specifying call-by-constant-reference, we
> don't have to hope that the compiler is very smart.  We simply eliminate
> even the possibility of calling the copy constructor and destructor.

In C++, every type (including int) has a constructor and destructor. This point 
of definition simplifies the exposition of language rules. We are saved from 
hopelessly inefficient implementations by the "as-if rule." It says the 
implementation can do what is wants as long as observable behavior is preserved. 
Multiple copies of temporary objects (as in parameter and returned-value 
passing) are not counted in "observable behavior" -- extra copies can be elided.

For POD types, I have never seen or heard of a compiler that actually generated 
a real constructor or destructor. Compilers perform a simple copy by whatever 
means is most efficient.

> 
> 
>>It is possible to construct a test case where pass-by-value gives worse
>>performance than pass-by-reference, and your example does indeed run
>>faster with pass-by-reference using Sun compilers at low optimization.
> 
> 
>    As noted, it should always be the case that pass-by-value is at least
> as slow as pass-by-constant-reference because of the overhead of calling
> the copy constructors and destructors, which are almost always
> unnecessary and can be trivially eliminated by specifying the calling
> convention.  If it's ever faster, I'd argue that it's because the
> compiler missed obvious optimizations for pass-by-constant-reference, or
> is allocating registers badly.
> 
> 
>>At high optimization, the compiler eliminated the loops and all but one
>>call to "add", which it inlined. I played with the test case for a short
>>time, but was unable to defeat the optimizer with minor changes.
> 
> 
>    Heh!  That's a smart compiler!  I had considered adding some
> randomization to the values to eliminate this possibility, but the
> timing values would have likely been swamped by the random number generator.
> 

In the original example, the call to "add" in the loop uses the same parameters. 
The compiler inlines the call, then hoists the computation out of the loop. The 
loop is now empty, so the compiler just computes the answer at compile time. 
Since the result of the computation was not used, the compiler can elide that as 
well!

I modified the loop to use the result by incrementing a variable that was later 
printed. (If the variable wasn't used, the compiler elided it, too. The "as-if" 
rule again.) To prevent hoisting the "add" out of the loop, I caused each 
iteration to add different values. Here is an example of two modified loops, and 
the output statements:

    Interval c(0.0,0.0);
    start = clock();
    for (i=0; i<upper; i++)
    {
       c.upper += addByValue( a, addByValue(Interval(i,0), b) ).upper;
    }
    end = clock();
    cout << "addByValue: \t" << (end-start) << " ticks " << c.upper << endl;

    c.upper = 0;
    start = clock();
    for (i=0; i<upper; i++)
    {
       c.upper += addByConstRef( a, addByConstRef(Interval(i,0), b) ).upper;
    }
    end = clock();
    cout << "addByConstRef: \t" << (end-start) << " ticks " << c.upper << endl;

I compiled and ran on 64-bit sparc (US II) and 64-bit amd64 (Opteron). According 
to my earlier claims, pass-by-value should have been faster.

64-bit sparc:
addByValue:     690000 ticks 4.1e+08
addByRef:       680000 ticks 4.1e+08
addByConstRef:  450000 ticks 4.1e+08

64-bit amd64:
addByValue:     1280000 ticks 4.1e+08
addByRef:        670000 ticks 4.1e+08
addByConstRef:   670000 ticks 4.1e+08

Color my face red. :-)

This result is quite different from other experiments with small structs that 
showed pass-by-value performing better. One possibility is that the compiler is 
missing some optimization opportunities. Another is that this example is not 
representative.

---
Steve Clamage, stephen.clamage@sun.com

From guillaume.melquiond@ens-lyon.fr Thu Apr  6 03:17:08 2006
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Subject: Re: [std-interval] C++ interval std
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
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Le jeudi 06 avril 2006 à 00:31 -0700, Steve Clamage a écrit :

> This result is quite different from other experiments with small structs that 
> showed pass-by-value performing better. One possibility is that the compiler is 
> missing some optimization opportunities. Another is that this example is not 
> representative.

Is your Interval class considered a "small struct" by the ABIs you
tested? According to the AMD64 ABI, it should be, since it is two
doubles; but I am not completely sure. If it is not, then pass-by-value
will go through the stack and will be a lot worse than pass-by-ref. This
would explain your results and it would mean that your example is not
representative at all.

I don't know if it is possible, but in this case it would be nice if you
could modify the ABI so that intervals are passed through registers.
This would tell if there really is a point in not simply using const
references.

Best regards,

Guillaume

From Stephen.Clamage@Sun.COM Thu Apr  6 04:11:05 2006
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Date: Thu, 06 Apr 2006 02:19:03 -0700
From: Steve Clamage <Stephen.Clamage@Sun.COM>
Subject: Re: [std-interval] C++ interval std
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The Interval class is the one posted by Alan Eliasen,
except that I removed the tag member from the Interval class,
leaving only 2 doubles.

In the compiled code, all the Interval functions were inlined,
so there are no calls to the functions. Here are two extracts
from the source code, along with the generated amd64 code.

I can also post the sparc code if you like.

First, the call-by-value part.
The compiler unrolled the loop 4 times.

     32     start = clock();
     33     for (i=0; i<upper; i++)
     34     {
     35        c.upper += addByValue( a, addByValue(Interval(i,0), b) ).upper;
     36     }
     37     end = clock();

         call       clock                                ;/ line : 32
         movq       %rax,%r12                            ;/ line : 32
         movlpd     .tim.0+32,%xmm0                              ;/ line : 26
         movlpd     %xmm0,72(%rsp)                               ;/ line : 33
         movq       48(%rsp),%r8                         ;/ line : 33
         movq       56(%rsp),%r9                         ;/ line : 33
         movq       %r8,160(%rsp)                                ;/ line : 33
         movq       %r9,168(%rsp)                                ;/ line : 33
         movq       32(%rsp),%r8                         ;/ line : 33
         movq       40(%rsp),%r9                         ;/ line : 33
         movq       %r8,224(%rsp)                                ;/ line : 33
         movq       %r9,232(%rsp)                                ;/ line : 33
.LP0.382:
         movlpd     160(%rsp),%xmm6                              ;/ line : 35
         movlpd     168(%rsp),%xmm5                              ;/ line : 35
         movlpd     224(%rsp),%xmm4                              ;/ line : 35
         movlpd     232(%rsp),%xmm3                              ;/ line : 35
         xorl       %eax,%eax                            ;/ line : 35
         movlpd     .tim.0+40,%xmm2                              ;/ line : 35
         movlpd     .tim.0+32,%xmm1
         movlpd     .tim.0+32,%xmm0
         movlpd     %xmm0,-8(%rbp)
         .zalign 16,8
.CGB.191:
         movlpd     %xmm1,64(%rsp)                               ;/ line : 35
         movq       64(%rsp),%r8                         ;/ line : 35
         movq       72(%rsp),%r9                         ;/ line : 35
         movq       %r8,176(%rsp)                                ;/ line : 35
         movq       %r9,184(%rsp)                                ;/ line : 35
         movlpd     176(%rsp),%xmm0                              ;/ line : 35
         addsd      %xmm6,%xmm0                          ;/ line : 35
         movlpd     %xmm0,192(%rsp)                              ;/ line : 35
         movlpd     184(%rsp),%xmm0                              ;/ line : 35
         addsd      %xmm5,%xmm0                          ;/ line : 35
         movlpd     %xmm0,200(%rsp)                              ;/ line : 35
         movq       192(%rsp),%xmm0                              ;/ line : 35
         movhpd     200(%rsp),%xmm0                              ;/ line : 35
         movq       %xmm0,208(%rsp)                              ;/ line : 35
         movhpd     %xmm0,216(%rsp)                              ;/ line : 35
         movlpd     208(%rsp),%xmm0                              ;/ line : 35
         addsd      %xmm4,%xmm0                          ;/ line : 35
         movlpd     %xmm0,240(%rsp)                              ;/ line : 35
         movlpd     216(%rsp),%xmm0                              ;/ line : 35
         addsd      %xmm3,%xmm0                          ;/ line : 35
         movlpd     %xmm0,248(%rsp)                              ;/ line : 35
         movq       240(%rsp),%r8                                ;/ line : 35
         movq       248(%rsp),%r9                                ;/ line : 35
         movq       %r8,80(%rsp)                         ;/ line : 35
         movq       %r9,88(%rsp)                         ;/ line : 35
         movlpd     -8(%rbp),%xmm0                               ;/ line : 35
         addsd      88(%rsp),%xmm0                               ;/ line : 35
         addsd      %xmm2,%xmm1                          ;/ line : 35
         movlpd     %xmm1,64(%rsp)                               ;/ line : 35
         movq       64(%rsp),%r8                         ;/ line : 35
         movq       72(%rsp),%r9                         ;/ line : 35
         movq       %r8,176(%rsp)                                ;/ line : 35
         movq       %r9,184(%rsp)                                ;/ line : 35
         movlpd     176(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm6,%xmm7                          ;/ line : 35
         movlpd     %xmm7,192(%rsp)                              ;/ line : 35
         movlpd     184(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm5,%xmm7                          ;/ line : 35
         movlpd     %xmm7,200(%rsp)                              ;/ line : 35
         movq       192(%rsp),%xmm7                              ;/ line : 35
         movhpd     200(%rsp),%xmm7                              ;/ line : 35
         movq       %xmm7,208(%rsp)                              ;/ line : 35
         movhpd     %xmm7,216(%rsp)                              ;/ line : 35
         movlpd     208(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm4,%xmm7                          ;/ line : 35
         movlpd     %xmm7,240(%rsp)                              ;/ line : 35
         movlpd     216(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm3,%xmm7                          ;/ line : 35
         movlpd     %xmm7,248(%rsp)                              ;/ line : 35
         movq       240(%rsp),%r8                                ;/ line : 35
         movq       248(%rsp),%r9                                ;/ line : 35
         movq       %r8,80(%rsp)                         ;/ line : 35
         movq       %r9,88(%rsp)                         ;/ line : 35
         addsd      88(%rsp),%xmm0                               ;/ line : 35
         addsd      %xmm2,%xmm1                          ;/ line : 35
         movlpd     %xmm1,64(%rsp)                               ;/ line : 35
         movq       64(%rsp),%r8                         ;/ line : 35
         movq       72(%rsp),%r9                         ;/ line : 35
         movq       %r8,176(%rsp)                                ;/ line : 35
         movq       %r9,184(%rsp)                                ;/ line : 35
         movlpd     176(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm6,%xmm7                          ;/ line : 35
         movlpd     %xmm7,192(%rsp)                              ;/ line : 35
         movlpd     184(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm5,%xmm7                          ;/ line : 35
         movlpd     %xmm7,200(%rsp)                              ;/ line : 35
         movq       192(%rsp),%xmm7                              ;/ line : 35
         movhpd     200(%rsp),%xmm7                              ;/ line : 35
         movq       %xmm7,208(%rsp)                              ;/ line : 35
         movhpd     %xmm7,216(%rsp)                              ;/ line : 35
         movlpd     208(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm4,%xmm7                          ;/ line : 35
         movlpd     %xmm7,240(%rsp)                              ;/ line : 35
         movlpd     216(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm3,%xmm7                          ;/ line : 35
         movlpd     %xmm7,248(%rsp)                              ;/ line : 35
         movq       240(%rsp),%r8                                ;/ line : 35
         movq       248(%rsp),%r9                                ;/ line : 35
         movq       %r8,80(%rsp)                         ;/ line : 35
         movq       %r9,88(%rsp)                         ;/ line : 35
         addsd      88(%rsp),%xmm0                               ;/ line : 35
         addsd      %xmm2,%xmm1                          ;/ line : 35
         movlpd     %xmm1,64(%rsp)                               ;/ line : 35
         movq       64(%rsp),%r8                         ;/ line : 35
         movq       72(%rsp),%r9                         ;/ line : 35
         movq       %r8,176(%rsp)                                ;/ line : 35
         movq       %r9,184(%rsp)                                ;/ line : 35
         movlpd     176(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm6,%xmm7                          ;/ line : 35
         movlpd     %xmm7,192(%rsp)                              ;/ line : 35
         movlpd     184(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm5,%xmm7                          ;/ line : 35
         movlpd     %xmm7,200(%rsp)                              ;/ line : 35
         movq       192(%rsp),%xmm7                              ;/ line : 35
         movhpd     200(%rsp),%xmm7                              ;/ line : 35
         movq       %xmm7,208(%rsp)                              ;/ line : 35
         movhpd     %xmm7,216(%rsp)                              ;/ line : 35
         movlpd     208(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm4,%xmm7                          ;/ line : 35
         movlpd     %xmm7,240(%rsp)                              ;/ line : 35
         movlpd     216(%rsp),%xmm7                              ;/ line : 35
         addsd      %xmm3,%xmm7                          ;/ line : 35
         movlpd     %xmm7,248(%rsp)                              ;/ line : 35
         movq       240(%rsp),%r8                                ;/ line : 35
         movq       248(%rsp),%r9                                ;/ line : 35
         movq       %r8,80(%rsp)                         ;/ line : 35
         movq       %r9,88(%rsp)                         ;/ line : 35
         addsd      88(%rsp),%xmm0                               ;/ line : 35
         movlpd     %xmm0,-8(%rbp)                               ;/ line : 35
         addsd      %xmm2,%xmm1                          ;/ line : 35
         addl       $4,%eax                              ;/ line : 35
.LU2.397:
         cmpl       $99999999,%eax                               ;/ line : 35
         jle        .CGB.191                             ;/ line : 35
.LX0.383:
.LE0.384:
.CGC.192:
         xorl       %ebx,%ebx                            ;/ line : 45
         call       clock                                ;/ line : 37
         movq       %rax,%r13                            ;/ line : 37


Now the call-by-const-ref part.
The compiler unrolled this loop 6 times.

     52     start = clock();
     53     for (i=0; i<upper; i++)
     54     {
     55        c.upper += addByConstRef( a, addByConstRef(Interval(i,0), b) ).upper;
     56     }
     57     end = clock();

         call       clock                                ;/ line : 52
         movq       %rax,%r12                            ;/ line : 52
         movlpd     56(%rsp),%xmm0                               ;/ line : 53
         movlpd     %xmm0,296(%rsp)                              ;/ line : 53
         movlpd     48(%rsp),%xmm4                               ;/ line : 55
         movlpd     32(%rsp),%xmm3                               ;/ line : 55
         movlpd     40(%rsp),%xmm2                               ;/ line : 55
         movlpd     .tim.0+40,%xmm5                              ;/ line : 55
         movlpd     .tim.0+32,%xmm1
         movlpd     .tim.0+32,%xmm0
         movlpd     %xmm0,-8(%rbp)
         .zalign 16,8
.CGF.195:
         movsd      %xmm1,%xmm0                          ;/ line : 55
         addsd      %xmm4,%xmm0                          ;/ line : 55
         movlpd     %xmm0,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm3,%xmm0                          ;/ line : 55
         movlpd     %xmm0,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm2,%xmm0                          ;/ line : 55
         movlpd     %xmm0,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         movlpd     -8(%rbp),%xmm0                               ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         movsd      %xmm1,%xmm6                          ;/ line : 55
         addsd      %xmm4,%xmm6                          ;/ line : 55
         movlpd     %xmm6,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm3,%xmm6                          ;/ line : 55
         movlpd     %xmm6,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm2,%xmm6                          ;/ line : 55
         movlpd     %xmm6,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         movsd      %xmm1,%xmm6                          ;/ line : 55
         addsd      %xmm4,%xmm6                          ;/ line : 55
         movlpd     %xmm6,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm3,%xmm6                          ;/ line : 55
         movlpd     %xmm6,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm2,%xmm6                          ;/ line : 55
         movlpd     %xmm6,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         movsd      %xmm1,%xmm6                          ;/ line : 55
         addsd      %xmm4,%xmm6                          ;/ line : 55
         movlpd     %xmm6,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm3,%xmm6                          ;/ line : 55
         movlpd     %xmm6,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm2,%xmm6                          ;/ line : 55
         movlpd     %xmm6,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         movsd      %xmm1,%xmm6                          ;/ line : 55
         addsd      %xmm4,%xmm6                          ;/ line : 55
         movlpd     %xmm6,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm3,%xmm6                          ;/ line : 55
         movlpd     %xmm6,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm2,%xmm6                          ;/ line : 55
         movlpd     %xmm6,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         movsd      %xmm1,%xmm6                          ;/ line : 55
         addsd      %xmm4,%xmm6                          ;/ line : 55
         movlpd     %xmm6,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm3,%xmm6                          ;/ line : 55
         movlpd     %xmm6,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm6                              ;/ line : 55
         addsd      %xmm2,%xmm6                          ;/ line : 55
         movlpd     %xmm6,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         movlpd     %xmm0,-8(%rbp)                               ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         addl       $6,%ebx                              ;/ line : 55
.LUF.414:
         cmpl       $99999994,%ebx                               ;/ line : 55
         jle        .CGF.195                             ;/ line : 55
.LX5.422:
.LE5.423:
.LU10.415:
         movlpd     48(%rsp),%xmm2                               ;/ line : 55
         movlpd     32(%rsp),%xmm3                               ;/ line : 55
         movlpd     40(%rsp),%xmm4                               ;/ line : 55
         movlpd     .tim.0+40,%xmm5                              ;/ line : 55
         .zalign 16,8
.LU11.416:
         movsd      %xmm1,%xmm0                          ;/ line : 55
         addsd      %xmm2,%xmm0                          ;/ line : 55
         movlpd     %xmm0,288(%rsp)                              ;/ line : 55
         movq       288(%rsp),%r8                                ;/ line : 55
         movq       296(%rsp),%r9                                ;/ line : 55
         movq       %r8,128(%rsp)                                ;/ line : 55
         movq       %r9,136(%rsp)                                ;/ line : 55
         movlpd     128(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm3,%xmm0                          ;/ line : 55
         movlpd     %xmm0,304(%rsp)                              ;/ line : 55
         movlpd     136(%rsp),%xmm0                              ;/ line : 55
         addsd      %xmm4,%xmm0                          ;/ line : 55
         movlpd     %xmm0,312(%rsp)                              ;/ line : 55
         movq       304(%rsp),%r8                                ;/ line : 55
         movq       312(%rsp),%r9                                ;/ line : 55
         movq       %r8,144(%rsp)                                ;/ line : 55
         movq       %r9,152(%rsp)                                ;/ line : 55
         movlpd     -8(%rbp),%xmm0                               ;/ line : 55
         addsd      152(%rsp),%xmm0                              ;/ line : 55
         movlpd     %xmm0,-8(%rbp)                               ;/ line : 55
         addsd      %xmm5,%xmm1                          ;/ line : 55
         incl       %ebx                         ;/ line : 55
         cmpl       $99999999,%ebx                               ;/ line : 55
         jle        .LU11.416                            ;/ line : 55
.LX6.424:
.LE6.425:
.LX2.387:
.LE2.388:
         call       clock                                ;/ line : 57

---
Steve Clamage, stephen.clamage@sun.com


Guillaume Melquiond wrote:

> Le jeudi 06 avril 2006 à 00:31 -0700, Steve Clamage a écrit :
> 
> 
>>This result is quite different from other experiments with small structs that 
>>showed pass-by-value performing better. One possibility is that the compiler is 
>>missing some optimization opportunities. Another is that this example is not 
>>representative.
> 
> 
> Is your Interval class considered a "small struct" by the ABIs you
> tested? According to the AMD64 ABI, it should be, since it is two
> doubles; but I am not completely sure. If it is not, then pass-by-value
> will go through the stack and will be a lot worse than pass-by-ref. This
> would explain your results and it would mean that your example is not
> representative at all.
> 
> I don't know if it is possible, but in this case it would be nice if you
> could modify the ABI so that intervals are passed through registers.
> This would tell if there really is a point in not simply using const
> references.
> 
> Best regards,
> 
> Guillaume
> 
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval


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Subject: Re: [std-interval] C++ interval std
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Le jeudi 06 avril 2006 à 02:19 -0700, Steve Clamage a écrit :
> The Interval class is the one posted by Alan Eliasen,
> except that I removed the tag member from the Interval class,
> leaving only 2 doubles.
> 
> In the compiled code, all the Interval functions were inlined,
> so there are no calls to the functions. Here are two extracts
> from the source code, along with the generated amd64 code.

If all the functions are inlined, you are not testing which argument
passing method is the best one for your architecture. You are only
testing whether the compiler is good enough to produce optimal assembly
in both cases, since no information is hidden behind function call. The
answer seems to be "no" for your compiler (SunCC?).

I know for example that GCC is really bad at handling and optimizing
pass-by-value arguments, and I have already submitted a few bug-reports
on this topic.

Best regards,

Guillaume

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 -------------- Original message ----------------------
From: std-interval-request@compgeom.poly.edu
> Send Std-interval mailing list submissions to
> 	std-interval@compgeom.poly.edu
> ------------------------------
> 
> Message: 2
> Date: 06 Apr 2006 00:25:57 +0200
> From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> Subject: Re: [std-interval] Parameter passing
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <m3fykrr762.fsf@uniton.integrable-solutions.net>
> Content-Type: text/plain; charset=iso-8859-1
> 
> first.i.last@comcast.net writes:
> 
> [...]
> 
> | A desirable property, but unnecessarily restrictive.  In particular interval 
> | objects with explicit properties might not be PODs.  
> 
> There are many PODs that do not have, nor need, a user-written copy
> constructor and destructor.  If the mental model of interval is that
> it is just a couple of floating point numbers, then Steve is
> exactly right.  Are you operating under the assumption that an
> interval is NOT essentially a couple of numbers?

Yes.

>  If yes, please be more specific.

First, there are properties that may need to be represented such as:
    -- openness of each end point
    -- domain filtration active flag (result is only partial)
    -- disjointness
    -- dependency list
    -- generative expression (built at run-time)
    -- and on non-IEEE machines, various flags/codes for
uninit, dead, and flavors of NaN (e.g., EIO, EDOM, ERANGE, div0, imag).

Second, and perhaps more important, while it is convenient to use a particular mental model of the internals of an interval, I doubt that it is strictly necessary.  Such a constraint upon the implementation will retard progress in developing innovative implementations. This is a non-trivial concern in that progress in the field is rapid and the goal of this effort is to establish a kind of best practice that will be emulated by implementations rather than to perform the classic standardization work of resolving conflicts among disparate existing implementations.

Third, the standard should not inhibit any existing practice without some consideration of the loss.  Algol's triplex type would be forbidden by the "an interval is two numbers" mental model.  It would still be a POD, and while natually substituable for an interval, could not comply with the "double interval[2]" mental model.  If necessary that kind of restriction is tolerable, but some showing of the necessity is called for.

> 
> [...]
> 
> | > Please note that our proposed interval type is meant to be a POD (plain
> | > old data) type and as such has no copy constructor nor destructor.
> | 
> | Is it your plan that the proposal include the POD-only requirement?  I would 
> | suggest that it is an obvious possibility that yeilds good performence 
> | improvements, but how important is it to get fat intervals quickly?
> | 
> | I would must prefer not to see such a requirement in the standard.
> 
> The proposal would need to be precise about whether internal<T> is a
> POD or not; that is unavoidable.

Why?  To the extent that concrete and abstract bound a range of degrees of specificity, what is lost by tending toward the abstract?

It appears to me that the fewer requirements we place upon implementations the greater the chance of acceptance and the greater the chance of implementors acting upon the opportunity.

In this regard I consider things like specific requirements of PODness to be a kind of fine print that should be minimized.

The only requirement for specificity I see would be to state whether or not the user is allowed to assume PODness.  And I would argue against that assumption.  But is such a statement in fact required?

> 
> [...]
> 
> | > Message: 3
> | > Date: Wed, 05 Apr 2006 05:49:41 -0700
> | > From: Lawrence.Crowl@Sun.com
> | > Subject: Re: [std-interval] Re: C++ interval std
> | > To: For discussions concerning the C++ standardization of intervals
> | > 	<std-interval@compgeom.poly.edu>
> | > Message-ID: <200604051249.k35Cnfbd008613@philmont.sfbay.sun.com>
> | > 
> | > first.i.last@comcast.net writes:
> | >  >> Lawrence feels strongly that the standard should be to pass by
> | >  >> value.  Intervals are small data structures;
> | >  >
> | >  >That perspective causes problems, just as it did for complex.
> | >  >Intervals should be considered atomic types whose internal structure
> | >  >is opaque.  We don't consider fp types as structures even though they
> | >  >consist of three distinct fields (and in fact are t reated as separate
> | >  >fields in software implementations of the run-time library).
> | > 
> | > The issue was the mechanism for passing the representation, not the
> | > logical opacity of the type.
> | 
> | The issue is the atomicity of the type.  Atomicity often implies effective 
> | opacity.  Opacity always implies atomicity.
> 
> Yet, at the end of the day the proposal needs to spell out the
> mechanism for passing the representation.  At the moment, I don't see
> how the committee would buy a proposal that is very vague about such
> issue.  Past experience with vagueness in that area has been a fertile
> source of programmer confusion, and defect reports (that the committee
> had to deal with).

Is an abstract type for parameters vague?

> 
> [...]
> 
> | > Message: 7
> | > Date: 05 Apr 2006 15:37:20 +0200
> | > From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> | > Subject: Re: [std-interval] passing by value vs reference
> | > To: For discussions concerning the C++ standardization of intervals
> | > 	<std-interval@compgeom.poly.edu>
> | > Message-ID: <m3d5fwcfe7.fsf@uniton.integrable-solutions.net>
> | > Content-Type: text/plain; charset=iso-8859-1
> | > 

> | > If done that way, in the typical cases, the "T" would then appear in
> | > non-deducible context. 
> | 
> | It need not be a dependent type.  It could easily by a parallel set of templates.
> 
> More specifically?

----- interval.h -----
    template< T > struct Interval    { ... };
    template< T > struct IntervalArg { ... };

Such an abstraction would require each implementor to document the calling convention actually used so that interfacing with other languages was possible, but implementations already have to document all kinds of calling convention properties of which parameter passing is only one.

Does the interval standard need to be specific about who cleans arguments off of the stack? Or whether external symbols get leading underbar warts? Or whether stack frame management is required (call/ret versus enter/leave).  Parameter access specs don't really belong in a high level language.  (I know, C is not a high level language and C++ drags much of that along, but we can try...).

> 
> 
> [ As I mentioned earlier, I'm not sure template aliases help in this
> case. ]

I don't understand the term template alias.  Coud you describe one?

> ------------------------------
> 
> Message: 3
> Date: Thu, 06 Apr 2006 09:18:02 +0200
> From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Subject: Re: [std-interval] Parameter passing
> To: std-interval@compgeom.poly.edu
> Message-ID: <1144307882.3988.78.camel@saline>
> Content-Type: text/plain; charset=ISO-8859-1
> 
> Le mercredi 05 avril 2006 à 21:48 +0000, first.i.last@comcast.net a
> écrit :
>  
> > > Please note that our proposed interval type is meant to be a POD (plain
> > > old data) type and as such has no copy constructor nor destructor.
> > 
> > Is it your plan that the proposal include the POD-only requirement?  I would 
> > suggest that it is an obvious possibility that yeilds good performence 
> > improvements, but how important is it to get fat intervals quickly?
> > 
> > I would must prefer not to see such a requirement in the standard.
> 
> If an implementation follows the specification of our proposal, then the
> resulting type is necessarily a POD. The interface has been specially
> designed so that it happens. With respect to the scope of our proposal,
> I don't see the point of adding a non-POD field to the interval class
> (what would it contain?) or of saying that the copy constructor and the
> destructor have side effects (what would they do?). Maybe we missed
> something in writing the proposal, but at least our toy implementation
> was clearly a POD.

I understand that the current version of the proposal requires that
intervals bs PODs and further than they are just two floating point values.  I suggest that both of those constraints be relaxed.
> 
> > > As a
> > > consequence, on some architectures and with non-broken compilers, they
> > > will behave no differently than if the function arguments were simply
> > > integers; except that the register will probably be bigger, or two
> > > registers will be used. When this happens, passing by value will be
> > > faster than passing by const-reference. Indeed there is no architecture
> > > such that foo(int) is slower than bar(int const &).
> > 
> > Of course there is.  When addresses are narrow (fit in a register) and ints 
> are 
> > wide (don't fit in a register).  64-bit code on 32-bit hardware.  32-bit code 
> on 
> > 16-bit hardware.  16-bit code on 8-bit hardware.  I've even worked on a 
> > bit-slice machine with 20-bit ints and 16-bit addresses.
> 
> It is not enough to consider only the part where the caller writes the
> arguments. You are missing the part where the callee reads the
> arguments. This requires an indirection when passing an argument by
> reference. Let us consider a non-trivial example like the successor
> function:
> 
>   int foo(int a)        { return a + 1; }
>   int bar(int const &a) { return a + 1; }
> 
> So I state it again, slightly modified: there is no architecture such
> that foo(int) is slower than bar(int const &) if the functions use the
> integer argument.

If the function call hierarchy is deep then many functions will accept and pass on parameters with only the leaf functions actually "using" the values.

But this is far afield from the real issue because floats aren't ints and many compilers will not pass floats in registers, much less structs in registers.  The standard should not make unnecessary assumptions about what implementations are willing and able to do at the lower levels.

> 
> > > I don't see any additional complexity in 4 with respect to 3. As already
> > > mentioned by Bill Clarke, you could simply have a typedef member in
> > > interval<T> to express the calling convention of the functions of the
> > > interval library: typedef interval<T> const &param_type;
> > > 
> > > This requires all the functions of the library to use the same calling
> > > convention.
> > 
> > How do you derive this requirement?  I don't see it.
> 
> If you have two functions with different calling conventions:
> 
>   interval foo(interval, interval);
>   interval bar(interval const &, interval const &);
> 
> then one of them is obviously not of the type
> 
>   interval binary_function(param_type, param_type);

Of course.

Does the existence of the type definition _require_ its use?  I think not.  On the assumption that some strange function (of which I am at present unable to conceive an example) needs to use the "other" convention, it can simply do so.  The only value in standardizing the convention lies in the assumption that users will emulate it.  If the library sets a default convention either implicitly via bare argument declarations or explicitly with a specific argument type definition then users will adopt the default convention.  That does not require that there be no exceptions to the default convention.

My dispute is with: "This REQUIRES [emphais added] all the functions of the library to use the same calling convention."  It permits/encourages the use of the same convention, but does not mandate it.

> ------------------------------
> 
> Message: 4
> Date: Thu, 06 Apr 2006 09:18:09 +0200
> From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Subject: Re: [std-interval] passing by value vs reference
> To: std-interval@compgeom.poly.edu
> Message-ID: <1144307889.3988.80.camel@saline>
> Content-Type: text/plain; charset=ISO-8859-1
> 
> Le mercredi 05 avril 2006 à 13:55 -0300, Fernando Cacciola a écrit :
> 
> > If  the FPU registers are stacked, like in the x86 family, it wouldn't
> > be too uncommon, IMHO, for a compiler to do:
> 
> [...]
> 
> As a matter of fact, it would be really uncommon. For example, x86 ABIs
> require the FPU stack to be empty (except maybe for arguments) at the
> beginning of every functions.

There are x86 systems without the (draconian) requirement for an empty FPU stack on function entry.  It is vary hard to evaluate a substantial expression efficiently under that requirement.

> Otherwise the functions would cause FPU
> stack overflows since they would have very little or no space left to do
> their computations.

That is what the stack overflow trap is for.

> Thanks to the empty stack, the compiler knows that
> it can use eight FPU registers without crashing the whole process. So
> for the particular example of (a*b)*(c*d), there is no way for a
> compiler to avoid temporarily storing the result of a*b on the memory stack.

Of course there is.  Pseudo code using FPU stack only with depth comments:

mulltree:      ; 0
    push a      ; 1
    push b      ; 2
    mul          ; 1
    push c      ; 2
    push d      ; 3
    mul          ; 2
    mul          ; 1

> 
> > That is, stacked FPU registers allows the compiler to allocate the
> > function frames (which is the problem in your example) without using
> > the external memory-based stack or rearranging the registers
> > manually. 
> 
> As a side note on this topic, stacked FPU registers seemed like a good
> idea thirty years ago. But now that the technology has evolved and has
> gone past GHz speeds, this good idea has become a nightmare for
> processor designers. Translating stack positions to standard bank
> positions incur a huge latency in decoding FPU instructions in the
> processor. This translation work is better done once and for all at
> compilation time. I would be really surprised if a modern processor
> (that is not plagued by backward compatibility concerns) implements
> stacked FPU registers.

If that were true (I am agnostic) then compilers would be better off generating explict register access instructions instead of implicit stack access instructions.  Even the x87 has both.

My understanding is that the opposite is occurring.  For instance, one well regarded compiler used to reserve some of the registers for explicit access and used the rest as a stack.  Fairly recently they discarded the direct access area and now use the entire register set as a stack.  This in a compiler known for decades to generate tight, fast code.

Point is that we should not be trying to shoehorn intervals into a single theoretical platform model unless it is absolutely necessary.

> ------------------------------
> 
> Message: 6
> Date: Thu, 06 Apr 2006 00:31:20 -0700
> From: Steve Clamage <Stephen.Clamage@Sun.COM>
> Subject: Re: [std-interval] C++ interval std
> To: For discussions concerning the C++ standardization of intervals
> 	<std-interval@compgeom.poly.edu>
> Message-ID: <4434C3C8.7050808@sun.com>
> Content-Type: text/plain; charset=us-ascii; format=flowed
> 
> Alan Eliasen wrote:
> > Steve Clamage wrote:
> > 
> > 
> > 
> >>>Bill Clarke wrote:
> >>>
> >>>
> >>>>This experiment is extremely platform specific, as you probably are
> >>>>aware.  Most platforms in use today other than x86 will be the other way
> >>>>around (add-by-value will be faster than add-by-const-ref).
> > 
> > 
> > Alan Eliasen wrote:
> > 
> >>>   How can that assertion possibly be made?  As you know, if a parameter
> >>>is passed by value, then the copy constructor is automatically called
> >>>for each object (e.g. twice for an add operator) on function entry, and
> >>>then the destructor is called (twice) on function exit.
> >>
> > 
> > Steve Clamage wrote:
> > 
> >>A simple object like complex or interval should have no user-defined
> >>copy constructor or destructor. That is, the default copy constructor
> >>generated by the compiler does the right thing and does not need to be
> >>user-defined. The destructor has nothing to do, and so should not be
> >>user-defined. In that case, pass-by-value can be optimized into register
> >>passing with no additional copying.
> > 
> > 
> >    You still agree, though, that even if the implementation doesn't do
> > memory allocation in the constructor, the compiler will still generate a
> > copy constructor and a destructor, (perhaps pretty simple and efficient)
> > and these will get normally get called in a pass-by-value.  Again, a
> > very smart compiler can optimize these away if it realizes that the copy
> > is unnecessary, but by simply specifying call-by-constant-reference, we
> > don't have to hope that the compiler is very smart.  We simply eliminate
> > even the possibility of calling the copy constructor and destructor.
> 
> In C++, every type (including int) has a constructor and destructor. This point 
> of definition simplifies the exposition of language rules. We are saved from 
> hopelessly inefficient implementations by the "as-if rule." It says the 
> implementation can do what is wants as long as observable behavior is preserved. 
> Multiple copies of temporary objects (as in parameter and returned-value 
> passing) are not counted in "observable behavior" -- extra copies can be elided.
> 
> For POD types, I have never seen or heard of a compiler that actually generated 
> a real constructor or destructor. Compilers perform a simple copy by whatever 
> means is most efficient.

You have stated the key point quite well.  It means that one writes code for correctness and efficiency (algorithm selection) but one leaves the low-level details to the compiler.

We can trust that the implementors will have at least as much interest in fast code as we do and that they will be far better informed as to what matters on their target platforms.  So the issue should be delegated to the implementors.

> ******************************************

-- Lee Winter

From gdr@integrable-solutions.net Thu Apr  6 11:01:48 2006
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first.i.last@comcast.net writes:

[...]

| > | > Please note that our proposed interval type is meant to be a POD (plain
| > | > old data) type and as such has no copy constructor nor destructor.
| > | 
| > | Is it your plan that the proposal include the POD-only requirement?  I would 
| > | suggest that it is an obvious possibility that yeilds good performence 
| > | improvements, but how important is it to get fat intervals quickly?
| > | 
| > | I would must prefer not to see such a requirement in the standard.
| > 
| > The proposal would need to be precise about whether internal<T> is a
| > POD or not; that is unavoidable.
| 
| Why?

because if the proposal is accepted, it is going to be part of a much
larger context.  They are some operations on can do on types depending
on whether they are PODs or not, like offsetof, initializations and
other fine details.  The standard needs to say whether such operations
are permitted or not.

[...]

| In this regard I consider things like specific requirements of
| PODness to be a kind of fine print that should be minimized. 

probably; but in the context we are talking about, you have to
specify.  You can't do without it -- and we learnt it the hard way. 

[...]

| > | > The issue was the mechanism for passing the representation, not the
| > | > logical opacity of the type.
| > | 
| > | The issue is the atomicity of the type.  Atomicity often implies effective 
| > | opacity.  Opacity always implies atomicity.
| > 
| > Yet, at the end of the day the proposal needs to spell out the
| > mechanism for passing the representation.  At the moment, I don't see
| > how the committee would buy a proposal that is very vague about such
| > issue.  Past experience with vagueness in that area has been a fertile
| > source of programmer confusion, and defect reports (that the committee
| > had to deal with).
| 
| Is an abstract type for parameters vague?

In C++, there is the notion of "abstract class" but I doubt that is
what you were refering to.  One has to be more specific than general
terms; this is not a language independent specification.

| > [...]
| > 
| > | > Message: 7
| > | > Date: 05 Apr 2006 15:37:20 +0200
| > | > From: Gabriel Dos Reis <gdr@integrable-solutions.net>
| > | > Subject: Re: [std-interval] passing by value vs reference
| > | > To: For discussions concerning the C++ standardization of intervals
| > | > 	<std-interval@compgeom.poly.edu>
| > | > Message-ID: <m3d5fwcfe7.fsf@uniton.integrable-solutions.net>
| > | > Content-Type: text/plain; charset=iso-8859-1
| > | > 
| 
| > | > If done that way, in the typical cases, the "T" would then appear in
| > | > non-deducible context. 
| > | 
| > | It need not be a dependent type.  It could easily by a parallel set of templates.
| > 
| > More specifically?
| 
| ----- interval.h -----
|     template< T > struct Interval    { ... };
|     template< T > struct IntervalArg { ... };

That is half of it; the other half is how are they used concretely in
specifying function parameters?  That is the most interesting bits.
Please don't be afraid to be concrete, otherwise I fear we would not
communicate effectively: the issue at hand is too concrete.

| Such an abstraction would require each implementor to document the
| calling convention actually used so that interfacing with other
| languages was possible, but implementations already have to document
| all kinds of calling convention properties of which parameter
| passing is only one. 

How is IntervalArg<T> is different from IntervalArg<T>?  What do they
contain? 

| Does the interval standard need to be specific about who cleans
| arguments off of the stack?

Once we know what IntervalArg<T> and Interval<T> contain and do, we
can get to that question.

[...]

| > [ As I mentioned earlier, I'm not sure template aliases help in this
| > case. ]
| 
| I don't understand the term template alias.  Coud you describe one?

A "template alias" is an alias for a family of types

   http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2003/n1489.pdf

-- Gaby
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 -------------- Original message ----------------------
From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> first.i.last@comcast.net writes:
> 
> [...]
> 
> | > | > Please note that our proposed interval type is meant to be a POD (plain
> | > | > old data) type and as such has no copy constructor nor destructor.
> | > | 
> | > | Is it your plan that the proposal include the POD-only requirement?  I 
> would 
> | > | suggest that it is an obvious possibility that yeilds good performence 
> | > | improvements, but how important is it to get fat intervals quickly?
> | > | 
> | > | I would must prefer not to see such a requirement in the standard.
> | > 
> | > The proposal would need to be precise about whether internal<T> is a
> | > POD or not; that is unavoidable.
> | 
> | Why?
> 
> because if the proposal is accepted, it is going to be part of a much
> larger context.  They are some operations on can do on types depending
> on whether they are PODs or not, like offsetof, initializations and
> other fine details.  The standard needs to say whether such operations
> are permitted or not.

OK, I did not ask a sufficiently precise question.  Why is "implementation defined" unacceptable?  I.e., why does PODness have to be a constant for all implementations?

I hope offsetof() is not going to be used much on intervals.  There would be little point in scrounging around inside an interval unless you are trying to cause (yourself) some trouble.

Initialization of an interval is almost certainly going to require a ctor due to the problem of compiler mangling of literal constants, so for purposes of initialization intervals aren't going to behave like PODs even if they are PODs.

Can you think of any other fine details (other than things like binary IO) that might influence the preference for PODs over "real" objects?

> 
> [...]
> 
> | In this regard I consider things like specific requirements of
> | PODness to be a kind of fine print that should be minimized. 
> 
> probably; but in the context we are talking about, you have to
> specify.  You can't do without it -- and we learnt it the hard way.

OK I accept your judgement that a specification is necessary.  That leaves the issue of whether it can be delegated to the implementation.  If it can be then its worth discussing whether it should be.
 
> 
> [...]
> 
> | > | > The issue was the mechanism for passing the representation, not the
> | > | > logical opacity of the type.
> | > | 
> | > | The issue is the atomicity of the type.  Atomicity often implies effective 
> | > | opacity.  Opacity always implies atomicity.
> | > 
> | > Yet, at the end of the day the proposal needs to spell out the
> | > mechanism for passing the representation.  At the moment, I don't see
> | > how the committee would buy a proposal that is very vague about such
> | > issue.  Past experience with vagueness in that area has been a fertile
> | > source of programmer confusion, and defect reports (that the committee
> | > had to deal with).
> | 
> | Is an abstract type for parameters vague?
> 
> In C++, there is the notion of "abstract class" but I doubt that is
> what you were refering to.  One has to be more specific than general
> terms; this is not a language independent specification.

Abstractions hide implementation details.  The previous suggestion (yours?) of interval::param_type would hide either "interval const &" or "interval" type definitions.  That would certainly be usefu, but  dependent types are problematic.  The only variation I'm suggesting is to make that parameter type independent of the interval template type.

> 
> | > [...]
> | > 
> | > | > Message: 7
> | > | > Date: 05 Apr 2006 15:37:20 +0200
> | > | > From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> | > | > Subject: Re: [std-interval] passing by value vs reference
> | > | > To: For discussions concerning the C++ standardization of intervals
> | > | > 	<std-interval@compgeom.poly.edu>
> | > | > Message-ID: <m3d5fwcfe7.fsf@uniton.integrable-solutions.net>
> | > | > Content-Type: text/plain; charset=iso-8859-1
> | > | > 
> | 
> | > | > If done that way, in the typical cases, the "T" would then appear in
> | > | > non-deducible context. 
> | > | 
> | > | It need not be a dependent type.  It could easily by a parallel set of 
> templates.
> | > 
> | > More specifically?
> | 
> | ----- interval.h -----
> |     template< T > struct Interval    { ... };
> |     template< T > struct IntervalArg { ... };
> 
> That is half of it; the other half is how are they used concretely in
> specifying function parameters?  That is the most interesting bits.
> Please don't be afraid to be concrete, otherwise I fear we would not
> communicate effectively: the issue at hand is too concrete.
> 
> | Such an abstraction would require each implementor to document the
> | calling convention actually used so that interfacing with other
> | languages was possible, but implementations already have to document
> | all kinds of calling convention properties of which parameter
> | passing is only one. 
> 
> How is IntervalArg<T> is different from IntervalArg<T>?  What do they
> contain? 

OK, I'll bite.  For this discussion assume Interval<T> is the same as the existing proposal.  If Interval<T> were not a template, say intervalf, interval, and intervalld, and intervalq in C99-style naming,  then we would use intervalf_arg_t, interval_arg_t, intervalld_arg_t, and intervalq_arg_t as corresponding argument types.  They would be implementation defined.  Everywhere that one wanted to pass in interval argument one would use the corresponding *arg_t to maintain platform optimization agility.

But Interval is going to be a template.  It is tempting to want to derive the argument type, hre named IntervalArg from the value type Interval.  But templates ahve weaknesses, one of which inhibits that derivation.

So I'm suggesting an independent template.  In crudest terms it would be something like this :
    
namespace pbr {

    template< typename T >
    struct IntervalArg { typedef T const & _t; };

    struct IntervalArg<float>
    { typedef Interval<float> const & _t; };

    struct IntervalArg<double>
    { typedef Interval<double> const & _t; };

    ... ditto for other fp types

} // pbr

namespace pbv {

    template< typename T >
    struct IntervalArg { typedef T const & _t; };

    struct IntervalArg<float>
    { typedef Interval<float> _t; };

    struct IntervalArg<double>
    { typedef Interval<double> _t; };

    ... ditto for other fp types

} // pbv

In use it would be a bit ugly:

    using namespace pbv; // or pbr
    template< typename T >
    Interval<T> agile_func( IntervalArg<T>::_t arg1 ) { ... }

A subtlety that may not be immediately apparent is that the purpose of the unspecialized template is to address contexts in which a template parameter T represents an interval type, whose base type is not specific.  Thus:

    template< typename T /* in truth Interval<U> */ >
    struct userdefined {
        ...
        T interval_func( IntervalArg<T>::_t arg );
        ...
    }; // userdefined

A more complex implementation would eliminate the unsightly ::_t along the lines of a proxy type.  It would rely upon the compiler to optimize away all of the bookkeepping:

namespace pbr {

    template < typename T >
    struct IntervalArg {  // for discussion purposes only
        IntervalArg( Interval<T> arg )
        : ref_( val )
        {}
        operator Interval<T> () const
        { return ref_; }
    private:
        Interval<T> const & ref_;
    };

} // pbr

namespace pbv { // all of this optimizes away

    template < typename T >
    struct IntervalArg {  // for discussion purposes only
        IntervalArg( Interval<T> arg )
        : val_( arg )
        {}
        operator Interval<T> () const
        { return val_; }
    private:
        Interval<T> val_;
    };

} // pbv

Usage is then straightforward:

    using namespace pbv; // or pbr
    template< typename T >
    Interval<T> agile_func( IntervalArg<T> arg1 ) { ... }

Lest any reader misunferstand, I am _not_ proposing that both pbr and pbv be available.  I only used the namespaces to separate the alternative implementations for the purposes of clarity within this discussion.

> 
> | Does the interval standard need to be specific about who cleans
> | arguments off of the stack?
> 
> Once we know what IntervalArg<T> and Interval<T> contain and do, we
> can get to that question.

I was being facetious.  I suppose that's an error in judgement when one is indulging in language laywering.  ;-)

Stack cleaning conventions don't belong in the standard IMHO.

> 
> [...]
> 
> | > [ As I mentioned earlier, I'm not sure template aliases help in this
> | > case. ]
> | 
> | I don't understand the term template alias.  Coud you describe one?
> 
> A "template alias" is an alias for a family of types
> 
>    http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2003/n1489.pdf

Nope.  I'm not going there!  Not now, and probably not ever.

Thanks for the info.

-- Lee Winter
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first.i.last@comcast.net writes:

[...]

| > | > The proposal would need to be precise about whether internal<T> is a
| > | > POD or not; that is unavoidable.
| > | 
| > | Why?
| > 
| > because if the proposal is accepted, it is going to be part of a much
| > larger context.  They are some operations on can do on types depending
| > on whether they are PODs or not, like offsetof, initializations and
| > other fine details.  The standard needs to say whether such operations
| > are permitted or not.
| 
| OK, I did not ask a sufficiently precise question.  Why is
| "implementation defined" unacceptable?  I.e., why does PODness have
| to be a constant for all implementations? 

Because whether the operations in question are permitted or not would
depend on the compiler; I don't see any compelling reason for that
sort of non-portability.

| I hope offsetof() is not going to be used much on intervals. 

It is a reasonable hope; others have other reasonable expectations
too.  The question is not whether it would be used "too much", but
whether it should be permitted at all.  I can see arguments both
ways; but none that convinces me of the non-portability you suggest.

| There
| would be little point in scrounging around inside an interval unless
| you are trying to cause (yourself) some trouble. 

That is your expectation; others expect to "serialize" things, using
offsetof among other things -- and we do have an open issue with
std::complex for example, from various point of view.

| Initialization of an interval is almost certainly going to require a
| ctor due to the problem of compiler mangling of literal constants,

I'm sorry; I don't see the connection.  Could you elaborate?

| so for purposes of initialization intervals aren't going to behave
| like PODs even if they are PODs. 

I don't see why.

| Can you think of any other fine details (other than things like
| binary IO) that might influence the preference for PODs over "real"
| objects? 

It all depends on the degree of non-PODness; there are ABIs out there
on popular platforms that make optimization decisions based on degree
of PODness.

[...]

| > | > | > The issue was the mechanism for passing the representation, not the
| > | > | > logical opacity of the type.
| > | > | 
| > | > | The issue is the atomicity of the type.  Atomicity often implies effective 
| > | > | opacity.  Opacity always implies atomicity.
| > | > 
| > | > Yet, at the end of the day the proposal needs to spell out the
| > | > mechanism for passing the representation.  At the moment, I don't see
| > | > how the committee would buy a proposal that is very vague about such
| > | > issue.  Past experience with vagueness in that area has been a fertile
| > | > source of programmer confusion, and defect reports (that the committee
| > | > had to deal with).
| > | 
| > | Is an abstract type for parameters vague?
| > 
| > In C++, there is the notion of "abstract class" but I doubt that is
| > what you were refering to.  One has to be more specific than general
| > terms; this is not a language independent specification.
| 
| Abstractions hide implementation details.  The previous suggestion
| (yours?) of interval::param_type

(no, it was not mine)

| would hide either "interval const
| &" or "interval" type definitions.  That would certainly be usefu,
| but  dependent types are problematic.  The only variation I'm
| suggesting is to make that parameter type independent of the
| interval template type. 

and that begs the question of to what degree the problem worths that
level of complexity.  

[...]

| > | ----- interval.h -----
| > |     template< T > struct Interval    { ... };
| > |     template< T > struct IntervalArg { ... };
| > 
| > That is half of it; the other half is how are they used concretely in
| > specifying function parameters?  That is the most interesting bits.
| > Please don't be afraid to be concrete, otherwise I fear we would not
| > communicate effectively: the issue at hand is too concrete.
| > 
| > | Such an abstraction would require each implementor to document the
| > | calling convention actually used so that interfacing with other
| > | languages was possible, but implementations already have to document
| > | all kinds of calling convention properties of which parameter
| > | passing is only one. 
| > 
| > How is IntervalArg<T> is different from IntervalArg<T>?  What do they
| > contain? 
| 
| OK, I'll bite.  For this discussion assume Interval<T> is the same
| as the existing proposal.  If Interval<T> were not a template, say
| intervalf, interval, and intervalld, and intervalq in C99-style
| naming,  then we would use intervalf_arg_t, interval_arg_t,
| intervalld_arg_t, and intervalq_arg_t as corresponding argument
| types.  They would be implementation defined.  Everywhere that one
| wanted to pass in interval argument one would use the corresponding
| *arg_t to maintain platform optimization agility. 
| 
| But Interval is going to be a template.  It is tempting to want to
| derive the argument type, hre named IntervalArg from the value type
| Interval.  But templates ahve weaknesses, one of which inhibits that
| derivation. 
| 
| So I'm suggesting an independent template.  In crudest terms it
| would be something like this : 
|     
| namespace pbr {
| 
|     template< typename T >
|     struct IntervalArg { typedef T const & _t; };
| 
|     struct IntervalArg<float>
|     { typedef Interval<float> const & _t; };
| 
|     struct IntervalArg<double>
|     { typedef Interval<double> const & _t; };
| 
|     ... ditto for other fp types
| 
| } // pbr
| 
| namespace pbv {
| 
|     template< typename T >
|     struct IntervalArg { typedef T const & _t; };
| 
|     struct IntervalArg<float>
|     { typedef Interval<float> _t; };
| 
|     struct IntervalArg<double>
|     { typedef Interval<double> _t; };
| 
|     ... ditto for other fp types
| 
| } // pbv
| 
| In use it would be a bit ugly:
| 
|     using namespace pbv; // or pbr
|     template< typename T >
|     Interval<T> agile_func( IntervalArg<T>::_t arg1 ) { ... }

Now, I can't call agile_func() using the "natural" syntax; I have to
explicitly specify the argument type.  It is a clutter and a level
of complexity that I'm having trouble finding convincing justification
for. 

| A subtlety that may not be immediately apparent is that the purpose
| of the unspecialized template is to address contexts in which a
| template parameter T represents an interval type, whose base type is
| not specific.  Thus: 
| 
|     template< typename T /* in truth Interval<U> */ >
|     struct userdefined {
|         ...
|         T interval_func( IntervalArg<T>::_t arg );
|         ...
|     }; // userdefined
| 
| A more complex implementation would eliminate the unsightly ::_t
| along the lines of a proxy type.  It would rely upon the compiler to
| optimize away all of the bookkeepping: 

So now, we have to add increasing levels of complexity to "solve"
something I'm not sure is a problem.  Simple things should be simple.

| namespace pbr {
| 
|     template < typename T >
|     struct IntervalArg {  // for discussion purposes only
|         IntervalArg( Interval<T> arg )
|         : ref_( val )
|         {}
|         operator Interval<T> () const
|         { return ref_; }
|     private:
|         Interval<T> const & ref_;
|     };
| 
| } // pbr

ABIs that unconditionally pass structs by "invisible" references would
now go through two indirections to access the data passed to the
function.  What really is the problem this is supposed to solve?

| namespace pbv { // all of this optimizes away
| 
|     template < typename T >
|     struct IntervalArg {  // for discussion purposes only
|         IntervalArg( Interval<T> arg )
|         : val_( arg )
|         {}
|         operator Interval<T> () const
|         { return val_; }
|     private:
|         Interval<T> val_;
|     };
| 
| } // pbv
| 
| Usage is then straightforward:
| 
|     using namespace pbv; // or pbr
|     template< typename T >
|     Interval<T> agile_func( IntervalArg<T> arg1 ) { ... }
| 
| Lest any reader misunferstand, I am _not_ proposing that both pbr
| and pbv be available.  I only used the namespaces to separate the
| alternative implementations for the purposes of clarity within this
| discussion. 

I understand that.  However, from my perspective -- because C++ has
template, argument deduction, overloading -- it really is
essential that non-portability be minimized when they can't be
avoided.  I'm not sure it cannot be avoided here.  Yes, we have
instances of such non-portability in the current standard; but past
lessons suggest that we don't multiply the existing troubles.

| > | Does the interval standard need to be specific about who cleans
| > | arguments off of the stack?
| > 
| > Once we know what IntervalArg<T> and Interval<T> contain and do, we
| > can get to that question.
| 
| I was being facetious.  I suppose that's an error in judgement when
| one is indulging in language laywering.  ;-) 

For the interest of the discussion, we should refrain from suggesting
people are "language lawyer" just because they don't agree with us.

| Stack cleaning conventions don't belong in the standard IMHO.
| 
| > 
| > [...]
| > 
| > | > [ As I mentioned earlier, I'm not sure template aliases help in this
| > | > case. ]
| > | 
| > | I don't understand the term template alias.  Coud you describe one?
| > 
| > A "template alias" is an alias for a family of types
| > 
| >    http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2003/n1489.pdf
| 
| Nope.  I'm not going there!  Not now, and probably not ever.

Good.  For the interest of the discussion, writing

    template<typename T>
      using IntervalArg = const Interval<T>&;

would make the "T" in a deducible context; remove needs for proxies
and such.  

>From my perspective, It is still a level of complexity (like any other
alternative you've suggested) for which I have not seen real
justification for -- e.g. what problems it supposed to solve, why that
problem is important, why that is a better alternative.

-- Gaby
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 -------------- Original message ----------------------
From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> first.i.last@comcast.net writes:
> 
> [...]
> 
> | > | > The proposal would need to be precise about whether internal<T> is a
> | > | > POD or not; that is unavoidable.
> | > | 
> | > | Why?
> | > 
> | > because if the proposal is accepted, it is going to be part of a much
> | > larger context.  They are some operations on can do on types depending
> | > on whether they are PODs or not, like offsetof, initializations and
> | > other fine details.  The standard needs to say whether such operations
> | > are permitted or not.
> | 
> | OK, I did not ask a sufficiently precise question.  Why is
> | "implementation defined" unacceptable?  I.e., why does PODness have
> | to be a constant for all implementations? 
> 
> Because whether the operations in question are permitted or not would
> depend on the compiler; I don't see any compelling reason for that
> sort of non-portability.

It is only non-portable if it is not detectable at compile time.

> 
> | I hope offsetof() is not going to be used much on intervals. 
> 
> It is a reasonable hope; others have other reasonable expectations
> too.  The question is not whether it would be used "too much", but
> whether it should be permitted at all.  I can see arguments both
> ways; but none that convinces me of the non-portability you suggest.
> 
> | There
> | would be little point in scrounging around inside an interval unless
> | you are trying to cause (yourself) some trouble. 
> 
> That is your expectation; others expect to "serialize" things, using
> offsetof among other things -- and we do have an open issue with
> std::complex for example, from various point of view.

Serialization suggests interval::operator<<() and interval::operator>>() rather than offsetof(), but the (non-)existence of those methods is a hugely contentious issue.  In fact serialization of the mental model "double interval[2]' could be handled by a user with upper() and lower().  Deserialization is just use of an appropriate constructor.  I have very little sympathy for users who insist on below-API access to objects.

Does anyone reading this list believe that using offsetof() on intervals is a healthy practice?  If so, to what end?

> 
> | Initialization of an interval is almost certainly going to require a
> | ctor due to the problem of compiler mangling of literal constants,
> 
> I'm sorry; I don't see the connection.  Could you elaborate?
> 
> | so for purposes of initialization intervals aren't going to behave
> | like PODs even if they are PODs. 
> 
> I don't see why.

If we allow classic static init then the compiler will be translating the text of literal values into binary.  If that translation occurs without directed rounding it will produce degenerate intervals that astonish the user and are in reality containment failures.  Consider this:

    static interval const tenths[] = 
    { { 0.0, 0.0 }
    , { 0.1, 0.1 } // oops
    , { 0.2, 0.2 } // oops
    , { 0.3, 0.3 } // oops
    , { 0.4, 0.4 } // oops
    , { 0.5, 0.5 }
    , { 0.6, 0.6 } // oops
    , { 0.7, 0.7 } // oops
    , { 0.8, 0.8 } // oops
    , { 0.9, 0.9 } // oops
    };

The array will contain the correct values only if the translation of the two members of each element is done with opposing directed rounding of the individual results.  So we might be force to use only dynamic initialization such as:

    static interval const tenths[] = 
    { interval( "[0.0]" }  // only used for consistency of notation
    { interval( "[0.1]" }
    { interval( "[0.2]" }
    { interval( "[0.3]" }
    { interval( "[0.4]" }
    { interval( "[0.5]" }  // only used for consistency of notation
    { interval( "[0.6]" }
    { interval( "[0.7]" }
    { interval( "[0.8]" }
    { interval( "[0.9]" }
    };

The above produces two degenerate intervals and eight non-degenerate intervals, will not astonish the user, and has no containment failures (assuming interval::interval( char const * ) works properly).

Thus PODness is not everywhere advantageous.

Is the distinction clear from the above example?

> | Can you think of any other fine details (other than things like
> | binary IO) that might influence the preference for PODs over "real"
> | objects? 
> 
> It all depends on the degree of non-PODness; there are ABIs out there
> on popular platforms that make optimization decisions based on degree
> of PODness.

Let's see if we can mutate a classic into something useful:

    Intervals should be as POD as possible and no PODer.
          -- apologies to Albert?

-- Lee Winter
From Stephen.Clamage@Sun.COM Fri Apr  7 02:19:44 2006
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Subject: Re: [std-interval] PODs and parameter passing
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first.i.last@comcast.net wrote:
>  -------------- Original message ----------------------
> From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> 
>>first.i.last@comcast.net writes:
>>
>>[...]
>>| OK, I did not ask a sufficiently precise question.  Why is
>>| "implementation defined" unacceptable?  I.e., why does PODness have
>>| to be a constant for all implementations? 
>>
>>Because whether the operations in question are permitted or not would
>>depend on the compiler; I don't see any compelling reason for that
>>sort of non-portability.
> 
> It is only non-portable if it is not detectable at compile time.

Scenario: A programmer develops on one platform, unaware that the code depends 
on a feature that varies among implementations. A colleague tries the code on a 
different platform, and it doesn't compile. The code requires a significant 
re-write to accomodate the differences.

Don't you agree this is a portability issue?

I'm a compiler developer. I find that the majority of customer questions and 
complaints are of the form, "My code works with compiler X, why doesn't it work 
with your compiler?"  Often the answer is that the code is not portable, in the 
sense of the scenario above.

Every time the standard says "undefined", "unspecified", or "implementation 
defined", it opens the door to problems like these. We need a compelling reason 
to leave issues like POD-ness and function signatures up to individual 
implementations.

[...]
>>
>>It all depends on the degree of non-PODness; there are ABIs out there
>>on popular platforms that make optimization decisions based on degree
>>of PODness.

Gaby, PODness is binary. If a type does not satisfy all the requirements of a 
POD, it is not a POD.

 > Let's see if we can mutate a classic into something useful:
 >
 >     Intervals should be as POD as possible and no PODer.
 >           -- apologies to Albert?
 >
 > -- Lee Winter

Let's paraphrase Tolstoy's "Anna Karenina" instead:
    All PODs are alike. Every non-POD is non-POD in its own way.

In particular, a POD does not have a user-defined constructor. If the only 
departure from PODness is the presence of user-defined initialization or 
converting constructors (but still no copy constructor), a compiler can generate 
efficient code for copying and passing values in and out of functions. (I think 
we could also allow private or protected members.)

---
Steve Clamage, stephen.clamage@sun.com

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From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
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Subject: Re: [std-interval] PODs and parameter passing
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I have the impression that the discussion is drifting a lot on details
which are really really minor.  I think that the issue of parameter
passing can be decided by the C++ committee, as it does not require
any expertise on intervals.

Therefore I propose to STOP the discussion on this issue now.

Lee, please try to refrain from monopolizing the mailing-list.
When you have points to make, please provide *concrete arguments*,
otherwise there is no need to give an opinion, and try to think
about the importance of all of them with respect to the goal of
this project.

We have a lot of more important issues that need attention so that
we converge to a consensus for them, and we don't have time to loose.

-- 
Sylvain
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Steve Clamage <Stephen.Clamage@Sun.COM> writes:

[...]

| >>It all depends on the degree of non-PODness; there are ABIs out there
| >>on popular platforms that make optimization decisions based on degree
| >>of PODness.
| 
| Gaby, PODness is binary. If a type does not satisfy all the
| requirements of a POD, it is not a POD.

you are exactly right.  

What I thinking of when I wrote that was scenario when the standard
says a class is a non-POD, but but the ABI treats it -- for calling
convention purpose -- as a POD because its copy-constructor is trivial
and it is sufficiently simple (e.g. does not have virtual functions,
not virtual base class etc.).  But, since we were discussing standard
matters, I should have been more specific.

-- Gaby
From first.i.last@comcast.net Fri Apr  7 03:14:22 2006
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Subject: Re: [std-interval] PODs and parameter passing
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 -------------- Original message ----------------------
From: Steve Clamage <Stephen.Clamage@Sun.COM>
> first.i.last@comcast.net wrote:
> >  -------------- Original message ----------------------
> > From: Gabriel Dos Reis <gdr@integrable-solutions.net>
> > 
> >>first.i.last@comcast.net writes:
> >>
> >>[...]
> >>| OK, I did not ask a sufficiently precise question.  Why is
> >>| "implementation defined" unacceptable?  I.e., why does PODness have
> >>| to be a constant for all implementations? 
> >>
> >>Because whether the operations in question are permitted or not would
> >>depend on the compiler; I don't see any compelling reason for that
> >>sort of non-portability.
> > 
> > It is only non-portable if it is not detectable at compile time.
> 
> Scenario: A programmer develops on one platform, unaware that the code depends 
> on a feature that varies among implementations. A colleague tries the code on a 
> different platform, and it doesn't compile. The code requires a significant 
> re-write to accomodate the differences.
> 
> Don't you agree this is a portability issue?
> 
> I'm a compiler developer. I find that the majority of customer questions and 
> complaints are of the form, "My code works with compiler X, why doesn't it work 
> with your compiler?"  Often the answer is that the code is not portable, in the 
> sense of the scenario above.
> 
> Every time the standard says "undefined", "unspecified", or "implementation 
> defined", it opens the door to problems like these. We need a compelling reason 
> to leave issues like POD-ness and function signatures up to individual 
> implementations.

I understand and agree with everything you wrote.  But you ignored the point I made, which is that "implementation defined and not detectable" is quite distinct from "implementation defined and detectable".  The former is a problem and typically involves user-supplied configuation variables/scripts/macros -- quite a hassle.  The latter is portable.  It takes a modicum of effort, but it is portable.

The whole point of things like std::numeric_limits<> is that machines differ.  Those differences matter.  Some of those differences matter a lot.  Thus for portable _performance_ rather than portable _compilation_, it is worth the investment of time to handle potential performace issues rather than glossing them over.

Now std::interval is not going to save the world WRT portable numeric software.  But if there ever was or will ever be time to address platform variations _with_which_users_must_contend_ then that time is prior to the adoption of the standard.  If the issues can be delegated to the implementors, leaving the users safely isolated, then there is no need for the standard to address them and we should not spend a lot of time on them.

Given the discussions over the impact of calling conventions it appears that many writers to this list belive calling conventions are important user-visible aspects performance.

> 
> [...]
> >>
> >>It all depends on the degree of non-PODness; there are ABIs out there
> >>on popular platforms that make optimization decisions based on degree
> >>of PODness.
> 
> Gaby, PODness is binary. If a type does not satisfy all the requirements of a 
> POD, it is not a POD.
> 
>  > Let's see if we can mutate a classic into something useful:
>  >
>  >     Intervals should be as POD as possible and no PODer.
>  >           -- apologies to Albert?
>  >
>  > -- Lee Winter
> 
> Let's paraphrase Tolstoy's "Anna Karenina" instead:
>     All PODs are alike. Every non-POD is non-POD in its own way.
> 
> In particular, a POD does not have a user-defined constructor. If the only 
> departure from PODness is the presence of user-defined initialization or 
> converting constructors (but still no copy constructor), a compiler can generate 
> efficient code for copying and passing values in and out of functions. (I think 
> we could also allow private or protected members.)

Are you implying that the existence or non-existence of copy ctors is a key determinant in efficiency?  If so, what portability would be lost if the standard stated that intervals are non-PODs and implementations varied in their support for copy ctors?

You didn't mention destructors, I assume because they has less impact on the callinc convention topic.  How much efficiency is lost due to the simpl presence of a desctructor?  I'm particularly concerned with temporaries generated during expression evaluation rather than copies generated during parameter passing.

Classic implementations of C's math.h always had to wrestle with speed versus correctness.  Some vendors appeased their customers by delegating the decision to them -- they provided a fast RTL and a good RTL that could be selected at link time.  As intervals become pervasive we should expect the kind of adaptive radiation that would drive vedors to offer alternative implementations.  The standard should not forbid that tradeoff without some compelling jusitification.

It is my expectation that some implementations might have variants of both forms.  For example, a blunt variant might be useful where fat intervals were rare and the extra overhead in time and space for dependency detection and correction was not desired.  A sharp variant would be useful where fat intervals are common and the extra overhead in time and space were worth it in order to obtain narrow results.

AFAIK dependency detection and correction are the only features that would require elaborate construction and destruction of interval objects.  All of the other features of which I have ever heard are simple state variables.  Does anyone have a contrary example?

-- Lee Winter
From Sylvain.Pion@sophia.inria.fr Fri Apr  7 04:00:42 2006
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Dear all,

I just raised the issue in front of the Library Working Group
of the ISO C++ committee, with the help of Steve.

The feedback is positive and encouraging.  A straw poll has been
taken, on whether we should continue the effort :
Strongly in favor = 4
Weakly   in favor = 5
Weakly   against  = 0
Strongly against  = 0

The question was also raised whether we should target C++0x or TR2,
the preference is for TR2 (10 votes against 1).

[
   TR2 is a non-normative document which serves as explicit exposure of
   the intent of the committee for the next standard.
   TRs are usually also implemented by compiler vendors and serve to make
   sure users are really happy with the specification before the final
   blessing.
   C++0x is the code-name for the next standard.
]


The goal is now to reach a consensus here and have a revision of the
proposal for the next meeting, beginning of october 2006.


We also discussed 2 issues briefly:
- pass-by-value versus pass-by-ref has already been debated by the
   committee for std::complex.  Seems like the debate was as hot as
   it is for intervals.  That's an issue for the committee.
- there are still concerns on the exact list of functions that we
   will propose, we need to make sure we have the good set (sufficiently
   useful, specified with enough details such as the width of intervals,
   and taking into account the difficulty of implementation).


Steve, please correct me if I did not get something correctly or if you
want to add something.

-- 
Sylvain
From Stephen.Clamage@Sun.COM Fri Apr  7 04:43:01 2006
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From: Steve Clamage <Stephen.Clamage@Sun.COM>
Subject: Re: [std-interval] PODs and parameter passing
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first.i.last@comcast.net wrote:

>  -------------- Original message ----------------------
> From: Steve Clamage <Stephen.Clamage@Sun.COM>
> 
...
>>In particular, a POD does not have a user-defined constructor. If the only 
>>departure from PODness is the presence of user-defined initialization or 
>>converting constructors (but still no copy constructor), a compiler can generate 
>>efficient code for copying and passing values in and out of functions. (I think 
>>we could also allow private or protected members.)
> 
> 
> Are you implying that the existence or non-existence of copy ctors is a key determinant in efficiency?  If so, what portability would be lost if the standard stated that intervals are non-PODs and implementations varied in their support for copy ctors?
> 
> You didn't mention destructors, I assume because they has less impact on the callinc convention topic.  How much efficiency is lost due to the simpl presence of a desctructor?  I'm particularly concerned with temporaries generated during expression evaluation rather than copies generated during parameter passing.

A POD has no user-defined constructors or destructor. If an object has a 
user-defined copy constructor or destructor, it affects what the compiler must 
do when passing and returning values. It's so much a question of how smart the 
compiler is, but what the language definition requires.

My point was that we can add an initialization constructor (but not a copy 
constructor) to what is otherwise a POD without affecting the efficiency of 
passing around values.

I expect an Interval type to be composed only of simple types (floating-point, 
pointer, enum, integer), and thus not need a user-defined copy constructor or 
destructor.

> Classic implementations of C's math.h always had to wrestle with speed versus correctness.  Some vendors appeased their customers by delegating the decision to them -- they provided a fast RTL and a good RTL that could be selected at link time.  As intervals become pervasive we should expect the kind of adaptive radiation that would drive vedors to offer alternative implementations.  The standard should not forbid that tradeoff without some compelling jusitification.

There is no problem with multiple library implementations co-existing and 
selectable at compile time or link time. For them to be most useful, the 
interfaces should be the same. The language standard would define only the 
interfaces, not the internals.

Example 1: Sun provides multiple versions of the basic C allocators 
malloc/calloc/realloc/free, each with different performance characteristics. 
Each of them conforms to the C (and C++) standards in that function signatures 
are identical in all versions. A programmer can select any one of the versions 
at link time, no source file editing or recompilation needed. If a programmer 
uses an extended interface offered by an allocator library, the code would not 
work with other libraries. The Standard allows extended interfaces, as long as a 
program using only the standard intefaces works correctly.  (The "as-if" rule 
again.)

Example 2:  Sun C++ comes with two different implementations of the C++ Standard 
Library: the default libCstd and the optional libstlport. The various Standard 
Library components are implemented very differently in the two libraries. Yet 
the public interfaces are identical, conforming to the C++ standard (except for 
some deficiencies in libCstd). To switch between libraries, one must recompile 
and re-link, but no source code editing is needed.

Getting back to Intervals, we should decide whether the Interval type supports a 
way (like a tag) to provide more information than just two floating-point 
values. I don't envision support for two kinds of Intervals, one with a 
tag-equivalent and one without.

As a quality of implementation (QOI) issue, the standard could allow the inquiry 
functions to return constant values, with no need to store and update the tag 
information. Different implementions with identical interfaces could offer 
tradeoffs among speed, accuracy, precision, and sharpness.

Example: The Standard requires types float, double, and long double, but says 
nothing about their representation or accuracy of computation. The only 
requirements are that arithmetic operations and sets of math functions be 
provided, and that minimum ranges are supported. All else is QOI. (Let the 
marketplace discard silly implementations instead of us trying to legislate 
against them.)

---
Steve Clamage, stephen.clamage@sun.com

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From: Steve Clamage <Stephen.Clamage@Sun.COM>
Subject: Re: [std-interval] C++ committee feedback
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Your summary looks right to me. The some points that helped persuade the group 
to move forward with intervals were these:

1. The domain experts (you guys) will reach consensus on what the library should 
look like by October. Except for Sylvain, nobody on the committe has the 
expertise to design the library or evaluate competing proposals. Without 
consensus, the project is doomed. So let's not get caught up in too much trivia. 
The goal should be a library interface that you all can live with.

2. Intervals are not just an academic exercise. Intervals are used widely in 
important industries to aid in critical designs.

3. Interval implementations exist and get a lot of use. The proposed library 
will be based on experience.

4. Although implementation is difficult, a reference implementation of the basic 
functions (arithmetic and transcendental functions) is freely available as Open 
Source from Sun.

---
Steve Clamage, stephen.clamage@sun.com

Sylvain Pion wrote:

> Dear all,
> 
> I just raised the issue in front of the Library Working Group
> of the ISO C++ committee, with the help of Steve.
> 
> The feedback is positive and encouraging.  A straw poll has been
> taken, on whether we should continue the effort :
> Strongly in favor = 4
> Weakly   in favor = 5
> Weakly   against  = 0
> Strongly against  = 0
> 
> The question was also raised whether we should target C++0x or TR2,
> the preference is for TR2 (10 votes against 1).
> 
> [
>   TR2 is a non-normative document which serves as explicit exposure of
>   the intent of the committee for the next standard.
>   TRs are usually also implemented by compiler vendors and serve to make
>   sure users are really happy with the specification before the final
>   blessing.
>   C++0x is the code-name for the next standard.
> ]
> 
> 
> The goal is now to reach a consensus here and have a revision of the
> proposal for the next meeting, beginning of october 2006.
> 
> 
> We also discussed 2 issues briefly:
> - pass-by-value versus pass-by-ref has already been debated by the
>   committee for std::complex.  Seems like the debate was as hot as
>   it is for intervals.  That's an issue for the committee.
> - there are still concerns on the exact list of functions that we
>   will propose, we need to make sure we have the good set (sufficiently
>   useful, specified with enough details such as the width of intervals,
>   and taking into account the difficulty of implementation).
> 
> 
> Steve, please correct me if I did not get something correctly or if you
> want to add something.
> 


From Mark.Woodyard@Sun.COM Fri Apr  7 09:31:56 2006
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Steve,

Steve Clamage wrote:

>
>
> 4. Although implementation is difficult, a reference implementation of 
> the basic functions (arithmetic and transcendental functions) is 
> freely available as Open Source from Sun.
>

I know that Sun has provided open source for FP transcendental 
functions; but for intervals?  If this is the case, can you give me a 
pointer to it?

Thanks,

Mark

-- 
<http://www.sun.com> 	* Mark Woodyard *
*Sun Microsystems, Inc.*
ubrm05-420, 500 Eldorado Blvd., Bldg 5
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From eliasen@mindspring.com Fri Apr  7 12:52:13 2006
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Guillaume Melquiond wrote:
> I know for example that GCC is really bad at handling and optimizing
> pass-by-value arguments, and I have already submitted a few bug-reports
> on this topic.

   Can you provide the bug report IDs so that we can see if these have
been fixed in subsequent releases, or verify their status?  Thanks!

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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Steve Clamage wrote:
> I compiled and ran on 64-bit sparc (US II) and 64-bit amd64 (Opteron).
> According to my earlier claims, pass-by-value should have been faster.
> 
> 64-bit sparc:
> addByValue:     690000 ticks 4.1e+08
> addByRef:       680000 ticks 4.1e+08
> addByConstRef:  450000 ticks 4.1e+08
> 
> 64-bit amd64:
> addByValue:     1280000 ticks 4.1e+08
> addByRef:        670000 ticks 4.1e+08
> addByConstRef:   670000 ticks 4.1e+08
> 
> Color my face red. :-)
> 
> This result is quite different from other experiments with small structs
> that showed pass-by-value performing better. One possibility is that the
> compiler is missing some optimization opportunities. Another is that
> this example is not representative.

   Well, it looks like in GCC that it's quite dependent on optimization
levels and inlining.  I rewrote my samples to include both inlined and
ordinary functions, and made some changes that apparently prevented the
compiler from optimizing out loops.  I should adopt your sample for the
inner loop, but here are my numbers:

x86_64, gcc 3.4.4, Linux:
-O0:
addByValue:             20020000 ticks  Sum: [1.7, 4.1]
addByRef:               19590000 ticks  Sum: [1.7, 4.1]
addByConstRef:          19590000 ticks  Sum: [1.7, 4.1]
addByValueInline:       22550000 ticks  Sum: [1.7, 4.1]
addByRefInline:         19460000 ticks  Sum: [1.7, 4.1]
addByConstRefInline:    19610000 ticks  Sum: [1.7, 4.1]

-O1:
addByValue:             12570000 ticks  Sum: [1.7, 4.1]
addByRef:               8350000 ticks   Sum: [1.7, 4.1]
addByConstRef:          8620000 ticks   Sum: [1.7, 4.1]
addByValueInline:       9980000 ticks   Sum: [1.7, 4.1]
addByRefInline:         5600000 ticks   Sum: [1.7, 4.1]
addByConstRefInline:    5600000 ticks   Sum: [1.7, 4.1]

-O2:
addByValue:             11490000 ticks  Sum: [1.7, 4.1]
addByRef:               7370000 ticks   Sum: [1.7, 4.1]
addByConstRef:          7960000 ticks   Sum: [1.7, 4.1]
addByValueInline:       2140000 ticks   Sum: [1.7, 4.1]
addByRefInline:         5590000 ticks   Sum: [1.7, 4.1]
addByConstRefInline:    5600000 ticks   Sum: [1.7, 4.1]

-O3:
addByValue:             2140000 ticks   Sum: [1.7, 4.1]
addByRef:               5590000 ticks   Sum: [1.7, 4.1]
addByConstRef:          5580000 ticks   Sum: [1.7, 4.1]
addByValueInline:       2000000 ticks   Sum: [1.7, 4.1]
addByRefInline:         5600000 ticks   Sum: [1.7, 4.1]
addByConstRefInline:    5590000 ticks   Sum: [1.7, 4.1]



and x86 Windows (mingw):

-O0:
addByValue:             115077 ticks    Sum: [1.7, 4.1]
addByRef:               85886 ticks     Sum: [1.7, 4.1]
addByConstRef:          85675 ticks     Sum: [1.7, 4.1]
addByValueInline:       128447 ticks    Sum: [1.7, 4.1]
addByRefInline:         90221 ticks     Sum: [1.7, 4.1]
addByConstRefInline:    90612 ticks     Sum: [1.7, 4.1]

-O1:
addByValue:             100967 ticks    Sum: [1.7, 4.1]
addByRef:               37254 ticks     Sum: [1.7, 4.1]
addByConstRef:          35842 ticks     Sum: [1.7, 4.1]
addByValueInline:       54780 ticks     Sum: [1.7, 4.1]
addByRefInline:         23334 ticks     Sum: [1.7, 4.1]
addByConstRefInline:    23495 ticks     Sum: [1.7, 4.1]

-O2:
addByValue:             63462 ticks     Sum: [1.7, 4.1]
addByRef:               38547 ticks     Sum: [1.7, 4.1]
addByConstRef:          38886 ticks     Sum: [1.7, 4.1]
addByValueInline:       82340 ticks     Sum: [1.7, 4.1]
addByRefInline:         26108 ticks     Sum: [1.7, 4.1]
addByConstRefInline:    21181 ticks     Sum: [1.7, 4.1]

-O3:
addByValue:             71995 ticks     Sum: [1.7, 4.1]
addByRef:               23043 ticks     Sum: [1.7, 4.1]
addByConstRef:          22283 ticks     Sum: [1.7, 4.1]
addByValueInline:       66817 ticks     Sum: [1.7, 4.1]
addByRefInline:         22082 ticks     Sum: [1.7, 4.1]
addByConstRefInline:    22653 ticks     Sum: [1.7, 4.1]

   Source for tests:

http://futureboy.us/temp/Interval.h
http://futureboy.us/temp/Interval.cc

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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>a POD type has a copy constructor and a destructor for the sake of
>language uniformity, but a compiler should _never_ call them. As a
>matter of fact, it should not even generate them. And this is not a
>matter of optimizing or not: this is explicitly the point of a POD type.

I ran into a problem using CodeWarrior to compile for both PPC and x86 where

  Interval stack[kStackSize];

created a huge performance penalty due to the compiler generating an 
empty default constructor and passing a pointer to it to 
__construct_array which called it repeatedly, even at the highest 
optimization levels. (Interval is a POD-type in my implementation.) 
The run-time penalty this imposed did not show up on profiles, being 
absorbed by the function containing the local variable which I 
expected to be expensive, so it took a while to discover the problem.

While this case is just a compiler bug, it illustrates an issue for the API.

Having the interval default constructor initialize to some reasonable 
value can protect against one class of typical program error, but may 
introduce other problems. Programmers reasonably expect declaring a 
stack array of doubles to have no run-time cost. Any non-empty 
default initialization changes a declaration which may be expected to 
be free or constant-time as in the case of an array of doubles, into 
an operation which depends on the array size.

Ron Avitzur
From Stephen.Clamage@Sun.COM Sun Apr  9 09:23:17 2006
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From: Steve Clamage <Stephen.Clamage@Sun.COM>
Subject: Re: [std-interval] C++ committee feedback
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Our C++ interface to the interval library is not open source. The headers come 
with the compiler, but a C++ runtime library is also needed.

Using Sun C++, you get access to the C++ interval library by including 
<suninterval.h> and adding -xia to all CC command lines.

There is nothing special about the C++ library. It is a thin layer of inline 
class functions to the underlying interval library that is open source, plus I/O 
functions in the runtime library. I don't have access to any computers inside 
Sun until Wednesday, so I can't be more specific than that.

---
Steve Clamage, stephen.clamage@sun.com

Mark Woodyard wrote:

> Steve,
> 
> Steve Clamage wrote:
> 
>>
>>
>> 4. Although implementation is difficult, a reference implementation of 
>> the basic functions (arithmetic and transcendental functions) is 
>> freely available as Open Source from Sun.
>>
> 
> I know that Sun has provided open source for FP transcendental 
> functions; but for intervals?  If this is the case, can you give me a 
> pointer to it?
> 
> Thanks,
> 
> Mark
> 



From george.corliss@marquette.edu Sun Apr  9 15:22:03 2006
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Subject: Re: [std-interval] C++ committee feedback
From: George Corliss <George.Corliss@marquette.edu>
To: For discussions concerning the C++ standardization of intervals
 <std-interval@compgeom.poly.edu>
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Sylvain,

Congratulations, and thanks to you and the rest of your team.

Can you point us to the most recent version of the proposal?

I would encourage you to send this report also to the reliable_computing
alias with a renewed invitation to subscribe here.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


> 
> I just raised the issue in front of the Library Working Group
> of the ISO C++ committee, with the help of Steve.
> 
> The feedback is positive and encouraging.  A straw poll has been
> taken, on whether we should continue the effort :
> Strongly in favor = 4
> Weakly   in favor = 5
> Weakly   against  = 0
> Strongly against  = 0
> 
> The question was also raised whether we should target C++0x or TR2,
> the preference is for TR2 (10 votes against 1).
> 
> [
>    TR2 is a non-normative document which serves as explicit exposure of
>    the intent of the committee for the next standard.
>    TRs are usually also implemented by compiler vendors and serve to make
>    sure users are really happy with the specification before the final
>    blessing.
>    C++0x is the code-name for the next standard.
> ]
> 
> 
> The goal is now to reach a consensus here and have a revision of the
> proposal for the next meeting, beginning of october 2006.
> 
> 
> We also discussed 2 issues briefly:
> - pass-by-value versus pass-by-ref has already been debated by the
>    committee for std::complex.  Seems like the debate was as hot as
>    it is for intervals.  That's an issue for the committee.
> - there are still concerns on the exact list of functions that we
>    will propose, we need to make sure we have the good set (sufficiently
>    useful, specified with enough details such as the width of intervals,
>    and taking into account the difficulty of implementation).
> 
> 
> Steve, please correct me if I did not get something correctly or if you
> want to add something.

From Sylvain.Pion@sophia.inria.fr Mon Apr 10 11:13:01 2006
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George,

George Corliss wrote:
> Sylvain,
> 
> Congratulations, and thanks to you and the rest of your team.

Thanks.

> Can you point us to the most recent version of the proposal?

So far this is still what Guillaume sent a few weeks ago.

> I would encourage you to send this report also to the reliable_computing
> alias with a renewed invitation to subscribe here.

Yes, but I would wait a bit more.  I think that there are still a
few big questions that need to be discussed here (and I would
appreciate if new people give a fresh look at a more polished
version of the proposal in some time):

1- the set of functions which we want to propose for standardization.
2- the required precision for these functions.
3- the mathematical semantic of intervals (cset versus other models...).
4- how to deal with comparisons of intervals.


I propose to begin by discussing the list of functions here.
The current proposal does not include cos/sin/exp/log for example,
which I think now is a mistake, but the question is to determine
what set we want exactly.
In a couple of days I expect to send a list of functions
(after having a look at the C89 and C99 standards "math.h"),
then proposing a list which matches the criteria of usefulness,
implementation difficulty, completeness, and existing implementations.
Does this sound OK ?


BTW, so far we have 51 subscribers here, and we got more than 40
answers to the questionnaire.

-- 
Sylvain
From george.corliss@marquette.edu Mon Apr 10 11:49:32 2006
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Date: Mon, 10 Apr 2006 11:59:07 -0500
Subject: Re: [std-interval] C++ committee feedback
From: George Corliss <George.Corliss@marquette.edu>
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Sylvain,

>> I would encourage you to send this report also to the reliable_computing
>> alias with a renewed invitation to subscribe here.
> 
> Yes, but I would wait a bit more.  I think that there are still a
> few big questions that need to be discussed here (and I would
> appreciate if new people give a fresh look at a more polished
> version of the proposal in some time):
> 
> 1- the set of functions which we want to propose for standardization.
> 2- the required precision for these functions.
> 3- the mathematical semantic of intervals (cset versus other models...).
> 4- how to deal with comparisons of intervals.
Good suggestion.  I think we benefit from as many participants in the
discussions as possible.  In particular, a friend notes that "the Germans"
have not been represented, although Juergen has.  I'd encourage sending the
meeting feedback and this agenda to reliable computing with a renewed
invitation.  You want discussion while the issues are debated, not after it
is too late.

Perhaps we should circulate the response John Pryce had sent you directly?
Many of his issues may be improved by further discussion, too.
> 
> I propose to begin by discussing the list of functions here.
> The current proposal does not include cos/sin/exp/log for example,
> which I think now is a mistake, but the question is to determine
> what set we want exactly.
> In a couple of days I expect to send a list of functions
> (after having a look at the C89 and C99 standards "math.h"),
> then proposing a list which matches the criteria of usefulness,
> implementation difficulty, completeness, and existing implementations.
> Does this sound OK ?
Yes.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


> 
> 
> BTW, so far we have 51 subscribers here, and we got more than 40
> answers to the questionnaire.

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Date: Tue, 11 Apr 2006 17:03:35 -0500
Subject: Re: [std-interval] response from ISL
From: George Corliss <George.Corliss@marquette.edu>
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 <std-interval@compgeom.poly.edu>
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> This message is in MIME format. Since your mail reader does not understand
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Sylvain,

In the interest of full and open discussion, I have attached copies of an
informal cover letter and a draft of a possible set of revisions to the
earlier standard proposal our 5SL team had forwarded to you a few weeks ago
so that everyone can read and comment on our comments.

Some of the issue have been extensively debated here in the mean time, but
others have not.  I am most interested in the question of whether the
standard should specify a mathematical model for intervals in the sense
discussed here, and if so, what that model should be.  The attached response
argues that there should be a mathematical model, but that it should be
implementation-defined, since there has not been a consensus.  One of the
threads over the past couple weeks seems to suggest that leaving such an
issue to be defined by the implementation guarantees lack of portability.

"ISL" (Interval Subroutine Library) is a beginning effort to draw together
much existing interval code into a comprehensive, quality library.  Our
current members are
  George F. Corliss  & Marquette University
  R. Baker Kearfott  & University of Louisiana at Lafayette
  Ned Nedialkov      & McMaster University and
                     & Lawrence Livermore National Laboratory
  John D. Pryce      & Cranfield University, RMCS Shrivenham
  Spencer Smith      & McMaster University

Clearly, if we are ever to have a portable interval library, it must depend
on a portable interval arithmetic, as this standardization process is
urging.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu



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--B_3227619819_5455820--

From first.i.last@comcast.net Tue Apr 11 23:17:51 2006
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	<std-interval@compgeom.poly.edu>
Subject: Re: [std-interval] response from ISL
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 -------------- Original message ----------------------
From: George Corliss <George.Corliss@marquette.edu>
> Sylvain,

[snip] 


> I am most interested in the question of whether the
> standard should specify a mathematical model for intervals in the sense
> discussed here, and if so, what that model should be.  The attached response
> argues that there should be a mathematical model, but that it should be
> implementation-defined, since there has not been a consensus.  One of the
> threads over the past couple weeks seems to suggest that leaving such an
> issue to be defined by the implementation guarantees lack of portability.

It may be worthwhile to place explicit limits on the future 
interpretation of the standard as far as restricting the models implementations may use.  For example, nothing in the standard should restrict an implementor from selecting a model wherein the elements contained in the set representing an interval can be from the union of all values representable on the underlying machine and all values representable in IEEE-754/854.  In addition to placing nothing in the standard indicating such a restriction, it may be useful to state that there is no such restriction.

-- Lee Winter
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	<std-interval@compgeom.poly.edu>
Subject: [std-interval] Parameter Passing Performance
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Steve Clamage wrote:
 >> I compiled and ran on 64-bit sparc (US II) and 64-bit amd64 (Opteron).
 >> According to my earlier claims, pass-by-value should have been faster.
 >> 
 >> 64-bit sparc:
 >> addByValue:     690000 ticks 4.1e+08
 >> addByRef:       680000 ticks 4.1e+08
 >> addByConstRef:  450000 ticks 4.1e+08
 >> 
 >> 64-bit amd64:
 >> addByValue:     1280000 ticks 4.1e+08
 >> addByRef:        670000 ticks 4.1e+08
 >> addByConstRef:   670000 ticks 4.1e+08
 >> 
 >> Color my face red. :-)
 >> 
 >> This result is quite different from other experiments with small structs
 >> that showed pass-by-value performing better. One possibility is that the
 >> compiler is missing some optimization opportunities. Another is that
 >> this example is not representative.

Sorry for the delay on responding, but I have been burdened with other
issues.  I decided to write my own benchmark that I found more
convincing in terms of likely use.  I chose to implement a simple
interval saxpy, but with the primitive operations out of line.  I will
not pretend this code is good interval arithmetic, but it should
provide a reasonable upper bound on the cost of parameters.  The source
is as follows.

% cat interval.h
#ifndef INTERVAL_H
#define INTERVAL_H

class interval;

#ifdef VALUE
typedef interval interval_in;
#else
typedef const interval & interval_in;
#endif

struct interval
{
        double lo, hi;
        interval() { }
        interval( double x, double y ) : lo( x ), hi( y ) { }
        interval & operator +=( interval_in x );
        friend interval operator +( interval_in x, interval_in y );
        friend interval operator *( interval_in x, interval_in y );
};

interval operator +( interval_in x, interval_in y );
interval operator *( interval_in x, interval_in y );

#endif

% cat interval.cc
#include "interval.h"

interval & interval::operator +=( interval_in x )
{
        lo += x.lo;
        hi += x.hi;
        return *this;
}

interval operator +( interval_in x, interval_in y )
{
        return interval( x.lo + y.lo, x.hi + y.hi );
}

interval operator *( interval_in x, interval_in y )
{
        double min = x.lo * y.lo;
        double max = min;
        double next = x.lo * y.hi;
        if ( next < min ) min = next;
        if ( next > max ) max = next;
        next = x.hi * y.lo;
        if ( next < min ) min = next;
        if ( next > max ) max = next;
        next = x.hi * y.hi;
        if ( next < min ) min = next;
        if ( next > max ) max = next;
        return interval( min, max );
}

% cat saxpy.h
#ifndef SAXPY_H
#define SAXPY_H

#include "interval.h"

interval saxpy( interval_in a, interval x[], interval y[], int n );

#endif

% cat saxpy.cc
#include "saxpy.h"

interval saxpy( interval_in a, interval x[], interval y[], int n )
{
        interval sum( 0.0, 0.0 );
        for ( int i = 0; i < n; ++i )
                sum += a * x[i] * y[i];
        return sum;
}

% cat benchmark.cc
#include <stdio.h>
#include "interval.h"
#include "saxpy.h"

const int size = 10000;

interval x[size];
interval y[size];
interval sum( 0.0, 0.0 );

int main()
{
        for ( int i = 0; i < size; ++i )
        {
                x[i].lo = 1.0 - i / (double)size;
                x[i].hi = 1.0 + i / (double)size;
                y[i].lo = -1.0 - i / (double)size;
                y[i].hi = -1.0 + i / (double)size;
        }
        for ( int i = 0; i < size; ++i )
        {
                sum += saxpy( x[i], x, y, size );
        }
        printf( "[%f;%f]\n", sum.lo, sum.hi );
        return 0;
}

I tested the result on four platforms and the two parameter
mechanisms.  The result is times in seconds.

    C++ param decl		refer	--------value-----------
    impl struct passing			pointer	stack	register

    SPARC v8 (32-bit)		6.3	11.3
    SPARC v9 (64-bit)		14.6			19.4
    IA32     (32-bit)		7.1		9.0
    AMD64    (64-bit)		2.8			4.3

In all cases, pass by const reference was faster.  I looked in detail
at the generated code and discovered that in all cases our compiler was
introducing an unnecessary copy for each value parameter.  It is a bug,
probably in the higher levels of the compiler.  Once one corrects for
the unnecessary copying, the value parameters are faster.

Note that performance is not the only criteria for choosing value
parameters.  The reduced aliasing means less exposure to program
errors.

  Lawrence Crowl             650-786-6146   Sun Microsystems, Inc.
                   Lawrence.Crowl@Sun.com   16 Network Circle, UMPK16-303
           http://www.Crowl.org/Lawrence/   Menlo Park, California, 94025
From guillaume.melquiond@ens-lyon.fr Wed Apr 26 10:51:52 2006
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From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
To: std-interval@compgeom.poly.edu
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Subject: [std-interval] Interval comparison operators
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Hi,

On the last draft of the proposal I posted, I had removed everything
related to interval comparisons because we felt this needed some more
work. Before tackling this issue, we would like to get your opinions on
the subject of comparing intervals.

For those who did not get to read our very first proposal, I will detail
what our approach was, so as to have a starting point for discussing.
The operators on intervals were directly derived from the order on real
numbers. Given two intervals X and Y, the result of (X < Y) was defined
as:
  - false if there are some values x in X and y in Y such that x >= y,
  - true if x < y for all the values x in X and y in Y,
  - a thrown exception if the intervals overlap or are empty.

As a first consequence, it reduces surprise for developers since a
property like (X < Y) == !(X >= Y) always holds true. But this is not
why we chose this definition in the first place. We wanted generic code
to be usable with intervals. Let's consider the following toy example:
computing accurately the sign of a 2x2 determinant. A generic C++
template implementation would look like:

        template< class T > sign_t det2(T a, T b, T c, T d) {
          T u = a * d, v = b * c;
          if (u < v) return negative;
          if (u > v) return positive;
          return zero;
        }

Now let's try to compute the sign of a floating-point determinant.
det2<double> is a fast but not reliable implementation. det2<exact>
(with "exact" being an exact arithmetic type) is reliable but slow. The
following implementation is generally fast and always reliable:

        sign_t good_det2(double a, double b, double c, double d) {
          try { return det2< interval<double> >(a, b, c, d); }
          catch(...) { return det2< exact >(a, b, c, d); }
        }

So first an interval evaluation is done, and if the result is not
guaranteed, an exception is thrown during the first comparison in the
generic code and the specific code falls back to the exact evaluation.
This example was inspired from the arithmetic filters of computational
geometry. Only generic code has to be written and it can then be used
with interval arithmetic to produce guaranteed results.

Now people may be reluctant to use exceptions (because of runtime cost,
code complexity, and so on) when specifically designing an interval
code. So, in our proposal, the comparison (X < Y) does not directly
throw; an exception is thrown only when the result of a comparison is
converted to a boolean value, for example in an "if" conditional
expression. This allows for other ways of comparing two intervals.

In particular, interval libraries usually provide explicit functions for
comparing intervals, something like "certainly less than" or "possibly
less than" functions that would always return a boolean value and never
throw. We believe C++ features should be used to provide a nicer syntax
though. Instead of cerlt(X,Y), a "certainly less than" comparison would
then be written as:

        if (certainly(X < Y)) ...

This should make a rather detailed overview of our opinion on comparison
operators for intervals. Now we are interested in what the opinions of
other interval developers are. Should the user be allowed to compare
intervals in C++? And if so, what should the semantic of these
comparisons be?

Best regards,

Guillaume

From rbk@louisiana.edu Wed Apr 26 11:34:15 2006
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To: std-interval@compgeom.poly.edu
From: "R. Baker Kearfott" <rbk@louisiana.edu>
Subject: Re: [std-interval] Interval comparison operators
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Guillaume et al,

I am glad you brought this point up again.

You are proposing an interesting way of handling the "three-valued"
logic of interval comparisons within existing boolean language
constructs.  I'll be interested in seeing what others think about it.

Actually, I have a small (possible) correction to your explanation.
You had:
>  - false if there are some values x in X and y in Y such that x >= y,
>  - true if x < y for all the values x in X and y in Y,
>  - a thrown exception if the intervals overlap or are empty.

Didn't you mean
   - false if there are ANY  values x in X and y in Y such that x >= y,

???

Best regards,

Baker


At 06:06 PM 4/26/2006 +0200, Guillaume Melquiond wrote:
>Hi,
>
>On the last draft of the proposal I posted, I had removed everything
>related to interval comparisons because we felt this needed some more
>work. Before tackling this issue, we would like to get your opinions on
>the subject of comparing intervals.
>
>For those who did not get to read our very first proposal, I will detail
>what our approach was, so as to have a starting point for discussing.
>The operators on intervals were directly derived from the order on real
>numbers. Given two intervals X and Y, the result of (X < Y) was defined
>as:
>  - false if there are some values x in X and y in Y such that x >= y,
>  - true if x < y for all the values x in X and y in Y,
>  - a thrown exception if the intervals overlap or are empty.
>
>As a first consequence, it reduces surprise for developers since a
>property like (X < Y) == !(X >= Y) always holds true. But this is not
>why we chose this definition in the first place. We wanted generic code
>to be usable with intervals. Let's consider the following toy example:
>computing accurately the sign of a 2x2 determinant. A generic C++
>template implementation would look like:
>
>        template< class T > sign_t det2(T a, T b, T c, T d) {
>          T u = a * d, v = b * c;
>          if (u < v) return negative;
>          if (u > v) return positive;
>          return zero;
>        }
>
>Now let's try to compute the sign of a floating-point determinant.
>det2<double> is a fast but not reliable implementation. det2<exact>
>(with "exact" being an exact arithmetic type) is reliable but slow. The
>following implementation is generally fast and always reliable:
>
>        sign_t good_det2(double a, double b, double c, double d) {
>          try { return det2< interval<double> >(a, b, c, d); }
>          catch(...) { return det2< exact >(a, b, c, d); }
>        }
>
>So first an interval evaluation is done, and if the result is not
>guaranteed, an exception is thrown during the first comparison in the
>generic code and the specific code falls back to the exact evaluation.
>This example was inspired from the arithmetic filters of computational
>geometry. Only generic code has to be written and it can then be used
>with interval arithmetic to produce guaranteed results.
>
>Now people may be reluctant to use exceptions (because of runtime cost,
>code complexity, and so on) when specifically designing an interval
>code. So, in our proposal, the comparison (X < Y) does not directly
>throw; an exception is thrown only when the result of a comparison is
>converted to a boolean value, for example in an "if" conditional
>expression. This allows for other ways of comparing two intervals.
>
>In particular, interval libraries usually provide explicit functions for
>comparing intervals, something like "certainly less than" or "possibly
>less than" functions that would always return a boolean value and never
>throw. We believe C++ features should be used to provide a nicer syntax
>though. Instead of cerlt(X,Y), a "certainly less than" comparison would
>then be written as:
>
>        if (certainly(X < Y)) ...
>
>This should make a rather detailed overview of our opinion on comparison
>operators for intervals. Now we are interested in what the opinions of
>other interval developers are. Should the user be allowed to compare
>intervals in C++? And if so, what should the semantic of these
>comparisons be?
>
>Best regards,
>
>Guillaume
>
>_______________________________________________
>Std-interval mailing list
>Std-interval@compgeom.poly.edu
>http://compgeom.poly.edu/mailman/listinfo/std-interval
>
>

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------

From rbk@louisiana.edu Wed Apr 26 11:36:37 2006
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Subject: OOPS Re: [std-interval] Interval comparison operators
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Guillaume et al,

OOPS, I meant my correction to read:

Didn't you mean
   - false if for every x in X and y in Y,  x >= y,

???

Otherwise, it includes the case of overlapping intervals.

Baker


>Date: Wed, 26 Apr 2006 11:49:11 -0500
>To: std-interval@compgeom.poly.edu
>From: "R. Baker Kearfott" <rbk@louisiana.edu>
>Subject: Re: [std-interval] Interval comparison operators
>
>Guillaume et al,
>
>I am glad you brought this point up again.
>
>You are proposing an interesting way of handling the "three-valued"
>logic of interval comparisons within existing boolean language
>constructs.  I'll be interested in seeing what others think about it.
>
>Actually, I have a small (possible) correction to your explanation.
>You had:
>>  - false if there are some values x in X and y in Y such that x >= y,
>>  - true if x < y for all the values x in X and y in Y,
>>  - a thrown exception if the intervals overlap or are empty.
>
>Didn't you mean
>   - false if there are ANY  values x in X and y in Y such that x >= y,
>
>???
>
>Best regards,
>
>Baker
>
>
>At 06:06 PM 4/26/2006 +0200, Guillaume Melquiond wrote:
>>Hi,
>>
>>On the last draft of the proposal I posted, I had removed everything
>>related to interval comparisons because we felt this needed some more
>>work. Before tackling this issue, we would like to get your opinions on
>>the subject of comparing intervals.
>>
>>For those who did not get to read our very first proposal, I will detail
>>what our approach was, so as to have a starting point for discussing.
>>The operators on intervals were directly derived from the order on real
>>numbers. Given two intervals X and Y, the result of (X < Y) was defined
>>as:
>>  - false if there are some values x in X and y in Y such that x >= y,
>>  - true if x < y for all the values x in X and y in Y,
>>  - a thrown exception if the intervals overlap or are empty.
>>
>>As a first consequence, it reduces surprise for developers since a
>>property like (X < Y) == !(X >= Y) always holds true. But this is not
>>why we chose this definition in the first place. We wanted generic code
>>to be usable with intervals. Let's consider the following toy example:
>>computing accurately the sign of a 2x2 determinant. A generic C++
>>template implementation would look like:
>>
>>        template< class T > sign_t det2(T a, T b, T c, T d) {
>>          T u = a * d, v = b * c;
>>          if (u < v) return negative;
>>          if (u > v) return positive;
>>          return zero;
>>        }
>>
>>Now let's try to compute the sign of a floating-point determinant.
>>det2<double> is a fast but not reliable implementation. det2<exact>
>>(with "exact" being an exact arithmetic type) is reliable but slow. The
>>following implementation is generally fast and always reliable:
>>
>>        sign_t good_det2(double a, double b, double c, double d) {
>>          try { return det2< interval<double> >(a, b, c, d); }
>>          catch(...) { return det2< exact >(a, b, c, d); }
>>        }
>>
>>So first an interval evaluation is done, and if the result is not
>>guaranteed, an exception is thrown during the first comparison in the
>>generic code and the specific code falls back to the exact evaluation.
>>This example was inspired from the arithmetic filters of computational
>>geometry. Only generic code has to be written and it can then be used
>>with interval arithmetic to produce guaranteed results.
>>
>>Now people may be reluctant to use exceptions (because of runtime cost,
>>code complexity, and so on) when specifically designing an interval
>>code. So, in our proposal, the comparison (X < Y) does not directly
>>throw; an exception is thrown only when the result of a comparison is
>>converted to a boolean value, for example in an "if" conditional
>>expression. This allows for other ways of comparing two intervals.
>>
>>In particular, interval libraries usually provide explicit functions for
>>comparing intervals, something like "certainly less than" or "possibly
>>less than" functions that would always return a boolean value and never
>>throw. We believe C++ features should be used to provide a nicer syntax
>>though. Instead of cerlt(X,Y), a "certainly less than" comparison would
>>then be written as:
>>
>>        if (certainly(X < Y)) ...
>>
>>This should make a rather detailed overview of our opinion on comparison
>>operators for intervals. Now we are interested in what the opinions of
>>other interval developers are. Should the user be allowed to compare
>>intervals in C++? And if so, what should the semantic of these
>>comparisons be?
>>
>>Best regards,
>>
>>Guillaume
>>
>>_______________________________________________
>>Std-interval mailing list
>>Std-interval@compgeom.poly.edu
>>http://compgeom.poly.edu/mailman/listinfo/std-interval
>>
>>
>

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------

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Subject: Re: OOPS Re: [std-interval] Interval comparison operators
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
To: std-interval@compgeom.poly.edu
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Le mercredi 26 avril 2006 à 11:51 -0500, R. Baker Kearfott a écrit :
> Guillaume et al,
> 
> OOPS, I meant my correction to read:
> 
> Didn't you mean
>    - false if for every x in X and y in Y,  x >= y,
> 
> ???
> 
> Otherwise, it includes the case of overlapping intervals.

Right. Thanks for spotting the mistake.

Best regards,

Guillaume

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Subject: Re: [std-interval] Interval comparison operators
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 -------------- Original message ----------------------
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Hi,

[...]

I expect to provide a detailed response, but I am confused by this section of your message:

> In particular, interval libraries usually provide explicit functions for
> comparing intervals, something like "certainly less than" or "possibly
> less than" functions that would always return a boolean value and never
> throw. We believe C++ features should be used to provide a nicer syntax
> though. Instead of cerlt(X,Y), a "certainly less than" comparison would
> then be written as:
> 
>         if (certainly(X < Y)) ...

Does this mean 

    if ( certainly_lt(X,Y) )

Or does operator<(interval,interval) return a specialized object that certainly(/*special object*/) reduces to a boolean or an exception?

If not, how do you expect the expression certainly(X<Y) to be evaluated?

-- Lee Winter

From guillaume.melquiond@ens-lyon.fr Wed Apr 26 13:34:01 2006
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Subject: Re: [std-interval] Interval comparison operators
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To: std-interval@compgeom.poly.edu
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Le mercredi 26 avril 2006 à 18:17 +0000, first.i.last@comcast.net a
écrit :

> >         if (certainly(X < Y)) ...
> 
> Does this mean 
> 
>     if ( certainly_lt(X,Y) )
> 
> Or does operator<(interval,interval) return a specialized object that
> certainly(/*special object*/) reduces to a boolean or an exception?

I really meant "certainly(X < Y)". And yes, this presumably requires the
use of some kind of an expression template as the return type of
operator<. So "certainly" will do the actual comparison and return a
boolean (and it will _never_ throw an exception).

Best regards,

Guillaume

From fernando_cacciola@datafull.com Wed Apr 26 14:25:36 2006
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Subject: Re: [std-interval] Interval comparison operators
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Guillaume Melquiond wrote:
> Le mercredi 26 avril 2006 à 18:17 +0000, first.i.last@comcast.net a
> écrit :
>
>>>         if (certainly(X < Y)) ...
>>
>> Does this mean
>>
>>     if ( certainly_lt(X,Y) )
>>
>> Or does operator<(interval,interval) return a specialized object that
>> certainly(/*special object*/) reduces to a boolean or an exception?
>
> I really meant "certainly(X < Y)". And yes, this presumably requires
> the use of some kind of an expression template as the return type of
> operator<. So "certainly" will do the actual comparison and return a
> boolean (and it will _never_ throw an exception).
>
FWIW the operator doesn't "have to" return an expression template letting 
"certainly" do the actual comparison.
It could also be that the operator returns a tribool, or a discrete interval 
over 'bool', so that "certainly" just turns that into a true/false.

The proposal itself could be more abstract, like:

Interval comparison operators return an object of an unspecified type 
representing a tristate boolean with valid states True, False and neither 
True nor False.
These states are accessible via:

bool certainly    (value) -> true if the state is True, false otherwise
bool certainly_not(value) -> true if the state is False, false otherwise
bool possibly     (value) -> true if the state is NOT False, false otherwise
bool possibly_not (value) -> true if the state is NOT True, false otherwise

and can be logically combined via:

valueR = valueL | valueR (OR)
valueR = valueL & valueR (AND)

In a boolean context, such object shows undefined behaviour if the state is 
not True or False.


That is, the specification of the comparison operator's result can be 
spelled as a Concept rather than a concrete type.
This leaves the details of the actual representation of the operator result 
to the implementator. The proposal itself would only list the "states" 
required for each result.

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com/


From guillaume.melquiond@ens-lyon.fr Wed Apr 26 14:37:46 2006
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Subject: Re: [std-interval] Interval comparison operators
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Le mercredi 26 avril 2006 à 16:42 -0300, Fernando Cacciola a écrit :

> > I really meant "certainly(X < Y)". And yes, this presumably requires
> > the use of some kind of an expression template as the return type of
> > operator<. So "certainly" will do the actual comparison and return a
> > boolean (and it will _never_ throw an exception).
> >
> FWIW the operator doesn't "have to" return an expression template letting 
> "certainly" do the actual comparison.
> It could also be that the operator returns a tribool, or a discrete interval 
> over 'bool', so that "certainly" just turns that into a true/false.

Right. And a discrete interval over bool is actually used in the
original draft and in our toy implementation :-). I just missed a part
of my sentence: I wanted to say that, _for performance reasons_, the
return type will presumably be an expression template. A discrete
interval works well, but since the comparison is not delayed, it
requires some more tests (usually three instead of one floating-point
comparison) and a compiler cannot optimize them away without some
interval arithmetic related knowledge. We also intended for the
comparison operators to produce such a discrete interval (originally
called interval<bool>, but there was a lot of complains about the name)
when needed.

Best regards,

Guillaume

From fernando_cacciola@datafull.com Wed Apr 26 13:47:09 2006
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Guillaume Melquiond wrote:
> Le mercredi 26 avril 2006 à 16:42 -0300, Fernando Cacciola a écrit :
>
>>> I really meant "certainly(X < Y)". And yes, this presumably requires
>>> the use of some kind of an expression template as the return type of
>>> operator<. So "certainly" will do the actual comparison and return a
>>> boolean (and it will _never_ throw an exception).
>>>
>> FWIW the operator doesn't "have to" return an expression template
>> letting "certainly" do the actual comparison.
>> It could also be that the operator returns a tribool, or a discrete
>> interval over 'bool', so that "certainly" just turns that into a
>> true/false.
>
> Right. And a discrete interval over bool is actually used in the
> original draft and in our toy implementation :-). I just missed a part
> of my sentence: I wanted to say that, _for performance reasons_, the
> return type will presumably be an expression template. A discrete
> interval works well, but since the comparison is not delayed, it
> requires some more tests (usually three instead of one floating-point
> comparison) and a compiler cannot optimize them away without some
> interval arithmetic related knowledge. We also intended for the
> comparison operators to produce such a discrete interval (originally
> called interval<bool>, but there was a lot of complains about the
> name)
> when needed.
>
Ineed.
I knew about interval<bool> and I also figured you were just considering an 
optimal implementation.

The goal of my post was to propose that you DO NOT include interval<bool> or 
any form of tribool in the proposal to make room for such clever 
implementations. Just state the requirements on suh a tribool type or branch 
out a separate "tribool CONCEPT" proposal (I know the std doesn't specfic 
mere concepts yet, but this one seems like a good candidate to start)

Best

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com/ 


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Friends,

My thoughts on this thread:

#1  In my own interval programming work, I don't think I have ever used
certainly/possibly operators or tri-valued logic, mostly because I have to
think too hard.  Instead, I use <double> tests on interval endpoints, e.g.,
lo(A) <= hi(B), and similar.  I must think carefully through all cases, but
boolean tests work as I am familiar.  I think I am not alone in that
practice.  I believe it leads to code that is more easily maintained by
people with only intermediate expertise.

#2  I do NOT favor making it as easy as possible for programmers to take
legacy code, change double to interval, and expect to get anything sensible.

If I ruled the world, I would have no interval to interval comparisons.  If
I did accept them, I'd use the CERTAINLY interpretation, that is
   X < Y is hi(X) < lo(Y)

I do not want the responsibility of ruling the world, and I am certainly
sympathetic to the argument that interval code should be as familiar as
possible to experienced programmers of <double>, suggesting the standard
should support interval to interval comparisons.

I also favor simplicity.  If this group argues about interpretations, what
is the plight of someone new to intervals.  Who would read the several pages
required to specify the semantics of several alternatives?

I am not sure what is the simplest solution, and I'll gladly follow further
discussions.  At the moment, I favor providing the CERTAINLY interpretation,
   X < Y is hi(X) < lo(Y), etc.,
although I am painfully aware that makes it easy to write code that violates
the Principle of Least Astonishment and can deliver results that a user
could interpret as violation of containment.

If we cannot accept
   1. No interval to interval comparisons
or
   2. Interpret comparisons as CERTAINLY,
my third choice is the interval<bool>.  When I first saw it, I was
horrified, but I've come to rather like the idea.  It has the advantage of
making boolean operators consistent with the cset interpretation for
numerical operators.  I like that design consistency.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


From avitzur@PacificT.com Wed Apr 26 17:28:46 2006
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From: Ron Avitzur <avitzur@PacificT.com>
Subject: Re: [std-interval] Interval comparison operators
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Hello,

I use the equivalents to certainly, possibly, and interval<bool> in 
interval graphics code.  Given both the care that must be taken to 
think through the cases, and that interval methods will be novel to 
many programmers using the library, I would tend towards an API which 
preferred safety over convenience.

If a programmer constructs an STL container of intervals which uses 
operator< by default, it would be safer if that failed to compile (if 
it has the wrong signature and there is no automatic conversion to 
bool, for example), rather than if it compiled but sometimes failed 
at run-time because either operator< or the automatic conversion to 
bool threw an exception, which is not allowed to happen for 
comparisons used in standard containers.

Being able to write certainly(X < Y) makes for readable code. 
Allowing if(X < Y) to compile with some default meaning introduces 
potential for confusion and subtle run-time errors.

A tradeoff is that then examples such as this need to be written in a 
way that is less elegant.

At 6:06 PM +0200 4/26/06, Guillaume Melquiond wrote:
>         template< class T > sign_t det2(T a, T b, T c, T d) {
>           T u = a * d, v = b * c;
>           if (u < v) return negative;
>           if (u > v) return positive;
>           return zero;
>         }
>
>         sign_t good_det2(double a, double b, double c, double d) {
>           try { return det2< interval<double> >(a, b, c, d); }
>           catch(...) { return det2< exact >(a, b, c, d); }
>         }

An appropriate question here is, how often is it useful to have 
functions template <class T> f(....) were T can be either scalar or 
interval?

- Ron Avitzur


>#1  In my own interval programming work, I don't think I have ever used
>certainly/possibly operators or tri-valued logic, mostly because I have to
>think too hard.  Instead, I use <double> tests on interval endpoints, e.g.,
>lo(A) <= hi(B), and similar.  I must think carefully through all cases, but
>boolean tests work as I am familiar.  I think I am not alone in that
>practice.  I believe it leads to code that is more easily maintained by
>people with only intermediate expertise.
>
>#2  I do NOT favor making it as easy as possible for programmers to take
>legacy code, change double to interval, and expect to get anything sensible.
>
>If I ruled the world, I would have no interval to interval comparisons.  If
>I did accept them, I'd use the CERTAINLY interpretation, that is
>    X < Y is hi(X) < lo(Y)
>
>I do not want the responsibility of ruling the world, and I am certainly
>sympathetic to the argument that interval code should be as familiar as
>possible to experienced programmers of <double>, suggesting the standard
>should support interval to interval comparisons.
>
>I also favor simplicity.  If this group argues about interpretations, what
>is the plight of someone new to intervals.  Who would read the several pages
>required to specify the semantics of several alternatives?
>
>I am not sure what is the simplest solution, and I'll gladly follow further
>discussions.  At the moment, I favor providing the CERTAINLY interpretation,
>    X < Y is hi(X) < lo(Y), etc.,
>although I am painfully aware that makes it easy to write code that violates
>the Principle of Least Astonishment and can deliver results that a user
>could interpret as violation of containment.
>
>If we cannot accept
>    1. No interval to interval comparisons
>or
>    2. Interpret comparisons as CERTAINLY,
>my third choice is the interval<bool>.  When I first saw it, I was
>horrified, but I've come to rather like the idea.  It has the advantage of
>making boolean operators consistent with the cset interpretation for
>numerical operators.  I like that design consistency.
From guillaume.melquiond@ens-lyon.fr Thu Apr 27 02:05:36 2006
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Subject: Re: [std-interval] Interval comparison operators
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Le mercredi 26 avril 2006 à 17:11 -0700, Ron Avitzur a écrit :

> A tradeoff is that then examples such as this need to be written in a 
> way that is less elegant.
[...]
> An appropriate question here is, how often is it useful to have 
> functions template <class T> f(....) were T can be either scalar or 
> interval?

Not that often, I would say. Yet, whenever you are using intervals to
control roundoff errors on a scalar type, it makes sense to use the same
syntax for both the code using the scalar type and the code using the
interval type. An exception is then thrown when two computed values are
too close for being comparable due to roundoff errors.

Anyway, the default implicit conversion to bool is a concern I
understand. A solution would be to require it to be explicit, something
similar to possibly and certainly (I don't have any idea of a good name
though). It would still be possible to annotate the scalar code with
dummy identity functions so that it remains generic.

Best regards,

Guillaume

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Subject: Re: [std-interval] Interval comparison operators
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Le mercredi 26 avril 2006 à 18:29 -0500, George Corliss a écrit :
> Friends,
> 
> My thoughts on this thread:
> 
> #1  In my own interval programming work, I don't think I have ever used
> certainly/possibly operators or tri-valued logic, mostly because I have to
> think too hard.  Instead, I use <double> tests on interval endpoints, e.g.,
> lo(A) <= hi(B), and similar.  I must think carefully through all cases, but
> boolean tests work as I am familiar.  I think I am not alone in that
> practice.  I believe it leads to code that is more easily maintained by
> people with only intermediate expertise.

I agree, but only partly. Handling bounds directly makes it look
simpler, but only as long as you are sure your intervals are not empty.
For example, "A.lower() <= B.upper()" will be undefined if one of the
intervals is empty, while "possibly(A <= B)" will return false. With
possibly empty intervals, it becomes necessary to add new tests and this
may decrease both performance and readability.

I suppose it's only a matter of habits though. People who are used to
handling bounds directly will keep handling bounds directly, while
people who are used to multi-valued logics will keep using them, and so
on. So, in a sense, the question could become: into which habits do we
want people who are new to interval arithmetic to get? Personally, I
wouldn't mind students using possibly / certainly so that they have to
think about what they really want to express rather than directly going
to lower level manipulation of bounds :-).

Best regards,

Guillaume

From george.corliss@marquette.edu Thu Apr 27 03:51:47 2006
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Subject: Re: [std-interval] Interval comparison operators
From: George Corliss <George.Corliss@marquette.edu>
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Guillaume,

>> #1  In my own interval programming work, I don't think I have ever used
>> certainly/possibly operators or tri-valued logic, mostly because I have to
>> think too hard.  Instead, I use <double> tests on interval endpoints, e.g.,
>> lo(A) <= hi(B), and similar.  I must think carefully through all cases, but
>> boolean tests work as I am familiar.  I think I am not alone in that
>> practice.  I believe it leads to code that is more easily maintained by
>> people with only intermediate expertise.
> 
> I agree, but only partly. Handling bounds directly makes it look
> simpler, but only as long as you are sure your intervals are not empty.
Absolutely, but I probably am checking for non-empty in my algorithms
anyway.

> For example, "A.lower() <= B.upper()" will be undefined if one of the
> intervals is empty, while "possibly(A <= B)" will return false. With
> possibly empty intervals, it becomes necessary to add new tests and this
> may decrease both performance and readability.
> 
> I suppose it's only a matter of habits though. People who are used to
> handling bounds directly will keep handling bounds directly, while
> people who are used to multi-valued logics will keep using them, and so
> on. So, in a sense, the question could become: into which habits do we
> want people who are new to interval arithmetic to get? Personally, I
> wouldn't mind students using possibly / certainly so that they have to
> think about what they really want to express rather than directly going
> to lower level manipulation of bounds :-).
Good point.

Any handling I can think of adds surprises, e.g.,
(X < Y) || (X == Y) || (X > Y)
is almost surely FALSE.

Add that to the list
    a - a != 0
    a^2 != a*a
    distributive law does not hold
of surprises awaiting the unwary.  These are unavoidable consequences of the
theory, but the longer is the list of surprises, the more challenging is
adoption.

I accept that we'll end up with interval to interval comparisons.  I urge a
simple alternative, (relatively) easy to understand, in some sense.

Dr. George F. Corliss
Electrical and Computer Engineering
Marquette University
PO Box 1881 
1515 W. Wisconsin Ave.
Milwaukee WI 53201-1881 USA
414-288-6599; Fax: 288-5579; Dept. 288-6280
Office: Haggerty Engineering 296
George.Corliss@Marquette.edu


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Ron Avitzur wrote:

> Hello,
>
> If a programmer constructs an STL container of intervals which uses 
> operator< by default, it would be safer if that failed to compile (if 
> it has the wrong signature and there is no automatic conversion to 
> bool, for example), rather than if it compiled but sometimes failed at 
> run-time because either operator< or the automatic conversion to bool 
> threw an exception, which is not allowed to happen for comparisons 
> used in standard containers.
>
> Being able to write certainly(X < Y) makes for readable code. Allowing 
> if(X < Y) to compile with some default meaning introduces potential 
> for confusion and subtle run-time errors.
>
OK, you make a good point. I'm inclined to agree, but it must be noticed 
that removing the throwing conversion to bool altogether requires a new 
level of complexity in the library. Consider:

template< class T > sign_t det2(T a, T b, T c, T d) {
          T u = a * d, v = b * c;
          if (u < v ) return negative;
          if ( u > v ) return positive;
          return zero;
        }

sign_t good_det2(double a, double b, double c, double d) {
          try { return det2< interval<double> >(a, b, c, d); }
          catch(...) { return det2< exact >(a, b, c, d); }
        }

And let's imagine that there are no throwing conversions to bool (not 
even explicit for the sake of the argument).
Since there are no exceptions one should be able to, after changing 
det2() accordingly, get rid of the try block right?
But how does the "filtering" function knows that the det2() wasn't 
computed robustly without exceptions?
det2() just can't return sign_t anymore.

A solution, which is the one that CGAL uses, could be:

template< class T >
interval<sign_t> det2(T a, T b, T c, T d)
{
  T u = a * d, v = b * c;
   if (certainly(u < v) ) return negative;
   if (certainly(u > v) ) return positive;
   if (certainly(u == v) ) return zero ;
   return interval<sign_t>::empty();
}

sign_t good_det2(double a, double b, double c, double d)
{
  sign_t r = det2< interval<double> >(a, b, c, d);
  if ( is_empty(r)  )
    r = det2< exact >(a, b, c, d);
  return r ;
}

But as you can see this is more complicated: first, there has to be a 
discrete interval<E> and not just interval<bool>; second, the programmer 
must be much more explicitly aware of the trivalued logic.
For instance, if det2() is written as this it won't work correctly:

template< class T >
interval<sign_t> det2(T a, T b, T c, T d)
{
  T u = a * d, v = b * c;
   if (certainly(u < v) ) return negative;
   if (certainly(u > v) ) return positive;
   return zero ; // WRONG. It will return zero when in reality the 
intervals overlapped
}

OTOH, the presence of the throwing conversion to bool _and_ inertial<E> 
can also lead to bugs.
That is, say I love to be utterly explicit so I try to stay away from 
conversion to bool, but I write:

template< class T >
interval<sign_t> det2(T a, T b, T c, T d)
{
  T u = a * d, v = b * c;
   if (certainly(u < v) ) return negative;
   if (certainly(u > v) ) return positive;
   if (u == v ) return zero ; // HERE
   return interval<sign_t>::empty();
}

The intention is to avoid having to put det2() in a try block (that's 
the purpose of the wrapped result type), but I made a mistake: the 
conversion to bool in (u==v) will throw instead of fall thru the final 
return as was the intention.

So, without a throwing conversion to bool, the proposal must incorporate 
interval<E> for all discrete types besides bool in order to let the user 
actually get away without exceptions.

FWIW, in CGAL interval<E> is spelled uncertain<E> to make it more clear 
and it has it's own set of functions (that is, there are no arithmetic 
or comparison operators for uncertain<E>, is_empty() is spelled 
is_indeterminate(), etc...)

But this goes out of the scope of the proposal (unless you bring it into 
scope :)

Best

Fernando Cacciola


From avitzur@PacificT.com Thu Apr 27 10:33:54 2006
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From: Ron Avitzur <avitzur@PacificT.com>
Subject: Re: [std-interval] Interval comparison operators
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>But how does the "filtering" function knows that the det2() wasn't 
>computed robustly without exceptions?
>det2() just can't return sign_t anymore.
>
>A solution, which is the one that CGAL uses, could be:
>
>template< class T >
>interval<sign_t> det2(T a, T b, T c, T d)
>{
>  T u = a * d, v = b * c;
>   if (certainly(u < v) ) return negative;
>   if (certainly(u > v) ) return positive;
>   if (certainly(u == v) ) return zero ;
>   return interval<sign_t>::empty();
>}
>So, without a throwing conversion to bool, the proposal must 
>incorporate interval<E> for all discrete types besides bool in order 
>to let the user actually get away without exceptions.

It is not clear from this example that interval<E> is required for discrete
types. All that is required is that det2 return an error, somehow. It may
throw an exception (explicitly or implicitly via an interval operator),
or it may return a separate error code in a parameter, or it may use an
enum type including {negative, positive, zero, and error}.

The question at hand is whether the interval library should throw
that exception itself. As long as one is explicitly considering the
interval cases, one could as easily write, for example:

  if (certainly(u < v) ) return negative;
  if (certainly(u > v) ) return positive;
  if (certainly(u == v) ) return zero ;
  throw (interval_comparison_exception); // or return error;

It is a tradeoff between being able to write concise code and requiring
one to write more explicitly what is intended in interval cases.

By the way, if anyone on the list would like a copy of our software
to play with (Mac or Windows), send me an e-mail privately.
  http://PacificT.com/Examples/ExampleB6.html

- Ron Avitzur

From Sylvain.Pion@sophia.inria.fr Thu Apr 27 15:32:40 2006
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I just read the thread.  Let me add a couple of comments.

First, concerning the "tribool", or "three-valued boolean logic":
since we have empty intervals, I think it is more sensible to
introduce a type which allows to store 4 values.  I was thinking
about naming it "bool_set", whose 4 possible values would have
been: {}, {true}, {false} and {true, false}.  With the operators &,
| and ^ defined on it (with semantics compatible with the inclusion
property of intervals), and mixed operations with bool, as well
as the certainly() and possibly() functions that Guillaume described.
I am unsure about the (throwing) conversion to bool, but it's appealing.
I think such a class can have its place in the standard library,
even independently from the interval class.

Concerning expression-templates.
I think I would prefer to have the compiler know the invariant
of interval<> and perform the optimizations based on that,
rather than adding more complexity in the standard for very
little gain here.
Moreover, thanks to my second remark below, users can also
provide such "expression-templates" comparison operators
if they wish the last bit of speed if the compiler does not
provide it.

Another note concerning the conversion to bool: currently the
language provides "implicit" conversion operators, and no
"explicit" ones.  But there is a proposal to add explicit
conversion operators, and it received good support in Berlin,
IIRC.  So this might be another option.  My next remark
should make this issue less important I hope.


Second, when I presented the interval comparisons in Dagstuhl,
a few people were surprised (to say the least...) about the
fact that they existed, and the choice of semantics.  What this
shows is that it is going to be hard to have a one-fits-all
solution.  We can choose to not offer anything, but I think
it would be nicer to provide something convenient if we can.
The argument of playing nicely with template code has been
raised by Guillaume and Fernando.  Let me add that we can
also anticipate that template code will in the future be
severely impacted by the new concepts and concept_maps (*).
In our case, it means that the semantic of operator< could
be chosen thanks to such a concept_map, and need not be
universal.
So, a soft solution could be to provide various sets of
comparison operators: a "certainly", a "possibly", and a
"returning bool_set" ones.  These 3 sets being defined
inside some namespaces like std::possibly, std::certainly
and std::???.
This way, template code can use concepts_maps, and non-template
code can use "using namespace" directives to choose the
set of comparison operators it prefers.  And code which
does nothing of this kind will simply fail to compile
inadvertant calls to "<" (and people who like the low
level comparisons between interval bounds should be happy).


-- 
Sylvain

(*) Concepts: there are some proposals floating around for
introducing this new feature in the language.  I heard in Berlin
that good progress had been made and that an updated proposal will
soon be available together with a first implementation based on GCC.

Note that the standard committee is currently debating whether
library proposals should depend on new language features or not.
My point of view is that we should anticipate positively concerning
the concepts, and I think we can offer something nice which
does not depend on it, but which will benefit a lot when/if it
will be added to the language.

One of the key feature is that, when a function is parameterized
by a concept (= list of requirements), the mapping between the
requirement list and the type you instantiate the function with,
can be specified via a concept_map, which allows to "redefine"
functions.
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 -------------- Original message ----------------------
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
>  Now we are interested in what the opinions of
> other interval developers are. Should the user be allowed to
> compare intervals in C++? And if so, what should the semantic
> of these comparisons be?

The attached file contains our detailed response to the issue of comparison of intervals.  Readers interested in specifics without explanation or rationale should not read it.

George Corliss wrote:

> #1  In my own interval programming work, I don't think
> I have ever used certainly/possibly operators or
> tri-valued logic, mostly because I have to think too hard.
> Instead, I use <double> tests on interval endpoints, e.g.,
> lo(A) <= hi(B), and similar.  I must think carefully through
> all cases, but boolean tests work as I am familiar.  I think
> I am not alone in that practice.  I believe it leads to code
> that is more easily maintained by people with only
> intermediate expertise.

This is an effective endorsement of the KISS principle.  We agree that comparison operations need to be as simple, clear, and readable as possible.  We believe that expresion templates or any other specialized technique, e.g., exceptions, that is not widely used in other comparison contexts will retard the widespread use of intervals.

Devil's Advocate question: how much of your habitual resistance to the use of higher level comparisons is due to the non-portability of the various implementations?  AFAICT tests of the bounds are the only reliable cross-platform conventions, so they may be the only reasonable habits at present.

> #2  I do NOT favor making it as easy as possible for
> programmers to take legacy code, change double to
> interval, and expect to get anything sensible.

This is a properly cautionary warnng, but with respect to comparison operators, we disagree.  The warning applies to retaining point-wise algorithms instead of adopting interval algorithms.  We do not believe it applies to primitive operations.  Rather, primitive interval operations should be as similar as possible to built-in floating point operations.

Ron Avitzur wrote:

> Being able to write certainly(X < Y) makes for readable
> code. Allowing if(X < Y) to compile with some default
> meaning introduces potential for confusion and subtle
> run-time errors.

The readability issue is important.  I suspect that to a typical C++ user "if ( certainly( X < Y ) )..." looks more like a syntax error than it does readable code.  Since "if ( certainly_lt(X, Y ) )..." is approximately as readable even to a person without knowledge of the specialized expression templates that affect only intervals, it is absolutely more readable than the former.

The issue of default meaning is even more important.  The default meaning of the comparison operators has to be so simple that it is hard to get it wrong.  And it has to work everywhere, including within the STL.

Guillaume Melquiond wrote:

> Ron Avitzur a écrit :
> > An appropriate question here is, how often is it useful to have 
> > functions template <class T> f(....) were T can be either scalar
> >  or interval?

> Not that often, I would say. Yet, whenever you are using
> intervals to control roundoff errors on a scalar type, it makes
> sense to use the same syntax for both the code using the
> scalar type and the code using the interval type. An exception
> is then thrown when two computed values are too close for
> being comparable due to roundoff errors.

In order to promote compatibility with the STL we suggest the avoidance of exceptions in favor of a handler function such as Interval::indistinct() modeled on _matherr() which would be called whenever an indistinct comparison was detected.  We have used this successfully, but found the principal value concept (detailed in the attached document) to be a simpler and thus superior solution.

>>>>>>

> I suppose it's only a matter of habits though. People who
> are used to handling bounds directly will keep handling bounds
> directly, while people who are used to multi-valued logics will
> keep using them, and so on. So, in a sense, the question could
> become: into which habits do we want people who are new to
> interval arithmetic to get? Personally, I wouldn't mind students
> using possibly / certainly so that they have to think about what
> they really want to express rather than directly going to lower
> level manipulation of bounds :-).

The question of the desirable habits for new users is absolutely fundamental.  The answer to that question forms the criteria that should be used to evaluate the entire interval proposal, particularly interval comparisons.  My company has spent a great deal of effort attempting to make it easy for C++ users to incorporate intervals into their programs, but our results are will not be ready for release for some months yet.

It may be worth soliciting an opinion from the author of the Frink programming language.  He added support for interval arithmetic in the form of triplex numbers a year or so ago.  His implementation is perfectly straightforward and lacks many of the features of other interval arithmetic implementations.  But due to the simplicity of his implementation he may be able to offer useful insiight into the issue of making intervals easy to use safely.

Lee Winter


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From Sylvain.Pion@sophia.inria.fr Sun May 28 02:18:29 2006
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Dear Lee,

Before going anywhere further on technical issues, I'm surprised by
the copyright statement of your document.  It seems to imply that
quoting/copying it from the text of the standard would add the
requirement to add your copyright notice to it.
I let you imagine what would happen if everybody did that for such
minor points.

If this is the case, then I'm not even willing to read it and take
any risk.

-- 
Sylvain
From first.i.last@comcast.net Sun May 28 06:22:38 2006
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Subject: Re: [std-interval] Interval comparison operators
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 -------------- Original message ----------------------
From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
> Dear Lee,
> 
> Before going anywhere further on technical issues, I'm surprised by
> the copyright statement of your document.  It seems to imply that
> quoting/copying it from the text of the standard would add the
> requirement to add your copyright notice to it.

That is not the intent.  When the interval  proposal is adopted or our implementation is released to the public our interest inconfidentiality expires.  Until one of those events occurs public dissemination of our documentation is premature, so we hope to limit it.

We have no interest in affecting the text of the standard, nor would we claim rights on the text of the standard nor anything published with it.

> I let you imagine what would happen if everybody did that for such
> minor points.

It would be a silly situation.

> 
> If this is the case, then I'm not even willing to read it and take
> any risk.

I understand.

In the interest of supporting the proposal we are willing to make a limited disclosure.  If the only acceptable support is public disclosure, then we cannot comply for some months yet.

-- Lee Winter
From guillaume.melquiond@ens-lyon.fr Sun May 28 06:50:23 2006
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Subject: Re: [std-interval] Interval comparison operators
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
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Le dimanche 28 mai 2006 à 05:02 +0000, first.i.last@comcast.net a
écrit :
> >  Now we are interested in what the opinions of
> > other interval developers are. Should the user be allowed to
> > compare intervals in C++? And if so, what should the semantic
> > of these comparisons be?
> 
> The attached file contains our detailed response to the issue of
> comparison of intervals.  Readers interested in specifics without
> explanation or rationale should not read it.

I have taken a quick look at your document and I have a few questions.

First, I'm a bit confused. You are speaking of "subsets of the machine
number line" while the proposal is clearly aimed at representing
(convex) subsets of the real number line. I hope this was only an
oversight.

I do not understand what you mean by "Present day STL experts may be
mislead by the set-based description of intervals, but would not be
confused by a line-segment-based description of intervals". According to
the previous paragraph of your document, I thought this was supposed to
be the exact same notion. Also how would it achieve not to confuse them?
STL comparison operators are lexicographic total ordering while your
line-segment comparison operators are inclusion partial ordering (or
perhaps they aren't?). Later you also say that "they are also fully
compatible with the STL". This does not strike me as obvious since STL
algorithms usually require this property to hold: !(x < y) && !(y < x)
implies that x and y are equivalent.

Concerning your neighborhood model, I disagree. You are saying that "the
certain and possible comparison functions are based on this model". But
somebody performing global optimization or value-range propagation will
use them, while the intervals are nothing like a neighborhood. So
certain and possible comparisons should not be associated to a "point
model" in my opinion.

Do you have some bibliographic references for the principal value model?
This looks like a center-radius model of intervals, but this isn't it,
so I'm a bit lost. For now, I will just ask how different is the "loose"
comparaison from the "possible" comparison. Since the "loose" comparison
is using "the implicit epsilon provided by the radius of the actual
intervals", it seems to me the results will always be the same. Also you
are saying this model appeals to a "much wider audience"; could you give
some examples where it is used?

Later, you say that "empty interval arguments should always yield
false". This statement contradicts your line-segment model, since the
empty set is included in every set. It also goes against your
neighborhood model, since the classical interpretation is: if something
is not possible, then its contrary is certain (and reciprocally).

Your overload of the shift operators looks like a nice idea to me.

Finally, you are proposing that the interval operators compare their
midpoint. This kind of goes against the whole point of providing
interval arithmetic so that people can do certified computations. So I
am a bit reluctant to consider your proposal.

Best regards,

Guillaume

From first.i.last@comcast.net Sun May 28 09:44:31 2006
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 -------------- Original message ----------------------
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Le dimanche 28 mai 2006 à 05:02 +0000, first.i.last@comcast.net a
> écrit :
> > >  Now we are interested in what the opinions of
> > > other interval developers are. Should the user be allowed to
> > > compare intervals in C++? And if so, what should the semantic
> > > of these comparisons be?
> > 
> > The attached file contains our detailed response to the issue of
> > comparison of intervals.  Readers interested in specifics without
> > explanation or rationale should not read it.
> 
> I have taken a quick look at your document and I have a
> few questions.
> 
> First, I'm a bit confused. You are speaking of "subsets of the
> machine number line" while the proposal is clearly aimed at
> representing (convex) subsets of the real number line. I hope
> this was only an oversight.

It was not an oversight.  It may have been a poor chioce of adjective in the document and a copy/paste omission on your part.  In fact it says "CONTIGUOUS subsets of the machine number line"[emphsis added].   Perhaps it should have said convex rather than contiguous.  In this context I think they mean the same thing (denotation) except that the term contiguous suggests (connotation) continuity, which is a fundamental property that line segments and typical intervals do have, but that sets in general do not have.

> 
> I do not understand what you mean by "Present day STL
> experts may be mislead by the set-based description of
> intervals, but would not be confused by a line-segment-
> based description of intervals". According to the previous
> paragraph of your document, I thought this was supposed
> to be the exact same notion. Also how would it achieve
> not to confuse them?

The set and segment implementations are identical.  It is the method of describing them that is different.  IMHO the term segment is better than the term set precisely because it indicates a fundamental property of typical intervals -- convexity.

Describing intervals as containing sets would suggest to an STL expert that they can hold any subset, which suggestion is false and thus misleading.  Describing intervals as containing line segments would suggest that they can only hold convex/contiguous subsets, which is accurate and thus not misleading.

> Later you also say that "they are also fully compatible with
> the STL". This does not strike me as obvious since STL
> algorithms usually require this property to hold:
> !(x < y) && !(y < x) implies that x and y are equivalent.

The sentence following the fragment you quoted states that they lack general applicability because they are often too strict.  In those two sentences I meant that they meet the general requirements, but aren't always useful because they may fail specific requirements such as the one you stated above about deducible equivalance.

> 
> Concerning your neighborhood model, I disagree. You are
> saying that "the certain and possible comparison functions
> are based on this model". But somebody performing global
> optimization or value-range propagation will use them, while
> the intervals are nothing like a neighborhood.  So certain and
> possible comparisons should not be associated to a "point
> model" in my opinion.

The sticking point here appears to be that "intervals are nothing like a 
neighborhood".  If they are not, what are they like?  I.e., what conceptual model do you believe the certain/possible comparisons to be based upon?  Note that the conceptual models are not used to describe to high levels of the software such as functions, algorithms, programs, or applications.  They are only useful to describe the rationale for having multiple sets of comparisons.  So they are properly applied only to distinguish the kinds of low-level 
operations available.

But we have a fundamental disagreement.  The reason certain and possible comparisons are characterized as based upon points is that the results of the comparisons desribe the presence or absence of points. Possible comparisons indicate that there exists some point in each object that satisfies the relation in question.  Certain comparisons indicate that there is one (and only one) point that satisfies the relation in question (except of course for cne() which 
indicates that there is no point that satisfies the relation).

> 
> Do you have some bibliographic references for the principal value model?

Not yet.  That is one of the reasons why it says that it would be understandable if they are not part of the standard.  The reasons for mentioning them at all is that it may benefit the team making the proposal to the committee to be aware that there is on-going research and development in this area.  It may be that there should be no operator notation for comparison until the various candidates have been evaluated in the field.  The candidates that have been suggested include set/segment, certainty, and principal value.

> This looks like a center-radius model of intervals, but this
> isn't it, so I'm a bit lost. For now, I will just ask how different
> is the "loose" comparaison from the "possible" comparison.
> Since the "loose" comparison is using "the implicit epsilon
> provided by the radius of the actual intervals", it seems to
> me the results will always be the same.

The results will not be the same.  The auithoritative definitions of the principal value comparisons can be found in Knuth, D.E. /The art of computer programming/ (vol II).  A brief description of its usage and utility can be found in the beginning of: <http://www.boost.org/libs/test/doc/components/     
test_tools/floating_point_comparison.html>

The difference between loose and possible is that peq() is true whenever one of the intervals overlaps any portion of the other, but leq() is true only whenever one of the intervals overlaps the center of the other.

> Also you are saying this model appeals to a "much wider
> audience"; could you give some examples where it is used?

At present it is not used AFAIK.  But one of the claims is that the PV model makes intervals suitable for direct replacement of built-in floating point types (in the sense of the Liskov substitution principle).   If that claim is valid then the PV model makes intervals appeal to every C++ programmer who uses built-in floating point types.

> Later, you say that "empty interval arguments should always
> yield false". This statement contradicts your line-segment
> model, since the empty set is included in every set.

What is the contradiction?  Equivalence and ordering comparisons do not deal with subsets.  The functions in() and contains() should affirm that an empty interval is included in every other interval.  But the empty interval is neither less then nor more than any other interval.  And given the the empty interval is not part of the machine number line one can claim that it is Not an Interval (NaI).  So, just as NaN is not equal to any other floating point value, not even an identical NaN, NaI should not be equal to any other interval, not even an identical NaI.

In fact this conflict illustrates some of the problems caused by the interval-as-set terminology.  It suggests that an empty interval is an empty set, and so seq(empty,empty) should return true.  But the interval-as-segment terminology suggests that an empty interval is not a segment.  (Nor is it a point.  The width is not zero, it is NaN).
So based upon the interval-as-segment terminology seq(empty,empty) should return false.

Is there a case to be made that empty intervals are less than or greater then non-empty intervals?

> It also goes against your neighborhood model, since the
> classical interpretation is: if something is not possible,
> then its contrary is certain (and reciprocally).

The classical interpretation fails anytime a NaN is encountered because they are not part of the number line.  Similarly empty intervals are not intervals (they need have no sensible bounds nor center/radius).  Moreover the classical interpretation cannot be applied to intervals at all because there are more relationships amoung intervals than there are among points on the machine number line.

> Finally, you are proposing that the interval operators compare their
> midpoint. This kind of goes against the whole point of providing
> interval arithmetic so that people can do certified computations.

The reason the conceptual models are worth discussing is that there is no single model for interval usage.  There can be a single model for the computation of interval values (i.e., outward rounding), but there cannot be a single model for interval applications.  C++ is often mentioned as a multi-paradigm language.  If conceptual models are paradigms then there are definitely multiple interval paradigms.

This is only a problem when one must choose a single paradigm to use in a linguistic feature such as operator notation.  The problme is that one must choose zero or one paradigm.  But selecting a single conceptual model for comparison operators does not "go against" the other models.  They still exist and are exactly as useful as they were prior to the selection.

In fact several accomplished users of intervals have written
that they prefer explicit bounds tests rather than comparison functions.  From this one can deduce that they can do certified computations without comparison functions, which certainly implies that they can do without an operator notation for those functions.

The point of operator notation is to make it easier to express simple concepts.  It may be that there is no simple concept related to intervals, in which case there should be no operator notation for comparison of intervals.

But there is an opposing viewpoint.  When adding up a column of figures, say measurements taken during an experiment, one might want to know how accurate the total was.  Adding up intervals constructed from the measurements and their associated errors makes it trivial to find the error for the total of the measurements.  So the utility of intervals for common-place calculcations is extremely high.  One need not be doing a global optimization to prefer intervals over built-in types.

Comparison operators are quite useful in common-place calculations, and they can be used quite naturally without danger of misleading the programmer.  For example given the need to sort some numbers the precise details of the sort mechanism are probably irrelevant.  The only universal concern is that the result of the sort operation be reasonably reproducible (e.g., swapping of identical items is usually well tolerated).  Comparison of principal values meets that need for simple and reasonably reproducible results.  None of the other conceptual models can meet that need.

> So I am a bit reluctant to consider your proposal.

I quite understand.  If you believe that the inclusion of PV comparisons would inhibit the development of certified computations you should definitely not add them to your standardization proposal.

-- Lee Winter
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Subject: Re: [std-interval] Interval comparison operators
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
To: std-interval@compgeom.poly.edu
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Le dimanche 28 mai 2006 à 16:55 +0000, first.i.last@comcast.net a
écrit :

> > First, I'm a bit confused. You are speaking of "subsets of the
> > machine number line" while the proposal is clearly aimed at
> > representing (convex) subsets of the real number line. I hope
> > this was only an oversight.
> 
> It was not an oversight.  It may have been a poor chioce of adjective
> in the document and a copy/paste omission on your part.  In fact it
> says "CONTIGUOUS subsets of the machine number line"[emphsis added].
> Perhaps it should have said convex rather than contiguous.  In this
> context I think they mean the same thing (denotation) except that the
> term contiguous suggests (connotation) continuity, which is a
> fundamental property that line segments and typical intervals do have,
> but that sets in general do not have.

Then I need to stress again that our proposal deals with intervals of
the _real_ number line. The machine number line is a discrete set of
values with its own arithmetic operators. An interval arithmetic can be
built on it, but this is not the one described in our proposal, while
the Boost interval library would support it for example (this interval
arithmetic is especially useful to statically certify the behavior of
floating-point applications).

[...]

> > Concerning your neighborhood model, I disagree. You are
> > saying that "the certain and possible comparison functions
> > are based on this model". But somebody performing global
> > optimization or value-range propagation will use them, while
> > the intervals are nothing like a neighborhood.  So certain and
> > possible comparisons should not be associated to a "point
> > model" in my opinion.
> 
> The sticking point here appears to be that "intervals are nothing like
> a neighborhood".  If they are not, what are they like?  I.e., what
> conceptual model do you believe the certain/possible comparisons to be
> based upon?

The natural interval extension of the comparison operators between real
numbers are comparison operators between intervals that return a value
in interval<bool> (which also happens to be the powerset of bool).
Certain and possible comparisons are two kind of maps from the powerset
of bool to bool. There is no need to speak of models, this is just a
reasonable way of constraining interval operators to a bool result.

[...]

> > Later, you say that "empty interval arguments should always
> > yield false". This statement contradicts your line-segment
> > model, since the empty set is included in every set.
> 
> What is the contradiction?  Equivalence and ordering comparisons do
> not deal with subsets.  The functions in() and contains() should
> affirm that an empty interval is included in every other interval.
> But the empty interval is neither less then nor more than any other
> interval.

It seems I didn't understand what your line-segment model is. I thought
its comparison operators were based on the set inclusion relation (hence
the functions slt, sle, and so on, as they are named in a few interval
arithmetic libraries, Sun's one for example).

> And given the the empty interval is not part of the machine number
> line one can claim that it is Not an Interval (NaI).  So, just as NaN
> is not equal to any other floating point value, not even an identical
> NaN, NaI should not be equal to any other interval, not even an
> identical NaI.

The empty interval _is_ an interval. It is not unreasonable to add a NaI
value in the same way there is a NaN floating-point value, but this does
not mean there is no empty interval. Would you forbid intersecting two
intervals that do not overlap?

> > It also goes against your neighborhood model, since the
> > classical interpretation is: if something is not possible,
> > then its contrary is certain (and reciprocally).
> 
> The classical interpretation fails anytime a NaN is encountered
> because they are not part of the number line.  Similarly empty
> intervals are not intervals (they need have no sensible bounds nor
> center/radius).  Moreover the classical interpretation cannot be
> applied to intervals at all because there are more relationships
> amoung intervals than there are among points on the machine number
> line.

NaN are not real numbers, they are never encountered in common
arithmetic on real numbers. Our proposal is about convex subsets of the
real numbers, not about convex subsets of machine numbers. I meant
classical interpretation to refer to computer science fields where the
"certain" and "possible" words are commonly used: probability
computations, fuzzy logic, and so on.

[...]

> But there is an opposing viewpoint.  When adding up a column of
> figures, say measurements taken during an experiment, one might want
> to know how accurate the total was.  Adding up intervals constructed
> from the measurements and their associated errors makes it trivial to
> find the error for the total of the measurements.  So the utility of
> intervals for common-place calculations is extremely high.  One need
> not be doing a global optimization to prefer intervals over built-in
> types.

How will it help to have comparison operators do midpoint comparisons on
this example?

[...]

Best regards,

Guillaume


From Sylvain.Pion@sophia.inria.fr Sun May 28 12:33:04 2006
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Subject: [std-interval] list of functions for intervals
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Dear all,

We have been thinking about the list of floating-point functions
which we could propose an interval version for.
More precisely, we have looked at the current list of floating-point
functions from the latest draft of C++0x
(http://www.open-std.org/JTC1/SC22/WG21/docs/papers/2006/n2009.pdf).

As a starting point, here is the list of functions coming from
<cmath> which operate over floating-point types (page 794):

abs       cosh   fmod     logb       rint
acos      erf    frexp    lrint      round
acosh     erfc   hypot    lround     scalbln
asin      exp    ilogb    modf       scalbn
asinh     exp2   ldexp    nan        sin
atan      expm1  lgamma   nearbyint  sinh
atan2     fabs   llrint   nextafter  sqrt
atanh     fdim   llround  nexttoward tan
cbrt      floor  log      pow        tanh
ceil      fma    log10    remainder  tgamma
copysign  fmax   log1p    remquo     trunc
cos       fmin   log2
fpclassify  isgreaterequal  islessequal    isnan     isunordered
isfinite    isinf           islessgreater  isnormal  signbit
isgreater   isless

A description of those functions can be found in the following
almost-final draft of the ISO C99 standard:
http://www.open-std.org/JTC1/SC22/WG14/www/docs/n869/n869.pdf.gz


We suggest to select the following functions for std::interval<T>:
abs       cosh     logb
acos
acosh     hypot    scalbln
asin      exp      scalbn
asinh     exp2     ldexp      sin
atan      expm1    sinh       cos
atan2     fabs     sqrt
atanh     fdim     tan
cbrt      log      pow        tanh
fma       log10    log2
fmin      fmax     log1p
erf       erfc     lgamma     tgamma


Notes:
- fmin, fmax : we propose to return interval<T>, while we could
   return double (the lower or upper bound), but we choose the
   consistency with the treatment done to other functions, and
   it is easy to extract the lower/upper bound of the resulting
   interval anyway.
- erf, erfc, lgamma, tgamma: we are not sure if interval versions
   of these functions would be useful.
- atan2, acos, asin: the range of the result interval should
   probably be specified differently than for floating-point
   (where it must be in [-pi,+pi] for atan2 for example).


We therefore propose to exclude the following functions,
for the following reasons:
- fmod, remainder, remquo : we do not see them useful for intervals.
   We did not find any good specification for interval counterparts.
- frexp, ilogb : because they would have to return an interval<int>,
   (or refer to it for ilogb) and they are probably not useful.
- copysign : no good specification found for intervals.
- rint, lrint, llrint, nearbyint, round, lround, llround, trunc,
   modf, floor, ceil:
   we believe that there is no typical use for intervals.
   It is however probably easy to define and implement them over
   intervals.
   In general, functions relating to Z (integers) probably do not make
   much sense for intervals, as intervals are expected to be used in a
   more numerical context.
- nan : does not make sense.
- nextafter, nexttoward : if an interval needs to be enlarged by
   one ulp (or more), then one can simply add interval<T>::min()
   (the smallest interval strictly containing 0 but not as bounds).
- fpclassify  isgreaterequal  islessequal    isnan     isunordered
   isfinite    isinf           islessgreater  isnormal  signbit
   isgreater   isless :
   do not make sense for intervals, as the treatment of NaNs,
   comparisons, infinities is different from what floating-point
   types do.



What do you think of these lists ?
Is something important excluded ?
Is there anything that should be excluded ?

Note that existing implementations do not necessarily offer all
proposed functions, so any comment on the implementation
difficulty (for interval<float>, interval<double> and
interval<long double>) would be appreciated.


-- 
Sylvain
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Subject: Re: [std-interval] Interval comparison operators
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All,

Warning: Rather long.  My comments are interspersed for the entire thread to
date.


On 5/28/06 12:02 AM, "first.i.last@comcast.net" <first.i.last@comcast.net>
wrote:

>  -------------- Original message ----------------------
> From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
>>  Now we are interested in what the opinions of
>> other interval developers are. Should the user be allowed to
>> compare intervals in C++? And if so, what should the semantic
>> of these comparisons be?
> 
> The attached file contains our detailed response to the issue of comparison of
> intervals.  Readers interested in specifics without explanation or rationale
> should not read it.

Some reactions ...

Copyright: Since I intend to quote portions of your document, I assert that
the quoted portions are subject to: "Permission is hereby granted to
distribute this document to all past, present, and future members of the
mailing list <std-interval@compgeom.poly.edu>; all past, present, and future
members of the team proposing the adoption of intervals into the C++
language; and all past, present, and future members of the C++ Standards
Committee and staff thereof.  Any such reproduction, distribution, or
copying of this document must include the above copyright statement and this
permission paragraph.  All other reproduction, distribution, or copying of
this document requires specific, written permission of the copyright
holder."

Personally, find find the requirement to include that slightly cumbersome.
However, I consider it a STRONG endorsement to the C++ committee of the
interest in an interval standard that your firm cares enough about intervals
to be that protective.  Hence, I joyfully comply with your copyright notice
(I hope).


Good analysis.  Well-thought out.  Thank you for the effort.


"... it is probably worth the effort to get as much as possible as right as
possible so long as it does not inhibit the timely adoption of the interval
proposal."

I'd even allow a modest delay in adoption, if we can develop a consensus on
what "right" is.


Principal Value Model: Hmmm.  Very interesting.  The purist side of me is
appalled; the engineering side of me applauds.  I agree that it can be a
stepping-stone.  I fear that it allows the less-than-careful programmer to
violate containment, which I consider the touch-stone of interval
algorithms.  I'd have to try it out in a non-trivial application to see
which side is stronger.


"Empty interval arguments should always yield false." and following.
Then you are including "I don't know" with FALSE?  Or TRUE means, "I am sure
this is true," and FALSE means, "I cannot assert TRUE."  I can live with
that, but I assert that is not the common understanding of FALSE.

I prefer exception-free (or exception-nearly-free) execution, too, but I
think you lose valuable information to lump "I don't know" with FALSE.
Tough issue.  I'll be interested to see whether we approach consensus.


"If improper intervals are not considered empty then improper intervals
should also always return false."
By "improper interval." do you mean semi-infinite, e.g., [1, inf]?  If so,
then shouldn't some of the 'possible' operators be able to return TRUE in
certain cases?


Standard Terminology:  Your proposal makes sense to me.



> George Corliss wrote:
> 
>> #1  In my own interval programming work, I don't think
>> I have ever used certainly/possibly operators or
>> tri-valued logic, mostly because I have to think too hard.
>> Instead, I use <double> tests on interval endpoints, e.g.,
>> lo(A) <= hi(B), and similar.  I must think carefully through
>> all cases, but boolean tests work as I am familiar.  I think
>> I am not alone in that practice.  I believe it leads to code
>> that is more easily maintained by people with only
>> intermediate expertise.
> 
> This is an effective endorsement of the KISS principle.  We agree that
> comparison operations need to be as simple, clear, and readable as possible.
> We believe that expresion templates or any other specialized technique, e.g.,
> exceptions, that is not widely used in other comparison contexts will retard
> the widespread use of intervals.
> 
> Devil's Advocate question: how much of your habitual resistance to the use of
> higher level comparisons is due to the non-portability of the various
> implementations?  AFAICT tests of the bounds are the only reliable
> cross-platform conventions, so they may be the only reasonable habits at
> present.
Answer to DA: None.  Even comparing endpoints has slightly different syntax
in different packages.

I'm an old Fortran programmer (in any of several parsing alternatives).  My
habits were formed long ago, when I wrote several of my own packages,
thinking they were for my own use, unconstrained by the practices of others.
Comparing endpoints gave me all the tools I ever needed.  In retrospect, I
think that habit encouraged me to think carefully through sometimes
exhaustive cases.  My codes are full of segments including character
graphics suggesting various cases of endpoint comparisons.
   //    [===========]
   //              [========>>>
I think at least I understand what I am doing.

I do not oppose more sophisticated comparisons as you propose.  However, I
am likely to advise non-experts to save themselves the effort of
understanding interval comparisons by restricting themselves to endpoint
comparisons until such time as they feel stifled.  But that's a question of
habit, as you suggest below.


>> #2  I do NOT favor making it as easy as possible for
>> programmers to take legacy code, change double to
>> interval, and expect to get anything sensible.
> 
> This is a properly cautionary warnng, but with respect to comparison
> operators, we disagree.  The warning applies to retaining point-wise
> algorithms instead of adopting interval algorithms.  We do not believe it
> applies to primitive operations.  Rather, primitive interval operations should
> be as similar as possible to built-in floating point operations.
The question, "Is A < B?" is different for floating point numbers A & B and
for intervals A & B.  As evidence of that assertion, I submit your document,
at least 25 years discussion in the interval community, and the fact that so
many variants exist.

Having primitive interval operators that LOOK like primitive floating-point
operators, but have different semantics OR that potentially violate
containment requires careful consideration.

If the floating-point and the interval question are different, ANY syntax
for posing the question is potentially confusing.  That is why I asserted
above I'd even accept a modest delay in adoption, if we can develop a
consensus on what "right" is.

That said, your proposal is a good step in that direction.  When I say
"potentially violate containment," I agree that your comparisons, used as
you intend, are (probably) safe.  My fear is that they may be easy to
miss-use.  I fear WAY too many examples of people writing code with
violations of containment and blaming us, rather than themselves.  I want to
make if hard to violate containment, even by miss-informed programmers.


> Ron Avitzur wrote:
> 
>> Being able to write certainly(X < Y) makes for readable
>> code. Allowing if(X < Y) to compile with some default
>> meaning introduces potential for confusion and subtle
>> run-time errors.
> 
> The readability issue is important.  I suspect that to a typical C++ user "if
> ( certainly( X < Y ) )..." looks more like a syntax error than it does
> readable code.  Since "if ( certainly_lt(X, Y ) )..." is approximately as
> readable even to a person without knowledge of the specialized expression
> templates that affect only intervals, it is absolutely more readable than the
> former.
> 
> The issue of default meaning is even more important.  The default meaning of
> the comparison operators has to be so simple that it is hard to get it wrong.
> And it has to work everywhere, including within the STL.
We are in violent agreement there!



>> I suppose it's only a matter of habits though. People who
>> are used to handling bounds directly will keep handling bounds
>> directly, while people who are used to multi-valued logics will
>> keep using them, and so on. So, in a sense, the question could
>> become: into which habits do we want people who are new to
>> interval arithmetic to get? Personally, I wouldn't mind students
>> using possibly / certainly so that they have to think about what
>> they really want to express rather than directly going to lower
>> level manipulation of bounds :-).
I agree it is a matter of habit, where we each see the rationale for OUR
habit.  Hence, it is wise to support multiple habits, UNLESS there is a
large complexity cost.

> The question of the desirable habits for new users is absolutely fundamental.
Agreed.

> The answer to that question forms the criteria that should be used to evaluate
> the entire interval proposal, particularly interval comparisons.  My company
> has spent a great deal of effort attempting to make it easy for C++ users to
> incorporate intervals into their programs, but our results are will not be
> ready for release for some months yet.
Wonderful.  You may not wish to say, but if you did sound usability testing
and can (eventually) publish your results for peer review, any reservations
I have for your proposal would disappear.

> It may be worth soliciting an opinion from the author of the Frink programming
> language.  He added support for interval arithmetic in the form of triplex
> numbers a year or so ago.  His implementation is perfectly straightforward and
> lacks many of the features of other interval arithmetic implementations.  But
> due to the simplicity of his implementation he may be able to offer useful
> insiight into the issue of making intervals easy to use safely.
Good suggestion.  Have you approached him?  If not, may I or someone else
use your message and your "Comparison of Intervals in C++" to approach him?



Lee Winter responds to response from Guillaume Melquiond:
>> I have taken a quick look at your document and I have a
>> few questions.
>> 
. . .

>> 
>> I do not understand what you mean by "Present day STL
>> experts may be mislead by the set-based description of
>> intervals, but would not be confused by a line-segment-
>> based description of intervals". According to the previous
>> paragraph of your document, I thought this was supposed
>> to be the exact same notion. Also how would it achieve
>> not to confuse them?
> 
> The set and segment implementations are identical.  It is the method of
> describing them that is different.  IMHO the term segment is better than the
> term set precisely because it indicates a fundamental property of typical
> intervals -- convexity.
> 
> Describing intervals as containing sets would suggest to an STL expert that
> they can hold any subset, which suggestion is false and thus misleading.
> Describing intervals as containing line segments would suggest that they can
> only hold convex/contiguous subsets, which is accurate and thus not
> misleading.
And talking about line segments might deflect the scorn of constructivists
who do not believe in set theory :-)

Do we all implicitly assume CLOSED line segments, with the possible
exception of semi-infinite [a, infinity)?  If whole is an interval, it is
closed, isn't it, because its complement is open (and closed)?  Then is the
semi-infinite line segment [a, infinity] closed because its complement
[-infinity, a) is open?

>> Later you also say that "they are also fully compatible with
>> the STL". This does not strike me as obvious since STL
>> algorithms usually require this property to hold:
>> !(x < y) && !(y < x) implies that x and y are equivalent.
> 
> The sentence following the fragment you quoted states that they lack general
> applicability because they are often too strict.  In those two sentences I
> meant that they meet the general requirements, but aren't always useful
> because they may fail specific requirements such as the one you stated above
> about deducible equivalence.
This example illustrates my point above that the questions are different for
floating-point and for intervals.  We are making progress, but we have not
yet converged on a consistent view of how to reconcile the differences.


>> Concerning your neighborhood model, I disagree. You are
>> saying that "the certain and possible comparison functions
>> are based on this model". But somebody performing global
>> optimization or value-range propagation will use them, while
>> the intervals are nothing like a neighborhood.  So certain and
>> possible comparisons should not be associated to a "point
>> model" in my opinion.
> 
> The sticking point here appears to be that "intervals are nothing like a
> neighborhood".  If they are not, what are they like?  I.e., what conceptual
> model do you believe the certain/possible comparisons to be based upon?  Note
> that the conceptual models are not used to describe to high levels of the
> software such as functions, algorithms, programs, or applications.  They are
> only useful to describe the rationale for having multiple sets of comparisons.
> So they are properly applied only to distinguish the kinds of low-level
> operations available.
Are neighborhoods open or closed line segments?

The AGREEMENT here is that a model is necessary to underlie the
specifications.

> But we have a fundamental disagreement.  The reason certain and possible
> comparisons are characterized as based upon points is that the results of the
> comparisons describe the presence or absence of points. Possible comparisons
> indicate that there exists some point in each object that satisfies the
> relation in question.  Certain comparisons indicate that there is one (and
> only one) point that satisfies the relation in question (except of course for
> cne() which 
> indicates that there is no point that satisfies the relation).
> 
>> 
>> Do you have some bibliographic references for the principal value model?
> 
> Not yet.  That is one of the reasons why it says that it would be
> understandable if they are not part of the standard.  The reasons for
> mentioning them at all is that it may benefit the team making the proposal to
> the committee to be aware that there is on-going research and development in
> this area.  It may be that there should be no operator notation for comparison
> until the various candidates have been evaluated in the field.  The candidates
> that have been suggested include set/segment, certainty, and principal value.
Have you plans to submit something for peer reviewed publication?  Or does
that await your commercial release?  I suspect several likely referees are
reading these discussions.

In my opinion, not-yet-published views deserve consideration, but
consideration more careful than published concepts.  I suspect the level of
community oversight may be higher in this forum than in many review
processes, so I am open to a position paper on the principal value model.

>> This looks like a center-radius model of intervals, but this
>> isn't it, so I'm a bit lost. For now, I will just ask how different
>> is the "loose" comparison from the "possible" comparison.
>> Since the "loose" comparison is using "the implicit epsilon
>> provided by the radius of the actual intervals", it seems to
>> me the results will always be the same.
> 
> The results will not be the same.  The authoritative definitions of the
> principal value comparisons can be found in Knuth, D.E. /The art of computer
> programming/ (vol II).  A brief description of its usage and utility can be
> found in the beginning of: <http://www.boost.org/libs/test/doc/components/
> test_tools/floating_point_comparison.html>
> 
> The difference between loose and possible is that peq() is true whenever one
> of the intervals overlaps any portion of the other, but leq() is true only
> whenever one of the intervals overlaps the center of the other.
Intriguing.  I would not mind being able to claim Knuth as an early, albeit
indirect, contributor to the theory of interval arithmetic.

>> Also you are saying this model appeals to a "much wider
>> audience"; could you give some examples where it is used?
> 
> At present it is not used AFAIK.  But one of the claims is that the PV model
> makes intervals suitable for direct replacement of built-in floating point
> types (in the sense of the Liskov substitution principle).   If that claim is
> valid then the PV model makes intervals appeal to every C++ programmer who
> uses built-in floating point types.
AFAIK = As Far As I Know?

>> Later, you say that "empty interval arguments should always
>> yield false". This statement contradicts your line-segment
>> model, since the empty set is included in every set.
> 
> What is the contradiction?  Equivalence and ordering comparisons do not deal
> with subsets.  The functions in() and contains() should affirm that an empty
> interval is included in every other interval.  But the empty interval is
> neither less then nor more than any other interval.  And given the the empty
> interval is not part of the machine number line one can claim that it is Not
> an Interval (NaI).  So, just as NaN is not equal to any other floating point
> value, not even an identical NaN, NaI should not be equal to any other
> interval, not even an identical NaI.
> 
> In fact this conflict illustrates some of the problems caused by the
> interval-as-set terminology.  It suggests that an empty interval is an empty
> set, and so seq(empty,empty) should return true.  But the interval-as-segment
> terminology suggests that an empty interval is not a segment.  (Nor is it a
> point.  The width is not zero, it is NaN).
In my Real Analyis class many years ago, I was told that inf(empty) =
+infinity.  I do NOT suggest that means empty == whole, but it might suggest
width(empty) = infinity.

The answer to width(empty) = ? Does not matter.  What matters is that we are
able to specify operator returns which
   are internally consistent, and
   do not lead to violations of containment.
The best (only?) way to achieve that is to have a single, sound underlying
model.

> So based upon the interval-as-segment terminology seq(empty,empty) should
> return false.
> 
> Is there a case to be made that empty intervals are less than or greater then
> non-empty intervals?
TRUE means, "I am sure this is true," and FALSE means, "I cannot assert
TRUE."  That is your convention?

>> It also goes against your neighborhood model, since the
>> classical interpretation is: if something is not possible,
>> then its contrary is certain (and reciprocally).
> 
> The classical interpretation fails anytime a NaN is encountered because they
> are not part of the number line.  Similarly empty intervals are not intervals
> (they need have no sensible bounds nor center/radius).  Moreover the classical
> interpretation cannot be applied to intervals at all because there are more
> relationships among intervals than there are among points on the machine
> number line.
NaN is taking a critical role in this discussion.

There is some sentiment to minimize dependence on NaN in the interests of
speed, although my understanding of the examples is missing.  One problem,
as I recall, is that in IEEE 754 arithmetic, -infinity + infinity yields
NaN, while we might prefer, at least in outwardly directed rounding modes,
to get whole.

I recall someone telling me that IEEE 754 NaN admits multiple bit patterns.
Hence, rather than overloading NaN as we seem to be doing, we might have
several NaNs, each with distinct meanings, all of which propagate as IEEE
754.  I suspect that is a BAD idea because propagation of different NaN bit
patterns is probably not portable across hardware.

The standard should specify the syntax and semantics, but not the
implementation.  However, it would be unwise to specify something whose best
implementation is "too" expensive, whatever "too" is.  Much of this NaN
discussion probably does not belong in the standard, although having it
available for implementers in another form should be a big help in having
the proposed standard accepted.  This discussion is VERY helpful in
formulating a wise specification.

It sounds to me as though reliance on the properties of IEEE 754 NaN buys us
so many benefits, that we probably prefer to accept any performance penalty
for now and add to the chorus for improved performance for any NaN
processing in future hardware.

Does anyone have hard experimental data on the performance costs of NaN?

>> Finally, you are proposing that the interval operators compare their
>> midpoint. This kind of goes against the whole point of providing
>> interval arithmetic so that people can do certified computations.
> 
> The reason the conceptual models are worth discussing is that there is no
> single model for interval usage.  There can be a single model for the
> computation of interval values (i.e., outward rounding), but there cannot be a
> single model for interval applications.  C++ is often mentioned as a
> multi-paradigm language.  If conceptual models are paradigms then there are
> definitely multiple interval paradigms.
> 
> This is only a problem when one must choose a single paradigm to use in a
> linguistic feature such as operator notation.  The problem is that one must
> choose zero or one paradigm.  But selecting a single conceptual model for
> comparison operators does not "go against" the other models.  They still exist
> and are exactly as useful as they were prior to the selection.
> 
> In fact several accomplished users of intervals have written
> that they prefer explicit bounds tests rather than comparison functions.  From
> this one can deduce that they can do certified computations without comparison
> functions, which certainly implies that they can do without an operator
> notation for those functions.
> 
> The point of operator notation is to make it easier to express simple
> concepts.  It may be that there is no simple concept related to intervals, in
> which case there should be no operator notation for comparison of intervals.
> 
> But there is an opposing viewpoint.  When adding up a column of figures, say
> measurements taken during an experiment, one might want to know how accurate
> the total was.  Adding up intervals constructed from the measurements and
> their associated errors makes it trivial to find the error for the total of
> the measurements.  So the utility of intervals for common-place calculations
> is extremely high.  One need not be doing a global optimization to prefer
> intervals over built-in types.
> 
> Comparison operators are quite useful in common-place calculations, and they
> can be used quite naturally without danger of misleading the programmer.  For
> example given the need to sort some numbers the precise details of the sort
> mechanism are probably irrelevant.  The only universal concern is that the
> result of the sort operation be reasonably reproducible (e.g., swapping of
> identical items is usually well tolerated).  Comparison of principal values
> meets that need for simple and reasonably reproducible results.  None of the
> other conceptual models can meet that need.
Excellent argument.

>> So I am a bit reluctant to consider your proposal.
> 
> I quite understand.  If you believe that the inclusion of PV comparisons would
> inhibit the development of certified computations you should definitely not
> add them to your standardization proposal.
I'm intrigued.  I insist on "Thou shalt not lie."  I favor simple.  I favor
considering carefully constructs which lead the unwary to write code that
appears to lie.

Let's continue the discussion.  Who else has opinions?

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From fernando_cacciola@datafull.com Mon May 29 15:31:22 2006
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Hello Lee,

For now just a question and a quick comment:

Can you justify your claim that:

given a non-degenerate interval X, the expression ceq(X,X) will return false


Maybe I'm just totally missing a point but your Prinicpal Model doesn't look 
to me like a usefull model of interval numbers. Aren't "bounds" the central 
notion of anything called an "interval"?? This models looks to me like the 
"arithmetic expansions" described by Priest here:

http://citeseer.ist.psu.edu/priest91algorithms.html

In such an expansion, roughly, a "result" is given explicitely as a 
"principal value" and a sequence of error terms.
The comparison semantics that you suggest are in line with those concepts, 
but not so much IMO with interval artihmetic.

IOW, the comparison semantics that take into account the "accumulated 
roundoff" (those you cite from Knuth) are well suited for a model which is 
centered around the fact that a result is always a real-point-value but 
which is represented as machine-point-value which differs from the actual 
value by some error. That's why these comparisons are essentiually 
point-based.
But IIUC the very purpose of interval arithmetic when applied to certified 
computations in the presence of roundoff is precisely to provide an 
alternative view centered not on the "principal" value but the error 
bounds...
If you want a number conceptually centered around an "actual value" which 
can't be exactly represented due to roundoff, OK, but I woudn't call that an 
interval.

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com/


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Subject: Re: [std-interval] Interval comparison operators
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 -------------- Original message ----------------------
From: "Fernando Cacciola" <fernando_cacciola@datafull.com>
> Hello Lee,
> 
> For now just a question and a quick comment:
> 
> Can you justify your claim that:
> 
> given a non-degenerate interval X, the expression ceq(X,X) will
> return false

In order to preserve the containment invariant ("not lie") it is necessary for ceq() to assume the independence of any variables that cannot be proven dependent.  So if intervals have no history (e.g., are PODs or close to) and the comparison function is declared as ...

    bool ceq(interval<T> lhs, interval<T> rhs);

... then it cannot distinguish the following cases:

    interval X("[1,2]"), Y("[1,2]");
    bool A = ceq(X,Y);  // independent arguments
    bool B = ceq(X,X);  // dependent arguments
    Y = X;  // create inter-variable dependency
    bool C = ceq(X,Y);  // dependent arguments

So ceq() must return false for all of them.

However, if the function is declared as ...
 
    bool ceq( interval<T> const & lhs, interval<T> const & lhs );

Then it can detect the dependency in case B and return true.  Sun's documentation states that they do this for arithmetic functions, but I am not certain what they do to comparison functions.

In order to detect the dependency in case C either intervals require history (non-PODs with deep copies etc.) or the compiler has to be much smarter than any I've ever heard of.

> Maybe I'm just totally missing a point but your Prinicpal Model
> doesn't look to me like a usefull model of interval numbers.

It isn't particularly useful when the goal is complete rigor as is typical of certified computation.  But it is useful when complete rigor is not required.

> Aren't "bounds" the central notion of anything called
> an "interval"??

I don't think so.  They are aften the exact focus of the user's attention when implementnig reliable computing, but my understanding of the central notion of IA is containment.  The implicit statement about which "thou shalt not lie" being "the true/exact result is contained in such-and-such region".  The region can be described by:
  -- explicit bounds: X..Y
  -- a point with a pair of directional error bounds: X +Y/-Z
  -- a point with symmetric error bounds such as:
  --  -- magnitude: X +/-Y
  --  -- precision limit: X to N sig. digits
  --  -- tolerance: X +/- Y%

Just to be clear, in addressing this issue it is necessary to distinguish representation from conceptual model.  The vast majority of interval implementations use bounds to represent intervals.  But alternate representations, such as center/radius are also useful, especially for problems/spaces of high dimension.

The conceptual models are not tied to the representation of intervals.  All of the conceptual models can be applied to all of the representations.

> This models looks to me like the 
> "arithmetic expansions" described by Priest here:
> 
> http://citeseer.ist.psu.edu/priest91algorithms.html
> 
> In such an expansion, roughly, a "result" is given explicitely as a 
> "principal value" and a sequence of error terms.
> The comparison semantics that you suggest are in line with
> those concepts, but not so much IMO with interval artihmetic.

Is it your conclusion that PV comparison semantics _cannot_ or _should_not_ be applied within interval arithmetic?

> IOW, the comparison semantics that take into account the
> "accumulated roundoff" (those you cite from Knuth) are
> well suited for a model which is centered around the fact
> that a result is always a real-point-value but which is
> represented as machine-point-value which differs from
> the actual value by some error. That's why these
> comparisons are essentiually point-based.

We are in complete agreement up to this point except that our definitions of the term "interval arithmetic" may be distinct.  I interpret your statements to indicate a belief that interval arithmetic consists only of operations that are useful for certified computations.

My definition of IA is the collection of techniques that apply to interval objects .AND. do not interfere with the definition of operations that are necessary for certified computations .AND. are useful for some reasonable purposes.  Thus I think my defintion would produce a proper superset of your definition.

> But IIUC the very purpose of interval arithmetic when applied
> to certified computations in the presence of roundoff is
> precisely to provide an alternative view centered not on
> the "principal" value but the error bounds...

The key phrase in your statement is "... when applied o certified computations...".  I believe that interval arithmetic has wider applicability than certified computations.  This is not to denigrate certified computations, but to suggest that there is a spectrum of rigor and utility ranging from certified computations at the end emphasizing rigor down to convenience for simple calculations at the end where rigor is less critical.

Is it your opinion that interval arithmethic should be used _only_ for certified computations?

> If you want a number conceptually centered around an
> "actual value" which can't be exactly represented due to
> roundoff, OK, but I woudn't call that an interval.

Is this simply a terminology issue?

Reductio:  Should we create a separate set of features whiich look/walk/quack like intervals and are implemented exactly as intervals are, but that we call something different, say "duplex numbers"?  Is this a branding issue where the term interval arithmetic should be reserved for only those systems and applications based on certified computations?

I suspect this issue is a consequence of the fact that there could be several goals for the standardization effort.  Is the goal to improve C++ for (only) users intending to create certified computations, or is the goal to improve C++ for as wide a set of users as possible?

The interest of my company is in the latter, but only to the extent that features designed for the wider audience do not detract from the utility of the proposal for users pursuing maximum rigor.

-- Lee Winter

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On 5/28/06, Sylvain Pion <Sylvain.Pion@sophia.inria.fr> wrote:
> - fmin, fmax : we propose to return interval<T>, while we could
>    return double (the lower or upper bound), but we choose the
>    consistency with the treatment done to other functions, and
>    it is easy to extract the lower/upper bound of the resulting
>    interval anyway.

How do you propose to define this interval? It is not clear to me.

-- 
Lawrence Crowl
From guillaume.melquiond@ens-lyon.fr Tue May 30 11:59:23 2006
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Subject: Re: [std-interval] list of functions for intervals
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Le mardi 30 mai 2006 à 10:57 -0700, Lawrence Crowl a écrit :
> On 5/28/06, Sylvain Pion <Sylvain.Pion@sophia.inria.fr> wrote:
> > - fmin, fmax : we propose to return interval<T>, while we could
> >    return double (the lower or upper bound), but we choose the
> >    consistency with the treatment done to other functions, and
> >    it is easy to extract the lower/upper bound of the resulting
> >    interval anyway.
> 
> How do you propose to define this interval? It is not clear to me.

The fmin(interval<T>,interval<T>) function is defined as the interval
extension of the fmin(T,T) function (so this is consistent with every
arithmetic operator of the proposal).

Mathematically, Min(X,Y) = { min(x,y) | x in X, y in Y }.

>From an implementation point of view, this means that if X and Y are not
empty, the result is
  [ fmin(X.lower(), Y.lower()), fmin(X.upper(), Y.upper()) ]

Best regards,

Guillaume

From eliasen@mindspring.com Wed May 31 18:13:36 2006
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George Corliss wrote:
> I recall someone telling me that IEEE 754 NaN admits multiple bit patterns.
> Hence, rather than overloading NaN as we seem to be doing, we might have
> several NaNs, each with distinct meanings, all of which propagate as IEEE
> 754.  I suspect that is a BAD idea because propagation of different NaN bit
> patterns is probably not portable across hardware.

   While bit patterns in NaNs may vary (they are represented as all 1s
in the exponent, and a non-zero fraction,) there are really only 2
categories of NaN that we should rely on, or expect to see : One is a
"quiet" NaN, (MSB of fraction = 1) and a "signaling" NaN, (MSB of
fraction = 0).  I know of no portable functions other than std::isnan()
(defined in cmath) which simply detects if it's a NaN or not, so you
shouldn't even expect to differentiate between these two.  You are also
not allowed to expect that if you set some specific bit pattern in the
fraction, that it will be maintained.

   The quiet NaN simply propagates itself when used in a calculation.
The signaling NaN, on the other hand, may trigger a floating-point
exception or trap when it is used in a calculation.  In UN*X-like
environments, you can set or modify the signal handler for SIGFPE to
handle/log the error condition when a signaling NaN is used.

   Using signaling NaNs is often very good, or necessary to prevent a
program that uses NaN from silently lying to you.

   For example, if variable "x" is set to a quiet NaN for some reason,
adding to it simply propagates the NaN value and you may see it:

   // x contains quiet NaN
   double b;
   b = x + 1.0;    // Value of b is now NaN, "tainted" by operation with x.

   If you display b, you'll see that its value is NaN, and you'll know
something is wrong.  However, if you do a boolean comparison, your
results may be silently poisoned and you'll never know you were wrong.

   // x contains (quiet) NaN
   if (x < 1.0)
       ... do the unintended thing, silently
   else
       ... do another unintended thing, silently

   What is going to happen when that comparison is made?  You'll never
know that a NaN was used in the comparison, and all further results of
your program may be wrong, or at the very least, untrustable!  (One
would be rather surprised and shocked to see how many of these
comparisons and invalid uses of NaNs there were in a product I worked on
until I added signaling NaN behavior to help enforce correctness.)

   Thus, an implementation that uses NaN should probably use signaling
NaNs to indicate the error condition.  When a *signaling* NaN is used in
the calculations above, a SIGFPE signal is generated, and the program's
incorrect behavior can be noted.  It would be nicer to flag an
exception, as signal handlers don't give you much chance to recover, but
it's probably better than continuing to run for two more weeks and lying
about your results.

   If used in a simple isnan() test, a signaling NaN doesn't trigger
signal handlers (at least in compilers I've seen.)  So that doesn't slow
you down.  If used in mathematical expressions, it does.

> The standard should specify the syntax and semantics, but not the
> implementation.  However, it would be unwise to specify something whose best
> implementation is "too" expensive, whatever "too" is.  Much of this NaN
> discussion probably does not belong in the standard, although having it
> available for implementers in another form should be a big help in having
> the proposed standard accepted.  This discussion is VERY helpful in
> formulating a wise specification.

   A clever implementer will probably make use of NaN for indicating
certain conditions and making the coding simpler.  A smart proposal will
probably be written as if NaN were being used.

> It sounds to me as though reliance on the properties of IEEE 754 NaN buys us
> so many benefits, that we probably prefer to accept any performance penalty
> for now and add to the chorus for improved performance for any NaN
> processing in future hardware.
> 
> Does anyone have hard experimental data on the performance costs of NaN?

   I've used NaNs widely in some large simulation/modelling projects.
Using them often buys quite a bit of performance *improvement* in
less-obvious ways.  The most obvious improvement is that memory usage is
often greatly reduced.  For example, if you want to have a large array
of double values, and have some way of indicating that each initialized
or not, NaN is an obvious choice.  The other options would be to
initialize to some number (dangerous, as that number might show up in
regular calculations), or to keep a separate flag indicating whether the
number was initialized or not.  Due to memory alignment issues, even
adding a boolean flag to your structure or class might double memory usage.

   This improves cache locality, and reduces the nonlinear performance
issues when swapping to disk or slower main memory.

   As for hard experimental data, here's some runs for a sample that
just adds either valid numbers (1.0) to a running sum, or NaN to that
same sum (which you'd never really want to do.)

Linux x86_64, g++ (GCC) 4.1.1 20060525 (Red Hat 4.1.1-1)

-O0:
add1:                   6880000 ticks   Sum: 1e+09
addQNaN:                5940000 ticks   Sum: nan
addSNaN:                6140000 ticks   Sum: nan

-O1:
add1:                   5970000 ticks   Sum: 1e+09
addQNaN:                5990000 ticks   Sum: nan
addSNaN:                6010000 ticks   Sum: nan

-O2:
add1:                   5800000 ticks   Sum: 1e+09
addQNaN:                5810000 ticks   Sum: nan
addSNaN:                5840000 ticks   Sum: nan

-O3:
add1:                   1830000 ticks   Sum: 1e+09
addQNaN:                1840000 ticks   Sum: nan
addSNaN:                1830000 ticks   Sum: nan


   In short, using NaNs in calculations don't make your program
significantly slower.  A real-world program would involve more memory
usage, and use of NaNs would possibly make it faster due to improved
cache locality.

   Program here:

   http://futureboy.us/temp/NaN.cc


-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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George Corliss wrote:
> Does anyone have hard experimental data on the performance costs of NaN?

   Here's some additional data on a different operating system,
processor, and compiler version.  This makes a huge difference!

Processor: Pentium III
Windows 2000
g++ (GCC) 3.4.2 (mingw-special)

-O0:
add1:                   10455 ticks     Sum: 1e+009
addQNaN:                166990 ticks    Sum: 1.#QNAN
addSNaN:                167741 ticks    Sum: 1.#QNAN

-O1:
add1:                   10344 ticks     Sum: 1e+009
addQNaN:                158759 ticks    Sum: 1.#QNAN
addSNaN:                159970 ticks    Sum: 1.#QNAN

-O2:
add1:                   10334 ticks     Sum: 1e+009
addQNaN:                163325 ticks    Sum: 1.#QNAN
addSNaN:                163405 ticks    Sum: 1.#QNAN

-O3:
add1:                   10344 ticks     Sum: 1e+009
addQNaN:                163496 ticks    Sum: 1.#QNAN
addSNaN:                163515 ticks    Sum: 1.#QNAN

   It looks like the cost of doing operations with NaN on this older
architecture is quite high!  I should reiterate that you almost never
actually want to *do* operations with NaN, (you usually just want to
test with isnan() ) but on this platform, it's about 16 times slower!

   As before, sample program is here:

   http://futureboy.us/temp/NaN.cc

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
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From: =?ISO-8859-1?Q?Herv=E9_Br=F6nnimann?= <hbr@poly.edu>
Subject: Re: [std-interval] Interval comparison operators
Date: Sat, 3 Jun 2006 11:37:39 +0200
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On Jun 1, 2006, at 3:25 AM, Alan Eliasen wrote:
> I know of no portable functions other than std::isnan()
> (defined in cmath) which simply detects if it's a NaN or not, so you
> shouldn't even expect to differentiate between these two.

FWIW, std::numeric_limits<T> has members has_quiet_NaN and  
has_signaling_NaN along with quiet_NaN and signaling_NaN.  What you  
can expect is to differentiate between them IF your platform supports  
them (and the numeric_limits given by your system is accurate for the  
platform, as it should).
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu
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Subject: Re: [std-interval] list of functions for intervals
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 -------------- Original message ----------------------
From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
> Dear all,
> 
> We have been thinking about the list of floating-point functions
> which we could propose an interval version for.
> More precisely, we have looked at the current list of floating-point
> functions from the latest draft of C++0x

[...] 

> What do you think of these lists ?
> Is something important excluded ?
> Is there anything that should be excluded ?
> 
> Note that existing implementations do not necessarily offer all
> proposed functions, so any comment on the implementation
> difficulty (for interval<float>, interval<double> and
> interval<long double>) would be appreciated.

Attached is a file containing comments on the issues you raised and suggested specifications for many of the functions at issue.  Having studied this issue in great detail, implemented all of the <cmath> functions, and designed implementations of the c99 functions I can assure you that the implementation of the interval versions of the <cmath> functions, including disjoint results, is quite reasonable.

Using typical elementary functions as a benchmark (trig, hyperbolics, and exponentials) all but two of the c99 functions require similar or lesser implementation effort.  We are still studying the recalcitrant pair of functions, beta() and ellint_1(), with an eye to efficient and robust implementation.

The attached document is a summary aimed at raising issues and identifying areas meriting additional discussion rather than a comprehensive specification with endless detail but no rationale.  Therefore readers who are only concerned with concrete suggestions should not read it.

-- Lee Winter

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Dear Prof. Corliss,

While I am quite interested in the issues you raised, I fear that the proposal team may not share that interest.  So I am responding privately in order to avoid the censure that an open discussion would court.

Liberal snippage in effect.

 -------------- Original message ----------------------
From: George Corliss <George.Corliss@marquette.edu>
> 
> On 5/28/06 12:02 AM, "first.i.last@comcast.net" <first.i.last@comcast.net>
> wrote:
> 
> >  -------------- Original message ----------------------
> > From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> >>  Now we are interested in what the opinions of
> >> other interval developers are. Should the user be allowed to
> >> compare intervals in C++? And if so, what should the semantic
> >> of these comparisons be?
> > 
> Some reactions ...
> 
> Copyright: Since I intend to quote portions of your document, I assert that
> the quoted portions are subject to: "Permission is hereby granted to
> distribute this document to all past, present, and future members of the
> mailing list <std-interval@compgeom.poly.edu>; all past, present, and future
> members of the team proposing the adoption of intervals into the C++
> language; and all past, present, and future members of the C++ Standards
> Committee and staff thereof.  Any such reproduction, distribution, or
> copying of this document must include the above copyright statement and this
> permission paragraph.  All other reproduction, distribution, or copying of
> this document requires specific, written permission of the copyright
> holder."
> 
> Personally, find find the requirement to include that
> slightly cumbersome.

That's hardly accurate.  It is a royale PITA all the way around.

> However, I consider it a STRONG endorsement to
> the C++ committee of the interest in an interval
> standard that your firm cares enough about intervals
> to be that protective.

An interesting perspective.  I hope the committee sees things that way.

>  Hence, I joyfully comply with your copyright notice
> (I hope).

Technically you did not because you omitted the actual copyright declaration.  ;-)

It's far more of a hassle than it first appears.  :-(

> 
> I'd even allow a modest delay in adoption, if we can
> develop a consensus on what "right" is.

I have hopes in that direction, but am skeptical.  Do you have reason to believe that a consensus is possible?  My understanding is that the FORTRAN proposal failed due to conflicts within the interval community.  I have no evidence to indicate that those conflicts have been resolved.  I fear that the disclosure of our approach to the issues may create additional conflicts.

> 
> 
> Principal Value Model: Hmmm.  Very interesting.  The purist
> side of me is appalled; the engineering side of me applauds.
> I agree that it can be a stepping-stone.  I fear that it allows
> the less-than-careful programmer to violate containment,
> which I consider the touch-stone of interval
> algorithms.

We are extremely interested in any example you have or find of a way to mis-use the proposed functions that produces a containment violation.  Of course they make better damned fools every year, so we are certain that nothing can be foolproof.  

> I'd have to try it out in a non-trivial application
> to see which side is stronger.

It may help to consider the difference in approach to numeric software that differentiates the PV model from classical interval designs.  In brief the classical interval designs are very careful about what is known and what is not known.  The value of outward rounding is that it efficiently provides an explicit boundary on the known/unkown which can be used in a sophisticated system to produce provably-good results.

The PV model is based upon the opposite approach.  Most numeric software is hopelessly bad.  Floating point is notoriously difficult to "get right", and even when you know how it takes a great deal of effort.  Intervals cannot cure that problem.  As you have written one cannot transform a point algorithm into an interval algorithm by substitution of intervals for floating point types.

But intervals can help.  Substitution of triplex numbers for floating point types does not alter the results of a calculation.  It does yield a bound on the error associated with the result.  That additional information, even if not used by the software, but simply reported as an output, is a tremendous improvement over the typical abysmal state of numeric software development.

Once you have triplex numbers in use then it becomes much easier to find and fix the bad parts of a software system.  In the limit you can gradually transform the software into a robust system for numerics.

The PV model arose from the fact that there are two semantics available to the user of triplex numbers.  One can use the point value or one can use the interval.  In fact we have an implementation where the semantics can be determined at run time, so a particular function can be exercised in both modes to determine what effect the change in semantics has on the result and the process by which the result is produced.

But what does it mean to "use the interval" in a typical numeric software package?  We needed a specification for intervals equivalent to the IEEE-754 for floating point types.  One that completely defined the results of every operation at the lowest level.  And one that was completely consistent.  That specification is deferred rounding.  Given deferred rounding, the principal value model does the same thing for intervals that round-to-nearest does for floating point -- it minimizes rounding error.

The initial goal was to get intervals into typical software development without the steep initial ramp required for classical intervals as used in reliable computing.  We succeeded in that because we found a seven-step process that takes an existing system using floating point and converts it to use intervals.  No source code changes needed.

The interesting thing about the conversion process is that the seven steps aren't large.  They are baby steps so simple that it is possible to test the system at each step of the conversion to determine that it still works as it originally did and fix anything that was broken by the conversion.  I/O and all.  Including <stdio.h>.  The only thing we do not support is overwriting numeric objects (via pointer casts, abuse of unions, binary IO, etc.).

But along the way we found that the PV model is so much better than classical floating point that it has very serious utility in its own right.  I would be interested in your reaction to the whole system once we are able to make it available.

> "Empty interval arguments should always yield false."
> and following. Then you are including "I don't know"
> with FALSE?

Nit: "I don't know" is not appropriate.  It suggests that there is or might be an answer that is either true or false but whose actual value is unknown even though knowable.  More accurate alternatives would be "I can't (ever) know", "meaningless" or "Bzzzzt -- bad question" (same as "meaningless").  Note that it does _not_ mean "indeterminate".

This is an interesting point, but it is not limited to intervals.  How about tan(pi/2)? sqrt(negative underflow)?  What is the ratio of one to zero (and no B.S. about limits)?  Any sane answer is complex because the result is undefined within the working number system.

Similarly, an empty interval does not have any relationship with any other interval.  Nor does it have any of the properties of an interval.  Since "undefined" is certainly not "true" it has to be lumped in with "false" if you ask a boolean query

>  Or TRUE means, "I am sure this is true," and FALSE means,
> "I cannot assert TRUE."  I can live with that, but I assert
> that is not the common understanding of FALSE.

I suspect the common understanding of false is defective.  Fuzzy systems have built a lot of good stuff on that defect.

> 
> I prefer exception-free (or exception-nearly-free) execution,
> too, but I think you lose valuable information to lump
> "I don't know" with FALSE.

I disagree.  If you ask an inappropriate question {such as plt([1],mpty)} you have not "lost" information due to the limitations on the response.  The info is still available if you ask a more sensible question {such as isempty(mpty)||plt([1],mpty)}.

IMHO the real issue appears to be how much support developers get in detecting inappropriate queries.

> Tough issue.  I'll be interested to see whether we approach consensus.

Definitely tough politically.  But even assuming the use of exceptions does not let us avoid finding a good answer.  When exceptions are disabled (e.g., in the no-throw() version) we still need to produce a sensible result.

> "If improper intervals are not considered empty then
> improper intervals should also always return false."
> By "improper interval." do you mean semi-infinite, e.g.,
> [1, inf]?

That was not my intent.  I don't comprehend what is improper about [1,inf].  Nor do I consider them to include infinity (another discussion some other time).

By "improper" I meant one whose lower bound was greater than its upper bound.  The typical response of "undefined behavior" is probably not acceptable in this context because we are looking for rigor rather than ease of implementation.

> > George Corliss wrote:
> > 
> >> #1  In my own interval programming work, I don't think
> >> I have ever used certainly/possibly operators or
> >> tri-valued logic, mostly because I have to think too hard.
> >> Instead, I use <double> tests on interval endpoints, e.g.,
> >> lo(A) <= hi(B), and similar.  I must think carefully through
> >> all cases, but boolean tests work as I am familiar.  I think
> >> I am not alone in that practice.  I believe it leads to code
> >> that is more easily maintained by people with only
> >> intermediate expertise.
> > 
> > This is an effective endorsement of the KISS principle.  We agree that
> > comparison operations need to be as simple, clear, and readable as possible.
> > We believe that expresion templates or any other specialized technique, e.g.,
> > exceptions, that is not widely used in other comparison contexts will retard
> > the widespread use of intervals.
> > 
> > Devil's Advocate question: how much of your habitual resistance to the use of
> > higher level comparisons is due to the non-portability of the various
> > implementations?  AFAICT tests of the bounds are the only reliable
> > cross-platform conventions, so they may be the only reasonable habits at
> > present.
> Answer to DA: None.  Even comparing endpoints has slightly
> different syntax in different packages.
> 
> I'm an old Fortran programmer (in any of several
> parsing alternatives).  My habits were formed long ago,
> when I wrote several of my own packages,
> thinking they were for my own use, unconstrained
> by the practices of others. Comparing endpoints gave
> me all the tools I ever needed.  In retrospect, I
> think that habit encouraged me to think carefully
> through sometimes exhaustive cases.  My codes
> are full of segments including character
> graphics suggesting various cases of endpoint comparisons.
>    //    [===========]
>    //              [========>>>
> I think at least I understand what I am doing.
> 
> I do not oppose more sophisticated comparisons as
> you propose.  However, I am likely to advise non-experts
> to save themselves the effort of understanding interval
> comparisons by restricting themselves to endpoint
> comparisons until such time as they feel stifled.  But that's
> a question of habit, as you suggest below.

I think Ron Avitur suggested it actually.

I think your suggestion re restraint until confidence grows is sensible when the domain is classical IA for reliable computing.  But the PV models are designed to be used "out of the box" as replacements for floating point comparisons.  OTOH, even with the Knuth variants it would be wise to make new users code their tolerance/epsilon tests explicitly until they have digested the concepts and can appreciate the higher-level concepts expressed by the comparison functions.  Note that the most important reason to use the higher-level comparisons is to make the code readable by others.

But for adoption in C++ I suspect powerful, succinct concepts are what will make the proposal fly.

> >> #2  I do NOT favor making it as easy as possible for
> >> programmers to take legacy code, change double to
> >> interval, and expect to get anything sensible.
> > 
> > This is a properly cautionary warnng, but with respect
>>  to comparison operators, we disagree.  The warning
> > applies to retaining point-wise algorithms instead of
> > adopting interval algorithms.  We do not believe it
> > applies to primitive operations.  Rather, primitive interval
> > operations should be as similar as possible to built-in 
> > floating point operations.
> The question, "Is A < B?" is different for floating point
> numbers A & B and for intervals A & B.  As evidence of
> that assertion, I submit your document, at least 25 years
> discussion in the interval community, and the fact that so
> many variants exist.

Stipulated.  But observe that your statement applies to classical interval arithmetic rather than the PV-based "duplex" arithmetic.  For PV-based arithmetic the expression "A < B" is the same for floating point and "duplex" numbers.

> 
> Having primitive interval operators that LOOK like primitive
> floating-point operators, but have different semantics OR
> that potentially violate containment requires careful
> consideration.

Yeah.  There's the rub.  No matter how good/useful the PV model is having them along side the classical interval relations is going to cause confusion.  The concepts are quite distinct, but I have oscillated from a desire for full integration to a desire to a completely separate naming convention (e.g., duplex numbers with all interval functionality rewrapped, repackaged, and repainted) many times.  The decision as to which is the most appropriate to propose is a bit of cart-before-horse.  The experiential data required to make a wise decision requires a great deal of exposure/usage by the target population.  But once that experience has been gained it becomes difficult to correct any mistakes in the original proposal.

I'm not that worried about containment violations (can you suggest how they might evolve?) but I am concerned about misuse due to misunderstood complexity -- too many choices.

> 
> If the floating-point and the interval question are different,
> ANY syntax for posing the question is potentially confusing.
> That is why I asserted above I'd even accept a modest
> delay in adoption, if we can develop a consensus on what
> "right" is.

Agreed, with the proviso that consensus on this kind of issue is no guarantee of wisdom.

> 
> That said, your proposal is a good step in that direction.
> When I say "potentially violate containment," I agree that
> your comparisons, used as you intend, are (probably) safe.
>  My fear is that they may be easy to miss-use.  I fear WAY
> too many examples of people writing code with violations
> of containment and blaming us, rather than themselves.
>  I want to make if hard to violate containment, even by
> miss-informed programmers.

I think we agree, but we might not.  I see the threat of naive programmers using the wrong function and thus getting a wrong answer.  But that does not create a containment violation as I understand the term.  Am I missing something?

> > Ron Avitzur wrote:
> > 
> >> I suppose it's only a matter of habits though. People who
> >> are used to handling bounds directly will keep handling bounds
> >> directly, while people who are used to multi-valued logics will
> >> keep using them, and so on. So, in a sense, the question could
> >> become: into which habits do we want people who are new to
> >> interval arithmetic to get? Personally, I wouldn't mind students
> >> using possibly / certainly so that they have to think about what
> >> they really want to express rather than directly going to lower
> >> level manipulation of bounds :-).
> I agree it is a matter of habit, where we each see the rationale
> for OUR habit.  Hence, it is wise to support multiple habits,
> UNLESS there is a large complexity cost.

There is not a large compile or run-time compleity cost.  There might be a perceptual or cognitive complexity cost.

The full triplex arithmetic has about eleven (11) distinct sets of comparison functions.  I don't find that complex because I comprehend each of the models on which they are based.  But if I spent 11 minutes describing them to an accomplished programmer, even an experienced interval arithmetic developer they would walk away hopelessly confused.  I'd guess it would take two hours to present them all intelligibly.  And 4-6 hours of problem sets to insure retention.  That's a lot.

This stuff is not simple.  We need powerful, abstract concepts to encapsulate the complexity and make it usable.  It is possible that C++ concept_maps might solve a lot of this packaging problem.

> > The answer to that question forms the criteria that should
> > be used to evaluate the entire interval proposal, particularly
> > interval comparisons.  My company has spent a great deal
> > of effort attempting to make it easy for C++ users to
> > incorporate intervals into their programs, but our results are
> > will not be ready for release for some months yet.
> Wonderful.  You may not wish to say, but if you did sound
> usability testing and can (eventually) publish your results for
> peer review, any reservations I have for your proposal
> would disappear.

We have some interest from the science departments at Harvard and have discussed a formal usability test to be performed by American Institutes for Research (specialists is human factors evaluation).  But neither of those projects can be actually started until we complete the implementation -- we probably won't have funds to repeat the projects if a major revision is needed.

Our testing philosophy is based on certification rather than evaluation.  We expect to find and fix all of the problems before we get into the field.  So we do a great deal of internal testing.  When we get independent test results they either pass/certify the results we expect or we go back to the drawing board and start over.  We are not comfortable with last-minute patches.

We definitely want as much rigor in the independent evaluations as we can get.

The bulk of this problem is not the functionality, but how to package and describe it to the user.  So it is basically a doc problem.  And the secret to good doc is the same as the secret to any kind or writing: lots of rewriting.  So that's what we do.

> > It may be worth soliciting an opinion from the author of the Frink programming
> > language.  He added support for interval arithmetic in the form of triplex
> > numbers a year or so ago.  His implementation is perfectly straightforward and
> > lacks many of the features of other interval arithmetic implementations.  But
> > due to the simplicity of his implementation he may be able to offer useful
> > insiight into the issue of making intervals easy to use safely.
> Good suggestion.  Have you approached him?

I have not.  I thought that decision should lie with the proposal team.

>  If not, may I or someone else use your message and
> your "Comparison of Intervals in C++" to approach him?

It appears that he is now a member of the mailing list so you are welcome to discuss any part of that paper with him.

Note that Frink only supports point semantics for its triplex numbers, so it does not have the PV-based comparisons.  I made the suggestion in the hope that he had considered additional functionality and would express an opinion about it that might be useful.

> Lee Winter responds to response from Guillaume Melquiond:
> >> I have taken a quick look at your document and I have a
> >> few questions.
> >> 
> . . .
> 
> Do we all implicitly assume CLOSED line segments, with the 
> possible exception of semi-infinite [a, infinity)?  If whole is
> an interval, it is closed, isn't it, because its complement is
> open (and closed)?  Then is the semi-infinite line segment
> [a, infinity] closed because its complement [-infinity, a) is
> open?

Grrrr.  All of the proposals I have seen assume closed intervals.

But there is a great deal of terminology abuse in the above (another discussion another time).

> >> Concerning your neighborhood model, I disagree. You are
> >> saying that "the certain and possible comparison functions
> >> are based on this model". But somebody performing global
> >> optimization or value-range propagation will use them, while
> >> the intervals are nothing like a neighborhood.  So certain and
> >> possible comparisons should not be associated to a "point
> >> model" in my opinion.
> > 
> > The sticking point here appears to be that "intervals are nothing like a
> > neighborhood".  If they are not, what are they like?  I.e., what conceptual
> > model do you believe the certain/possible comparisons to be based upon?  Note
> > that the conceptual models are not used to describe to high levels of the
> > software such as functions, algorithms, programs, or applications.  They are
> > only useful to describe the rationale for having multiple sets of comparisons.
> > So they are properly applied only to distinguish the kinds of low-level
> > operations available.
> Are neighborhoods open or closed line segments?

Closed AFAICT.

> 
> The AGREEMENT here is that a model is necessary to underlie the
> specifications.

Meaning a single model?  I believe that systems like Sun's forte already have at least two models in use (set/segment and neighborhood of uncertainty).  I proposed a third model (PV) for use in "bottom up" improvements to numeric software.

> 
> > But we have a fundamental disagreement.  The reason certain and possible
> > comparisons are characterized as based upon points is that the results of the
> > comparisons describe the presence or absence of points. Possible comparisons
> > indicate that there exists some point in each object that satisfies the
> > relation in question.  Certain comparisons indicate that there is one (and
> > only one) point that satisfies the relation in question (except of course for
> > cne() which 
> > indicates that there is no point that satisfies the relation).
> > 
> >> 
> >> Do you have some bibliographic references for the principal value model?
> > 
> > Not yet.  That is one of the reasons why it says that it would be
> > understandable if they are not part of the standard.  The reasons for
> > mentioning them at all is that it may benefit the team making the proposal to
> > the committee to be aware that there is on-going research and development in
> > this area.  It may be that there should be no operator notation for comparison
> > until the various candidates have been evaluated in the field.  The candidates
> > that have been suggested include set/segment, certainty, and principal value.
> Have you plans to submit something for peer reviewed
> publication?

Interest but no plans.  We do not have experience or skill in that process.

>  Or does that await your commercial release?

Definitely.

We are taking a great risk by the premature disclosure to the C++ standardization effort.  We aren't worried about competition -- the more the merrier.  We are worried about premature evaluation such that when the complete system description is available people will already have made up their minds and dismissed it due to a shallow/incomplete description such as is going on re the standardization proposal.

After all we are going to be making claims that violate most of the existing body of knowledge about interval arithmetic.  So we'll be easy to dismiss as cranks.

> I suspect several likely referees are reading these discussions.

I do not doubt it.

> 
> In my opinion, not-yet-published views deserve consideration, but
> consideration more careful than published concepts.

Of course.

> I suspect the level of community oversight may be higher
> in this forum than in many review processes, so I am open
> to a position paper on the principal value model.

In addition to lack of skill and experience, we also lack bandwidth.  You want to volunteer?  An objective and thorough white paper would be quite valuable to us.
 
> >> Also you are saying this model appeals to a "much wider
> >> audience"; could you give some examples where it is used?
> > 
> > At present it is not used AFAIK.  But one of the claims is that the PV model
> > makes intervals suitable for direct replacement of built-in floating point
> > types (in the sense of the Liskov substitution principle).   If that claim is
> > valid then the PV model makes intervals appeal to every C++ programmer who
> > uses built-in floating point types.
> AFAIK = As Far As I Know?

Yes.

> 
> >> Later, you say that "empty interval arguments should always
> >> yield false". This statement contradicts your line-segment
> >> model, since the empty set is included in every set.
> > 
> > What is the contradiction?  Equivalence and ordering comparisons do not deal
> > with subsets.  The functions in() and contains() should affirm that an empty
> > interval is included in every other interval.  But the empty interval is
> > neither less then nor more than any other interval.  And given the the empty
> > interval is not part of the machine number line one can claim that it is Not
> > an Interval (NaI).  So, just as NaN is not equal to any other floating point
> > value, not even an identical NaN, NaI should not be equal to any other
> > interval, not even an identical NaI.
> > 
> > In fact this conflict illustrates some of the problems caused by the
> > interval-as-set terminology.  It suggests that an empty interval is an empty
> > set, and so seq(empty,empty) should return true.  But the interval-as-segment
> > terminology suggests that an empty interval is not a segment.  (Nor is it a
> > point.  The width is not zero, it is NaN).
> In my Real Analyis class many years ago, I was told that inf(empty) =
> +infinity.

Presumably that was before in-band error values such as NaN were available.  That kind of convention is still in use in both C and C++ in the <math.h> symbol HUGE_VAL.  In specific situation you describe with lower(empty)>upper(empty) the properties indicate that empty is an improper interval, so while the properties were well defined, they were not meaningful.  

Is that a violation of interval consistency?  Is that a lie?  IMHO it is, but only a white one -- i.e. not hidden and justified by necessity.

>  I do NOT suggest that means empty == whole, but it might suggest
> width(empty) = infinity.

I suggest that extension of that concept indicates width(empty) = -infinity rather han +infinity.  That difference is probably the more recent availability of affine systems whereas most legacy systems that even have an infinity were projective.

> 
> The answer to width(empty) = ? Does not matter.  What matters is that we are
> able to specify operator returns which
>    are internally consistent, and
>    do not lead to violations of containment.
> The best (only?) way to achieve that is to have a single, sound underlying
> model.

That's a blivet.  Certainly soundness of the underlying theory is a necessity.  But the theory cannot have a single conceptual model because there is more than one way to view/use/interpret an interval.  There are at least two mutually incompatible such models widely used within the existing community of interval practitioners.  I expect we will have to settle for well defined operations over intervals, and all based upon outward rounding and containment.  But we'll have a variety of operations not all combinations of which will be useful.

Formally we have to expect that because any useful interval system is as least as powerful as basic arithmetic [Godel] and the language of which it is a part is complete [Turing].

> 
> > So based upon the interval-as-segment terminology seq(empty,empty) should
> > return false.
> > 
> > Is there a case to be made that empty intervals are less than or greater then
> > non-empty intervals?
> TRUE means, "I am sure this is true," and FALSE means, "I cannot assert
> TRUE."  That is your convention?

That is the convention I suggest should be used.  I'll take the blame for it, but I would be hesitant to take credit for it.  It is common in many domains.

> 
> >> It also goes against your neighborhood model, since the
> >> classical interpretation is: if something is not possible,
> >> then its contrary is certain (and reciprocally).
> > 
> > The classical interpretation fails anytime a NaN is encountered because they
> > are not part of the number line.  Similarly empty intervals are not intervals
> > (they need have no sensible bounds nor center/radius).  Moreover the classical
> > interpretation cannot be applied to intervals at all because there are more
> > relationships among intervals than there are among points on the machine
> > number line.
> NaN is taking a critical role in this discussion.

Not as a necessary component of intervals, but as a model for the consistent extension of a system.  I raised the the topic of NaN to indicate that the classical interpretation of logic (where !false implies true) already does not apply to modern numerics.  So insisting upon the classical interpretation within interval operations is a serious mistake.

> There is some sentiment to minimize dependence on NaN in the interests of
> speed, although my understanding of the examples is missing.  One problem,
> as I recall, is that in IEEE 754 arithmetic, -infinity + infinity yields
> NaN, while we might prefer, at least in outwardly directed rounding modes,
> to get whole.

I understand that desire and can sympathize.  But it is a containment violation.  The interval [-inf,+inf] does not contain all possible results of operations on intervals.  In only contains the numeric results.  So using it in place of the IEEE-defined result is unacceptable if the goal is complete rigor.

If one is willing to ignore non-numeric results then [-inf,+inf] is a panacea.  But ignoring non-numeric results is not acceptable because it to bad software.  This is directly related to one of the aspects of the incompleteness of Pryce's cset paper.  I don't know where we've gotten on that, but I will find out.

> 
> I recall someone telling me that IEEE 754 NaN admits multiple bit patterns.
> Hence, rather than overloading NaN as we seem to be doing, we might have
> several NaNs, each with distinct meanings, all of which propagate as IEEE
> 754.  I suspect that is a BAD idea because propagation of different NaN bit
> patterns is probably not portable across hardware.

It is not yet portable.  But it will be.  It is not an important issue though because given two NaN inputs getting either out is good enough even if arbitrary.

IMHO we should not worry about bad hardware.  We should be designing good software and then building machines to execute it.  We should not be designing (and limiting) software to tell bad hardware what to do [Dijkstra '72 I think].

> 
> The standard should specify the syntax and semantics, but not the
> implementation.  However, it would be unwise to specify something whose best
> implementation is "too" expensive, whatever "too" is.

Why?

Changing rounding modes is extremely expensive on commodity hardware.  We can show a trivial hardware change that eliminates the need for mode changes and thus eliminates all of the pipeline flushes that plague interval implementations.  It only requires a single, non-sticky bit in the FPU status register and a tiny amount of logic.  If performance were a grave concern it would be quickly adopted.  But there is little interest in the public discussions about it, even in math fora.

If some CPUs don't handle NaNs quickly, that's too bad for those CPUs.  Other CPUs will handle them quickly.  Any other approach will crippled interval sofware by embedding (and thus tacitly approving) support for bad CPU designs.

> Much of this NaN
> discussion probably does not belong in the standard, although having it
> available for implementers in another form should be a big help in having
> the proposed standard accepted.  This discussion is VERY helpful in
> formulating a wise specification.
> 
> It sounds to me as though reliance on the properties of IEEE 754 NaN buys us
> so many benefits, that we probably prefer to accept any performance penalty
> for now and add to the chorus for improved performance for any NaN
> processing in future hardware.

That is my opinion.

> 
> Does anyone have hard experimental data on the performance costs of NaN?

It does not matter how bad they are today, so those performance numbers are irrelevant to the issues under discussion.

However, as a point of reference, recent intel CPUs are unbelievably bad.  They are documented to be 1000x slower on special values (such as NaN, inf, denorm) than on non-special values.  AMDs recent CPUs are orders of magnitude better on special values, even though their handling of special values has slipped somewhat over time.

> > 
> > I quite understand.  If you believe that the inclusion of PV comparisons would
> > inhibit the development of certified computations you should definitely not
> > add them to your standardization proposal.
>
> I'm intrigued.  I insist on "Thou shalt not lie."  I favor simple.  I favor
> considering carefully constructs which lead the unwary to write code that
> appears to lie.
> 
> Let's continue the discussion.  Who else has opinions?

I think the dynamics of the std-interval forum are not as vigorous as one might find in a typical discussion forum.  That might be on purpose.

-- Lee Winter
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 -------------- Original message ----------------------
From: first.i.last@comcast.net

> Dear Prof. Corliss,

[...]

The message was addressed incorrectly.  Please discard.

-- Lee Winter
 
From rbk@louisiana.edu Sun Jun  4 10:59:04 2006
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Subject: Re: [std-interval] Interval comparison operators
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Lee,

At 05:15 PM 6/4/2006 +0000, first.i.last@comcast.net wrote:
>Dear Prof. Corliss,
>
.
.
.

>
>> 
>> I'd even allow a modest delay in adoption, if we can
>> develop a consensus on what "right" is.
>
>I have hopes in that direction, but am skeptical.  Do you have reason to
believe that a consensus is possible?  My understanding is that the FORTRAN
proposal failed due to conflicts within the interval community.  I have no
evidence to indicate that those conflicts have been resolved.  I fear that
the disclosure of our approach to the issues may create additional conflicts.
>

The failure within the Fortran community was more complicated than
that, although lack of consensus within the interval community 
was a factor.  I am much more optimistic with the C++ proposal, due
to various facets of the discussion.

My view is that, if there is a hopeless lack of consensus, it may
indicate that there isn't a single "right" way, but choosing 
a particular way and having a standard is better than having none.
However, we should strive to maximize the utility of the language
in the standard.

Sincerely,

Baker
  

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------


From george.corliss@marquette.edu Sun Jun  4 18:26:34 2006
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Lee and all,

Excellent.  I like your proposal better than mine, but (of course?) I have
some questions for you and the list.  I had in mind a minimalist standard;
you are more ambitious.  If we can summon support for an ambitious standard,
LET'S DO IT. 


Q1, p. 1, par. 2.  "Standardization of the interval functions should not
mandate that containment, which is a QoI issue."  Do you mean containment in
the sense that the set of interval standard functions should contain the
floating point ones?  Or that (shudder) containment of values returned
should not be mandated?

Q2, par. 4.  "the result of an interval version of a <cmath> function is the
hull of all of the results ..." is close to the cset definition, except that
csets enclose also results of limits.  Several of us are preparing a cset
draft for posting here within a few days.  _IF_ csets are accepted, say, for
divide, it would be natural to use them to specify results of cmath
functions, too?  I'd have to look more closely for differences in returned
values.

Q3, par. 7. "existence of a type designed to hold multiple instances of
values"  Such a type could improve the practicality of our cset proposal,
too.  Thank you!

Q4, par. 9. "wrong" and "nacceptably wide"
--> "wrong" and "unacceptably wide"


Q5. isnan() and nan().  I see where you are going with the "Set of interval
functions must contain the set of floating-point functions, and interval
functions on singleton intervals must agree with their floating-point
counterpart" argument.  I'm sympathetic.

It is a mistake for a standard to give too detailed an implementation, but
many are concerned that the standard also should not mandate a slow
implementation.  I assume we want to represent an <empty> set and probably a
<whole> set.  If we use [NaN, NaN] as an internal, opaque implementation of
<empty>, there are very few performance-robbing tests.  If an implementation
DOES decide to use NaN to represent <empty>, I guess isnan() does no harm,
and I guess nan() would be the equivalent of <empty>.

Q6.  Additions?
   interval square( interval X )?

Many interval coders are accustomed to
   double mag( interval X ); // or magnitude := max abs(X)
   double mig( interval X ); // or mignitude := min abs(X),
where "abs(X)" is the interval abs as I imagine you'd specify it.

Q7. Function forms of operators: Hooray!  Then the C++ interval is (nearly)
a C interval library plus a C++ wrapper class?  Then I can use it if I am
restricted to C, for some reason.  Or is that an empty opportunity?

I appreciate you suggesting that implementations are not too hard.  In
addition, we should note there are at least a couple quite good (tight)
implementations of most of the common elementary functions, more evidence
that a vendor's barrier to entry is not high.

My reservation is that by putting more advanced tools (your twin functions)
in the hands of people inexperienced with interval algorithms, you provide
more opportunities for screwing up :-)

(In preparing this response, I have consulted on some, but not all, of these
points with John Pryce, R. Baker Kearfott, Ned Nedialkov, and Spencer
Smith.)

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


On 6/3/06 7:30 PM, "first.i.last@comcast.net" <first.i.last@comcast.net>
wrote:

>  -------------- Original message ----------------------
> From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
>> Dear all,
>> 
>> We have been thinking about the list of floating-point functions
>> which we could propose an interval version for.
>> More precisely, we have looked at the current list of floating-point
>> functions from the latest draft of C++0x
> 
> [...] 
> 
>> What do you think of these lists ?
>> Is something important excluded ?
>> Is there anything that should be excluded ?
>> 
>> Note that existing implementations do not necessarily offer all
>> proposed functions, so any comment on the implementation
>> difficulty (for interval<float>, interval<double> and
>> interval<long double>) would be appreciated.
> 
> Attached is a file containing comments on the issues you raised and suggested
> specifications for many of the functions at issue.  Having studied this issue
> in great detail, implemented all of the <cmath> functions, and designed
> implementations of the c99 functions I can assure you that the implementation
> of the interval versions of the <cmath> functions, including disjoint results,
> is quite reasonable.
> 
> Using typical elementary functions as a benchmark (trig, hyperbolics, and
> exponentials) all but two of the c99 functions require similar or lesser
> implementation effort.  We are still studying the recalcitrant pair of
> functions, beta() and ellint_1(), with an eye to efficient and robust
> implementation.
> 
> The attached document is a summary aimed at raising issues and identifying
> areas meriting additional discussion rather than a comprehensive specification
> with endless detail but no rationale.  Therefore readers who are only
> concerned with concrete suggestions should not read it.
> 
> -- Lee Winter
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval


From j.d.pryce@ntlworld.com Sun Jun  4 21:48:00 2006
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Lee, and participants in this group

At 19:12 04/06/06, R. Baker Kearfott wrote:
>My view is that, if there is a hopeless lack of consensus, it may
>indicate that there isn't a single "right" way, but choosing
>a particular way and having a standard is better than having none.
>However, we should strive to maximize the utility of the language
>in the standard.

Like Baker, I feel optimistic that a consensus will emerge. I 
STRONGLY agree with Baker's paragraph above.

Lee, you have written eloquently of the Principal Value (PV) model 
that you have been working on. If it is as different in 
concept/philosophy/goals (I don't know enough about it to know which 
of those words are most appropriate) from the "classical interval 
model" as you say, then certainly it needs a different standard from 
one that supports the classical model. Therefore, I do not see you as 
in conflict with the classical intervallers, but as complementary.

However I speak as the principal author of containment set (cset) 
theory for the last few years. Csets are NOT the most widely held 
view of classical intervals, and when I started working on them for 
Bill Walster under contract to Sun around 2001 they were generally 
seen as an eccentricity that would soon die out.

Evaluation of cset theory by the interval community was delayed 
slightly by commercial confidentiality. That prohibited putting some 
aspects of csets in the public domain - mainly Sun's implementation 
detail. The main reason for delay was that Bill and I had serious 
disagreement, not over what a cset-based interval implementation 
should do, but about what the results *meant*. I believed, and still 
do, that Bill's philosophy of csets at that time was mathematically 
inconsistent. As a result we could not agree on a paper to submit to 
the open literature. We spoke at conferences etc, but some of the 
assertions we made were incompatible, which was not good for credibility.

Maybe it was a blessing in disguise, because then I joined the ISL 
project steering committee, and working with 3 guys who have jointly 
over 50 years interval programming experience, plus a professional 
software engineer, widened my outlook so that the paper I eventually 
wrote, Pryce and Corliss "Interval arithmetic with containment sets" 
(2006), submitted to "Computing", see
     http://homepage.ntlworld.com/j.d.pryce/isloct05/IntvlArithCsets.pdf
was far clearer and more concise than it would otherwise have been.

And, to my surprise, my ISL colleagues decided of their own accord 
that a cset-based interval system was the one they preferred, though 
the well-known packages they had up to then used, and in one case 
written, were based on what I call the Simple System.

How did this come about? I believe it was because I had been able to 
write an account that showed such a system is
- rock-solid mathematically,
- actually useful.

Both are necessary conditions for acceptance in this corner of 
scientific computing (sadly, not sufficient). I urge you to move the 
task of writing up what PV intervals are all about to near the top of 
your priorities, if not the actual top. And get it into the open 
literature so that people can pull your ideas to pieces (as my cset 
ideas have been for several years), force you to refine them, and 
eventually be convinced you are making sense.

I find many things you write very weird or downright false (e.g. 
distinctions between line segments and sets, and tests on the empty 
set). That is because I am matching it against my model, which is 
firmly based on classical set theory. You have work to do to convince 
me, but my mind is open. As I am a mathematician, the "rock-solid 
mathematically" interests me more, initially, than the "actually 
useful". I think many people with more interval experience and/or 
more influence in the scientific world than I would agree with me.

PV intervals must be mathematically consistent, or they will die. But 
there is more than that. You must have an underlying purpose for 
them, or philosophy about them, that explains why this consistent bit 
of mathematics actually helps humans solve real life problems. From 
what you write, you are a fair way towards having both, but you won't 
convince the world unless you WRITE IT UP for public evaluation.

Best wishes for that project.

John Pryce

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 -------------- Original message ----------------------
From: George Corliss <George.Corliss@marquette.edu>
> Lee and all,

[...]

> Q1, p. 1, par. 2.  "Standardization of the interval functions
> should not mandate that containment, which is a QoI issue."
>  Do you mean containment in the sense that the set of
> interval standard functions should contain the floating point
> ones?  Or that (shudder) containment of values returned
> should not be mandated?

The latter.  The standard should require that the mathematically correct answer be contained within the interval result.  However, the result of the corresponding floating point function can be arbitrarily far from the mathematically correct answer (QoI of the FP library).  Thus requiring that the FP result be contained within the interval result can have an adverse effect upon the sharpness of the interval result.  So it comes down to a choice between the QoI of the interval implementation versus the consistency between the FP and interval implementations.

We choose consistency for our implementation.  But as much we have a very strong preference for systems that are consistent, we do not believe the standard should make that consistency mandatory because we suspect it would operate to the detriment of the QoI of the interval library.  So we reluctantly suggest that it be left as a recommendation rather than a requirement..  (I would love for 
the consensus to form the opposite conclusion!)

> Q2, par. 4.  "the result of an interval version of a <cmath>
> function is the hull of all of the results ..." is close to the cset
> definition, except that csets enclose also results of limits.

And except that cset theory as I comprehend it considers only the numeric values rather than the full spectrum of function results.

> Several of us are preparing a cset draft for posting here
> within a few days.  _IF_ csets are accepted, say, for
> divide, it would be natural to use them to specify results of
> cmath functions, too?  I'd have to look more closely for
> differences in returned values.

We would love the safe expression rearrangement that a comprehensive cset theory would allow.  And of course that rearrangement should be viable for elementary functions.  So it would appear to be a natural extension of the theory.  But I 
am concerned about the completeness of the theory.  There are function domain issues, the handling of special vaules (Nan & Inf), and the mapping between the real and machine number lines.

The cset issue is certainly bigger than the <cmath> discussion, and might be bigger (or longer) than the standardization discussion. 

> Q4, par. 9. "wrong" and "nacceptably wide"
> --> "wrong" and "unacceptably wide"

Yes.

> Q5. isnan() and nan().  I see where you are going with the
> "Set of interval functions must contain the set of
> floating-point functions, and interval functions on singleton
> intervals must agree with their floating-point counterpart"
> argument.  I'm sympathetic.
> 
> It is a mistake for a standard to give too detailed an
> implementation, but many are concerned that the
> standard also should not mandate a slow implementation.

On whose hardware?  We intend to buy hardware that will execute a good implementation quickly.  People who buy slow hardware should not blame the standard.

Certainly the standard should not mandate an implementation that _cannot_ be executed efficiently.  But we are far from that.

Historical note: One of the very contentious issues in the original adoption of the IEEE-754 standard was that some major vendors (IBM, DEC, etc.) felt that the extra features such as NaN, Inf, and especially denormal numbers would slow down the processing of normal numbers.  The story is that DEC lost a lot of credit as 
a leader in the field when their rep stated categorically that the proposed features _could_not_ be implemented efficiently.  Of course he was wrong, Intel already had an efficient implementation.

Let us not take counsel of our fears.

> I assume we want to represent an <empty> set and
> probably a <whole> set.  If we use [NaN, NaN] as an
> internal, opaque implementation of <empty>, there are
> very few performance-robbing tests.

My understanding is that Sun choose NaNs for empty due to the similarity of the propagation rules for NaN and empty.  Which means that same thing you said above.

But the standard should neither prohibit nor mandate any implementation of empty.  It should describe the properties of empty completely.  In our view all of those properties (lower, upper, midpt, radius, diameter, etc.) are not numbers.  So they should be NaN or HUGE_VAL depending upon the platform capabilities.

> If an implementation DOES decide to use NaN to represent
> <empty>, I guess isnan() does no harm, and I guess nan()
> would be the equivalent of <empty>.

Is there a problem with that?  We tend to view it as a feature.  In fact we support a variety of NaN-based values including:
    "none"   empty
    "init"      uninitialized
    "dead"   destroyed
    "div0"    division by zero
    "imag"   sqrt(negative)
    "EIO "    IO error (read)
    "EDOM" domain error
    "ERNG"  range error

All of these are treated as empty.
    
> 
> Q6.  Additions?
>    interval square( interval X )?

It is a very specific solution to a widespread problem: inconsistent evaluation of dependencies.  Sun uses automatic identity checking which is a slightly more general solution.

There should be a general solution such as rearrangement at compile time and dependency tracking at run-time.  Note that some kind of ru-time is inevitable because of separate compilation and/or irreducible expressions.

> 
> Many interval coders are accustomed to
>    double mag( interval X ); // or magnitude := max abs(X)
>    double mig( interval X ); // or mignitude := min abs(X),
> where "abs(X)" is the interval abs as I imagine you'd specify it.

We have a "little list" but the functions are not part of <cmath>, which was the subject the proposal team wanted addressed.  I attached a list of examples to this message for the benefit of those interested.

> 
> Q7. Function forms of operators: Hooray!  Then the
> C++ interval is (nearly) a C interval library plus a C++
> wrapper class?

Yes.  There are still template and overloading problems that require a set of adapter declarations, but the layer we implemented is quite thin.

> Then I can use it if I am restricted to C, for some reason.

Or FORTRAN.

>  Or is that an empty opportunity?

In terms of new code the opportunity is probably not large for general applications.  For embedded applications where reliability is very highly prized, we believe there will be substantial demand.

And in terms of maintaining and enhancing existing sofware the opportunity is quite large.

> 
> I appreciate you suggesting that implementations are not
> too hard.  In addition, we should note there are at least a
> couple quite good (tight) implementations of most of the
> common elementary functions, more evidence that a
> vendor's barrier to entry is not high.

We do not have information on the effort required to produce sharp implementations.  But ours is designed for extreme portability, complete consistency (which blunts some results), and maximum rigor with little or no concern for performance.  We expect fast/tight implementations on specific plaforms to be about the same level of difficulty.

> My reservation is that by putting more advanced tools
> (your twin functions) in the hands of people inexperienced
> with interval algorithms, you provide more opportunities
> for screwing up :-)

Other than the multiplication of entities, part of which is mitigated by a simple naming convention, how do twin functions pose a risk?

We have the expectation (based on a small sample of users) that they solve the problem of user frustration with very wide results leading to abandonment of the interval forms.  For example, a user who gets what he considers silly results, such as interval::f() returning [-inf +inf], is tempted to revert to using std::f() because he has no interval alternative that gives him an answer he considers useful.  That is the threat the twin functions tend to counter.

-- Lee Winter

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Le dimanche 04 juin 2006 à 00:30 +0000, first.i.last@comcast.net a
écrit :

> The attached document is a summary aimed at raising issues and
> identifying areas meriting additional discussion rather than a
> comprehensive specification with endless detail but no rationale.
> Therefore readers who are only concerned with concrete suggestions
> should not read it.

If I correctly understand your document, you have extended the atan2
function as three interval functions. For Y=[-1,1] and X=[-2,-1], they
will answer:

        twin_atan2  => [-Pi,-Pi/2] | [Pi/2,Pi]
        atan2_sharp => [Pi/2,3Pi/2]
        atan2_blunt => [-Pi,Pi]

In our current proposal, we have preferred to provide less functions yet
be more generic; this idea was inspired by interval arithmetic libraries
like gaol. First there is an atan2 function which is the natural
interval extension, namely your atan2_blunt function. Second there is a
relational function atan2_rel defined as:

        atan2_rel(Y,X,R) contains { r in R ; cos(r) in X and sin(r) in
        Y }

Because of its two arguments, the atan2 example may not be the clearest
one. So let's consider the acos function instead.two interval functions
are defined:

        acos(X) contains { acos(x) ; x in X } = { r in [0,Pi] ; cos(r) in X }
        acos_rel(X,R) contains { r in R ; cos(r) in X }

Note: if Pi was exactly representable by a floating-point number, only
one function would be needed. The result of acos(X) would be defined as
acos_rel(X,[0,Pi]).

Why provide this function acos_rel? Because it is needed when doing
global optimization and constraints programming. Indeed, after doing
some forward and backward propagations, you usually come to the point
where you have an equality "b = cos(a)" and constraints "a in A" and "b
in B". Then you can compute improved constraints:

        B' <- intersection(cos(A), B)
        A' <- acos_rel(B, A)

If acos_rel was not available, the second assignation could be written
A' <- intersection(acos(B), A). But the set A' would then be wrong if
the initial sets were A = B = [-1,1].

Best regards,

Guillaume

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John and George,

Thanks for the link to your paper "Interval arithmetic with containment 
sets" (2006), submitted to Computing.
It is a fine effort. I think you are on the right track with containment 
sets.
Good luck with the ISL Project !

Ray Moore


----- Original Message ----- 
From: <std-interval-request@compgeom.poly.edu>
To: <std-interval@compgeom.poly.edu>
Sent: Monday, June 05, 2006 6:04 AM
Subject: Std-interval Digest, Vol 5, Issue 5


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> Today's Topics:
>
>   1. Re: list of functions for intervals (George Corliss)
>   2. Re: Interval comparison operators (Dr John Pryce)
>   3. Re: extra functions for intervals (first.i.last@comcast.net)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sun, 04 Jun 2006 20:40:04 -0500
> From: George Corliss <George.Corliss@marquette.edu>
> Subject: Re: [std-interval] list of functions for intervals
> To: For discussions concerning the C++ standardization of intervals
> <std-interval@compgeom.poly.edu>
> Cc: ISL List <isl@interval.louisiana.edu>
> Message-ID: <C0A8F5A4.9C0%George.Corliss@Marquette.edu>
> Content-Type: text/plain; charset="US-ASCII"
>
> Lee and all,
>
> Excellent.  I like your proposal better than mine, but (of course?) I have
> some questions for you and the list.  I had in mind a minimalist standard;
> you are more ambitious.  If we can summon support for an ambitious 
> standard,
> LET'S DO IT.
>
>
> Q1, p. 1, par. 2.  "Standardization of the interval functions should not
> mandate that containment, which is a QoI issue."  Do you mean containment 
> in
> the sense that the set of interval standard functions should contain the
> floating point ones?  Or that (shudder) containment of values returned
> should not be mandated?
>
> Q2, par. 4.  "the result of an interval version of a <cmath> function is 
> the
> hull of all of the results ..." is close to the cset definition, except 
> that
> csets enclose also results of limits.  Several of us are preparing a cset
> draft for posting here within a few days.  _IF_ csets are accepted, say, 
> for
> divide, it would be natural to use them to specify results of cmath
> functions, too?  I'd have to look more closely for differences in returned
> values.
>
> Q3, par. 7. "existence of a type designed to hold multiple instances of
> values"  Such a type could improve the practicality of our cset proposal,
> too.  Thank you!
>
> Q4, par. 9. "wrong" and "nacceptably wide"
> --> "wrong" and "unacceptably wide"
>
>
> Q5. isnan() and nan().  I see where you are going with the "Set of 
> interval
> functions must contain the set of floating-point functions, and interval
> functions on singleton intervals must agree with their floating-point
> counterpart" argument.  I'm sympathetic.
>
> It is a mistake for a standard to give too detailed an implementation, but
> many are concerned that the standard also should not mandate a slow
> implementation.  I assume we want to represent an <empty> set and probably 
> a
> <whole> set.  If we use [NaN, NaN] as an internal, opaque implementation 
> of
> <empty>, there are very few performance-robbing tests.  If an 
> implementation
> DOES decide to use NaN to represent <empty>, I guess isnan() does no harm,
> and I guess nan() would be the equivalent of <empty>.
>
> Q6.  Additions?
>   interval square( interval X )?
>
> Many interval coders are accustomed to
>   double mag( interval X ); // or magnitude := max abs(X)
>   double mig( interval X ); // or mignitude := min abs(X),
> where "abs(X)" is the interval abs as I imagine you'd specify it.
>
> Q7. Function forms of operators: Hooray!  Then the C++ interval is 
> (nearly)
> a C interval library plus a C++ wrapper class?  Then I can use it if I am
> restricted to C, for some reason.  Or is that an empty opportunity?
>
> I appreciate you suggesting that implementations are not too hard.  In
> addition, we should note there are at least a couple quite good (tight)
> implementations of most of the common elementary functions, more evidence
> that a vendor's barrier to entry is not high.
>
> My reservation is that by putting more advanced tools (your twin 
> functions)
> in the hands of people inexperienced with interval algorithms, you provide
> more opportunities for screwing up :-)
>
> (In preparing this response, I have consulted on some, but not all, of 
> these
> points with John Pryce, R. Baker Kearfott, Ned Nedialkov, and Spencer
> Smith.)
>
> Dr. George Corliss
> Electrical and Computer Engineering
> Marquette University
> P.O. Box 1881
> 1515 W. Wisconsin Ave.
> Milwaukee, WI 53201-1881
> George.Corliss@Marquette.edu
> 414-288-6599 (office); 288-4400 (GasDay);
>    288-6280 (Dept.); 288-5579 (fax)
> Office: Haggerty Engineering 296
> Www.eng.mu.edu/corlissg
>
>
> On 6/3/06 7:30 PM, "first.i.last@comcast.net" <first.i.last@comcast.net>
> wrote:
>
>>  -------------- Original message ----------------------
>> From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
>>> Dear all,
>>>
>>> We have been thinking about the list of floating-point functions
>>> which we could propose an interval version for.
>>> More precisely, we have looked at the current list of floating-point
>>> functions from the latest draft of C++0x
>>
>> [...]
>>
>>> What do you think of these lists ?
>>> Is something important excluded ?
>>> Is there anything that should be excluded ?
>>>
>>> Note that existing implementations do not necessarily offer all
>>> proposed functions, so any comment on the implementation
>>> difficulty (for interval<float>, interval<double> and
>>> interval<long double>) would be appreciated.
>>
>> Attached is a file containing comments on the issues you raised and 
>> suggested
>> specifications for many of the functions at issue.  Having studied this 
>> issue
>> in great detail, implemented all of the <cmath> functions, and designed
>> implementations of the c99 functions I can assure you that the 
>> implementation
>> of the interval versions of the <cmath> functions, including disjoint 
>> results,
>> is quite reasonable.
>>
>> Using typical elementary functions as a benchmark (trig, hyperbolics, and
>> exponentials) all but two of the c99 functions require similar or lesser
>> implementation effort.  We are still studying the recalcitrant pair of
>> functions, beta() and ellint_1(), with an eye to efficient and robust
>> implementation.
>>
>> The attached document is a summary aimed at raising issues and 
>> identifying
>> areas meriting additional discussion rather than a comprehensive 
>> specification
>> with endless detail but no rationale.  Therefore readers who are only
>> concerned with concrete suggestions should not read it.
>>
>> -- Lee Winter
>> _______________________________________________
>> Std-interval mailing list
>> Std-interval@compgeom.poly.edu
>> http://compgeom.poly.edu/mailman/listinfo/std-interval
>
>
>
> ------------------------------
>
> Message: 2
> Date: Sun, 04 Jun 2006 23:04:43 +0100
> From: Dr John Pryce <j.d.pryce@ntlworld.com>
> Subject: Re: [std-interval] Interval comparison operators
> To: For discussions concerning the C++ standardization of intervals
> <std-interval@compgeom.poly.edu>, "R. Baker Kearfott"
> <rbk@louisiana.edu>
> Message-ID: <6.2.5.6.0.20060604213551.02ecd4f0@ntlworld.com>
> Content-Type: text/plain; charset="us-ascii"; format=flowed
>
> Lee, and participants in this group
>
> At 19:12 04/06/06, R. Baker Kearfott wrote:
>>My view is that, if there is a hopeless lack of consensus, it may
>>indicate that there isn't a single "right" way, but choosing
>>a particular way and having a standard is better than having none.
>>However, we should strive to maximize the utility of the language
>>in the standard.
>
> Like Baker, I feel optimistic that a consensus will emerge. I
> STRONGLY agree with Baker's paragraph above.
>
> Lee, you have written eloquently of the Principal Value (PV) model
> that you have been working on. If it is as different in
> concept/philosophy/goals (I don't know enough about it to know which
> of those words are most appropriate) from the "classical interval
> model" as you say, then certainly it needs a different standard from
> one that supports the classical model. Therefore, I do not see you as
> in conflict with the classical intervallers, but as complementary.
>
> However I speak as the principal author of containment set (cset)
> theory for the last few years. Csets are NOT the most widely held
> view of classical intervals, and when I started working on them for
> Bill Walster under contract to Sun around 2001 they were generally
> seen as an eccentricity that would soon die out.
>
> Evaluation of cset theory by the interval community was delayed
> slightly by commercial confidentiality. That prohibited putting some
> aspects of csets in the public domain - mainly Sun's implementation
> detail. The main reason for delay was that Bill and I had serious
> disagreement, not over what a cset-based interval implementation
> should do, but about what the results *meant*. I believed, and still
> do, that Bill's philosophy of csets at that time was mathematically
> inconsistent. As a result we could not agree on a paper to submit to
> the open literature. We spoke at conferences etc, but some of the
> assertions we made were incompatible, which was not good for credibility.
>
> Maybe it was a blessing in disguise, because then I joined the ISL
> project steering committee, and working with 3 guys who have jointly
> over 50 years interval programming experience, plus a professional
> software engineer, widened my outlook so that the paper I eventually
> wrote, Pryce and Corliss "Interval arithmetic with containment sets"
> (2006), submitted to "Computing", see
>     http://homepage.ntlworld.com/j.d.pryce/isloct05/IntvlArithCsets.pdf
> was far clearer and more concise than it would otherwise have been.
>
> And, to my surprise, my ISL colleagues decided of their own accord
> that a cset-based interval system was the one they preferred, though
> the well-known packages they had up to then used, and in one case
> written, were based on what I call the Simple System.
>
> How did this come about? I believe it was because I had been able to
> write an account that showed such a system is
> - rock-solid mathematically,
> - actually useful.
>
> Both are necessary conditions for acceptance in this corner of
> scientific computing (sadly, not sufficient). I urge you to move the
> task of writing up what PV intervals are all about to near the top of
> your priorities, if not the actual top. And get it into the open
> literature so that people can pull your ideas to pieces (as my cset
> ideas have been for several years), force you to refine them, and
> eventually be convinced you are making sense.
>
> I find many things you write very weird or downright false (e.g.
> distinctions between line segments and sets, and tests on the empty
> set). That is because I am matching it against my model, which is
> firmly based on classical set theory. You have work to do to convince
> me, but my mind is open. As I am a mathematician, the "rock-solid
> mathematically" interests me more, initially, than the "actually
> useful". I think many people with more interval experience and/or
> more influence in the scientific world than I would agree with me.
>
> PV intervals must be mathematically consistent, or they will die. But
> there is more than that. You must have an underlying purpose for
> them, or philosophy about them, that explains why this consistent bit
> of mathematics actually helps humans solve real life problems. From
> what you write, you are a fair way towards having both, but you won't
> convince the world unless you WRITE IT UP for public evaluation.
>
> Best wishes for that project.
>
> John Pryce
>
>
> ------------------------------
>
> Message: 3
> Date: Mon, 05 Jun 2006 10:17:46 +0000
> From: first.i.last@comcast.net
> Subject: Re: [std-interval] extra functions for intervals
> To: For discussions concerning the C++ standardization of intervals
> <std-interval@compgeom.poly.edu>
> Message-ID:
> <060520061017.1343.448404CA0003420D0000053F22092299279B9C0E04D207D29B9C9D0700@comcast.net>
>
> Content-Type: text/plain; charset="us-ascii"
>
> -------------- Original message ----------------------
> From: George Corliss <George.Corliss@marquette.edu>
>> Lee and all,
>
> [...]
>
>> Q1, p. 1, par. 2.  "Standardization of the interval functions
>> should not mandate that containment, which is a QoI issue."
>>  Do you mean containment in the sense that the set of
>> interval standard functions should contain the floating point
>> ones?  Or that (shudder) containment of values returned
>> should not be mandated?
>
> The latter.  The standard should require that the mathematically correct 
> answer be contained within the interval result.  However, the result of 
> the corresponding floating point function can be arbitrarily far from the 
> mathematically correct answer (QoI of the FP library).  Thus requiring 
> that the FP result be contained within the interval result can have an 
> adverse effect upon the sharpness of the interval result.  So it comes 
> down to a choice between the QoI of the interval implementation versus the 
> consistency between the FP and interval implementations.
>
> We choose consistency for our implementation.  But as much we have a very 
> strong preference for systems that are consistent, we do not believe the 
> standard should make that consistency mandatory because we suspect it 
> would operate to the detriment of the QoI of the interval library.  So we 
> reluctantly suggest that it be left as a recommendation rather than a 
> requirement..  (I would love for
> the consensus to form the opposite conclusion!)
>
>> Q2, par. 4.  "the result of an interval version of a <cmath>
>> function is the hull of all of the results ..." is close to the cset
>> definition, except that csets enclose also results of limits.
>
> And except that cset theory as I comprehend it considers only the numeric 
> values rather than the full spectrum of function results.
>
>> Several of us are preparing a cset draft for posting here
>> within a few days.  _IF_ csets are accepted, say, for
>> divide, it would be natural to use them to specify results of
>> cmath functions, too?  I'd have to look more closely for
>> differences in returned values.
>
> We would love the safe expression rearrangement that a comprehensive cset 
> theory would allow.  And of course that rearrangement should be viable for 
> elementary functions.  So it would appear to be a natural extension of the 
> theory.  But I
> am concerned about the completeness of the theory.  There are function 
> domain issues, the handling of special vaules (Nan & Inf), and the mapping 
> between the real and machine number lines.
>
> The cset issue is certainly bigger than the <cmath> discussion, and might 
> be bigger (or longer) than the standardization discussion.
>
>> Q4, par. 9. "wrong" and "nacceptably wide"
>> --> "wrong" and "unacceptably wide"
>
> Yes.
>
>> Q5. isnan() and nan().  I see where you are going with the
>> "Set of interval functions must contain the set of
>> floating-point functions, and interval functions on singleton
>> intervals must agree with their floating-point counterpart"
>> argument.  I'm sympathetic.
>>
>> It is a mistake for a standard to give too detailed an
>> implementation, but many are concerned that the
>> standard also should not mandate a slow implementation.
>
> On whose hardware?  We intend to buy hardware that will execute a good 
> implementation quickly.  People who buy slow hardware should not blame the 
> standard.
>
> Certainly the standard should not mandate an implementation that _cannot_ 
> be executed efficiently.  But we are far from that.
>
> Historical note: One of the very contentious issues in the original 
> adoption of the IEEE-754 standard was that some major vendors (IBM, DEC, 
> etc.) felt that the extra features such as NaN, Inf, and especially 
> denormal numbers would slow down the processing of normal numbers.  The 
> story is that DEC lost a lot of credit as
> a leader in the field when their rep stated categorically that the 
> proposed features _could_not_ be implemented efficiently.  Of course he 
> was wrong, Intel already had an efficient implementation.
>
> Let us not take counsel of our fears.
>
>> I assume we want to represent an <empty> set and
>> probably a <whole> set.  If we use [NaN, NaN] as an
>> internal, opaque implementation of <empty>, there are
>> very few performance-robbing tests.
>
> My understanding is that Sun choose NaNs for empty due to the similarity 
> of the propagation rules for NaN and empty.  Which means that same thing 
> you said above.
>
> But the standard should neither prohibit nor mandate any implementation of 
> empty.  It should describe the properties of empty completely.  In our 
> view all of those properties (lower, upper, midpt, radius, diameter, etc.) 
> are not numbers.  So they should be NaN or HUGE_VAL depending upon the 
> platform capabilities.
>
>> If an implementation DOES decide to use NaN to represent
>> <empty>, I guess isnan() does no harm, and I guess nan()
>> would be the equivalent of <empty>.
>
> Is there a problem with that?  We tend to view it as a feature.  In fact 
> we support a variety of NaN-based values including:
>    "none"   empty
>    "init"      uninitialized
>    "dead"   destroyed
>    "div0"    division by zero
>    "imag"   sqrt(negative)
>    "EIO "    IO error (read)
>    "EDOM" domain error
>    "ERNG"  range error
>
> All of these are treated as empty.
>
>>
>> Q6.  Additions?
>>    interval square( interval X )?
>
> It is a very specific solution to a widespread problem: inconsistent 
> evaluation of dependencies.  Sun uses automatic identity checking which is 
> a slightly more general solution.
>
> There should be a general solution such as rearrangement at compile time 
> and dependency tracking at run-time.  Note that some kind of ru-time is 
> inevitable because of separate compilation and/or irreducible expressions.
>
>>
>> Many interval coders are accustomed to
>>    double mag( interval X ); // or magnitude := max abs(X)
>>    double mig( interval X ); // or mignitude := min abs(X),
>> where "abs(X)" is the interval abs as I imagine you'd specify it.
>
> We have a "little list" but the functions are not part of <cmath>, which 
> was the subject the proposal team wanted addressed.  I attached a list of 
> examples to this message for the benefit of those interested.
>
>>
>> Q7. Function forms of operators: Hooray!  Then the
>> C++ interval is (nearly) a C interval library plus a C++
>> wrapper class?
>
> Yes.  There are still template and overloading problems that require a set 
> of adapter declarations, but the layer we implemented is quite thin.
>
>> Then I can use it if I am restricted to C, for some reason.
>
> Or FORTRAN.
>
>>  Or is that an empty opportunity?
>
> In terms of new code the opportunity is probably not large for general 
> applications.  For embedded applications where reliability is very highly 
> prized, we believe there will be substantial demand.
>
> And in terms of maintaining and enhancing existing sofware the opportunity 
> is quite large.
>
>>
>> I appreciate you suggesting that implementations are not
>> too hard.  In addition, we should note there are at least a
>> couple quite good (tight) implementations of most of the
>> common elementary functions, more evidence that a
>> vendor's barrier to entry is not high.
>
> We do not have information on the effort required to produce sharp 
> implementations.  But ours is designed for extreme portability, complete 
> consistency (which blunts some results), and maximum rigor with little or 
> no concern for performance.  We expect fast/tight implementations on 
> specific plaforms to be about the same level of difficulty.
>
>> My reservation is that by putting more advanced tools
>> (your twin functions) in the hands of people inexperienced
>> with interval algorithms, you provide more opportunities
>> for screwing up :-)
>
> Other than the multiplication of entities, part of which is mitigated by a 
> simple naming convention, how do twin functions pose a risk?
>
> We have the expectation (based on a small sample of users) that they solve 
> the problem of user frustration with very wide results leading to 
> abandonment of the interval forms.  For example, a user who gets what he 
> considers silly results, such as interval::f() returning [-inf +inf], is 
> tempted to revert to using std::f() because he has no interval alternative 
> that gives him an answer he considers useful.  That is the threat the twin 
> functions tend to counter.
>
> -- Lee Winter
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To: For discussions concerning the C++ standardization of intervals
	<std-interval@compgeom.poly.edu>
From: "R. Baker Kearfott" <rbk@louisiana.edu>
Subject: Re: [std-interval] list of functions for intervals
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Guillaume, Lee,

I am just getting around to reading this thread.  Also, note that the opinions
I give here are my personal ones, subject to change after additional
discussion within this group and within the ISL group.

I quote from the "Example Specifications for Interval Verions (sic) of
<cmath> Functions:"

"A more aggressive interpretation of the compatibility requirement is that 
the result of an interval version of a <cmath> function is the hull of all 
of the results that would be generated by the non-interval version of the 
function if it were fed every combination of non-interval arguments implied 
by the argument intervals."

I agree with the above as a guide for specification of interval
functions.   More precisely, John Pryce's cset theory clarifies
this statement in limiting cases.  

Also, I suggest the the modification,
"contains the hull," rather
than "is the hull."  To demand that it be exactly the hull may be
too difficult in some cases.  In your parlance, "white lies" (meaning
that the returned result isn't the exact range to within roundout,
but merely contains it) are less destructive from a logical point
of view than "outright lies" (where there are values in the range
that are outside the returned result).  The coiners of the idea
"thou shalt not lie" in conjunction with interval arithmetic meant
that the returned result contain the mathematically correct result.
In limiting cases, what is the mathematically correct result is
specified, at least partially, by cset theory.  (There are also
other considerations, such as extending acos to acos_rel, as 
Guillaume suggests.)

If I understand "twin," you envision it to hold two results,
such as returning [-\infty,-1] .union. [1,\infty] as the result
of [1,2] / [-1,1].  I can see a use for that.  However, there is a
"twin arithmetic" in the interval literature that is something else,
so I would recommend using a word other than "twin" in this context. 
I also recommend, if we go this route, that the actual results returned
be set based on the cset theory.

Guillaume,  I understand the  acos_rel can be useful for constraint
propagation.  It seems that similar utility cannot be gained
within Lee's "twin" structure, since the set of all r such that
cos(r) is in X is countably infinite, for a particular x \in X,
-1 <= x <= 1.  Also, results with disjoint intervals as cset,
such as  \sqrt([1,4]) (which yields [-2,1] .union. [1,2] as cset) 
could indeed be handled with sqrt_rel.  All in all, my first impressions
are that this does seem to be somewhat simpler than the "twin" structure.

Sincerely,

Baker

At 03:52 PM 6/5/2006 +0200, Guillaume Melquiond wrote:
>Le dimanche 04 juin 2006 à 00:30 +0000, first.i.last@comcast.net a
>écrit :
>
>> The attached document is a summary aimed at raising issues and
>> identifying areas meriting additional discussion rather than a
>> comprehensive specification with endless detail but no rationale.
>> Therefore readers who are only concerned with concrete suggestions
>> should not read it.
>
>If I correctly understand your document, you have extended the atan2
>function as three interval functions. For Y=[-1,1] and X=[-2,-1], they
>will answer:
>
>        twin_atan2  => [-Pi,-Pi/2] | [Pi/2,Pi]
>        atan2_sharp => [Pi/2,3Pi/2]
>        atan2_blunt => [-Pi,Pi]
>
>In our current proposal, we have preferred to provide less functions yet
>be more generic; this idea was inspired by interval arithmetic libraries
>like gaol. First there is an atan2 function which is the natural
>interval extension, namely your atan2_blunt function. Second there is a
>relational function atan2_rel defined as:
>
>        atan2_rel(Y,X,R) contains { r in R ; cos(r) in X and sin(r) in
>        Y }
>
>Because of its two arguments, the atan2 example may not be the clearest
>one. So let's consider the acos function instead.two interval functions
>are defined:
>
>        acos(X) contains { acos(x) ; x in X } = { r in [0,Pi] ; cos(r) in X }
>        acos_rel(X,R) contains { r in R ; cos(r) in X }
>
>Note: if Pi was exactly representable by a floating-point number, only
>one function would be needed. The result of acos(X) would be defined as
>acos_rel(X,[0,Pi]).
>
>Why provide this function acos_rel? Because it is needed when doing
>global optimization and constraints programming. Indeed, after doing
>some forward and backward propagations, you usually come to the point
>where you have an equality "b = cos(a)" and constraints "a in A" and "b
>in B". Then you can compute improved constraints:
>
>        B' <- intersection(cos(A), B)
>        A' <- acos_rel(B, A)
>
>If acos_rel was not available, the second assignation could be written
>A' <- intersection(acos(B), A). But the set A' would then be wrong if
>the initial sets were A = B = [-1,1].
>
>Best regards,
>
>Guillaume
>
>_______________________________________________
>Std-interval mailing list
>Std-interval@compgeom.poly.edu
>http://compgeom.poly.edu/mailman/listinfo/std-interval
>
>

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------


From rbk@louisiana.edu Mon Jun  5 09:51:47 2006
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From: "R. Baker Kearfott" <rbk@louisiana.edu>
Subject: more Re: [std-interval] list of functions for intervals
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Guillaume,

What if, in your example below, R contains two disjoint segments
of points r such that cos(r) \in R?  Would you return the interval
hull?  In fact, R could possibly contain an arbitrary number of
such segments.  Thus, acos_rel does give additional utility for
constraint propagation, but can't give the exact cset in all cases.
Also, I note that Lee's "twin" idea, if I understand it correctly,
doesn't handle the case with more than two disjoint intervals in the
cset.  At some point, I'm guessing that we need to accept what
Lee calls "white lies" in some cases, and design a standard that is
a good balance between simplicity and utility in a wide variety
of applications.  (We should also try to not prohibit vendors from
doing more, if they see a market.)

Best regards,

Baker

>Date: Mon, 05 Jun 2006 10:26:11 -0500
>To: For discussions concerning the C++ standardization of intervals
>	<std-interval@compgeom.poly.edu>
>From: "R. Baker Kearfott" <rbk@louisiana.edu>
>Subject: Re: [std-interval] list of functions for intervals
>
>Guillaume, Lee,
>
>I am just getting around to reading this thread.  Also, note that the opinions
>I give here are my personal ones, subject to change after additional
>discussion within this group and within the ISL group.
>
>I quote from the "Example Specifications for Interval Verions (sic) of
><cmath> Functions:"
>
>"A more aggressive interpretation of the compatibility requirement is that 
>the result of an interval version of a <cmath> function is the hull of all 
>of the results that would be generated by the non-interval version of the 
>function if it were fed every combination of non-interval arguments implied 
>by the argument intervals."
>
>I agree with the above as a guide for specification of interval
>functions.   More precisely, John Pryce's cset theory clarifies
>this statement in limiting cases.  
>
>Also, I suggest the the modification,
>"contains the hull," rather
>than "is the hull."  To demand that it be exactly the hull may be
>too difficult in some cases.  In your parlance, "white lies" (meaning
>that the returned result isn't the exact range to within roundout,
>but merely contains it) are less destructive from a logical point
>of view than "outright lies" (where there are values in the range
>that are outside the returned result).  The coiners of the idea
>"thou shalt not lie" in conjunction with interval arithmetic meant
>that the returned result contain the mathematically correct result.
>In limiting cases, what is the mathematically correct result is
>specified, at least partially, by cset theory.  (There are also
>other considerations, such as extending acos to acos_rel, as 
>Guillaume suggests.)
>
>If I understand "twin," you envision it to hold two results,
>such as returning [-\infty,-1] .union. [1,\infty] as the result
>of [1,2] / [-1,1].  I can see a use for that.  However, there is a
>"twin arithmetic" in the interval literature that is something else,
>so I would recommend using a word other than "twin" in this context. 
>I also recommend, if we go this route, that the actual results returned
>be set based on the cset theory.
>
>Guillaume,  I understand the  acos_rel can be useful for constraint
>propagation.  It seems that similar utility cannot be gained
>within Lee's "twin" structure, since the set of all r such that
>cos(r) is in X is countably infinite, for a particular x \in X,
>-1 <= x <= 1.  Also, results with disjoint intervals as cset,
>such as  \sqrt([1,4]) (which yields [-2,1] .union. [1,2] as cset) 
>could indeed be handled with sqrt_rel.  All in all, my first impressions
>are that this does seem to be somewhat simpler than the "twin" structure.
>
>Sincerely,
>
>Baker
>
>At 03:52 PM 6/5/2006 +0200, Guillaume Melquiond wrote:
>>Le dimanche 04 juin 2006 à 00:30 +0000, first.i.last@comcast.net a
>>écrit :
>>
>>> The attached document is a summary aimed at raising issues and
>>> identifying areas meriting additional discussion rather than a
>>> comprehensive specification with endless detail but no rationale.
>>> Therefore readers who are only concerned with concrete suggestions
>>> should not read it.
>>
>>If I correctly understand your document, you have extended the atan2
>>function as three interval functions. For Y=[-1,1] and X=[-2,-1], they
>>will answer:
>>
>>        twin_atan2  => [-Pi,-Pi/2] | [Pi/2,Pi]
>>        atan2_sharp => [Pi/2,3Pi/2]
>>        atan2_blunt => [-Pi,Pi]
>>
>>In our current proposal, we have preferred to provide less functions yet
>>be more generic; this idea was inspired by interval arithmetic libraries
>>like gaol. First there is an atan2 function which is the natural
>>interval extension, namely your atan2_blunt function. Second there is a
>>relational function atan2_rel defined as:
>>
>>        atan2_rel(Y,X,R) contains { r in R ; cos(r) in X and sin(r) in
>>        Y }
>>
>>Because of its two arguments, the atan2 example may not be the clearest
>>one. So let's consider the acos function instead.two interval functions
>>are defined:
>>
>>        acos(X) contains { acos(x) ; x in X } = { r in [0,Pi] ; cos(r) in X }
>>        acos_rel(X,R) contains { r in R ; cos(r) in X }
>>
>>Note: if Pi was exactly representable by a floating-point number, only
>>one function would be needed. The result of acos(X) would be defined as
>>acos_rel(X,[0,Pi]).
>>
>>Why provide this function acos_rel? Because it is needed when doing
>>global optimization and constraints programming. Indeed, after doing
>>some forward and backward propagations, you usually come to the point
>>where you have an equality "b = cos(a)" and constraints "a in A" and "b
>>in B". Then you can compute improved constraints:
>>
>>        B' <- intersection(cos(A), B)
>>        A' <- acos_rel(B, A)
>>
>>If acos_rel was not available, the second assignation could be written
>>A' <- intersection(acos(B), A). But the set A' would then be wrong if
>>the initial sets were A = B = [-1,1].
>>
>>Best regards,
>>
>>Guillaume
>>
>>_______________________________________________
>>Std-interval mailing list
>>Std-interval@compgeom.poly.edu
>>http://compgeom.poly.edu/mailman/listinfo/std-interval
>>
>>
>
>---------------------------------------------------------------
>R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
>(337) 482-5270 (work)                     (337) 993-1827 (home)
>URL: http://interval.louisiana.edu/kearfott.html
>Department of Mathematics, University of Louisiana at Lafayette
>(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
>Box 4-1010, Lafayette, LA 70504-1010, USA
>---------------------------------------------------------------
>
>
>_______________________________________________
>Std-interval mailing list
>Std-interval@compgeom.poly.edu
>http://compgeom.poly.edu/mailman/listinfo/std-interval
>
>

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------


From first.i.last@comcast.net Mon Jun  5 10:15:12 2006
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Subject: Re: [std-interval] cset theory as fundamental
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 -------------- Original message ----------------------
From: "R. Baker Kearfott" <rbk@louisiana.edu>
> Guillaume, Lee,
> 

[...]

> I quote from the "Example Specifications for Interval Verions
> (sic) of <cmath> Functions:"
> 
> "A more aggressive interpretation of the compatibility
> requirement is that the result of an interval version
> of a <cmath> function is the hull of all  of the results
> that would be generated by the non-interval version
> of the function if it were fed every combination of
> non-interval arguments implied by the argument intervals."
> 
> I agree with the above as a guide for specification of interval
> functions.   More precisely, John Pryce's cset theory clarifies
> this statement in limiting cases. 

As I understand the cset theory it contains only the numeric function results (including +/-inf) and does not address the issue of a function whose return values could be NaN.

In addition the cset theory appears to apply to the mathemetically correct value is if computed with arbitrary precision, while the above was intended to propose the inclusion of the result computed by the coresponding finite precision floating point implementation.  The mathematically correct result and the floating point result are usually not identical.
 
> 
> Also, I suggest the the modification, "contains the hull," rather
> than "is the hull."  To demand that it be exactly the hull may be
> too difficult in some cases.

I understand the issue, but stand by the proposed criteria in the sense that it sets the desired standard.  IFF there are cases that are too hard/slow they should be described in some way as exceptions from the normal/general expectations.  Those exceptions should be implementation defined.

The rationale we used for propsing that standard is that "contains the hull" (of the floating point implementation) is quite a general permission for bluntness.  The existence of that permission tends to erode the confidence of new users.  Like maintaining a public bug list demonstrates the confidence of software develpers and builds confidence in the sofware users (that they will not be blind-sided), so too do explicit bluntness specs demonstrate the confidence of the implementors and build confidence in the interval users that they will not get useless results.

This may be more of a sales issue than a correctness issue.  But there are a very large number of users who need to be convinced that intervals are worth considering as a replacement for floating point.

> In your parlance, "white lies" (meaning
> that the returned result isn't the exact range to within roundout,
> but merely contains it) are less destructive from a logical point
> of view than "outright lies" (where there are values in the range
> that are outside the returned result).  The coiners of the idea
> "thou shalt not lie" in conjunction with interval arithmetic meant
> that the returned result contain the mathematically correct result.
> In limiting cases, what is the mathematically correct result is
> specified, at least partially, by cset theory.  (There are also
> other considerations, such as extending acos to acos_rel, as 
> Guillaume suggests.)

Understood.  My version of the proposal is clearly out of date with respect to relational extensions (2005-08-01).

> 
> If I understand "twin," you envision it to hold two results,
> such as returning [-\infty,-1] .union. [1,\infty] as the result
> of [1,2] / [-1,1].  I can see a use for that.  However, there is a
> "twin arithmetic" in the interval literature that is something else,
> so I would recommend using a word other than "twin" in this context. 

OK.  Good point.

> I also recommend, if we go this route, that the actual
> results returned be set based on the cset theory.

What is it about disjoint results in particular that recommends the cset theory over the alternative classical interval theories?

-- Lee Winter

From rbk@louisiana.edu Mon Jun  5 11:07:25 2006
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Lee (C++ standardization, and ISL),

At 05:29 PM 6/5/2006 +0000, first.i.last@comcast.net wrote:
> -------------- Original message ----------------------
>From: "R. Baker Kearfott" <rbk@louisiana.edu>
>> Guillaume, Lee,
>> 
>
>[...]
>

>> 
>> If I understand "twin," you envision it to hold two results,
>> such as returning [-\infty,-1] .union. [1,\infty] as the result
>> of [1,2] / [-1,1].  I can see a use for that.  However, there is a
>> "twin arithmetic" in the interval literature that is something else,
>> so I would recommend using a word other than "twin" in this context. 
>
>OK.  Good point.
>
>> I also recommend, if we go this route, that the actual
>> results returned be set based on the cset theory.
>
>What is it about disjoint results in particular that recommends the cset
theory over the alternative classical interval theories?
>

I am recommending cset arithmetic generally because it is an extensively
well-thought-out theory that guides specification of results and gives
results that are provable.  Having worked with extended interval
arithmetic for quite some time, I've found specifications to sometimes
be ad-hoc and to perhaps give unexpected results to someone not
familiar with the particular implementation. For instance, there is a
significant (>3) number of different ways I have seen division by 
an interval that contains zero defined. With a solid mathematical
theory, it both constrains the way the results can be define and 
allows one to predict what the computations will do. 

There is nothing about disjoint results in particular that leads me
to recommend cset theory, other than in cases, such as division by
an interval that contains zero, when the disjoint results are obtained
as limiting cases.

To what "alternative classical theory" are you referring?

In any case, John may have some additional comment on this.

Sincerely,

Baker

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------

From guillaume.melquiond@ens-lyon.fr Mon Jun  5 12:02:11 2006
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Subject: Re: more Re: [std-interval] list of functions for intervals
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
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Le lundi 05 juin 2006 à 12:05 -0500, R. Baker Kearfott a écrit :
> What if, in your example below, R contains two disjoint segments
> of points r such that cos(r) \in R?  Would you return the interval
> hull?

Yes, the result is an interval and it contains all the values matching
the relation, so that the result does not lie. But I don't see this
truth as an issue. Indeed, lots of interval applications tend to split
their domain into sub-domains if the results they have computed are not
precise enough. In that case, they will get to a point where the various
Rs contain only one single contiguous interval.

> In fact, R could possibly contain an arbitrary number of
> such segments.  Thus, acos_rel does give additional utility for
> constraint propagation, but can't give the exact cset in all cases.

Right, but this is a proposal for interval arithmetic, not for arbitrary
set arithmetic. Having acos_rel([0,1], [-inf,inf]) return an infinite
set of implicitly defined intervals is possible but it goes well beyond
what we want to propose here.

And obtaining the "exact" cset is anyway out-of-reach because of bounds
rounding. As a matter of fact, this rounding phenomenon is why I'm not
really fond of cset intervals when they have floating-point bounds (I'm
only speaking for myself here). For example, it means that multiplying
four intervals containing positive and finite numbers can lead to an
interval containing negative values. But I'm digressing.

> Also, I note that Lee's "twin" idea, if I understand it correctly,
> doesn't handle the case with more than two disjoint intervals in the
> cset.  At some point, I'm guessing that we need to accept what
> Lee calls "white lies" in some cases, and design a standard that is
> a good balance between simplicity and utility in a wide variety
> of applications.

Note that Lee's twin idea is fundamentally different from the idea I
presented. First, it only applies to atan2 with respect to trigonometric
functions. For example, there is no meaning in a twin version of acos
since the set extension of acos only returns intervals when it is fed
with intervals. Second, the result of the twin version of atan2 is
constrained to [-Pi,Pi] while cosine and sine on the whole real line.

I'm not saying that the twin idea is a bad idea. As a matter of fact we
have used it for the division in the Boost library, and I still think it
was a good idea. I'm just saying that this is not what people doing
constraints programming are expecting in my opinion. But this could be
useful for other people.

Best regards,

Guillaume

From rbk@louisiana.edu Mon Jun  5 12:29:23 2006
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Guillaume,

At 09:16 PM 6/5/2006 +0200, Guillaume Melquiond wrote:
>Le lundi 05 juin 2006 à 12:05 -0500, R. Baker Kearfott a écrit :
>> What if, in your example below, R contains two disjoint segments
>> of points r such that cos(r) \in R?  Would you return the interval
>> hull?
>
>Yes, the result is an interval and it contains all the values matching
>the relation, so that the result does not lie. But I don't see this
>truth as an issue. Indeed, lots of interval applications tend to split
>their domain into sub-domains if the results they have computed are not
>precise enough. In that case, they will get to a point where the various
>Rs contain only one single contiguous interval.
>
>> In fact, R could possibly contain an arbitrary number of
>> such segments.  Thus, acos_rel does give additional utility for
>> constraint propagation, but can't give the exact cset in all cases.
>
>Right, but this is a proposal for interval arithmetic, not for arbitrary
>set arithmetic. Having acos_rel([0,1], [-inf,inf]) return an infinite
>set of implicitly defined intervals is possible but it goes well beyond
>what we want to propose here.
>

I agree fully with the above choice.  I have previously thought 
a bit about arbitrary set arithmetic, and am of the opinion that
it is more complicated than something we want to standardize at
present.

>And obtaining the "exact" cset is anyway out-of-reach because of bounds
>rounding. As a matter of fact, this rounding phenomenon is why I'm not
>really fond of cset intervals when they have floating-point bounds (I'm
>only speaking for myself here). For example, it means that multiplying
>four intervals containing positive and finite numbers can lead to an
>interval containing negative values. But I'm digressing.
>

Picking up on your "digression," I don't see how multiplying four positive
intervals and getting an interval containing negative numbers as 
a result is related to cset arithmetic.  Isn't this related to
the definition of interval multiplication, which, for finite intervals,
is the same as the old-fashioned definition of multiplication
of intervals?  That is, isn't this a quality of implementation issue?
(Lower bounds that are positive but rounded down should be rounded
down to exactly zero, and a result that is exactly zero shouldn't 
be rounded down. Isn't that what IEEE-754 does?)  Otherwise, are
you thinking of an example with infinite end points that I missed?

>> Also, I note that Lee's "twin" idea, if I understand it correctly,
>> doesn't handle the case with more than two disjoint intervals in the
>> cset.  At some point, I'm guessing that we need to accept what
>> Lee calls "white lies" in some cases, and design a standard that is
>> a good balance between simplicity and utility in a wide variety
>> of applications.
>
>Note that Lee's twin idea is fundamentally different from the idea I
>presented. 

Yes, it is different, for a different purpose.

>First, it only applies to atan2 with respect to trigonometric
>functions. For example, there is no meaning in a twin version of acos
>since the set extension of acos only returns intervals when it is fed
>with intervals. Second, the result of the twin version of atan2 is
>constrained to [-Pi,Pi] while cosine and sine on the whole real line.
>
>I'm not saying that the twin idea is a bad idea. As a matter of fact we
>have used it for the division in the Boost library, and I still think it
>was a good idea. I'm just saying that this is not what people doing
>constraints programming are expecting in my opinion. But this could be
>useful for other people.
>


Yes, I understand the use of the acos_rel function in constraint
propagation.  I also think I understand that Lee's idea is to extend
all floating point functions in a natural way, using the classically
restricted domains of the inverse trig functions.
 
Best regards,

Baker

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------


From rmoore17@columbus.rr.com Mon Jun  5 12:46:48 2006
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John and all,

The one thing that bothers me about the cset approach is=20
returning a result like [0, 1] when feeding the argument=20
[-4, 1] to the square root function. I mean there is a very useful =
extension of the square root function to complex values, for which the =
result would be something else, like
[0, 1] U [-2, 2] i.

I understand the difficulty of allowing complex values. To make it =
complete would be another huge project on top of all that is already =
underway.

However, otherwise it will necessary to explain the restriction to real =
results. Furthermore, things like
(sqrt [-4, 1])^4 would produce [0, 1] without including complex numbers, =
whereas it should produce [0, 16]
with complex numbers allowed.=20

What is the proposal for dealing with such concerns ?

Ray Moore
 
------=_NextPart_000_000D_01C688B9.34289540
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	charset="iso-8859-1"
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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charset=3Diso-8859-1">
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<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>John and all,</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>The one thing that bothers me about the =
cset=20
approach is </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>returning a result like [0, 1] when =
feeding the=20
argument </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>[-4, 1] to the square root function. I =
mean there=20
is a very useful extension of the square root function to complex =
values, for=20
which the result would be something else,&nbsp;like</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>[0, 1] U [-2, 2] i.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>I understand the difficulty of allowing =
complex=20
values. To make it complete would be another huge project on top of all =
that is=20
already underway.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>However, otherwise&nbsp;it&nbsp;will =
necessary to=20
explain the restriction to real results. Furthermore, things =
like</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>(sqrt [-4, 1])^4 would produce [0, 1] =
without=20
including complex numbers, whereas it should produce [0, =
16]</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>with complex numbers allowed. =
</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>What is the proposal for dealing with =
such concerns=20
?</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Ray Moore</FONT></DIV>
<DIV>&nbsp;</DIV></BODY></HTML>

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From guillaume.melquiond@ens-lyon.fr Mon Jun  5 12:47:51 2006
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Le lundi 05 juin 2006 à 14:43 -0500, R. Baker Kearfott a écrit :

> Picking up on your "digression," I don't see how multiplying four positive
> intervals and getting an interval containing negative numbers as 
> a result is related to cset arithmetic.  Isn't this related to
> the definition of interval multiplication, which, for finite intervals,
> is the same as the old-fashioned definition of multiplication
> of intervals?  That is, isn't this a quality of implementation issue?
> (Lower bounds that are positive but rounded down should be rounded
> down to exactly zero, and a result that is exactly zero shouldn't 
> be rounded down. Isn't that what IEEE-754 does?)  Otherwise, are
> you thinking of an example with infinite end points that I missed?

Yes, an infinite end-point is involved. But this is unfortunately easy
to obtain because of rounding. For example,

interval<double>
  a(1.3e-200, 5), b(2.7e-150, 8), c(0.8, 4.2e100), d(17, 7.3e250),
  e = (a * b) * (c * d);

The lower bound of a * b is rounded to zero and the upper bound of c * d
is rounded to infinity in double precision floating-point arithmetic. As
a consequence, their product e will contain negative values. Indeed the
cset of 0*inf contains -inf; hence e is forced to include the whole
extended real line. Without rounding (e.g. with rational bounds),
interval e would have contained only positive and finite values. With
rounding and without cset, interval e would have been [0,+inf).

By reverting the bounds, it is possible to distinguish between
overflowed infinities and real infinities (I think there is a paper by
Hickey on this subject) and hence prevent this issue. But interval
computations will get a bit expensive because of this trick.

Best regards,

Guillaume

From hbr@poly.edu Mon Jun  5 13:00:19 2006
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Dear Ray:
In the interval proposal as it stands, we have considered this and  
also proposed to ignore negative values in sqrt. There is an item in  
the rationale about this:

> — What is the behavior on out-of-range argument values? E.g.,  
> should sqrt(x) throw if interval
> x contains negative values?

> We decided to interpret the inclusion property as allowing negative  
> values for sqrt without throwing
> exception, simply saying that sqrt(i) contains sqrt(x) for any  
> positive x in i (and is empty if i is
> entirely negative). Similarly for any function whose domain is a  
> subset of the representable T. This is
> the most inclusive view since it allows for silent error  
> propagation and recovery for sqrt(i) where
> i is (in theory) guaranteed to represent a positive number but its  
> interval enclosure contains negative
> numbers.

Note that this will be the overwhelmingly common case, due to  
roundoff errors. Thus likely sqrt(x) will be invoked with very small  
values for inf(x). And the user should either be guaranteed that x  
represents a non-negative number (hence the inclusion property is not  
violated), or manually test that x>=0, which if this is done using  
intervals, will also correctly detect the cases where x could be  
negative, in which case the user will necessarily have to handle the  
situation.

> Note that, it is always possible for the user to check manually the  
> range of the arguments (e.g.,
> does i contain negative numbers) and to choose the appropriate  
> action. As Bill Walster puts it:
> “Depending on the context, an empty result of an arithmetic  
> operation or function evaluation may
> or may not indicate that an error has been made. An exception-like  
> feature is needed to provide
> a test for expression continuity, which is an assumption for the  
> interval Newton algorithm and the
> Brouwer fixed-point theorem. This will only be needed in special  
> circumstances and therefore needs
> to be invokable only when required.”

In response to your concern about imaginary numbers:  if (sqrt [-4,  
1])^4 is indeed intended to return [0,16], then special handling is  
necessary from the user of the class interval<> since the class won't  
do it by itself.  On the other hand, it's not impossible to extend  
complex< interval<T> > (although the effect is unspecified in the C++  
standard, and therefore non-portable). But that is clearly not what  
we intend to standardize.

Regards,
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu


On Jun 5, 2006, at 10:00 PM, Ray Moore wrote:

> John and all,
>
> The one thing that bothers me about the cset approach is
> returning a result like [0, 1] when feeding the argument
> [-4, 1] to the square root function. I mean there is a very useful  
> extension of the square root function to complex values, for which  
> the result would be something else, like
> [0, 1] U [-2, 2] i.
>
> I understand the difficulty of allowing complex values. To make it  
> complete would be another huge project on top of all that is  
> already underway.
>
> However, otherwise it will necessary to explain the restriction to  
> real results. Furthermore, things like
> (sqrt [-4, 1])^4 would produce [0, 1] without including complex  
> numbers, whereas it should produce [0, 16]
> with complex numbers allowed.
>
> What is the proposal for dealing with such concerns ?
>
> Ray Moore
>
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval


From fernando_cacciola@datafull.com Mon Jun  5 13:00:25 2006
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Guillaume Melquiond wrote:
>
>        A' <- acos_rel(B, A)
>
> If acos_rel was not available, the second assignation could be written
> A' <- intersection(acos(B), A). But the set A' would then be wrong if
> the initial sets were A = B = [-1,1].
>
Hmm, I thought I understood the xyz_rel(X,R) functions to be precisely the 
equivalent of intersection(xyz(X),R), yet you explicetely state here that is 
not; but I can't follow: why would intersection(acos([-1,1]),[-1,1]) be 
wrong? That is, what exactly is the result of acos_rel([-1,1],[-1,1]) and 
how is that different from the explicit restriction to R?

TIA

Fernando Cacciola
SciSoft
http://fcacciola.50webs.com/


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Guillaume,

At 10:01 PM 6/5/2006 +0200, Guillaume Melquiond wrote:
>Le lundi 05 juin 2006 à 14:43 -0500, R. Baker Kearfott a écrit :
>
>> Picking up on your "digression," I don't see how multiplying four positive
>> intervals and getting an interval containing negative numbers as 
>> a result is related to cset arithmetic.  Isn't this related to
>> the definition of interval multiplication, which, for finite intervals,
>> is the same as the old-fashioned definition of multiplication
>> of intervals?  That is, isn't this a quality of implementation issue?
>> (Lower bounds that are positive but rounded down should be rounded
>> down to exactly zero, and a result that is exactly zero shouldn't 
>> be rounded down. Isn't that what IEEE-754 does?)  Otherwise, are
>> you thinking of an example with infinite end points that I missed?
>
>Yes, an infinite end-point is involved. But this is unfortunately easy
>to obtain because of rounding. For example,
>
>interval<double>
>  a(1.3e-200, 5), b(2.7e-150, 8), c(0.8, 4.2e100), d(17, 7.3e250),
>  e = (a * b) * (c * d);
>
>The lower bound of a * b is rounded to zero and the upper bound of c * d
>is rounded to infinity in double precision floating-point arithmetic. As
>a consequence, their product e will contain negative values. Indeed the
>cset of 0*inf contains -inf; hence e is forced to include the whole
>extended real line. Without rounding (e.g. with rational bounds),
>interval e would have contained only positive and finite values. With
>rounding and without cset, interval e would have been [0,+inf).
>

Thank you.  That clarifies it.  

Let me think about this some more and also allow (possibly) others to
respond.  I'm thinking there are possibly other cases where not including
the -\infty will result in a set that does not contain points that
are expected.

>By reverting the bounds, it is possible to distinguish between
>overflowed infinities and real infinities (I think there is a paper by
>Hickey on this subject) and hence prevent this issue. But interval
>computations will get a bit expensive because of this trick.
>

That is true.  Also, certainly, we'd like the interval arithmetic to
be reasonably fast.  However, regardless of exactly how the extended
interval arithmetic is defined in the standard, it should be possible
to make it clear to users, in a simple explanation, what particular
results will be.  If cset arithmetic is used, hopefully there aren't
too many cases in which what classically has been called "overflows"
and "underflows" occur :-)

Best regards,

Baker
 

---------------------------------------------------------------
R. Baker Kearfott,    rbk@louisiana.edu   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------


From eliasen@mindspring.com Mon Jun  5 14:00:03 2006
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> On Jun 1, 2006, at 3:25 AM, Alan Eliasen wrote:
> 
>> I know of no portable functions other than std::isnan()
>> (defined in cmath) which simply detects if it's a NaN or not, so you
>> shouldn't even expect to differentiate between these two.

Hervé Brönnimann wrote:
> FWIW, std::numeric_limits<T> has members has_quiet_NaN and 
> has_signaling_NaN along with quiet_NaN and signaling_NaN.  What you  can
> expect is to differentiate between them IF your platform supports  them
> (and the numeric_limits given by your system is accurate for the 
> platform, as it should).

   If the implementations I've looked at are proper, has_quiet_NaN and
has_signaling_NaN are only boolean fields (not functions!) which only
tell you if a particular numeric type (e.g. double or int) has a special
value which could represent those NaNs.  They tell you nothing about
whether a particular number *is* a NaN of either type.

   In, say, gcc 4.1.1, has_signaling_NaN is simply defined as:

 static const bool has_signaling_NaN = has_quiet_NaN;

   So, again, without lack of evidence to the contrary, I stand by my
assertion that isnan() is the only standard function available to detect
if a number is a NaN or not, and it can't distinguish between quiet and
signaling NaNs.

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu

From guillaume.melquiond@ens-lyon.fr Mon Jun  5 14:11:31 2006
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Subject: Re: [std-interval] list of functions for intervals
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Le lundi 05 juin 2006 à 17:17 -0300, Fernando Cacciola a écrit :
> Guillaume Melquiond wrote:
> >
> >        A' <- acos_rel(B, A)
> >
> > If acos_rel was not available, the second assignation could be written
> > A' <- intersection(acos(B), A). But the set A' would then be wrong if
> > the initial sets were A = B = [-1,1].
> >
> Hmm, I thought I understood the xyz_rel(X,R) functions to be precisely the 
> equivalent of intersection(xyz(X),R), yet you explicetely state here that is 

If they simply were some intersections, there wouldn't be much point in
adding these functions :-).

> not; but I can't follow: why would intersection(acos([-1,1]),[-1,1]) be 
> wrong? That is, what exactly is the result of acos_rel([-1,1],[-1,1]) and 
> how is that different from the explicit restriction to R?

When R is included in the domain of the reciprocal function and the set
intersection of the set result with R is contiguous, then both
expressions will have the same result. For acos_rel([-1,1],[-1,1]), the
intersection is indeed contiguous, but R is not included in the domain
(for acos it is [0,Pi]), so this will give different results:

intersection(acos([-1,1]), [-1,1]) = [0,1]
acos_rel([-1,1], [-1,1]) = [-1,1]

Indeed, the set of values x in [-1,1] such that cos(x) is in [-1,1]
(always true) is simply [-1,1]. This example may seem idiotic so let's
consider smaller intervals: what are the values x in [-0.2,-0.1] such
that cos(x) is in [0.99,1]?

The answer as a set is [-0.142,-0.1]. Since this is a contiguous set,
this will be the interval result given by acos_rel. On the other hand,
acos([0.99,1]) = [0,0.142], so the intersection would have given the
empty set (meaning that there is no solution, this is wrong). The
xyz_rel functions are meant as a tool to correctly solve (in)equations
involving trigonometric functions.

Best regards,

Guillaume

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 -------------- Original message ----------------------
From: Alan Eliasen <eliasen@mindspring.com>

> So, again, without lack of evidence to the contrary, I stand
> by my assertion that isnan() is the only standard function
> available to detect if a number is a NaN or not, and it
> can't distinguish between quiet and signaling NaNs.

Do you not like the use of fpclassify() to detect NaNs?  On x86 platforms there is hardware support for classification based on the fxam instruction.

-- Lee Winter
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 -------------- Original message ----------------------
From: Guillaume Melquiond <guillaume.melquiond@ens-lyon.fr>
> Le lundi 05 juin 2006 à 14:43 -0500, R. Baker Kearfott a écrit :
> 

[...]

> Indeed the cset of 0*inf contains -inf; hence e is forced to include the whole extended real line. 

[...]

> Without rounding (e.g. with rational bounds),
> interval e would have contained only positive and finite values. With
> rounding and without cset, interval e would have been [0,+inf).

This is an issue with the present state-of-the-art in csets, but I believe it to be fixable.  It derives from the concern over the topology of the number line near zero, but I believe there at least one sensible and rigorous definition that can be used to eliminate the issue and restore the IEEE-754 sense of rounding.

-- Lee Winter
From eliasen@mindspring.com Mon Jun  5 22:25:53 2006
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Alan Eliasen wrote:
>> So, again, without lack of evidence to the contrary, I stand by my
>> assertion that isnan() is the only standard function available to
>> detect if a number is a NaN or not, and it can't distinguish
>> between quiet and signaling NaNs.

Lee Winter wrote:
> Do you not like the use of fpclassify() to detect NaNs?  On x86
> platforms there is hardware support for classification based on the
> fxam instruction.

   Thanks; I was not aware of fpclassify, only the boolean conditions
like isnan().  It appears from the documentation in gcc 4.1.1 that
isnan() "returns a non-zero value if (fpclassify(x) == FP_NAN)", so one
is simply defined in terms of the other, and confers no clear advantages
when testing for NaN.

   Still, it doesn't affect my point that there isn't a standardized
function to distinguish between quiet and signaling NaNs, other than
working directly with the bit patterns as I noted in my first posting on
the subject.

-- 
  Alan Eliasen                 |  "When trouble is solved before it
  eliasen@mindspring.com       |    forms, who calls that clever?"
  http://futureboy.us/         |              --Sun Tzu
From j.d.pryce@ntlworld.com Tue Jun  6 02:20:39 2006
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Subject: Re: [std-interval] csets
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Ray and all

At 21:00 05/06/06, Ray Moore wrote:
>The one thing that bothers me about the cset approach is
>returning a result like [0, 1] when feeding the argument
>[-4, 1] to the square root function. I mean there is a very useful 
>extension of the square root function to complex values, for which 
>the result would be something else, like
>[0, 1] U [-2, 2] i.
>
>I understand the difficulty of allowing complex values. To make it 
>complete would be another huge project on top of all that is already underway.
>
>However, otherwise it will necessary to explain the restriction to 
>real results. Furthermore, things like
>(sqrt [-4, 1])^4 would produce [0, 1] without including complex 
>numbers, whereas it should produce [0, 16]
>with complex numbers allowed.
>
>What is the proposal for dealing with such concerns ?

I will answer the query "how to apply csets over the complex 
numbers?" (mathematics). That leaves aside the important question of 
"when, in a program, to decide to move from the reals to the complex 
numbers?" (language and library design and semantics).-

To set up a cset system you need
- An underlying number system S - preferably a field such as the 
reals or complex numbers of course.
- A compact topological space S* in which S is embedded as a dense subset.

Then the cset value of any (possibly vector) "function of 
S-variables", i.e. f : S^n -> S^m, is defined for any subset of 
(S*)^n to be a subset of (S*)^m, defined in terms of graph closure. 
Compactness implies the Fundamental Theorem holds, which ensures 
containment in the resulting interval system.

To convert this into an interval cset system you need
- A set I of subsets of S* that you deem to be "intervals". They must 
be compact, and the S* must be a member of I.
- An algorithm "interval hull" that encloses an arbitrary subset X of 
S* in a member of I, call it hull(X). This is the "exact arithmetic" version.

To convert this to a machine interval cset system you need
- A subset I_T of I, deemed to be the "machine intervals" for a given 
machine version T of the underlying system S.
- An algorithm "machine interval hull" that encloses an arbitrary 
subset of S* in a member of I_T, call it hull_T(X).

   I guess hull_T(X) must always enclose hull(X). Not a problem when 
intervals are boxes in (R*)^m, but a bit tricky when intervals are 
wrap-around ones (not always an obvious UNIQUE exact hull), or discs 
in the complex plane (easily get a good-enough, but not easily a 
best, machine hull).

That summarizes the theoretical needs. Rump's INTLAB has an 
implementation with intervals being *finite* discs in the complex 
plane C. The most natural compact extension C* is C plus one point at 
infinity, as used for 150 years in complex analysis. The set I could 
then be all the finite discs, plus the "infinite discs" which are 
half-planes, plus the whole of C*, plus the empty set. This set is 
closed under +, - and reciprocal (not multiplication or division).

The set I_T could be all discs that have machine-representable centre 
and radius - with a special way to represent the half planes.

I haven't worked on this system, so I don't know any of the practical 
snags. But it makes sense in principle.

John

Dr John and Mrs Kate Pryce
142 Kingshill Rd
Swindon, Wiltshire SN1 4LW
UK
Tel (+44)1793-331062 

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All,

We have prepared a completely revised a draft of a proposed
standard based on the draft of March 2006 by Br\"onnimann,
Melquiond, and Pion. Although the attached document bears
the names of Br\"onnimann, Melquiond, and Pion, it is the
result of work by John Pryce on their earlier version, and
there has not yet been discussion on whether they accept
the document in this revised form.

The document is too large to send as an attachment to this
Alias.  The draft is available for download from
    http://homepage.ntlworld.com/j.d.pryce/isloct05/

This draft differs from the March 2006 draft primarily in its explanation of
an underlying abstract mathematical model based on containment sets and (we
think) simplifications which follow from that.  We have tried to strengthen
considerably the conceptual rationale for interval arithmetic.

This version has been the subject of extensive discussions among Interval
Subroutine Library (ISL) project members John Pryce, George Corliss, R.
Baker Kearfott, Ned Nedialkov, and Spencer Smith.  We intend this draft as a
catalyst for further discussion. We argue for the importance of specifying
an abstract mathematical model.  We favour a one-model cset-based standard,
but a standard that supports both this and the Simple System would be
acceptable.

In preparing this revision, the ISL project has focused in the interval
abstract mathematical model and the semantics.  We intend that C++ experts
in the community continue to refine the C++ aspects.

This draft does not reflect recent discussions of cmath or of comparison
operators.  We continue to follow those discussion threads with interest.

John Pryce, George Corliss, R. Baker Kearfott, Ned Nedialkov, and Spencer
Smith 



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On 6/7/06, George Corliss <George.Corliss@marquette.edu> wrote:
> We have prepared a completely revised a draft of a proposed
> standard based on the draft of March 2006 by Br\"onnimann,
> Melquiond, and Pion.

IV.4 : API issues : Internal and external form for intervals

I don't recall that "infty" is a standard form for writing infinities.
I think the C++ standard should not introduce yet another form, as it
make interoperability and shared implementations harder.

26.6 : Interval numbers

Do not use "abstract model" as a short form for "abstract interval model".
There is too great a chance of confusion in the full standard, where
the context is much broader.

26.6.3 paragraph 3 : interval( const char *s )

You must state which exception is raised.

26.6.3 paragraph 6 : interval( const T& lo, const T& hi)

Likewise.

26.6.3 paragraph 7 bullet 3

The functions to specify semi-infinite intervals must be defined.
Alternatively, one could require NaN/infinity support.

26.6.3 paragraph 9

Again, needs to state which exception.

26.6.4 : Interval member operators

All assignment operators should return references to objects,
not values.

26.6.5 : Interval non-member operations

The definition "Returns: interval<T>(lhs) += rhs" is incorrect.
The result of the assignment operator is a reference.  The result
of an addition operator should be an object.  Likewise for the
others.

2.6.6 : Extended division function

Is there a particular reason that you did not define xdiv to
write to non-const reference parameters?  E.g.,

template< typename T >
void xdiv( const interval<T>& dividend, const interval<T>& divisor,
           interval<T>& primary, interval<T>& secondary );

It strikes me that one is likely to want to unpack the pair immediately,
and therefore directly setting variables would be better.

26.6.9 : Interval value operations

I note the potential confusion between "inf" as a floating point value
and an interval operation.  I don't think it is a bit problem, nor
do I have a solution.

26.6.12 : Interval static value operations

Given pi, why not e, etc.?

26.6.13 : External numbers and intervals

The statement "An implementation may provide features beyone the above"
is dangerous.  It grants permission to vendors to claim that non-portable
code is standards-conformant.  Vendors can always add extensions, but
sanctioning them without enumeration is dangerous.  Define what you want
all compilers to conform to and do not mention the rest.  Under that rule,

    [2*pi] requires an expression interpreter in the input library,
    and therefore is difficult to define, annoying to implement, and
    potentially expensive at run time.  So, I would not standardize it.

    [1.1;1.2]e15 is difficult to parse effectively and I would exclude it.

    hexidecimal base numbers are permitted in the C99 standard, and I see
    no particular difficulty in defining them.  Furthermore, they provide
    a means to avoid extending intervals on I/O, and so I recommend putting
    them into the standard.

-- 
Lawrence Crowl
From george.corliss@marquette.edu Mon Jun 12 18:28:06 2006
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If you are not on the RC mailing alias ...

------ Forwarded Message
> From: "Kreinovich, Vladik" <vladik@utep.edu>
> Date: Mon, 12 Jun 2006 19:14:00 -0600
> To: <reliable_computing@interval.louisiana.edu>
> Cc: "Kosheleva, Olga" <olgak@utep.edu>, "Kreinovich, Vladik" <vladik@utep.edu>
> Conversation: Intervals mentioned  in an education paper
> Subject: Intervals mentioned  in an education paper
> 
> Dear Friends, 
> 
> This is just FYI.
> 
> The latest issue (Vol. 25, No. 3, 2006) of the Journal of Computers in
> Mathematics and Science Teaching published by the Association for the
> Advancement of Computing in Education (AACE) starts with an article by
> William Richardson from Francis Marion University on the treatment of
> computational precision etc. in an introduction programming course for
> scientists and engineers.
> 
> The article starts with a known problem - that round off errors
> sometimes make results of numerical computations unreliable - and cites
> interval arithmetic as the most natural solution to this problem (with a
> reference to Hayes' 2003 popular article in American Scientist).
> Following Hayes, Richardson cites the lack of hardware support and the
> lack of standardized treatment of intervals in programming langauges
> among the main reasons why interval computations are not as widely used
> as they could be.
> 
> He also mentions the need for operations with large integers and large
> reals. 
> 
> It is very good that intervals are mentioned in an article aimed at
> those who teach math and science, additional exposure is never a bad
> idea. 
> 
> Anecdotal evidence shows that (while there is only 1-2 pages about
> intervals, still) thos article is a good exposure: I learned about this
> article from my wife Olga who is now teaching future math teachers at
> our College of Education and who is subscibed to this joirnal as part of
> her membership in AACE; the article is first in this issue.
> 
> Maybe someone from our field can submit, to this (or similar
> education-orineted) journal an education-oriented article specifically
> devoted to intervals?
> 
> Vladik
> 
> 

------ End of Forwarded Message


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Dear all,

We have worked on separating the bool_set type (previously named
interval<bool>) into its own proposal.  Let me remind you that
this is used as the return type for the comparisons of intervals,
and it implements multi-valued logic (akeen to Boost.Tribool).

It is going to be document number N2046 in the mid-term mailing.
The PDF is available at :
http://www-sop.inria.fr/geometrica/team/Sylvain.Pion/cxx/bool_set/bool_set_N2046.pdf

Some sample code can also be found here :
http://www-sop.inria.fr/geometrica/team/Sylvain.Pion/cxx/


We plan to release an updated interval proposal at some point
(as soon as possible...).  And we are currently reading through
the cset documents.

-- 
Herve, Guillaume, Sylvain
From avitzur@PacificT.com Wed Jun 21 10:56:31 2006
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To: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>,
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From: Ron Avitzur <avitzur@PacificT.com>
Subject: Re: [std-interval] separate bool_set proposal available
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>We have worked on separating the bool_set type (previously named
>interval<bool>) into its own proposal.  Let me remind you that
>this is used as the return type for the comparisons of intervals,
>and it implements multi-valued logic (akeen to Boost.Tribool).
>
>It is going to be document number N2046 in the mid-term mailing.
>The PDF is available at :
>http://www-sop.inria.fr/geometrica/team/Sylvain.Pion/cxx/bool_set/bool_set_N2046.pdf
>
>Some sample code can also be found here :
>http://www-sop.inria.fr/geometrica/team/Sylvain.Pion/cxx/
>
>
>We plan to release an updated interval proposal at some point
>(as soon as possible...).  And we are currently reading through
>the cset documents.

Hello,

I've made this point on the list before, but it might be
worth mentioning in the discussion of tradeoffs in N2046.

Under the rationale:

>It is primarily used for the result of uncertain comparisons of
>types where comparisons can return a trivalent state (e.g.,
>intervals can be compared or overlap), to avoid systematically
>throwing an exception when the comparison returns a result other
>than true or false.

>In this way, bool_set can be used wherever a bool is used and the
>user can expect the same result except if an exception is raised,
>which she then has to handle.

>The benefits are that the code will not compile when bool is
>changed into bool_set and will trigger a code review. The problem is
>that it may not be possible for the programmer to modify the code if
>it belongs to a library

This mostly covers the tradeoffs involved in choosing an implicit
conversion to bool. However, I would suggest also considering a
discussion of std::set<interval>.

In this case, if interval defines

  bool_set interval::operator<(interval&, interval&)

and bool_set offers an implicit conversion to bool, set<interval>
will compile without error and have an unhandled exception if any of
the intervals overlap. The combination of an automatic conversion to
bool while using bool_set with libraries unaware of the tri-valued
logic is at odds with the desire to avoid systematically throwing an
exception when the comparison returns a result other than true or false.

Here the problem is that set wasn't designed to consider that operator<
might throw an exception, the programmer can't modify the library code
to handle the exception, and it is not useful for the programmer using
set<> to handle the exception outside of set. Of course, you can invoke
set<interval, user_supplied_ordering> with some other comparison
which doesn't throw if you are aware of the risk. The convenience of an
automatic conversion creates runtime errors that would otherwise be caught
at compile time in this case.

- Ron Avitzur
From hbr@poly.edu Wed Jun 21 11:40:51 2006
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Subject: Re: [std-interval] separate bool_set proposal available
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Ron:

On Jun 21, 2006, at 2:13 PM, Ron Avitzur wrote:
> In this case, if interval defines
>
>  bool_set interval::operator<(interval&, interval&)
>
> and bool_set offers an implicit conversion to bool, set<interval>
> will compile without error and have an unhandled exception if any of
> the intervals overlap.

Please note that in the current (working) version of the interval  
proposal, we do not define an operator< for intervals.  Instead, we  
offer the "bool_set operator<(interval,interval)" in a separate  
namespace bool_set_ops.  Presumably, if the user includes this  
namespace, he/she is aware of bool_set and how it should be used wrt  
exceptions.  (BTW, there are also other namespaces for certainly and  
possibly comparisons.) Without this, you'll get a compile-time  
failure when using set<interval>.  Hope that answers your concerns,
--
Hervé Brönnimann
CIS, Polytechnic University
hbr@poly.edu


From Sylvain.Pion@sophia.inria.fr Sun Jul  9 08:09:59 2006
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Dear George and the ISL team,

I have read through your modified proposal as well as your cset paper.
They contain interesting ideas, and many should be integrated in
the final proposal.  As far as I understood them, it seems that many
of these ideas are orthogonal to csets, so, for the purpose of
discussion here, it would be nice to consider them separately.
In this mail, I will focus on the cset model itself.

As far as I understood, the cset approach is mostly motivated by
the needs to handle :
1- discontinuity of functions (e.g. division by zero)
2- construction from floating-point infinity
3- re-association capabilities
(am I missing other important ones ?)

In practice, the cset model implies that intervals are enlarged so
as to verify new properties.  To define the cset functions, you have
to look at how the function is defined outside the input intervals,
and take all possible limits of values of the function outside the
intervals. (forgive the short imprecise summary).

This produces "strange" effects, like :
- [0;+inf]*[0;+inf] returns [-inf;+inf], whereas "the simple" model
   can simply return the more "natural" [0;+inf].
- 1/[0;1] returns [-inf;+inf]  ([1;+inf] for the "simple" case)
- sign([0;5]) returns [-1;1] ([0;1] for the "simple" case)
You mention these effects in your paper, although you do not really
propose a way to take care of this.

I understand that the cset model brings in some consistency, which
is a most definitely desired feature.  But it does not come without
constraints.  I am also not convinced that the same kind of consistency
cannot be achieved using a non-cset model.

The main question I have is that I do not find convincing arguments,
in practice, to justify the cset model.  For example, the wrap-around
model is nicely motivated by functions like : f(a,b) = 1/(1/a+1/b).
I miss the equivalent for csets.  I believe that, in the 3 main
reasons listed above, 1- and 3- can be specified in a non-cset model
as well (by a non-cset or "simple" model, I mean a model which does
not have to take into account values of functions outside the input
intervals, this is the most distinctive feature of cset, and the most
problematic to me).
For 2-, I am not sure yet what to think, but I hardly see this as a
reason to justify the cset cost anyway.  I see this cost as :
- larger intervals
- slightly slower implementation
- more complicated definition/specification


As far as the proposal is concerned, we can still propose several
models.  The std::interval could have a policy parameter specifying
the model.  If we do that, we add a lot of complexity to the proposal,
which really needs to be motivated.  We are already not considering
the integration of a wrap-around model or Kaucher model (is it a
mistake ?).  I believe that most people care about speed and tightness
of the intervals, so if we need to choose one model, my current
personnal opinion is that a (well-defined of course) non-cset is
the best choice.


I would be more than happy to read opinions of interval experts on
this issue.  Concrete use-cases requiring csets would be a must.

-- 
Sylvain

From george.corliss@marquette.edu Sun Jul  9 08:47:51 2006
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Subject: Re: [std-interval] Draft standard based on csets
From: George Corliss <George.Corliss@marquette.edu>
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Sylvain,

Thank you for your response.  The ISL team is meeting this week in
Milwaukee.  We will be working on further clarifications  One of the
suggestions of Lee Winter is that we construct a model which is subset-able
in the sense that by omitting certain features, you get recognizable, valid
systems for interval arithmetic.  For example, one subset of the theory
might be "simple," and one might be "cset."  We are working on such a
unification, so far without complete success.  We even think there is some
hope that the unified theory might be simpler in the sense that it is more
general.  Work continues.

George Corliss

> Dear George and the ISL team,
> 
> I have read through your modified proposal as well as your cset paper.
> They contain interesting ideas, and many should be integrated in
> the final proposal.  As far as I understood them, it seems that many
> of these ideas are orthogonal to csets, so, for the purpose of
> discussion here, it would be nice to consider them separately.
> In this mail, I will focus on the cset model itself.
> 
> As far as I understood, the cset approach is mostly motivated by
> the needs to handle :
> 1- discontinuity of functions (e.g. division by zero)
> 2- construction from floating-point infinity
> 3- re-association capabilities
> (am I missing other important ones ?)
> 
> In practice, the cset model implies that intervals are enlarged so
> as to verify new properties.  To define the cset functions, you have
> to look at how the function is defined outside the input intervals,
> and take all possible limits of values of the function outside the
> intervals. (forgive the short imprecise summary).
> 
> This produces "strange" effects, like :
> - [0;+inf]*[0;+inf] returns [-inf;+inf], whereas "the simple" model
>    can simply return the more "natural" [0;+inf].
> - 1/[0;1] returns [-inf;+inf]  ([1;+inf] for the "simple" case)
> - sign([0;5]) returns [-1;1] ([0;1] for the "simple" case)
> You mention these effects in your paper, although you do not really
> propose a way to take care of this.
> 
> I understand that the cset model brings in some consistency, which
> is a most definitely desired feature.  But it does not come without
> constraints.  I am also not convinced that the same kind of consistency
> cannot be achieved using a non-cset model.
> 
> The main question I have is that I do not find convincing arguments,
> in practice, to justify the cset model.  For example, the wrap-around
> model is nicely motivated by functions like : f(a,b) = 1/(1/a+1/b).
> I miss the equivalent for csets.  I believe that, in the 3 main
> reasons listed above, 1- and 3- can be specified in a non-cset model
> as well (by a non-cset or "simple" model, I mean a model which does
> not have to take into account values of functions outside the input
> intervals, this is the most distinctive feature of cset, and the most
> problematic to me).
> For 2-, I am not sure yet what to think, but I hardly see this as a
> reason to justify the cset cost anyway.  I see this cost as :
> - larger intervals
> - slightly slower implementation
> - more complicated definition/specification
> 
> 
> As far as the proposal is concerned, we can still propose several
> models.  The std::interval could have a policy parameter specifying
> the model.  If we do that, we add a lot of complexity to the proposal,
> which really needs to be motivated.  We are already not considering
> the integration of a wrap-around model or Kaucher model (is it a
> mistake ?).  I believe that most people care about speed and tightness
> of the intervals, so if we need to choose one model, my current
> personnal opinion is that a (well-defined of course) non-cset is
> the best choice.
> 
> 
> I would be more than happy to read opinions of interval experts on
> this issue.  Concrete use-cases requiring csets would be a must.


From george.corliss@marquette.edu Sat Aug 12 06:09:52 2006
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As this groups does not yet appear to have reached a consensus on comparison
operators, there are some additional thoughts.

I've been asked to teach a database class for the first time in my career,
so I am reading about SQL (Structured Query Language).  Interestingly, SQL
uses a three-valued logic with values TRUE, FALSE, and UNKNOWN.

The rationale seems to be
   1. Fields in a database often have values NULL
   2. Comparisons with NULL yield UNKNOWN
   3. Need "Boolean" operators on results of comparisons

The analogy with intervals is not perfect, but it is informative.  Since
databases are more widely used than intervals, their standards have endured
severe scrutiny and extensive practical applications.  We may have something
to learn.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From Sylvain.Pion@sophia.inria.fr Sat Aug 12 08:47:47 2006
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George Corliss wrote:
> As this groups does not yet appear to have reached a consensus on comparison
> operators, there are some additional thoughts.

As far as I'm concerned, I understand that several different semantics
are desired.  I am unsure about the best way to provide these in C++,
but so far the proposal puts them in separate namespaces, so at least
they are easily available.  I am keeping an eye on the evolution of the
language, most importantly the concepts, if we can find better ways to
provide the various semantics.

> I've been asked to teach a database class for the first time in my career,
> so I am reading about SQL (Structured Query Language).  Interestingly, SQL
> uses a three-valued logic with values TRUE, FALSE, and UNKNOWN.
> 
> The rationale seems to be
>    1. Fields in a database often have values NULL
>    2. Comparisons with NULL yield UNKNOWN
>    3. Need "Boolean" operators on results of comparisons
> 
> The analogy with intervals is not perfect, but it is informative.  Since
> databases are more widely used than intervals, their standards have endured
> severe scrutiny and extensive practical applications.  We may have something
> to learn.

Thanks for the information, George.  It's good to see that
the SQL semantic is covered by our bool_set proposal.  It
makes one more motivation to standardize something like this.

I would be curious about the details, though.  What happens
if you do "if(UNKNOWN)" (or the equivalent in SQL, if there
is an equivalent) ?

-- 
Sylvain
From george.corliss@marquette.edu Sun Aug 13 05:52:31 2006
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Subject: Re: [std-interval] Comparisons
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Sylvain,

>> I've been asked to teach a database class for the first time in my career,
>> so I am reading about SQL (Structured Query Language).  Interestingly, SQL
>> uses a three-valued logic with values TRUE, FALSE, and UNKNOWN.
>> 
>> The rationale seems to be
>>    1. Fields in a database often have values NULL
>>    2. Comparisons with NULL yield UNKNOWN
>>    3. Need "Boolean" operators on results of comparisons
>> 
>> The analogy with intervals is not perfect, but it is informative.  Since
>> databases are more widely used than intervals, their standards have endured
>> severe scrutiny and extensive practical applications.  We may have something
>> to learn.
> 
> Thanks for the information, George.  It's good to see that
> the SQL semantic is covered by our bool_set proposal.  It
> makes one more motivation to standardize something like this.
> 
> I would be curious about the details, though.  What happens
> if you do "if(UNKNOWN)" (or the equivalent in SQL, if there
> is an equivalent) ?

Yes, I think it strengthens our case to say, "We are similar to the
heavily-used SQL practice," if we are.

Others more knowledgeable may correct me, but I do not find control
structures.  SQL is a declarative language, so conditionals act more like
guards, for example,
   SELECT name FROM employees WHERE birthdate > '1936-08-12';

If birthdate has the value NULL, (birthdate > '1936-08-12') evaluates to
UNKNOWN, and the record is NOT selected.  In general, only those
combinations that evaluate to TRUE are selected.  UNKNOWN propagates from
comparisons (birthdate > '1936-08-12'), through logical operators (AND, OR,
NOT), but when SQL needs to make a select/no-select decision, TRUE means,
"I'm sure the condition is true," and FALSE means, "I cannot safely assert
TRUE."

In our context, Boolean TRUE is what we sometimes call CERTAINLY TRUE, and
FALSE is not TRUE.  With a careful interpretation, FALSE is an enclosure of
TRUE, in the sense that the correct value is true, but we cannot guarantee
that, so we return a "larger interval."

At least, that is how I interpret the SQL practice in an interval analogy.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From george.corliss@marquette.edu Tue Aug 15 13:55:25 2006
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From: George Corliss <George.Corliss@marquette.edu>
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Friends,

Ned Neddialkov had sent this pointer which may be of interest to this list
for use as "ammunition" that intervals are good.

------ Forwarded Message
> From: Ned Nedialkov <nedialk@mcmaster.ca>
> Date: Thu, 27 Jul 2006 13:45:01 -0400
> Subject: applications
> 
> I discovered recently a very thorough study of applications of
> interval methods, in particular integration, to space flight mechanics:
http://www.esa.int/gsp/ACT/doc/ACT-RPT-04-4105-ARIADNA-Assessing_the_Accurac
y_of_Interval_arithmetic_Estimates.pdf

------ End of Forwarded Message

The ESA Technical Officer, Mihaly Markot, was a student of Tibor Tsendes.


Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From lawrence.crowl@gmail.com Wed Aug 16 14:45:46 2006
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I'm not an expert in the domain, but my read of the conclusions
is that the interval approach wasn't helpful.  Apparently, the
integration process failed far earlier than non-interval integration.
How are we interpreting the conclusions differently?

On 8/15/06, George Corliss <George.Corliss@marquette.edu> wrote:
> Friends,
>
> Ned Neddialkov had sent this pointer which may be of interest to this list
> for use as "ammunition" that intervals are good.
>
> ------ Forwarded Message
> > From: Ned Nedialkov <nedialk@mcmaster.ca>
> > Date: Thu, 27 Jul 2006 13:45:01 -0400
> > Subject: applications
> >
> > I discovered recently a very thorough study of applications of
> > interval methods, in particular integration, to space flight mechanics:
> http://www.esa.int/gsp/ACT/doc/ACT-RPT-04-4105-ARIADNA-Assessing_the_Accurac
> y_of_Interval_arithmetic_Estimates.pdf
>
> ------ End of Forwarded Message
>
> The ESA Technical Officer, Mihaly Markot, was a student of Tibor Tsendes.
>
>
> Dr. George Corliss
> Electrical and Computer Engineering
> Marquette University
> P.O. Box 1881
> 1515 W. Wisconsin Ave.
> Milwaukee, WI 53201-1881
> George.Corliss@Marquette.edu
> 414-288-6599 (office); 288-4400 (GasDay);
>     288-6280 (Dept.); 288-5579 (fax)
> Office: Haggerty Engineering 296
> Www.eng.mu.edu/corlissg
>
>
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval
>


-- 
Lawrence Crowl
From markot@sztaki.hu Thu Aug 17 02:44:03 2006
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Dear Colleagues,

I would like to add some comments to the discussion as a Technical 
Officer of the mentioned study: (The T.O. title means that I represented 
the ESA side which awarded a research contract in this subject.)

- The study was intended to be a very initial assessment of the 
applicability of interval ODE solvers for special space flight problems. 
Because of the short contract period (4 months) I did not expect any 
particularly detailed results.

- The numerical results indeed proved that the tested existing 
general-purpose, "off-the-shelf" interval solvers are not comparable 
with non-interval ones in term of the time of propagation, due to the 
overestimation. Nothing really surprising...

- Note that the study was done by a team which has primary focus on 
space research and had less previous expertize with interval tools. 
Unfortunately, I was not successful with my plan to award a parallel 
contract also to a primarily interval-oriented team. This way I got a 
report on "what happens in some simple scenarios", but nothing on "why 
the interval solvers fail so earlier" and "how to improve/tune these 
solvers to achieve better results".

- All in all, I still find this study as a good "ammunition" - not 
because of the achieved results but because we pointed out the need of 
reliable methods in this field and made some initial contacts with the 
space science community - in the hope of further collaborations.

Regards,
Mihaly

-- 
Dr. Mihaly Csaba Markot
Computer and Automation Research Institute
Hungarian Academy of Sciences
Phone: +36 1 279 6112, Fax: +36 1 209 5267

----------------------------- Original message -----------------------------
Subject:   Re: [std-interval] FW: applications
Sent by:  "Lawrence Crowl" <lawrence.crowl@gmail.com>
Date:   Thu, August 17, 2006 12:24 am
Address: "For discussions concerning the C++ standardization of 
intervals" <std-interval@compgeom.poly.edu>
--------------------------------------------------------------------------

I'm not an expert in the domain, but my read of the conclusions
is that the interval approach wasn't helpful.  Apparently, the
integration process failed far earlier than non-interval integration.
How are we interpreting the conclusions differently?

On 8/15/06, George Corliss <George.Corliss@marquette.edu> wrote:
 > > Friends,
 > >
 > > Ned Neddialkov had sent this pointer which may be of interest to 
this list
 > > for use as "ammunition" that intervals are good.
 > >
 > > ------ Forwarded Message
 >> > > From: Ned Nedialkov <nedialk@mcmaster.ca>
 >> > > Date: Thu, 27 Jul 2006 13:45:01 -0400
 >> > > Subject: applications
 >> > >
 >> > > I discovered recently a very thorough study of applications of
 >> > > interval methods, in particular integration, to space flight 
mechanics:
 > > 
http://www.esa.int/gsp/ACT/doc/ACT-RPT-04-4105-ARIADNA-Assessing_the_Accurac
 > > y_of_Interval_arithmetic_Estimates.pdf
 > >
 > > ------ End of Forwarded Message
 > >
 > > The ESA Technical Officer, Mihaly Markot, was a student of Tibor 
Tsendes.
 > >
 > >
 > > Dr. George Corliss
 > > Electrical and Computer Engineering
 > > Marquette University
 > > P.O. Box 1881
 > > 1515 W. Wisconsin Ave.
 > > Milwaukee, WI 53201-1881
 > > George.Corliss@Marquette.edu
 > > 414-288-6599 (office); 288-4400 (GasDay);
 > >     288-6280 (Dept.); 288-5579 (fax)
 > > Office: Haggerty Engineering 296
 > > Www.eng.mu.edu/corlissg
 > >
 > >
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-- Lawrence Crowl _______________________________________________ 
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From george.corliss@marquette.edu Thu Aug 17 03:00:33 2006
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Subject: Re: [std-interval] Re: applications in space science
From: George Corliss <George.Corliss@marquette.edu>
To: For discussions concerning the C++ standardization of intervals
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Mihaly,

Great to hear from you.  Thanks for putting in your perspective.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg



On 8/17/06 5:23 AM, "Mihály Csaba Markót" <markot@sztaki.hu> wrote:

> Dear Colleagues,
> 
> I would like to add some comments to the discussion as a Technical
> Officer of the mentioned study: (The T.O. title means that I represented
> the ESA side which awarded a research contract in this subject.)
> 
> - The study was intended to be a very initial assessment of the
> applicability of interval ODE solvers for special space flight problems.
> Because of the short contract period (4 months) I did not expect any
> particularly detailed results.
> 
> - The numerical results indeed proved that the tested existing
> general-purpose, "off-the-shelf" interval solvers are not comparable
> with non-interval ones in term of the time of propagation, due to the
> overestimation. Nothing really surprising...
> 
> - Note that the study was done by a team which has primary focus on
> space research and had less previous expertize with interval tools.
> Unfortunately, I was not successful with my plan to award a parallel
> contract also to a primarily interval-oriented team. This way I got a
> report on "what happens in some simple scenarios", but nothing on "why
> the interval solvers fail so earlier" and "how to improve/tune these
> solvers to achieve better results".
> 
> - All in all, I still find this study as a good "ammunition" - not
> because of the achieved results but because we pointed out the need of
> reliable methods in this field and made some initial contacts with the
> space science community - in the hope of further collaborations.
> 
> Regards,
> Mihaly



From markus.neher@math.uni-karlsruhe.de Fri Aug 18 00:25:24 2006
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From: Markus Neher <markus.neher@math.uni-karlsruhe.de>
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Dear colleagues,

> Message: 1
> Date: Wed, 16 Aug 2006 15:24:41 -0700
> From: "Lawrence Crowl" <lawrence.crowl@gmail.com>
> Subject: Re: [std-interval] FW: applications
> To: "For discussions concerning the C++ standardization of intervals"
> 	<std-interval@compgeom.poly.edu>
> Message-ID:
> 	<90228e530608161524v5f4b390dk2998b0afe741aad4@mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> I'm not an expert in the domain, but my read of the conclusions
> is that the interval approach wasn't helpful.  Apparently, the
> integration process failed far earlier than non-interval integration.
> How are we interpreting the conclusions differently?

In my opinion, the ESA study only shows that two existing interval
solvers for ODEs failed earlier than non-interval integration.

It is well known that validated integration with Taylor model methods
performes much better for these IVPs than the tested interval solvers,
see for example

@article{HoBeMa03a,
      author    = "J. Hoefkens and M. Berz and K. Makino",
      title     = "Controlling the Wrapping Effect in the Solution of
                   {ODEs} for Asteroids",
      journal   = "Reliable Computing",
      volume    = "9",
      pages     = "21-41",
      year      = "2003",
      }

Regards,

Markus
From rmoore17@columbus.rr.com Fri Aug 18 12:43:00 2006
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Markus and All:

Indeed, among the conclusions of the ESA study, we find:
"All interval integrators which have been tested in this work try to avoid 
the wrapping effect using a linear expansion of the solution of the ODE with 
respect to the initial conditions. However, the works of Berz and Makino 
showed that important improvements on the control of this effect cam be 
achieved when higher order methods on initial conditions are applied. As a 
consequence, further intensive investigations should be accomplished, aimed 
at estimating the performances of such promising methods on the integration 
of typical space-related problems."

Ray Moore


----- Original Message ----- 
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Subject: Std-interval Digest, Vol 7, Issue 5


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>   1. Re: ESA Study on Interval Methods for Inegration (Markus Neher)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 18 Aug 2006 10:04:43 +0200
> From: Markus Neher <markus.neher@math.uni-karlsruhe.de>
> Subject: [std-interval] Re: ESA Study on Interval Methods for
> Inegration
> To: std-interval@compgeom.poly.edu
> Message-ID: <44E5749B.6050008@math.uni-karlsruhe.de>
> Content-Type: text/plain; charset=us-ascii
>
> Dear colleagues,
>
>> Message: 1
>> Date: Wed, 16 Aug 2006 15:24:41 -0700
>> From: "Lawrence Crowl" <lawrence.crowl@gmail.com>
>> Subject: Re: [std-interval] FW: applications
>> To: "For discussions concerning the C++ standardization of intervals"
>> <std-interval@compgeom.poly.edu>
>> Message-ID:
>> <90228e530608161524v5f4b390dk2998b0afe741aad4@mail.gmail.com>
>> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>>
>> I'm not an expert in the domain, but my read of the conclusions
>> is that the interval approach wasn't helpful.  Apparently, the
>> integration process failed far earlier than non-interval integration.
>> How are we interpreting the conclusions differently?
>
> In my opinion, the ESA study only shows that two existing interval
> solvers for ODEs failed earlier than non-interval integration.
>
> It is well known that validated integration with Taylor model methods
> performes much better for these IVPs than the tested interval solvers,
> see for example
>
> @article{HoBeMa03a,
>      author    = "J. Hoefkens and M. Berz and K. Makino",
>      title     = "Controlling the Wrapping Effect in the Solution of
>                   {ODEs} for Asteroids",
>      journal   = "Reliable Computing",
>      volume    = "9",
>      pages     = "21-41",
>      year      = "2003",
>      }
>
> Regards,
>
> Markus
>
> ------------------------------
>
> _______________________________________________
> Std-interval mailing list
> Std-interval@compgeom.poly.edu
> http://compgeom.poly.edu/mailman/listinfo/std-interval
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>
> End of Std-interval Digest, Vol 7, Issue 5
> ******************************************
> 


From lcglopes@sapo.pt Tue Aug 22 16:23:14 2006
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Dear colleagues,
Does anyone know any implementation of real and/or complex interval
arithmetic (with outward rounding) in Python?
Thank you in advance for your advice.
Luiz Lopes

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Luiz C. G. Lopes
Dept. of Mathematics and Engineering
University of Madeira, Penteada Campus
9000-390 Funchal, Madeira Is., Portugal
Phone: +351 291 705 151
Fax:   +351 291 705 199
E-mail: lopes@uma.pt
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 
 

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rounding) in Python?</SPAN></FONT></DIV>
<DIV><FONT face=3DArial size=3D2><SPAN class=3D109414723-22082006>Thank =
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<DIV><FONT face=3DArial size=3D2><SPAN class=3D109414723-22082006>Luiz=20
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Dear colleagues,
Does anyone know any implementation of real and/or complex interval
arithmetic (with outward rounding) in Python?
Thank you in advance for your advice.
Luiz Lopes

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Luiz C. G. Lopes
Dept. of Mathematics and Engineering
University of Madeira, Penteada Campus
9000-390 Funchal, Madeira Is., Portugal
Phone: +351 291 705 151
Fax:   +351 291 705 199
E-mail: lopes@uma.pt
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 
 

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<DIV><FONT face=3DArial size=3D2><SPAN class=3D109414723-22082006>Does =
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rounding) in Python?</SPAN></FONT></DIV>
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<DIV><FONT face=3DArial size=3D2><SPAN class=3D109414723-22082006>Luiz=20
Lopes</SPAN></FONT></DIV>
<DIV><FONT face=3DArial size=3D2><SPAN class=3D109414723-22082006><FONT =
face=3DArial=20
size=3D2><BR>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>Luiz C. G. =
Lopes<BR>Dept.=20
of Mathematics and Engineering<BR>University of Madeira, Penteada=20
Campus<BR>9000-390 Funchal, Madeira Is., Portugal<BR>Phone: +351 291 705 =

151<BR>Fax:&nbsp;&nbsp; +351 291 705 199<BR>E-mail: <A =
title=3Dmailto:lopes@uma.pt=20
href=3D"mailto:lopes@uma.pt">lopes@uma.pt</A><BR>~~~~~~~~~~~~~~~~~~~~~~~~=
~~~~~~~~~~~~~~~<BR></DIV></FONT></SPAN></FONT>
<DIV><FONT face=3DArial size=3D2><SPAN=20
class=3D109414723-22082006></SPAN></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2><SPAN=20
class=3D109414723-22082006></SPAN></FONT>&nbsp;</DIV></FONT></DIV></BODY>=
</HTML>

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From Sylvain.Pion@sophia.inria.fr Tue Sep 12 00:28:03 2006
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Dear std-intervalers,

A revised version of the proposal is now available at:
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2067.pdf

The accompanying "bool_set" proposal is still at:
http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2046.pdf

Any comment is more than welcome, especially before the ISO/WG21
meeting in Portland in October.

Best regards,
-- 
Sylvain
From george.corliss@marquette.edu Tue Sep 12 18:18:53 2006
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Sylvain,

I appreciate the clear effort your team has put into this version.  I hope
it generates additional discussion.

A couple of easy points, in the title, I'd capitalize Add.

On p. 31 Acknowledgments, I ask that you mention John Pryce instead of (or
in addition) to me.  John did FAR more of the work in crafting our
discussions than I did.

Reference [15] is no longer available from that URL, as I lost my account on
that server some time ago.  It is probably most appropriate to say a
preprint is available from the author.

I'll be working with John Pryce to offer other comments.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


On 9/12/06 3:16 AM, "Sylvain Pion" <Sylvain.Pion@sophia.inria.fr> wrote:

> Dear std-intervalers,
> 
> A revised version of the proposal is now available at:
> http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2067.pdf
> 
> The accompanying "bool_set" proposal is still at:
> http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2046.pdf
> 
> Any comment is more than welcome, especially before the ISO/WG21
> meeting in Portland in October.
> 
> Best regards,


From Sylvain.Pion@sophia.inria.fr Wed Sep 13 00:25:56 2006
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George Corliss wrote:
> I appreciate the clear effort your team has put into this version.  I hope
> it generates additional discussion.

Thanks.  We did the best we could with our limited time.

> A couple of easy points, in the title, I'd capitalize Add.
> 
> On p. 31 Acknowledgments, I ask that you mention John Pryce instead of (or
> in addition) to me.  John did FAR more of the work in crafting our
> discussions than I did.
> 
> Reference [15] is no longer available from that URL, as I lost my account on
> that server some time ago.  It is probably most appropriate to say a
> preprint is available from the author.

I agree on these points, I will fix these for the next iteration.

> I'll be working with John Pryce to offer other comments.

Thanks in advance.

-- 
Sylvain
From Jean-Pierre.Merlet@sophia.inria.fr Wed Sep 13 02:41:10 2006
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Nice job by Herve, Guillaume and Sylvain.

I have two questions:

-should not be some definition about the returned enclosure of inverse 
functions such as:
2 Returns: an enclosure of {acos(x) | x in X and x in [ 1,1]}. template 
< class T> interval <T> acosh ( interval <T> X);
Should we impose that the enclosure be include in the range [0,pi] ?


-you are not talking about interval vectors and matrices except in VI.2.
where you are using is[s], s being the index, starting at s=0. This will 
not be compatible with PROFIL notations using is(s) with s starting at 
1. I am not that familiar with C++ but I guess we may template another 
vector definition compatible with PROFIL while still using the C++ 
standard ?

Otherwise sound good at a first look. Best


From guillaume.melquiond@ens-lyon.fr Wed Sep 13 04:13:45 2006
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Subject: Re: [std-interval] Re:proposed C++ Interval standard
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Le mercredi 13 septembre 2006 à 12:28 +0200, Jean-Pierre Merlet a
écrit :
> Nice job by Herve, Guillaume and Sylvain.

Thanks.

> I have two questions:
> 
> -should not be some definition about the returned enclosure of inverse 
> functions such as:
> 2 Returns: an enclosure of {acos(x) | x in X and x in [ 1,1]}. template 
> < class T> interval <T> acosh ( interval <T> X);
> Should we impose that the enclosure be include in the range [0,pi] ?

In the current draft, this is left as a matter of quality of
implementation. Due to Pi not being representable by a floating-point
matter, writing a specification is not simple. Let's name Pi+ the first
floating-point number after Pi.

The floating-point enclosure of acos([-1,-1]) has to contain Pi+, so we
are necessarily outside the mathematical range [0,Pi]. Due to the
mathematical properties of acos, we could still avoid this problem by
saying: unless the input interval contains -1, the output interval has
to be included in the mathematical range [0,Pi].

The problem becomes, however, more difficult for the atan function. A
lot of floating-point bounds require the output interval to contain Pi
+/2 and/or its opposite. So we can't have a simple specification that
requires the output to be included in [-Pi/2,Pi/2].

Now we could write a specification that simply requires the output
interval to be included in [-Pi+/2,Pi+/2]. I don't really see the point
of such a specification, as it allows for values outside the
mathematical range. It the user algorithm supports a bound like Pi+/2,
but not the next few floating-point numbers, then it should simply
perform an interval intersection to remove these values.

As a consequence, I would say that there is no need to impose more than
this design decision: "the standard should not require implementations
to return the sharpest intervals possible, but only preserve the
containment property for all functions."

> -you are not talking about interval vectors and matrices except in VI.2.
> where you are using is[s], s being the index, starting at s=0. This will 
> not be compatible with PROFIL notations using is(s) with s starting at 
> 1. I am not that familiar with C++ but I guess we may template another 
> vector definition compatible with PROFIL while still using the C++ 
> standard ?

This question is easier to answer. Section VI.2 contains an example that
relies on features that have existed since the first standardization of
C++, namely std::vector. C++ provides three kinds of vector/matrix
structures: classical C arrays, std::vector, and std::valarray. They can
all be used with an interval value type, and they all use the square
brackets and start at index 0. If the C++ standard ever describes a
generic linear algebra library, I'm quite sure it will rely on the same
syntax. So, with the array syntax you describe, PROFIL is quite off from
C++ practice in my opinion.

But this is actually irrelevant. Our proposal only describes the basic
interval type. If we start to define vector and matrix types, we will
have to define arithmetic operators on them, and so on. This is out of
the scope of our proposal. An additional proposal could be written
afterwards (though I think C++ developers would be a lot more receptive
to a generic linear algebra library rather than a specific interval
linear algebra library).

Best regards,

Guillaume

From Frederic.Goualard@univ-nantes.fr Thu Sep 14 00:33:01 2006
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Subject: [std-interval] Mathematical relations and default initialization
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Dear all,

I have just read the latest revision of the proposal (2006-09-05
revision 1) and I would like to comment on two specific issues:

* Mathematical relations
As I understand it from the discussion on the list, these methods
(acos_rel, ...) were inspired from the ones that exist in the gaol
library (the idea is much older, though, and such operators were already
present in BNR Prolog back in the 80s).
Gaol provides an nth_root_rel() operator to compute the relational
inverse nth root of an interval J wrt. an interval I. With constraint
programming methods, this operator is necessary to solve constraints
involving exponentiations.
The nth_root_rel() operator does not appear in the standard. Is this
omission on purpose? If indeed it is, why is it so?

Side notes:
  - on Page 12, the signatures for the mathematical relations are wrong
(compare with page 27).
  - div_rel() does not appear on page 27 while it is listed on page 12


* Default initialization
I see on page 15 that the default constructor creates an empty interval.
 At some point in the discussion, Sylvain gave 6 possible ways of
implementing this constructor:

1- no default constructor at all
2- [0,0]
3- empty
4- whole
5- uninitialized tag
6- see below (something a la "singular iterator")

Possibility 4 was brushed away from the start, and the remaining
possibilities heavily debated. In my opinion, it makes sense to have the
default constructor return "whole" since interval arithmetic is often
used in processes that try to gain some information on the possible
value of a variable (that is, we start from a wide interval and narrow
it down to some reasonably small one).


Best regards,

FG.
-- 
Frédéric Goualard                                 LINA - FRE CNRS 2729
                           Univ. of Nantes - Ecole des Mines de Nantes
Tel.: +33 2 51 12 58 38            2, rue de la Houssinière - BP 92208
Fax.: +33 2 51 12 58 12                         F-44322 NANTES CEDEX 3
http://goualard.free.fr/
From j.d.pryce@ntlworld.com Thu Sep 14 02:58:25 2006
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Dear all

At 09:21 14/09/06, Frédéric Goualard wrote:
>* Default initialization
>I see on page 15 that the default constructor creates an empty interval.
>  At some point in the discussion, Sylvain gave 6 possible ways of
>implementing this constructor:
>
>1- no default constructor at all
>2- [0,0]
>3- empty
>4- whole
>5- uninitialized tag
>6- see below (something a la "singular iterator")
>
>Possibility 4 was brushed away from the start, and the remaining
>possibilities heavily debated. In my opinion, it makes sense to have the
>default constructor return "whole" since interval arithmetic is often
>used in processes that try to gain some information on the possible
>value of a variable (that is, we start from a wide interval and narrow
>it down to some reasonably small one).

I am delighted that someone else takes this view. 
The ISL team came down in favour of returning 
"whole" many months ago, for exactly the reason you cite.

Regards

John Pryce
Dr John and Mrs Kate Pryce
142 Kingshill Rd
Swindon, Wiltshire SN1 4LW
UK
Tel (+44)1793-331062


From george.corliss@marquette.edu Thu Sep 14 06:04:45 2006
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Friends,

On 9/14/06 3:21 AM, "Frédéric Goualard" <Frederic.Goualard@univ-nantes.fr>
wrote:

> * Default initialization
> I see on page 15 that the default constructor creates an empty interval.
>  At some point in the discussion, Sylvain gave 6 possible ways of
> implementing this constructor:
> 
> 1- no default constructor at all
> 2- [0,0]
> 3- empty
> 4- whole
> 5- uninitialized tag
> 6- see below (something a la "singular iterator")
> 
> Possibility 4 was brushed away from the start, and the remaining
> possibilities heavily debated. In my opinion, it makes sense to have the
> default constructor return "whole" since interval arithmetic is often
> used in processes that try to gain some information on the possible
> value of a variable (that is, we start from a wide interval and narrow
> it down to some reasonably small one).

My first choice is #5, assuming that tags are permitted.

A close second is #4. If we read "[a, b]" as "If an answer exists, it
satisfies a <= x <= b," then #4 does not lie, while #3 often does lie.  If
there is a number, but we have no constraints on its value, it must belong
to R*.

The argument for #3, as I understand it, is that <empty> propagates through
most operations, so that if a coder unintentionally computes with an
uninitialized variable, the eventual result is likely to be <empty>, or some
other obviously incorrect value, and the error is more likely to be caught.
I am sympathetic to that argument, too.

There is no perfect answer.  The danger is that we unintentionally use an
uninitialized variable as if it were initialized.  The trouble comes about
because using two bit patterns, usually interpreted as hi and lo, does not
have enough expressive power.  Raising an exception is one means of adding
expressive power, but there seems to be agreement that intervals should
raise exceptions rarely, if ever.

To express "uninitialized" and several other states an interval object might
have, I favor tags, a concept which has not proven itself in practice.

I suggest the standard should PERMIT a tagged implementation.  I believe the
current proposal does.  Page 9, paragraph 3 says in interval is specified by
two values of type T, but I find on where the proposal forbids the memory
footprint being more.

For the mathematical result to be returned by a default constructor, I favor
#4, <whole> because I value containment above ease of debugging.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg



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Subject: Re: [std-interval] Revised document available
From: George Corliss <George.Corliss@marquette.edu>
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Sylvain and all,

> A revised version of the proposal is now available at:
> http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2067.pdf

Can you help me understand the difference between "undefined" and
"implementation-dependent" or "implementation-defined"?

I am not familiar with the vocabulary of standards, but it would seem to me
that "undefined" means that not only does the standard not specify what the
result should be, but that no one else does, either.  In principle, the
result is permitted to be non-deterministic on a single machine, let alone
on a single implementation.

I would expect "implementation-dependent" to mean that the choice is up to
the implementation.  I see you often use "implementation-defined," which I
would interpret to mean that it is the responsibility of the implementation
to specify what it will do and then to do what it specified?

If those interpretations are consistent with standard writing practice, is
there a reason to leave ANYTHING "undefined?"  If we cannot specify results
for each implementation, should not the implementers be required to specify,
that is, to be "implementation-defined"?

If that makes sense, would it also make sense to specify that
implementations on IEEE machines take advantage of IEEE support?  For
example, one might say, "On machines that support infinities, ... On other
machines, ... is implementation-defined."  That would be a MUCH stronger
specification of portability without imposing additional requirements in
practice.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From Stephen.Clamage@Sun.COM Thu Sep 14 09:48:29 2006
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George Corliss wrote:

> 
> Can you help me understand the difference between "undefined" and
> "implementation-dependent" or "implementation-defined"?


The C and C++ standards define these terms.

1. Undefined behavior means the standard places no requirements on the 
compile-time or run-time systems. Common responses to code having undefined 
behavior are
- refuse to compile
- compile, but fail to link
- link, but crash at run time
- run, but produce an undesired result
- run and produce the result the programmer wanted
Other responses are possible, such as the legendary "reformat the hard drive."
(Suppose a wild jump via an uninitialized pointer goes to the BIOS reformat 
command.)

An implementation is allowed to define the behavior of code that is formally 
undefined in the standard. Example: Divide-by-zero has undefined behavior, but 
an implementation could say that it will always raise a signal, or always abort, 
or always return a particular value.


2. Implementation defined means that the standard allows a list or range of 
possible behaviors, and the implementation is required to tell you what it does. 
Example: Type int must be capable of representing values in the range 
[-32767,32767]. The implementation must document what the actual range is, which 
almost always wider.


3. Unspecified (a category you didn't list) is similar to 
implementation-defined, but the implementation need not tell you what it does. 
Example: All the arguments to a function must be fully evaluated before the 
function is called, but the evaluation order is unspecified. An implementation 
can evaluate them in any order, and does not have to document the order. The 
order need not be consistent.


4. Implementation dependent is a generic term that means that the behavior can 
vary among systems. The term includes undefined, implementation-defined, and 
unspecified behavior.

---
Steve Clamage, stephen.clamage@sun.com
From guillaume.melquiond@ens-lyon.fr Thu Sep 14 10:22:14 2006
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Subject: Re: [std-interval] Mathematical relations and default
	initialization
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Le jeudi 14 septembre 2006 à 10:21 +0200, Frédéric Goualard a écrit :

> The nth_root_rel() operator does not appear in the standard. Is this
> omission on purpose? If indeed it is, why is it so?

The nth_root_rel is purposely out of the proposal because nth_root is
out too :-). I don't think the omission is on purpose though. If people
feel it is useful, it can be added.

> Side notes:
>   - on Page 12, the signatures for the mathematical relations are wrong
> (compare with page 27).
>   - div_rel() does not appear on page 27 while it is listed on page 12

Thanks, I will take a look.

> * Default initialization
> I see on page 15 that the default constructor creates an empty interval.
>  At some point in the discussion, Sylvain gave 6 possible ways of
> implementing this constructor:
> 
> 1- no default constructor at all
> 2- [0,0]
> 3- empty
> 4- whole
> 5- uninitialized tag
> 6- see below (something a la "singular iterator")
> 
> Possibility 4 was brushed away from the start, and the remaining
> possibilities heavily debated. In my opinion, it makes sense to have the
> default constructor return "whole" since interval arithmetic is often
> used in processes that try to gain some information on the possible
> value of a variable (that is, we start from a wide interval and narrow
> it down to some reasonably small one).

I don't remember 4 being brushed right away (proposition 1 was). As a
matter of fact, propositions 3 and 4 have reached a point in my opinion
where I consider them to be equally useful. So, at least on my side, it
is still 4 in the proposal, only because of inertia.

Best regards,

Guillaume

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Subject: Re: [std-interval] Revised document available
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	<std-interval@compgeom.poly.edu>
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Le jeudi 14 septembre 2006 à 10:59 -0500, George Corliss a écrit :
> Sylvain and all,
> 
> > A revised version of the proposal is now available at:
> > http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2067.pdf
> 
> Can you help me understand the difference between "undefined" and
> "implementation-dependent" or "implementation-defined"?

I don't think we put "implementation-dependent" situations on purpose.
It may simply be mistakes at places where we meant "implementation-
defined". I should review them.

"Implementation-defined" means "behavior, for a well-formed program
construct and correct data, that depends on the implementation and that
each implementation shall document." So it is a documented yet not
portable behavior. For example, the number of bits of an int is
implementation-defined.

"Undefined" (not "unspecified") applies when using "an erroneous program
construct or erroneous data". For example, overflowing signed integers
brings about undefined behavior in C and C++. It could fail an assertion
in debug mode or simplify execution paths when optimizing. In
particular, the compiler is allowed to assume that the sum of two
negative numbers is a negative number. Note that undefined behavior
situations are generally perfectly identified in the Standard.

> I am not familiar with the vocabulary of standards, but it would seem to me
> that "undefined" means that not only does the standard not specify what the
> result should be, but that no one else does, either.  In principle, the
> result is permitted to be non-deterministic on a single machine, let alone
> on a single implementation.

Yes, non-deterministic describes it fine.

> I would expect "implementation-dependent" to mean that the choice is up to
> the implementation.  I see you often use "implementation-defined," which I
> would interpret to mean that it is the responsibility of the implementation
> to specify what it will do and then to do what it specified?

Exactly. The behavior could even depend on a compiler option.

> If those interpretations are consistent with standard writing practice, is
> there a reason to leave ANYTHING "undefined?"  If we cannot specify results
> for each implementation, should not the implementers be required to specify,
> that is, to be "implementation-defined"?

When you specify that, for some entries, the result is implementation-
defined, it means you force the implementer to test for these specific
entries, to define a result, and to document it. Let us consider the two
ways of querying a lower bound in the proposal.

On one hand, x.lower() returns the lower bound of x. But if x is empty,
the result is undefined. On the other hand, inf(x) returns the lower
bound of x, or infinity if x is empty. But if x is empty and infinities
do not exist, the result is implementation-defined.

As a consequence, a library implementer is allowed to write a trivial
version of lower: this is just a memory read. It is also possible to
assert that the interval is not empty. Indeed, a failed assertion is a
typical example of undefined behavior, so this is allowed.

For inf, the situation is different: the behavior is always defined,
whether x is empty or not. The implementation has to test for this case
and deal with it in a documented manner. If the implementation provides
infinities, the standard specify what the result is. Otherwise, it is up
to the implementation to specify it.

I hope this illustrates that allowing undefined behavior on some inputs
allows to write more efficient code. The lower member could have been
changed to "implementation-defined", but then it may have considerably
slowed down codes that are known not to generate empty intervals. On the
other hand, it means the user has to be careful and use inf if the code
can generate empty intervals. I think this is a good compromise.

> If that makes sense, would it also make sense to specify that
> implementations on IEEE machines take advantage of IEEE support?  For
> example, one might say, "On machines that support infinities, ... On other
> machines, ... is implementation-defined."  That would be a MUCH stronger
> specification of portability without imposing additional requirements in
> practice.

Note that this is already the case for inf(). For other functions, it
would depend on what you put behind your "..." dots. Note also that the
current wording impose the use of infinities for arithmetic functions if
the implementation supports them, as they are the only way to enclose
some theoretical interval results. So the question becomes: should we
impose implementations to document the results they return when they
would have to return an interval containing an infinite bound? I'm not
sure it is worth it, as I don't see how such a documentation would help
developers.

Best regards,

Guillaume

From george.corliss@marquette.edu Thu Sep 14 10:40:49 2006
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Guillaume,

Thank you for your response.

>> * Default initialization
>> I see on page 15 that the default constructor creates an empty interval.
>>  At some point in the discussion, Sylvain gave 6 possible ways of
>> implementing this constructor:
>> 
>> 1- no default constructor at all
>> 2- [0,0]
>> 3- empty
>> 4- whole
>> 5- uninitialized tag
>> 6- see below (something a la "singular iterator")
>> 
>> Possibility 4 was brushed away from the start, and the remaining
>> possibilities heavily debated. In my opinion, it makes sense to have the
>> default constructor return "whole" since interval arithmetic is often
>> used in processes that try to gain some information on the possible
>> value of a variable (that is, we start from a wide interval and narrow
>> it down to some reasonably small one).
> 
> I don't remember 4 being brushed right away (proposition 1 was). As a
> matter of fact, propositions 3 and 4 have reached a point in my opinion
> where I consider them to be equally useful. So, at least on my side, it
> is still 4 in the proposal, only because of inertia.
P. 15, 26.6.4, par. 1 & 2 says empty, which is #3.

As I discussed in an earlier message, I favor <whole>

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From george.corliss@marquette.edu Thu Sep 14 11:06:53 2006
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Subject: Re: [std-interval] Revised document available
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Guillaume,

Very helpful response.  Thank you.

>> If that makes sense, would it also make sense to specify that
>> implementations on IEEE machines take advantage of IEEE support?  For
>> example, one might say, "On machines that support infinities, ... On other
>> machines, ... is implementation-defined."  That would be a MUCH stronger
>> specification of portability without imposing additional requirements in
>> practice.
> 
> Note that this is already the case for inf(). For other functions, it
> would depend on what you put behind your "..." dots.
I am not studying every line of the proposal for instances such as this, but
I hope you are, and that you are satisfied with what you see.

> Note also that the
> current wording impose the use of infinities for arithmetic functions if
> the implementation supports them, as they are the only way to enclose
> some theoretical interval results.
Correct.  That should be clear:  Implementations on IEEE machines are
required to use IEEE features :-)

> So the question becomes: should we
> impose implementations to document the results they return when they
> would have to return an interval containing an infinite bound? I'm not
> sure it is worth it, as I don't see how such a documentation would help
> developers.
I favor the clearest warnings I can convince you to accept.  For example,
suppose x = [1, max_real]; y = x^2.  If the implementation supports
infinity, we are safe with [1, +oo] (really meaning the mathematical
semi-open [1, +oo)).  If we have no infinity, what are our choices?
   1. LIE with something like [1, max_real]
   2. Raise an exception, which no one likes
   3. Some other special bit pattern
   4. Tag to indicate overflow, but we still need to return a value

I believe the most common implementation decision (with no infinities) is to
choose to lie, #1.  I have written a couple packages myself that did that.
I am willing to accept that as an engineering design choice, but with ANY
possible violation of containment, I prefer the strongest, clearest possible
warnings.  I'd like a run-time warning, although that is nearly equivalent
to unpopular exceptions.  AT LEAST mandate a strong warning in the
documentation that an overflow can introduce a containment failure.

We are in violent agreement on most of the proposal.  At points like this, I
think I am a bit more focused on the guarantee of containment, and you are a
bit more focused on speed.

I certainly agree that speed is important.  In fact, I suggest somewhere,
perhaps in the first half of p. 3, you include a reminder to the effect that
EVERYTHING in this standard will perform MUCH better is there is built-in
hardware support for intervals [credit two anonymous referees of one of my
recent papers for reminding us].

I know you agree that containment is important.

Hence, many of these points of discussion are about where on the
speed-safety spectrum we want to be.  Whatever compromises we settle on, we
should clearly document so developers know where they are.

Dr. George Corliss
Electrical and Computer Engineering
Marquette University
P.O. Box 1881
1515 W. Wisconsin Ave.
Milwaukee, WI 53201-1881
George.Corliss@Marquette.edu
414-288-6599 (office); 288-4400 (GasDay);
    288-6280 (Dept.); 288-5579 (fax)
Office: Haggerty Engineering 296
Www.eng.mu.edu/corlissg


From Frederic.Goualard@univ-nantes.fr Thu Sep 14 13:15:45 2006
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Guillaume Melquiond wrote:
> Le jeudi 14 septembre 2006 à 10:21 +0200, Frédéric Goualard a écrit :
> 
>> The nth_root_rel() operator does not appear in the standard. Is this
>> omission on purpose? If indeed it is, why is it so?
> 
> The nth_root_rel is purposely out of the proposal because nth_root is
> out too :-). I don't think the omission is on purpose though. If people
> feel it is useful, it can be added.

In my experience, nth_root() may safely be excluded from the standard 
because it is seldom used. On the other hand, nth_root_rel() is *very* 
important since it is necessary to handle constraints with 
exponentiations, such as constraints on polynomials!

For example, to handle the constraint

x^5 = y

with a backward/forward algorithm (see "Revising hull and box 
consistency". F. Benhamou, F. Goualard, L. Granvilliers, and J.-F. 
Puget, Procs. of ICLP'99, pp. 230-244, MIT Press), we would use:

y <- y \cap pow(x,5)
x <- x \cap nth_root_rel(y,5,x)

Excluding nth_root_rel() from the standard makes the introduction of the 
other relational operators basically useless since I believe we have 
more often to deal with constraints containing exponentiations than with 
constraints involving, say, trigonometric functions.

> 
>> Side notes:
>>   - on Page 12, the signatures for the mathematical relations are wrong
>> (compare with page 27).
>>   - div_rel() does not appear on page 27 while it is listed on page 12
> 
> Thanks, I will take a look.
> 
>> * Default initialization
>> I see on page 15 that the default constructor creates an empty interval.
>>  At some point in the discussion, Sylvain gave 6 possible ways of
>> implementing this constructor:
>>
>> 1- no default constructor at all
>> 2- [0,0]
>> 3- empty
>> 4- whole
>> 5- uninitialized tag
>> 6- see below (something a la "singular iterator")
>>
>> Possibility 4 was brushed away from the start, and the remaining
>> possibilities heavily debated. In my opinion, it makes sense to have the
>> default constructor return "whole" since interval arithmetic is often
>> used in processes that try to gain some information on the possible
>> value of a variable (that is, we start from a wide interval and narrow
>> it down to some reasonably small one).
> 
> I don't remember 4 being brushed right away (proposition 1 was). As a
> matter of fact, propositions 3 and 4 have reached a point in my opinion
> where I consider them to be equally useful. So, at least on my side, it
> is still 4 in the proposal, only because of inertia.

You mean "3" of course :o)



Cheers,

FG.
-- 
Frédéric Goualard                                 LINA - FRE CNRS 2729
Tel.: +33 2 51 12 58 38    Univ. of Nantes - Ecole des Mines de Nantes
Fax.: +33 2 51 12 58 12            2, rue de la Houssinière - BP 92208
http://goualard.free.fr/                        F-44322 NANTES CEDEX 3

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Guillaume Melquiond wrote:
> Le jeudi 14 septembre 2006 à 10:21 +0200, Frédéric Goualard a écrit :
> 
>> The nth_root_rel() operator does not appear in the standard. Is this
>> omission on purpose? If indeed it is, why is it so?
> 
> The nth_root_rel is purposely out of the proposal because nth_root is
> out too :-). I don't think the omission is on purpose though. If people
> feel it is useful, it can be added.

Let's be careful with the list of functions, especially those hard
to implement.  Having too many may trigger resistance from the C++
committee.  I already fear that the changes done in the revision
won't be appreciated a lot on that aspect...  But we'll see.


>> * Default initialization
>> I see on page 15 that the default constructor creates an empty interval.
>>  At some point in the discussion, Sylvain gave 6 possible ways of
>> implementing this constructor:
>>
>> 1- no default constructor at all
>> 2- [0,0]
>> 3- empty
>> 4- whole
>> 5- uninitialized tag
>> 6- see below (something a la "singular iterator")
>>
>> Possibility 4 was brushed away from the start, and the remaining
>> possibilities heavily debated. In my opinion, it makes sense to have the
>> default constructor return "whole" since interval arithmetic is often
>> used in processes that try to gain some information on the possible
>> value of a variable (that is, we start from a wide interval and narrow
>> it down to some reasonably small one).
> 
> I don't remember 4 being brushed right away (proposition 1 was). As a
> matter of fact, propositions 3 and 4 have reached a point in my opinion
> where I consider them to be equally useful. So, at least on my side, it
> is still 4 in the proposal, only because of inertia.

As George says, there is indeed no perfect choice.  I can see good
arguments supporting 2, 3, 4, 6 (I see 5 as a debug mode allowed by 6).

The debug mode, 5, (e.g. using a tag) can be envisioned for the
other cases than 6 as well, but then it's not a bug anymore to not
initialize, so it might become hard to distinguish forgotten
initializations from correct code assuming the documented default
constructed value.

"empty" can help for propagating uninitialized-ness, as George
mentioned, and it was my argument for picking this choice in the
proposal.  But it's incomplete, since there are cases where it
does not propagate (e.g. with branches).
(while at it : concerning the propagation of empty, the current
proposal does not say anything, since any function taking empty
can return any interval: are there opinions on the sharpness of
returned intervals in this case?  we could easily enforce empty
as returned interval)

6 also has the advantage of speed, I'm thinking especially of array
initialization.

I'm not very convinced by the arguments which have been given so
far in favor of "whole", because I think they mix the correctness
issue of forgotten initializations, with the preferred value of
the initializations of variables in *some* algorithms.
Such algorithms should initialize variables explicitly to "whole",
IMO.  And given that there is no clear intuitive default, users
will never remember that "whole" is used as default value, so
in practice it will be better to use "whole" explicitly anyway
for these cases, so no need to make it the default constructed
value.  If somebody thinks it would be too inconvenient to require
an explicit initialization to "whole" for some codes, I would be
interesting in seeing such codes.

My personal preference goes to 6 (i.e. producing an "uninitialized
interval", similar to the behavior of iterators, that is, only
copies/assignments are allowed on them, basically).

-- 
Sylvain
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(Ron, I guess you mistakenly replied to me personally,
  so I re-reply on the list).

Ron Avitzur wrote:
>>>>  1- no default constructor at all
>>>>  2- [0,0]
>>>>  3- empty
>>>>  4- whole
>>>>  5- uninitialized tag
>>>>  6- see below (something a la "singular iterator")
>>
>> As George says, there is indeed no perfect choice.  I can see good
>> arguments supporting 2, 3, 4, 6 (I see 5 as a debug mode allowed by 6).
> 
> In defense of 1, I'll reiterate my concern from April that folks expect
> declaring  { double foo[kSize]; ...} is free while having any default
> constructor can make { interval<double> foo[kSize]; ... } in an inner
> loop be very costly.
> 
> I encountered precisely this a few years ago in a context that made it
> very difficult to recognize the inefficiency.

So, you are arguing for 6, like me.

1 means no default constructor, that is, a private one.
At least, this is how I understood 1.

-- 
Sylvain
From chu@uca.edu Thu Sep 14 14:22:12 2006
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Agree with George that there is no perfect answer. Not seeing explicit
support for 2 - [0,0] yet. However, it saves initialization time
significantly for applications involving large-scale sparse systems.

Chenyi

>>> Sylvain Pion <Sylvain.Pion@sophia.inria.fr> 9/14/2006 5:01 PM >>>

Ron Avitzur wrote:
>>>>  1- no default constructor at all
>>>>  2- [0,0]
>>>>  3- empty
>>>>  4- whole
>>>>  5- uninitialized tag
>>>>  6- see below (something a la "singular iterator")
>>
>> As George says, there is indeed no perfect choice.  I can see good
>> arguments supporting 2, 3, 4, 6 (I see 5 as a debug mode allowed by
6).
> 
> In defense of 1, I'll reiterate my concern from April that folks
expect
> declaring  { double foo[kSize]; ...} is free while having any
default
> constructor can make { interval<double> foo[kSize]; ... } in an
inner
> loop be very costly.
> 
> I encountered precisely this a few years ago in a context that made
it
> very difficult to recognize the inefficiency.

So, you are arguing for 6, like me.

1 means no default constructor, that is, a private one.
At least, this is how I understood 1.

-- 
Sylvain
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Chenyi Hu wrote:
> Agree with George that there is no perfect answer. Not seeing explicit
> support for 2 - [0,0] yet. However, it saves initialization time
> significantly for applications involving large-scale sparse systems.

6 is even faster than 2 anyway, since it does not require to do
anything.

2 may indeed be faster than 3 and 4, if zero-initialization of memory
is faster than initialization to something else.  I don't know if some 
platforms show such behavior.

The only argument I see for 2 is that is it similar to std::complex,
and similar to built-in floating-point types for the explicit
zero-initialization (i.e. "double d = double();" actually initializes
to 0).


> Chenyi
> 
>>>> Sylvain Pion <Sylvain.Pion@sophia.inria.fr> 9/14/2006 5:01 PM >>>
> 
> Ron Avitzur wrote:
>>>>>  1- no default constructor at all
>>>>>  2- [0,0]
>>>>>  3- empty
>>>>>  4- whole
>>>>>  5- uninitialized tag
>>>>>  6- see below (something a la "singular iterator")
>>> As George says, there is indeed no perfect choice.  I can see good
>>> arguments supporting 2, 3, 4, 6 (I see 5 as a debug mode allowed by
> 6).
>> In defense of 1, I'll reiterate my concern from April that folks
> expect
>> declaring  { double foo[kSize]; ...} is free while having any
> default
>> constructor can make { interval<double> foo[kSize]; ... } in an
> inner
>> loop be very costly.
>>
>> I encountered precisely this a few years ago in a context that made
> it
>> very difficult to recognize the inefficiency.
> 
> So, you are arguing for 6, like me.
> 
> 1 means no default constructor, that is, a private one.
> At least, this is how I understood 1.
> 


-- 
Sylvain
From avitzur@PacificT.com Thu Sep 14 14:35:09 2006
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>>>>>   1- no default constructor at all
>>>>>   2- [0,0]
>>>>>   3- empty
>>>>>   4- whole
>>>>>   5- uninitialized tag
>>>>>   6- see below (something a la "singular iterator")
>
>So, you are arguing for 6, like me.
>
>1 means no default constructor, that is, a private one.
>At least, this is how I understood 1.

Yes. I had misremembered the earlier discussion. Going back to

  http://compgeom.poly.edu/pipermail/std-interval/2006-April/000040.html

6 most closely resembles the behavior of built-in types.
From avitzur@PacificT.com Thu Sep 14 15:09:05 2006
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>if zero-initialization of memory is faster than initialization to
>something else.  I don't know if some platforms show such behavior.

Zero initialization of arrays can be much faster on PowerPC with the
dcbz instruction which zeros a cache line. This is much faster than
assigning the 0 value to memory because the assignment may first cause the
entire cache line to be read in from main memory which can be very slow.
That's unnecessary when the entire cache line is to be overwritten anyway.

Also, if I recall correctly on Mac OS X, the Mach kernel zero-fills
memory as a security feature when an anonymous memory page is used
for the first time.

However, I'm just responding to the specific question about
initialization to zero. I don't think this level of system-specific
performance lore is relevant to the discussion.
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Sylvain and all,

>>> 1- no default constructor at all
>>> 2- [0,0]
>>> 3- empty
>>> 4- whole
>>> 5- uninitialized tag
>>> 6- see below (something a la "singular iterator")
Could someone fill me in?  I'm not familiar with "singular iterator", and I
found nothing "below" in the original message that helped me understand what
is #6.  Is #6 equivalent to "undefined," in the sense that what you get is
whatever bit pattern happened to be in that memory location from its
previous use?

> (while at it : concerning the propagation of empty, the current
> proposal does not say anything, since any function taking empty
> can return any interval: are there opinions on the sharpness of
> returned intervals in this case?  we could easily enforce empty
> as returned interval)
Ouch!  Yes, that is a (unintended?) consequence of not specifying tightness.

> 6 also has the advantage of speed, I'm thinking especially of array
> initialization.
My understanding of C++ is that happens often, since in some parameter
passing, a default constructor is called and then the appropriate values are
copied into those locations.  Is that close?  Is that why is is a TOTAL
waste of time to initialize an array that is about to be filled anyway?

> I'm not very convinced by the arguments which have been given so
> far in favor of "whole", because I think they mix the correctness
> issue of forgotten initializations, with the preferred value of
> the initializations of variables in *some* algorithms.
> Such algorithms should initialize variables explicitly to "whole",
> IMO.  
No, we agree that it is bad programming practice to rely on default
initializations, no matter what they are.  I am talking about the extent to
which we can protect the careless programmer who forgets to initialize the
variable before using it.

> And given that there is no clear intuitive default, users
> will never remember that "whole" is used as default value, so
> in practice it will be better to use "whole" explicitly anyway
> for these cases, so no need to make it the default constructed
> value.  If somebody thinks it would be too inconvenient to require
> an explicit initialization to "whole" for some codes, I would be
> interesting in seeing such codes.
Does the same argument apply for empty?

I think whole and empty are equivalent in that argument.

Here are two careless programs:

Example 1.
Interval X I think is 1, but it is built with a default constructor that
defaults to empty.
Y = [-1]
Z = HULL (X, Y) 
I think Z encloses all values of sin, but it does not because it is [-1]
I assert that is a containment failure.

Example 2.
Interval X I think is 1, but it is built with a default constructor that
defaults to whole.
Y = [2, 4]
Z = [-3] + set difference Y \ X.
I think Z encloses all values of sin, but it does not because it is empty
I assert that is a containment failure.

Conclusion: NEITHER empty nor whole are immune to containment failure.

I think whole and empty are equivalent in that argument.

Conclusion 2: My case against #6 is pretty weak.

My case favoring whole over empty is not very good, either.


> My personal preference goes to 6 (i.e. producing an "uninitialized
> interval", similar to the behavior of iterators, that is, only
> copies/assignments are allowed on them, basically).
Assuming I have understood what you mean by #6, I am forced to agree.

George


From j.d.pryce@ntlworld.com Thu Sep 14 14:37:53 2006
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--=====================_135644110==_
Content-Type: text/plain; charset="us-ascii"; format=flowed

Dear std-intervalers,

At 09:16 12/09/06, Sylvain Pion wrote:
>A revised version of the proposal is now available at:
>http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2067.pdf

I aim to comment on the revised proposal in several separate messages 
addressing various aspects. Here is the first one. The views are my 
own, but mostly shared by the other four members of the ISL project team.

As you will know, ISL favours a cset-based standard. In case readers 
have missed them, please find attached the following.
- The current version of ISL's interval standard proposal, dated 7 June 2006.
   We are working on a revision in the light of [std-interval] discussions.
   In particular we support Lee Winter's arguments in favour of allowing (but
   not mandating) tags.
- The paper by Pryce and Corliss "Interval Arithmetic with Containment
   Sets", accepted for publication in Springer "Computing". This is a
   wide ranging discussion of theoretical and practical issues.

Herve, Guillaume, Sylvain: Your current version improves on the 
previous in many ways. In particular the specifications of arithmetic 
operations are now much cleaner and closer to the mathematics. It is 
now mandatory for I/O to respect inclusion. The C++ code has been 
tidied up, e.g. by removing the "numeric specializations" to float, 
double & long double, which turned out to be unnecessary.

I want to comment first on the use of "undefined". Is it appropriate 
to specify an "undefined" result in so many cases?
E.g. p15-16 #4,10,12,15,... These are functions central to the 
interval system, yet using any of them, even once, makes it 
impossible to assert portability of a program. For a package aimed at 
high-integrity programming this makes no sense.

For instance. At present "interval(NaN)" is mandated to return empty, 
but "interval(NaN, NaN)" need not. What happens if a safety-critical 
program developed on a system where "interval(NaN, NaN)" returns 
empty is ported to one where it returns whole, or some other value, 
or raises an exception?

The vast majority of machines on which interval computation will be used are
- IEEE-conforming;
- used by the general scientific community, for whom portability and
   future-proofing of code is vastly important.

On a non-IEEE machine, if interval computation is used I believe it 
will be for a specialist purpose (e.g. embedded processor in 
avionics). Portability FROM such a machine TO a different platform 
will not be so important.

The standard should respect the needs of both these types of application.

I propose that it leave NOTHING undefined on IEEE platforms, while 
allowing "undefined", "unspecified" or "implementation-defined" on 
non-IEEE platforms. (Maybe the choice between these three options, 
for a platform whose users are not concerned with portability, should 
be left to the house-rules defined by their managers.) Actually, of 
the 10 occurrences of "undefined" in your draft standard text, I 
don't see a reason against changing them all to 
"implementation-defined" for non-IEEE, and giving a specific 
definition for IEEE.

Regards

John Pryce  
--=====================_135644110==_
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