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Re: Combining Practicality with Perfection

From John Levine <johnl@taugh.com>
Newsgroups comp.arch
Subject Re: Combining Practicality with Perfection
Date 2026-02-12 03:31 +0000
Organization Taughannock Networks
Message-ID <10mjhhm$cli$1@gal.iecc.com> (permalink)
References <10llhkk$34374$2@dont-email.me> <JH8jR.3$O41.2@fx07.iad> <10mj5el$1gf9$1@gal.iecc.com> <1770861898-5857@newsgrouper.org>

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According to MitchAlsup  <user5857@newsgrouper.org.invalid>:
>
>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.

Oh I forgot that using hex exponents meant there was no hidden bit, so
in practice it lost three bits of precision on every operation.  There was
a great deal of grumbling that people with 709x Fortran codes had to
make everything double precision to keep getting reasonably good 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). ...

The VAX is the first machine I know that used the hidden bit trick to
get an extra bit of significance.  The PDP-6/10 was pretty close but
their format was two's complement which meant no hidden bit but they
could use integer comparisons on normalized floating point numbers.

-- 
Regards,
John Levine, johnl@taugh.com, Primary Perpetrator of "The Internet for Dummies",
Please consider the environment before reading this e-mail. https://jl.ly

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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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