Re: Computer arithmetic problems worth exploring

Message-ID	<4DCAF7BA.3010700@SPAM.comp-arch.net> (permalink)
Date	2011-05-11 13:55 -0700
From	"Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net>
Organization	comp-arch.net
Newsgroups	comp.arch
Subject	Re: Computer arithmetic problems worth exploring
References	<bc3f766d-88d5-448e-a344-0b840020b2d9@u12g2000vbf.googlegroups.com> <4DC5C0AE.5000200@SPAM.comp-arch.net> <8l9gs6d9ckhfqcmq4u261qqgtu3mu0a1ft@4ax.com> <4DC854BF.8090308@SPAM.comp-arch.net> <iqark9$oqa$1@gosset.csi.cam.ac.uk>

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On 5/10/2011 1:05 AM, nmm1@cam.ac.uk wrote:
> In article<4DC854BF.8090308@SPAM.comp-arch.net>,
> Andy \"Krazy\" Glew<andy@SPAM.comp-arch.net>  wrote:

>> If we don't go that far, IEEE FP is about as good of a floating point
>> standard as can be achieved. It eliminates most of the FP surprises for
>> unsophisticated programmers that can be eliminated, and still remain FP.
>
> Grrk.  It doesn't do it significantly better than most of the better
> traditional arithmetics do.

Is  IEEE FP better than IBM hex FP?  IMHO yes.

Better than CDC 60 bit FP?  IMHO yes.

But I concede the point:  yes, we can imagine better FP.  I vaguely 
remember reading some of the proposals considered and rejected during 
the IEEE FP standardization effort - or perhaps I saw or read one of 
Kahan's presentations.


Now, the real question:  is it worth fixing?  Is it feasible to fix? 
Could, for example, some SW guy build a "Better FP" library that uses 
some of the things Nick has mentioned, like -0,0,+0, and popularize it? 
  If it was in wide use, then HW might add support?
      Or could some  really brave HW company add  the support, probably 
with an enable that allowed conventional IEEE FP to be supported.
      My guess is that this could not be done in 32 bit - the encodings 
are too tight.  Perhaps in 64 bit. Or in a new, wider, format.


> The thing that IEEE gets spectacularly wrong is its handling of
> exceptional values (including zero, but that's not visible except
> via infinities).  And I mean WRONG.
>
> It is completely and utterly wrong that x = y does not mean that
> 1/x = 1/y.
>
> The argument that it sets a flag would hold water if it were not
> for the fact that the flag handling is seriously sick, as well as
> incompatible with the arithmetic model of all relevant computing
> languages.  And, by sick, I mean false positive, false negatives
> and dubious semantics.

Yes, the idea of setting sticky flags seems to have been a compromise 
that made almost nobody happy.

Personally, I'm all for traps and exceptions as the standard way of 
reporting errors.
    * http://andyglew.blogspot.com/2009/07/error-handling.html
    * http://semipublic.comp-arch.net/wiki/Error_Reporting

But,. it's hard to get traction.

> And its NaN handling is utterly and completely broken, though it
> wasn't half as bad when it was designed.  Blame the fanatics who
> got that into C99, but not only them.
>
> If IEEE 754 had the following modifications, then it would be
> about as good as could be achieved:
>
>      1) There is a mandatory trap-diagnose-and-terminate mode, as
> on traditional mainframes and in LIA-1.  The objection to this
> is and was purely dogmatic.
>
>      2) Division by zero creates a NaN, not an infinity, thus
> removing the main gotch caused by the inconsistent interpretation
> of the sign bit.

Which is better:

-0,0,+0 such that 1/-0=-inf, 1/+0=+inf, 1/0=inf of unknown sign?

Or 1/0 = NaN?



>      3) ALL numeric operations on NaNs return a NaN or raise a
> (hard) exception if they can't (including comparison), and the
> ONLY way to lose a NaN is by an explicit non-numeric test for
> such a value.

Wasn't Kahan conducting a survey about this in CAM a few years ago?

No, actually, it looked like he was  asking leading questions that 
pointed in the direction of getting rid of silent NaNs.

Thread

Re: Computer arithmetic problems worth exploring George Neuner <gneuner2@comcast.net> - 2011-05-07 03:06 -0400
  Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-07 09:44 +0100
    Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-07 11:38 +0100
      Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-07 12:21 +0100
        Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-07 13:47 +0100
          Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-07 09:55 -0700
            Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-07 19:27 +0100
              Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-07 13:54 -0700
                Re: Computer arithmetic problems worth exploring George Neuner <gneuner2@comcast.net> - 2011-05-09 13:38 -0400
                Re: Computer arithmetic problems worth exploring Robert A Duff <bobduff@shell01.TheWorld.com> - 2011-05-10 12:40 -0400
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-10 20:32 +0200
            Re: Computer arithmetic problems worth exploring torbenm@diku.dk (Torben Ægidius Mogensen) - 2011-05-09 13:42 +0200
    Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-07 04:26 -0700
      Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-07 12:13 +0100
  Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-07 14:59 -0700
    Re: Computer arithmetic problems worth exploring George Neuner <gneuner2@comcast.net> - 2011-05-09 14:14 -0400
      Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-09 20:38 +0100
      Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-09 13:55 -0700
        Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-10 09:05 +0100
          Re: Computer arithmetic problems worth exploring Jason Riedy <jason@lovesgoodfood.com> - 2011-05-10 13:24 -0400
            Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-10 18:41 +0100
            Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-11 13:56 -0700
            Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-11 14:04 -0700
            Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-11 14:06 -0700
          Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-11 13:55 -0700
            Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-11 22:15 +0100
              Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-12 20:52 +0100
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-12 20:20 +0100
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-12 14:55 -0700
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-13 12:25 +0200
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-13 11:18 +0100
                Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-14 13:19 -0700
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-14 19:11 -0700
              Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-12 20:08 -0700
            Re: Computer arithmetic problems worth exploring Jason Riedy <jason@lovesgoodfood.com> - 2011-05-12 23:54 -0400
        Re: Computer arithmetic problems worth exploring George Neuner <gneuner2@comcast.net> - 2011-05-12 01:08 -0400
          Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-12 09:27 +0100
            Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-12 05:41 -0700
              Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-12 13:22 +0100
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-12 07:22 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-12 14:58 +0100
                Re: Computer arithmetic problems worth exploring MitchAlsup <MitchAlsup@aol.com> - 2011-05-12 09:23 -0700
                Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-12 22:59 +0000
                Re: Non-constant initializers Ian Collins <ian-news@hotmail.com> - 2011-05-13 11:07 +1200
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-12 23:17 +0000
                Re: Non-constant initializers Ian Collins <ian-news@hotmail.com> - 2011-05-13 11:20 +1200
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-12 23:30 +0000
                Re: Non-constant initializers Ian Collins <ian-news@hotmail.com> - 2011-05-13 11:34 +1200
                Re: Non-constant initializers Keith Thompson <kst-u@mib.org> - 2011-05-12 16:52 -0700
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-14 00:13 +0000
                Re: Non-constant initializers kym@kymhorsell.com - 2011-05-14 01:54 +0000
                Re: Non-constant initializers Columbus sailed the ocean China Blue <chine.bleu@yahoo.com> - 2011-05-14 01:07 -0700
                Re: Non-constant initializers kym@kymhorsell.com - 2011-05-14 09:22 +0000
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-14 17:14 +0000
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-14 00:11 +0000
                Re: Non-constant initializers Columbus sailed the ocean China Blue <chine.bleu@yahoo.com> - 2011-05-12 16:15 -0700
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-12 23:28 +0000
                Re: Non-constant initializers Joe Pfeiffer <pfeiffer@cs.nmsu.edu> - 2011-05-12 18:01 -0600
                Re: Non-constant initializers Keith Thompson <kst-u@mib.org> - 2011-05-12 18:15 -0700
                Re: Non-constant initializers Joe Pfeiffer <pfeiffer@cs.nmsu.edu> - 2011-05-12 22:56 -0600
                Re: Non-constant initializers Seebs <usenet-nospam@seebs.net> - 2011-05-13 05:18 +0000
                Re: Non-constant initializers Fred the Freshwater Catfish <usenet.fred@bdtd.invalid> - 2011-05-13 23:57 +0000
            Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-12 20:20 -0700
              Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-13 09:48 +0100
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-13 12:55 +0200
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-13 11:25 +0100
                Re: Computer arithmetic problems worth exploring MitchAlsup <MitchAlsup@aol.com> - 2011-05-13 08:57 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-13 16:42 +0100
                Re: Computer arithmetic problems worth exploring MitchAlsup <MitchAlsup@aol.com> - 2011-05-13 13:17 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-13 21:03 +0100
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-14 06:43 +0200
                Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-14 06:55 +0100
                Re: Computer arithmetic problems worth exploring "Ken Hagan" <k.hagan@thermoteknix.com> - 2011-05-17 12:59 +0100
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-17 12:44 +0100
                Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-17 14:07 +0100
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-17 17:20 +0100
                Re: Computer arithmetic problems worth exploring "Ken Hagan" <k.hagan@thermoteknix.com> - 2011-05-17 15:03 +0100
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-14 08:43 +0100
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-14 09:17 +0100
                Re: Computer arithmetic problems worth exploring Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-05-14 09:04 -0700
                Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-14 17:00 -0700
                Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-14 16:58 -0700
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-14 19:07 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-15 09:40 +0100
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-16 11:05 +0200
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-16 06:44 -0700
                Re: Computer arithmetic problems worth exploring mac <acolvin@efunct.com> - 2011-05-19 20:17 +0000
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-19 15:20 -0700
                Re: Computer arithmetic problems worth exploring George Neuner <gneuner2@comcast.net> - 2011-05-19 18:51 -0400
                Re: Computer arithmetic problems worth exploring Petter Gustad <newsmailcomp6@gustad.com> - 2011-05-20 08:01 +0200
                Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-20 15:09 -0700
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-20 08:54 +0200
                Re: Computer arithmetic problems worth exploring "Ken Hagan" <k.hagan@thermoteknix.com> - 2011-05-23 11:11 +0100
                Re: Computer arithmetic problems worth exploring George Neuner <gneuner2@comcast.net> - 2011-05-23 18:20 -0400
                Re: Computer arithmetic problems worth exploring Morten Reistad <first@last.name> - 2011-06-03 08:21 +0200
                Re: Computer arithmetic problems worth exploring Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-05-19 13:31 -0700
                Re: Computer arithmetic problems worth exploring Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-05-16 09:05 -0700
                Re: Computer arithmetic problems worth exploring Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-05-16 22:37 +0200
                Re: Computer arithmetic problems worth exploring Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-05-18 23:16 -0700
                Re: Computer arithmetic problems worth exploring ChrisQ <meru@devnull.com> - 2011-05-17 17:10 +0100
                Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-17 17:27 +0100
                Re: Computer arithmetic problems worth exploring ChrisQ <meru@devnull.com> - 2011-05-17 23:08 +0100
                Re: Computer arithmetic problems worth exploring Tom <tggzzz@blueyonder.co.uk> - 2011-05-17 22:37 +0000
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-18 09:25 +0100
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-18 06:25 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-18 14:06 +0100
                Re: Computer arithmetic problems worth exploring Tom Gardner <spamjunk@blueyonder.co.uk> - 2011-05-18 19:23 +0100
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-18 13:48 -0700
                Re: Computer arithmetic problems worth exploring Andrew Reilly <areilly---@bigpond.net.au> - 2011-05-19 00:29 +0000
                Re: Computer arithmetic problems worth exploring "Ken Hagan" <k.hagan@thermoteknix.com> - 2011-05-19 13:12 +0100
                Re: Computer arithmetic problems worth exploring Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-05-18 23:27 -0700
                Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-19 15:19 -0700
                Re: Computer arithmetic problems worth exploring Stephen Fuld <SFuld@alumni.cmu.edu.invalid> - 2011-05-20 07:33 -0700
                Re: Computer arithmetic problems worth exploring Michael S <already5chosen@yahoo.com> - 2011-05-16 03:14 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-16 10:43 +0100
                Re: Computer arithmetic problems worth exploring Michael S <already5chosen@yahoo.com> - 2011-05-16 04:58 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-16 12:40 +0100
                Re: Computer arithmetic problems worth exploring MitchAlsup <MitchAlsup@aol.com> - 2011-05-15 10:12 -0700
                Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-14 13:22 -0700
                Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-15 09:02 +0100
                Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-14 14:02 -0700
          Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-12 20:18 -0700
      Re: Computer arithmetic problems worth exploring Robert Myers <rbmyersusa@gmail.com> - 2011-05-09 14:32 -0700
        Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-09 16:08 -0700

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