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Re: Computer arithmetic problems worth exploring

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  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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#1374 — Re: Computer arithmetic problems worth exploring

On Sun, 27 Feb 2011 19:13:30 -0800 (PST), Quadibloc
<jsavard@ecn.ab.ca> wrote:

>On Feb 26, 10:41 pm, MitchAlsup <MitchAl...@aol.com> wrote:
>
>> Minor note: One CAN build a reciprocator tree and its only about 2X
>> the logic of a multiplier tree (ala CRAY). We don't for two reasons,
>> programmers seem to want division, and IEEE 754 accuracy cannot be
>> maintained with reciprocation.
>
>Programmers lived for a long time without IEEE 754 accuracy, though...
>
>John Savard

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

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#1375

In article <vir9s650jhccr639kr9s3bofe6rqc9ih1t@4ax.com>,
George Neuner  <gneuner2@comcast.net> wrote:
>On Sun, 27 Feb 2011 19:13:30 -0800 (PST), Quadibloc
><jsavard@ecn.ab.ca> wrote:
>>On Feb 26, 10:41 pm, MitchAlsup <MitchAl...@aol.com> wrote:
>>
>>> Minor note: One CAN build a reciprocator tree and its only about 2X
>>> the logic of a multiplier tree (ala CRAY). We don't for two reasons,
>>> programmers seem to want division, and IEEE 754 accuracy cannot be
>>> maintained with reciprocation.
>>
>>Programmers lived for a long time without IEEE 754 accuracy, though...
>
>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.

And how :-(  Most of the claims for the benefits of IEEE 754 are
based on a complete misunderstanding of this area.  For example,
it does have increased accuracy - in some restricted senses - but
using it does NOT necessarily give any more accuracy in a final
result than using any other reasonable scheme.  As you know,
but very few do, consistency and repeatability are not closely
associated with accuracy.

And using its advanced properties is WAY beyond the ability of
99.9% of modern programmers :-(


Regards,
Nick Maclaren.

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#1377

nmm1@cam.ac.uk wrote:
> As you know,
> but very few do, consistency and repeatability are not closely
> associated with accuracy.

Regrettably that kind of misapprehension is not limited to
programmers: engineers (and especially engineers-mutated-into-managers)
are also prone to it. I've lost count of the times I've been asked for
"accurate measurements" (or similar), with zero comprehension of the
inadequacy of that type of question.

When it is important, i.e. typically a manager, I take the time to
tell them the story of a very expensive attenuation test set with a
repeatability of 0.001dB - even though its accuracy was only 0.1dB.

It usually takes a couple of minutes to be sure that they haven't
misheard and have understood the 100-fold "discrepancy". Unless they
are especially clueless, they are sufficiently interested to learn that
it was use for testing the attenuation of transatlantic telephone
cables as a function of temperature. Since the cable drums were rather
large, it took a week in an oven to change the cable's temperature,
and the attenuation only changed by a small fraction of a dB. Nobody
cared what the actual attenuation was - only the change in attenuation.

And don't get me started on what I once saw inside an application for
a financial payments system. Basically it was frig the floating point
arithmetic until the small number of specified unit tests passed.
I damn near resigned on the spot.

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#1381

In article <vi9xp.6$lm2.1@newsfe17.ams2>,
Tom Gardner  <spamjunk@blueyonder.co.uk> wrote:
>
>> As you know,
>> but very few do, consistency and repeatability are not closely
>> associated with accuracy.
>
>Regrettably that kind of misapprehension is not limited to
>programmers: engineers (and especially engineers-mutated-into-managers)
>are also prone to it. I've lost count of the times I've been asked for
>"accurate measurements" (or similar), with zero comprehension of the
>inadequacy of that type of question.

Rregrettably, also applies to many scientists :-(  The worst I
ever saw was a physicist who refused to be persuaded that the
numbers displayed by a machine to 5 D.P. would not lead to
results accurate to 12 D.P., and asserted that our mainframe
was broken and needed fixing.  After an hour and a half, my
colleague (a numerical analyst) and I threw him out and I rang
his supervisor and mentioned his name.  "Oh, God, what has he
done NOW?"

>And don't get me started on what I once saw inside an application for
>a financial payments system. Basically it was frig the floating point
>arithmetic until the small number of specified unit tests passed.
>I damn near resigned on the spot.

Sigh.  Been there - seen that.  It's VERY hard to persuade Superior
People (e.g. executives or senior professors) of their delusions.


Regards,
Nick Maclaren.

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#1382

nmm1@cam.ac.uk wrote:
> In article<vi9xp.6$lm2.1@newsfe17.ams2>,
> Tom Gardner<spamjunk@blueyonder.co.uk>  wrote:
>>
>>> As you know,
>>> but very few do, consistency and repeatability are not closely
>>> associated with accuracy.
>>
>> Regrettably that kind of misapprehension is not limited to
>> programmers: engineers (and especially engineers-mutated-into-managers)
>> are also prone to it. I've lost count of the times I've been asked for
>> "accurate measurements" (or similar), with zero comprehension of the
>> inadequacy of that type of question.
>
> Rregrettably, also applies to many scientists :-(  The worst I
> ever saw was a physicist who refused to be persuaded that the
> numbers displayed by a machine to 5 D.P. would not lead to
> results accurate to 12 D.P.,

Which reminds me of a two hour argument with an (alleged) software
engineer about why it isn't possible to get a more accurate value
simply by doing a linear interpolation between two successive
samples in a sampled data system. Directing him to reference on
the sampling theorem worked, but probably because he couldn't
understand it.

> and asserted that our mainframe
> was broken and needed fixing.  After an hour and a half, my
> colleague (a numerical analyst) and I threw him out and I rang
> his supervisor and mentioned his name.  "Oh, God, what has he
> done NOW?"

You were lucky: you got some satisfaction!


>> And don't get me started on what I once saw inside an application for
>> a financial payments system. Basically it was frig the floating point
>> arithmetic until the small number of specified unit tests passed.
>> I damn near resigned on the spot.
>
> Sigh.  Been there - seen that.  It's VERY hard to persuade Superior
> People (e.g. executives or senior professors) of their delusions.

Or, in my case, plain old engineers (technicians really, but
they didn't know that), who needed to get management off their
back. Unfortunately it was engineering management (not commercial
management) that ought to have known and cared - hence my near
resignation.

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#1383

On May 7, 6:47 am, Tom Gardner <spamj...@blueyonder.co.uk> wrote:

> Or, in my case, plain old engineers (technicians really, but
> they didn't know that), who needed to get management off their
> back.

One would think that even the lowliest technician would understand -
the purpose of testing some cases is to determine that the system is
likely to give the correct answer in _all_ cases.

Was someone in management *telling* them they had to use floating-
point arithmetic, because it performed better? That is the only excuse
I could imagine for such conduct. They should have known that instead
of coding special cases, what they had to do was use integer
arithmetic so as to get the answers right.

Most floating-point representations, though, as long as you don't
exceed their precision, do allow integers to be handled accurately.
So, if, for example, their machine didn't have a long enough binary
integer, and they were programming in FORTRAN and not PL/I or COBOL,
so they couldn't use the decimal data type (if it was a 360 which even
had one)... so they had to use double-precision floating point...

then just multiply the amounts by 100 so it's an integer number of
pennies! (Or 240 in the United Kingdom before decimalisation.)

John Savard

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#1384

Quadibloc wrote:
> On May 7, 6:47 am, Tom Gardner<spamj...@blueyonder.co.uk>  wrote:
>
>> Or, in my case, plain old engineers (technicians really, but
>> they didn't know that), who needed to get management off their
>> back.
>
> One would think that even the lowliest technician would understand -
> the purpose of testing some cases is to determine that the system is
> likely to give the correct answer in _all_ cases.

Well, yes.

However, testing was a new concept to them: previously they
coded then threw the code over a wall to the testers.
Repeatedly. So that a 2 day job took 6 months.

They had recently been through a training course by external
consultants that taught that first you write the tests, then
fiddle with your code until the code gives the right results.
That's actually a reasonable technique (and better than many),
provided that it in addition to sane engineering practices
(or, if you believe in the concept, "common  sense" engineering
practices).


> Was someone in management *telling* them they had to use floating-
> point arithmetic, because it performed better?

I didn't dare ask. I suspect it was completely inadequate supervision
by people that *did* know better but couldn't afford to rock the boat
(I've never had such qualms).


> That is the only excuse
> I could imagine for such conduct. They should have known that instead
> of coding special cases, what they had to do was use integer
> arithmetic so as to get the answers right.

Actually, for the application under consideration, it wasn't clear
that the properties of integer arithmetic led to fewer "problems"
than the properties of floating point arithmetic.


> Most floating-point representations, though, as long as you don't
> exceed their precision, do allow integers to be handled accurately.
> So, if, for example, their machine didn't have a long enough binary
> integer, and they were programming in FORTRAN and not PL/I or COBOL,
> so they couldn't use the decimal data type (if it was a 360 which even
> had one)... so they had to use double-precision floating point...
>
> then just multiply the amounts by 100 so it's an integer number of
> pennies! (Or 240 in the United Kingdom before decimalisation.)

Fine, until you have to divide by 60, then multiply by 60 and expect
to get the number you first thought of :)

Yes, I can guess what you're going to say next.

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#1386

On May 7, 12:27 pm, Tom Gardner <spamj...@blueyonder.co.uk> wrote:

> Yes, I can guess what you're going to say next.

Well, of course *you* could; the trouble, of course, was that they
couldn't. But then I remember helping a programmer with his shiny new
IBM PC AT who was drawing a pie chart... but was making a mess of it.
Because he had never heard of something called "radians".

Thus, I am well aware that even in the old days, before people
programmed their own computers and learned BASIC on the street, as it
were, people were often thrown at computers, having been taught only
the essentials of a programming language, but without knowledge of
such matters as numerical analysis.

John Savard

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#1403

On Sat, 7 May 2011 13:54:22 -0700 (PDT), Quadibloc <jsavard@ecn.ab.ca>
wrote:

>On May 7, 12:27 pm, Tom Gardner <spamj...@blueyonder.co.uk> wrote:
>
>> Yes, I can guess what you're going to say next.
>
>Well, of course *you* could; the trouble, of course, was that they
>couldn't. But then I remember helping a programmer with his shiny new
>IBM PC AT who was drawing a pie chart... but was making a mess of it.
>Because he had never heard of something called "radians".

To be fair, I've always thought forcing drawing APIs to work only in
radians is a mistake ... the functions at minimum should accept
radians, DMS and decimal degrees.  

You have to remember that most people in the US are under-educated.
Many never took trigonometry (or don't remember it if they did), nor
do they handle fractions or long decimals well.  

Most people IME quickly understand DMS, but many people have trouble
with radians - there's something about having 2 PIs in a pie that jams
the mental machinery.  Everyone knows 1 pie is a circle so why is 1 PI
half a circle?  "What jackass came up with that?".   And then
fractions are thrown in on top and everything collapses.

I also think having the y-axis reversed by default is a mistake.  What
little graphing most people did in school almost invariably involved
the origin at bottom left of the paper.  While most every API allows
to relocate the origin, IMO the default should be the bottom left of
the screen/window/surface.

I don't think newbies should be coddled, but I do believe it's
important that they get positive feedback quickly when they do
something right.  Scale and coordinate conversions should not be
required as part of the initial experience of drawing a simple graph
like they learned in algebra (which is all some people may ever want
to do).  They can discover the delights of trigonometry later when
they try something harder.

YMMV,
George

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#1423

George Neuner <gneuner2@comcast.net> writes:

> Most people IME quickly understand DMS, but many people have trouble
> with radians - there's something about having 2 PIs in a pie that jams
> the mental machinery.  Everyone knows 1 pie is a circle so why is 1 PI
> half a circle?  "What jackass came up with that?".

Google for the paper "pi is wrong".

- Bob

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#1427

Robert A Duff wrote:
> George Neuner<gneuner2@comcast.net>  writes:
>
>> Most people IME quickly understand DMS, but many people have trouble
>> with radians - there's something about having 2 PIs in a pie that jams
>> the mental machinery.  Everyone knows 1 pie is a circle so why is 1 PI
>> half a circle?  "What jackass came up with that?".
>
> Google for the paper "pi is wrong".

Personally I prefer to use circle count, i.e.

2*pi radians == 360 degrees == 1 circle.

This is worthwhile simply because it makes trig argument reduction both 
(almost) trivial and exact.

Terje

-- 
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"

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#1397

Quadibloc <jsavard@ecn.ab.ca> writes:


> One would think that even the lowliest technician would understand -
> the purpose of testing some cases is to determine that the system is
> likely to give the correct answer in _all_ cases.

With emphasis on "likely", as no amount of testing can prove the absense
of errors.

	Torben

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#1379

On May 7, 2:44 am, n...@cam.ac.uk wrote:

> And using its advanced properties is WAY beyond the ability of
> 99.9% of modern programmers :-(

This is true, but so is avoiding getting into *worse* trouble when
floating-point misbehaves, like IBM 360 floating-point.

I agree that for the most part, the added benefits of IEEE 754 usually
make very little difference - floating-point numbers are usually used
in ways that make thinking of them as inherently approximate *not* a
mistake, and, thus, the effort used to get the absolutely closest
possible result is largely wasted (and increases the latency or
expense of division).

John Savard

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#1380

In article <42a8e7d9-f8fc-433d-83fe-4a96998c90f3@s9g2000yqm.googlegroups.com>,
Quadibloc  <jsavard@ecn.ab.ca> wrote:
>
>> And using its advanced properties is WAY beyond the ability of
>> 99.9% of modern programmers :-(
>
>This is true, but so is avoiding getting into *worse* trouble when
>floating-point misbehaves, like IBM 360 floating-point.

Actually, no, not at all - I am pretty sure that you were responding
to a different assertion.  I agree that IEEE 754 has fewer gotchas
than IBM 360, but that's not what I said.

I was specifically talking about using its advanced features:
directed rounding, use of its flags, use of infinities and NaNs,
and a few more obscure aspects.  And using THOSE is a HELL of a
lot harder than just using IBM 360 - at least if you need to get
it right!


Regards,
Nick Maclaren.

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#1387

On 5/7/2011 12:06 AM, George Neuner wrote:
> On Sun, 27 Feb 2011 19:13:30 -0800 (PST), Quadibloc
> <jsavard@ecn.ab.ca>  wrote:
>
>> On Feb 26, 10:41 pm, MitchAlsup<MitchAl...@aol.com>  wrote:
>>
>>> Minor note: One CAN build a reciprocator tree and its only about 2X
>>> the logic of a multiplier tree (ala CRAY). We don't for two reasons,
>>> programmers seem to want division, and IEEE 754 accuracy cannot be
>>> maintained with reciprocation.
>>
>> Programmers lived for a long time without IEEE 754 accuracy, though...
>>
>> John Savard
>
> 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
(1) are unlikely to be hurt by IEEE accuracy
(2) are less likely to be surprised by things like x-y=0 not being 
equivalent to x=y

It's not a substitute for numerical analysis, but it helps a bit.

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#1405

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:
>> On Sun, 27 Feb 2011 19:13:30 -0800 (PST), Quadibloc
>> <jsavard@ecn.ab.ca>  wrote:
>>
>>> On Feb 26, 10:41 pm, MitchAlsup<MitchAl...@aol.com>  wrote:
>>>
>>>> Minor note: One CAN build a reciprocator tree and its only about 2X
>>>> the logic of a multiplier tree (ala CRAY). We don't for two reasons,
>>>> programmers seem to want division, and IEEE 754 accuracy cannot be
>>>> maintained with reciprocation.
>>>
>>> Programmers lived for a long time without IEEE 754 accuracy, though...
>>>
>>> John Savard
>>
>> 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
>(1) are unlikely to be hurt by IEEE accuracy

Yes.

>(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.  

Even having arbitrary precision they can get into trouble quickly
enough ... more than half of the newbie questions in the Lisp and Java
forums are related to arithmetic and "why is this answer wrong".  Lisp
has arbitrary integer fractions but not arbitrary decimals, so the
moment there is a conversion from exact fraction to inexact FP (or the
reverse)  the newbie gets an unexpected answer.  In Java BigDecimal is
not the default floating point type (and is harder than it should be
to use) so newbie questions start with the typical "the answer is
wrong", progress to "how do I use this stupid BD package to get the
right answer?" and end with whining about why BD isn't the default.

>It's not a substitute for numerical analysis, but it helps a bit.

Forget numerical analysis - most students in the US never take
calculus.  Many colleges don't require any more than 2 algebra courses
to get a non-math liberal arts degree.  Even business majors typically
only need add a statistics course.  Unless the person went to a top
tier school or was ambitiously taking electives, the odds are low that
a liberal arts major will have had any higher maths.

George

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#1408

In article <8l9gs6d9ckhfqcmq4u261qqgtu3mu0a1ft@4ax.com>,
George Neuner  <gneuner2@comcast.net> wrote:
>On Sat, 07 May 2011 14:59:10 -0700, "Andy \"Krazy\" Glew"
><andy@SPAM.comp-arch.net> wrote:
>
>>Unsophisticated programmers
>>(1) are unlikely to be hurt by IEEE accuracy
>
>Yes.

Not entirely.  They may be unlucky enough to trip over a really
unstable calculation.  Of course, increasing the accuracy wouldn't
actually help ....

>>(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.  

The former is one of the arguments in favour of denormals.  My
counter-example is that they don't need to be very sophisticated
to be caught by x .ne. 0 but x+1.1 = x.  It's seriously bad news
in many numerical algorithms!


Regards,
Nick Maclaren.

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#1409

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.

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#1418

In article <4DC854BF.8090308@SPAM.comp-arch.net>,
Andy \"Krazy\" Glew <andy@SPAM.comp-arch.net> wrote:
>
>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.

As I posted, it does better than some arithmetics, but breaks
some rules that others preserve.

>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.

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.

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.

    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.


Regards,
Nick Maclaren.

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#1425

And Nick Maclaren writes:
> 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.

Not everyone agrees with you, and I'm tired of laying out the
same text again and again.

> It is completely and utterly wrong that x = y does not mean
> that 1/x = 1/y.

Unless you're tracing either side of an air foil, where that
matters.  (Or other conformal mapping with a slice.)  Blame the
standard for supporting users and most architects for insisting
the mode you want be dropped.  (Yes, projective mode was in the
original proposal and was removed because it sank the whole
effort.)

> And, by sick, I mean false positive, false negatives and
> dubious semantics.

Again, not everyone agrees with you, although I do only for
allowing a choice on when to signal underflow.  But then
architects blow a fuse.

> 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.

Again, not everyone agrees with you.  I found it quite handy even
before going to Berkeley and being told the "right" way to use
NaN propagation.

> 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.

If by "dogmatic" you mean "motivated by vector operations at the
time and still in use" and "motivated by the mainframe policies
in operation then".  Nothing in 754 precludes such a mode.
Standardizing such a mode requires standardizing *what* is being
terminated.  Good luck with that.

> 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 a choice that screws a set of users who participated
with code and text during initial standardization.

> 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.

Which is a choice that screws a set of users who participated
with code and text both during initial standardization and during
its "re-visioning."

While I don't like all of the resulting sausage, I know how and
why it happened.
-- 
Jason

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