Re: Computer arithmetic problems worth exploring

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Date	Mon, 09 May 2011 13:55:27 -0700
From	"Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net>
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Subject	Re: Computer arithmetic problems worth exploring
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On 5/9/2011 11:14 AM, George Neuner wrote:
> On Sat, 07 May 2011 14:59:10 -0700, "Andy \"Krazy\" Glew"
> <andy@SPAM.comp-arch.net>  wrote:
>
>> On 5/7/2011 12:06 AM, George Neuner wrote:
>>>
>>> Not only that, but increasingly modern programmers do not understand
>>> floating point arithmetic or how to use it correctly, so additional
>>> accuracy from using 754 algorithms largely is wasted.
>>>
>>> George
>>
>> Although I think that is part of the  point:
>>
>> Unsophisticated programmers
>> (2) are less likely to be surprised by things like x-y=0 not being
>> equivalent to x=y
>
> No.  IME unsophisticated programmers are dumbfounded to discover
> things like x-y=0<>  x=y  and  9(x/9)<>  x.   The simple arithmetic
> they learned in school fails almost immediately unless they happen to
> be lucky enough to be using arbitrary precision arithmetic.

It is possible I expressed myself poorly, that you misunderstood what I 
was trying to say, and that we actually agree:

Unsophisticated programmers are the ones who need as much help as 
possible, preserving simple rules lile x-y=0 <=> x=y.  Which, IIRC, IEEE 
FP provides.

Unfortunately, IEEE FP does not eliminate all of  the gotchas. In 
particular, y(x/y) <> x.

So it is possible that you are arguing that IEEE FP is not safe enough. 
Perhaps you advocate universal default use of rational bignum and 
bigdecimal arithmetic, possibly with symbolic treatment of irrational 
numbers like pi and e and ...

There's good arguments for that, but I'm not going to go that far yet. 
(And, IMHO, just providing bignum rationals  without supporting 
symbolically exact computations involving pi is just a bandaid.)

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.

---

Regulars on comp.arch will know that I am a fan of computer hardware 
instruction set support for "security" like Milo Martin's HardBound. 
Really, this is support that tries to minimize, catch, prevent, many 
common programming bugs that lead to security holes.

IEEE FP, with things like denorms and gradual underflow, is to numerical 
analysis what HardBound is to buffer overflow errors. It's not perfect, 
but it helps, and  is, IMHO, probably a good use of hardware.
     Actually, IEEE FP has much better  arguments for it than the 
"security" support.  It is much less different than existing machines.

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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