Re: Combining Practicality with Perfection

From	MitchAlsup <user5857@newsgrouper.org.invalid>
Newsgroups	comp.arch
Subject	Re: Combining Practicality with Perfection
References	(2 earlier) <10mj1tj$10hdv$1@dont-email.me> <JH8jR.3$O41.2@fx07.iad> <10mj5el$1gf9$1@gal.iecc.com> <1770861898-5857@newsgrouper.org> <20260212104947.000078dc@yahoo.com>
Date	2026-02-12 17:10 +0000
Message-ID	<1770916245-5857@newsgrouper.org> (permalink)

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Michael S <already5chosen@yahoo.com> posted:

> On Thu, 12 Feb 2026 02:04:58 GMT
> MitchAlsup <user5857@newsgrouper.org.invalid> wrote:
> 
> > John Levine <johnl@taugh.com> posted:
> > 
> > > According to David Schultz  <david.schultz@earthlink.net>:  
> > > >This reminds me of when I took a numerical analysis course. (The
> > > >many ways that computer calculations can go wrong and how to deal
> > > >with it.) The professor said that the schools IBM (360 or 370, ca.
> > > >1980) was perfect for the course because of the defects in its
> > > >floating point system. Guard digits and rounding sorts of things
> > > >as near as I can recall.  
> > > 
> > > The 360's floating point is a famous and somewhat puzzling failure,
> > > considering how much else they got right.
> > > 
> > > It does hex normalization rather than binary. They assumed that
> > > leading digits are evenly distributed so there's be on average one
> > > zero bit, but in fact they're geometrically distributed, so on
> > > average there's two. They got one bit back by making the exponent
> > > units of 16 rather than 2, but that's still one bit gone. It
> > > truncated rather than rounding, another bit gone.  They also
> > > truncated rather than rounding results.
> > > 
> > > Originally there wre no guard digits which made the results
> > > comically bad but IBM retrofitted them at great cost to all the
> > > installed machines.
> > > 
> > > IEEE floating point can be seen as a reaction to that, how do you
> > > use the same number of bits but get good results.  
> > 
> > VAX got this correct too (the VAX format not the one inherited from 
> > PDP-11/45; PDP-11/40* FP was worse). VAX FP is arguably as good as
> > IEEE 754 with the exception that more IEEE numbers have reciprocals 
> > due to the change in exponent bias by 1. {{One can STILL argue whether
> > deNormals were a plus or a minus in IEEE}}
> 
> From the perspective of stability of convergence of few common
> algorithms denormals are significant plus.
> From the perspective of minimizing surprises it is also plus. On VAX 
> (a > b) does not necessarily guarantee (a-b > 0).
> I wonder in which situation it can be seen as a minus?

a-b underflows and takes a trap.
 
> There are several things that I don't like about IEEE-754 Standard, but
> none of them related to format of binary numbers.
> 
> > 
> > CMU had a PDP-11/40 with writable control store 1974. I programmed it 
> > to do PDP-11/45 FP instead of PDP-11/40 FP as a Jr. project.
> > >   
> 
>

Thread

Combining Practicality with Perfection John Savard <quadibloc@invalid.invalid> - 2026-01-31 18:28 +0000
  Re: Combining Practicality with Perfection jgd@cix.co.uk (John Dallman) - 2026-01-31 22:36 +0000
  Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-05 01:57 +0000
    Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-05 06:06 +0000
      Re: Combining Practicality with Perfection Robert Finch <robfi680@gmail.com> - 2026-02-05 08:10 -0500
      Re: Combining Practicality with Perfection scott@slp53.sl.home (Scott Lurndal) - 2026-02-05 14:50 +0000
      Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-05 23:58 +0000
        Re: Combining Practicality with Perfection jgd@cix.co.uk (John Dallman) - 2026-02-06 16:37 +0000
          Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-06 22:32 +0000
            Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-06 22:34 +0000
            Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-07 00:57 +0000
              Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-07 02:45 +0000
          Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-06 22:40 +0000
        Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-09 22:46 +0000
          Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-10 03:49 +0000
            Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-10 19:10 +0000
              Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-11 23:04 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-11 23:55 +0000
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-12 06:04 +0000
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-24 00:22 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-10-24 19:32 +0000
                Re: Combining Practicality with Perfection jgd@cix.co.uk (John Dallman) - 2026-10-25 06:00 +0000
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-25 17:38 +0000
                Re: Combining Practicality with Perfection Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-10-25 22:43 -0700
                Re: Combining Practicality with Perfection jgd@cix.co.uk (John Dallman) - 2026-10-26 09:35 +0000
                Re: Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-10-26 19:53 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-10-26 13:40 +0000
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-26 22:05 +0000
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-26 22:12 +0000
                Re: Combining Practicality with Perfection Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-10-26 20:13 -0700
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-27 14:30 +0000
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-26 22:09 +0000
                Re: Combining Practicality with Perfection EricP <ThatWouldBeTelling@thevillage.com> - 2026-10-26 18:20 -0400
                Re: Combining Practicality with Perfection quadibloc@invalid.com (John Savard) - 2026-10-27 03:00 +0000
                Re: Combining Practicality with Perfection antispam@fricas.org (Waldek Hebisch) - 2026-10-26 22:51 +0000
                Re: Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-10-25 18:47 +0000
                Re: Combining Practicality with Perfection David Schultz <david.schultz@earthlink.net> - 2026-02-11 17:57 -0600
                Re: Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-02-12 00:04 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-12 02:04 +0000
                Re: Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-02-12 03:31 +0000
                Hex floating point (was: Combining Practicality with Perfection) Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 16:53 +0000
                Re: Combining Practicality with Perfection anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-02-12 08:45 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-12 17:09 +0000
                Re: Combining Practicality with Perfection Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-14 18:03 +0100
                Re: Combining Practicality with Perfection BGB <cr88192@gmail.com> - 2026-02-19 02:10 -0600
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-19 17:30 +0000
                Re: Combining Practicality with Perfection Michael S <already5chosen@yahoo.com> - 2026-02-19 20:15 +0200
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-19 19:55 +0000
                Re: Combining Practicality with Perfection BGB <cr88192@gmail.com> - 2026-02-20 05:08 -0600
                Re: Combining Practicality with Perfection Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-20 15:22 +0100
                Re: Combining Practicality with Perfection BGB <cr88192@gmail.com> - 2026-02-20 15:26 -0600
                Re: Combining Practicality with Perfection Paul Clayton <paaronclayton@gmail.com> - 2026-02-21 20:27 -0500
                Re: Combining Practicality with Perfection Michael S <already5chosen@yahoo.com> - 2026-02-12 10:49 +0200
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-12 17:10 +0000
                Re: Combining Practicality with Perfection Michael S <already5chosen@yahoo.com> - 2026-02-12 23:38 +0200
                Re: Combining Practicality with Perfection Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-12 14:28 +0100
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-12 05:51 +0000
                Re: Combining Practicality with Perfection Michael S <already5chosen@yahoo.com> - 2026-02-12 10:53 +0200
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-12 18:40 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-12 20:02 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-12 20:33 +0000
                Re: Combining Practicality with Perfection Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-11 19:50 -0800
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-12 05:55 +0000
                Re: Combining Practicality with Perfection Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-12 08:40 -0800
                Re: Combining Practicality with Perfection scott@slp53.sl.home (Scott Lurndal) - 2026-02-12 16:51 +0000
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-12 18:49 +0000
                Re: Combining Practicality with Perfection scott@slp53.sl.home (Scott Lurndal) - 2026-02-12 15:54 +0000
                Re: Combining Practicality with Perfection Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-12 08:52 -0800
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-12 18:37 +0000
                Re: Combining Practicality with Perfection antispam@fricas.org (Waldek Hebisch) - 2026-02-14 16:33 +0000
                Re: floating pain, Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-02-14 18:12 +0000
                Re: floating pain, Combining Practicality with Perfection antispam@fricas.org (Waldek Hebisch) - 2026-02-17 01:16 +0000
                Re: floating pain, Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-02-17 01:24 +0000
                Re: floating pain, Combining Practicality with Perfection antispam@fricas.org (Waldek Hebisch) - 2026-02-17 16:21 +0000
                Re: floating pain, Combining Practicality with Perfection John Levine <johnl@taugh.com> - 2026-02-17 19:20 +0000
                Re: floating pain, Combining Practicality with Perfection antispam@fricas.org (Waldek Hebisch) - 2026-02-17 19:52 +0000
                Re: floating pain, Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-17 19:09 +0000
                Re: Combining Practicality with Perfection jgd@cix.co.uk (John Dallman) - 2026-02-15 14:37 +0000
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-17 18:57 +0000
                Re: Combining Practicality with Perfection antispam@fricas.org (Waldek Hebisch) - 2026-02-17 20:43 +0000
                Re: Combining Practicality with Perfection MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-18 00:50 +0000
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-18 08:52 +0000
                Re: Combining Practicality with Perfection Robert Finch <robfi680@gmail.com> - 2026-02-18 08:40 -0500
                Re: Combining Practicality with Perfection quadi <quadibloc@ca.invalid> - 2026-02-20 08:14 +0000
                Re: Combining Practicality with Perfection Thomas Koenig <tkoenig@netcologne.de> - 2026-02-19 18:49 +0000

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