Re: complex number in struct form in C

From	Kaz Kylheku <kaz@kylheku.com>
Newsgroups	comp.lang.c
Subject	Re: complex number in struct form in C
Date	2014-12-29 19:40 +0000
Organization	Aioe.org NNTP Server
Message-ID	<20141229112747.367@kylheku.com> (permalink)
References	(7 earlier) <62472149-c09e-42d6-9789-3d62b9b3cdf0@googlegroups.com> <cg5tkrFdk2bU1@mid.individual.net> <m7oa2p$m7a$1@speranza.aioe.org> <onTnw.296096$812.264879@fx20.am4> <m7r9bb$lgf$1@speranza.aioe.org>

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On 2014-12-29, glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote:
> BartC <bc@freeuk.com> wrote:
>
> (snip, I wrote)
>>> Two things that it is generally believed should not be done in
>>> floating point (besides cryptography) are finance and typesetting.
>  
>> The issues with the uses in finance ones we all know about (whether we 
>> agree or not).
>  
>> What problems are you going to get in typesetting?
>
> Knuth wrote that when working on TeX.  For that reason, TeX uses only
> fixed point math for typesetting computation, though some floating
> point is used for messages. Computations in TeX are done in 32 bits,
> with 16 bits after the binary point, giving the value in printers
> points. (72.27 pt/in.)  

If you use floating-point arithmetic for typesetting, it will look fine to the
naked eye. However, the results will not be bit-exact.

This means it will be more difficult to develop a regression test suite which
works on every supported target machine.

The test suite will have to have some tolerances built in. Say, it could
judge how closely the typeset output is to some ideal value, and give that
a score from 0 to 1, and then the regression test suite is looking for,
say, 0.98 as a passing mark.

In the area of encoding voice for telephony, you can do this with PESQ
scores, for instance. A regression suite for a bunch of voice codecs
can pass stock audio samples through them and measure PESQ. If the scores
deviate from the previously established "golden values", then there is
a problem. (This is useful to do even if the codecs could be tested
for bit-exactness. Why? Because the test can be done end-to-end, involving
analog components also. A failure could indicate not only that the
work on some codec has a bug, but that the equipment has problems, like
noisy amplifiers, distortion, or externaly induced noise.)

On the other hand, suppose your floating-point numbers give you 15 decimal
digits of significance, and say the output is quantized into around 16 bits.
You can still get bit-exact results, even if there are discrepancies in the
last digit from one machine to the next. It may require some cunning in some of
the corner cases.

> He has an example where they were typesetting on a machine that they
> were told was 5333 dpi, and the results looked bad. When they found
> that it was actually 5333 1/3 dpi, everything worked fine.  Just a
> tiny difference in rounding makes a big visual difference.

If you have a 5333 1/3 DPI black device, and you try to render 5333
stripes which alternate between black and white, there will be a nasty
moiré effect.

A 1/3 difference out of 5333 is quite large. Much, much larger than
the fractional difference that arises from incrementing the least signficant
decimal digit when there are fifteen.

> Also, at that time different computers used different floating point
> systems with different rounding.

Audio and video codecs use floating-point. You will not hear or see a
difference between different floating-point systems.

If, say, the type double is used, and gives you about 15 significant decimal
figures, your senses are not going to discern a discrepancy in the least
significant figure.

The quantization of the data to the amplitude resolution of the video
or audio DAC destroys more significant figures than any machine-dependent
truncation or rounding.

Thread

complex number in struct form in C Dexterr <dejangru@gmail.com> - 2014-12-21 07:20 -0800
  Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-21 11:30 -0500
    Re: complex number in struct form in C Dexterr <dejangru@gmail.com> - 2014-12-21 08:35 -0800
      Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-21 10:54 -0600
        Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-21 12:00 -0500
          Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-21 11:08 -0600
            Re: complex number in struct form in C Barry Schwarz <schwarzb@dqel.com> - 2014-12-21 10:12 -0800
              Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-21 13:22 -0600
                Re: complex number in struct form in C Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-21 22:21 +0000
              Re: complex number in struct form in C asetofsymbols@gmail.com - 2014-12-26 11:34 -0800
                Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-26 14:10 -0600
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-28 07:04 +0000
                Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-28 13:14 +0000
                Re: complex number in struct form in C Robert Wessel <robertwessel2@yahoo.com> - 2014-12-28 10:45 -0600
                Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-28 08:56 -0800
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-29 10:10 +0000
                Re: complex number in struct form in C Kaz Kylheku <kaz@kylheku.com> - 2014-12-29 19:40 +0000
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-29 20:54 +0000
                Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-29 21:55 +0000
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-30 03:07 +0000
                Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-30 10:51 +0000
                Re: complex number in struct form in C Rosario193 <Rosario@invalid.invalid> - 2014-12-30 12:15 +0100
                Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-30 03:31 -0800
                Re: complex number in struct form in C Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-30 12:17 +0000
                Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-30 13:18 +0000
                Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-30 05:28 -0800
                Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-30 13:53 +0000
                Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-30 08:53 -0600
                Re: complex number in struct form in C "Chris M. Thomasson" <no@spam.invalid> - 2014-12-30 20:05 -0800
                Re: complex number in struct form in C Jeff Higgins <jeff@invalid.invalid> - 2014-12-30 17:40 -0500
                Re: complex number in struct form in C Tim Rentsch <txr@alumni.caltech.edu> - 2015-03-24 08:58 -0700
                Re: complex number in struct form in C Les Cargill <lcargill99@comcast.com> - 2015-03-24 19:41 -0500
                Re: complex number in struct form in C Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-30 14:59 +0000
                Re: complex number in struct form in C David Thompson <dave.thompson2@verizon.net> - 2015-01-12 15:33 -0500
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2015-01-12 22:51 +0000
                Re: complex number in struct form in C Ben Bacarisse <ben.usenet@bsb.me.uk> - 2015-01-12 23:34 +0000
                Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-26 15:25 -0500
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-28 07:17 +0000
                Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-26 20:49 +0000
                Re: complex number in struct form in C asetofsymbols@gmail.com - 2014-12-27 00:22 -0800
                Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-27 08:25 -0600
                Re: complex number in struct form in C Geoff <geoff@invalid.invalid> - 2014-12-27 10:20 -0800
                Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-27 13:21 -0600
                Re: complex number in struct form in C Geoff <geoff@invalid.invalid> - 2014-12-27 13:11 -0800
                Re: complex number in struct form in C "Osmium" <r124c4u102@comcast.net> - 2014-12-27 15:36 -0600
                Re: complex number in struct form in C Geoff <geoff@invalid.invalid> - 2014-12-27 14:54 -0800
                Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-27 15:45 -0800
                Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-27 13:40 -0800
                Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-28 06:50 -0500
                Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-28 04:25 -0800
                Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-28 06:44 -0500
                Re: complex number in struct form in C Richard Damon <Richard@Damon-Family.org> - 2014-12-28 08:33 -0500
                Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-27 11:46 -0500
                Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-28 07:28 +0000
                Re: complex number in struct form in C Kaz Kylheku <kaz@kylheku.com> - 2014-12-27 17:23 +0000
            Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-21 14:37 -0500
          Re: complex number in struct form in C Keith Thompson <kst-u@mib.org> - 2014-12-21 12:37 -0800
          Re: complex number in struct form in C glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2014-12-22 00:54 +0000
      Re: complex number in struct form in C James Kuyper <jameskuyper@verizon.net> - 2014-12-21 11:54 -0500
      Re: complex number in struct form in C Vincenzo Mercuri <nomail@yahoo.it> - 2014-12-21 18:07 +0100
        Re: complex number in struct form in C Dexterr <dejangru@gmail.com> - 2014-12-21 10:37 -0800
          Re: complex number in struct form in C "Chris M. Thomasson" <no@spam.invalid> - 2014-12-21 10:55 -0800
          Re: complex number in struct form in C raltbos@xs4all.nl (Richard Bos) - 2014-12-22 12:15 +0000
            Re: complex number in struct form in C Dexterr <dejangru@gmail.com> - 2014-12-22 05:51 -0800
              Re: complex number in struct form in C BartC <bc@freeuk.com> - 2014-12-22 14:01 +0000
                Re: complex number in struct form in C Keith Thompson <kst-u@mib.org> - 2014-12-22 08:02 -0800
            Re: complex number in struct form in C Keith Thompson <kst-u@mib.org> - 2014-12-22 08:03 -0800
    Re: complex number in struct form in C Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-12-21 22:27 +0000
  Re: complex number in struct form in C "Chris M. Thomasson" <no@spam.invalid> - 2014-12-21 10:51 -0800
    Re: complex number in struct form in C Dexterr <dejangru@gmail.com> - 2014-12-21 11:14 -0800
  Re: complex number in struct form in C Malcolm McLean <malcolm.mclean5@btinternet.com> - 2014-12-21 17:17 -0800

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