Re: C arithmetic, was Software proofs, was Are there different

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From	gah4 <gah4@u.washington.edu>
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Subject	Re: C arithmetic, was Software proofs, was Are there different
Date	Fri, 10 Feb 2023 23:47:40 -0800 (PST)
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On Friday, February 10, 2023 at 10:18:49 AM UTC-8, Hans-Peter Diettrich wrote:

(snip)

> Please explain the provenience or purpose of that hidden bit with
> integral numbers. How can integral values be *normalized* so that a
> previously required bit can be hidden? Sign extension to a higher number
> of bits does not increase the value or accuracy of an integral number.

> [He said "mantissa", so it's floating point. I've certainly seen scaled
> integer arithmetic, but normalized integers other than +/- zero in systems
> with signed zeros seems unlikely. -John]

Normalized binary floating point, with hidden one, is pretty common.
I knew IBM S/360 floating point for some years before learning about
those, and it seemed surprising at the time.

As for integers, though, there are some processors with a floating
point format that does not left normalize values.

Some CDC processors, if the value can be shifted, normalized,
as an integer value without losing bits on either end, choose that.
Even more, the exponent is zero for that case.  I think some
Burroughs processors also do that.

The result of doing that is that, for values in the appropriate range,
the floating point instructions work for integer values. No instructions
are needed to convert (in range) integers to floating point.

There is so much fun history to the different floating point
formats used over the years.  Now almost forgotten.
[I am not aware of any hidden bit formats before IEEE but the 704
manual noted that normalized mantissas always have a 1 in the high
bit so it wasn't a big leap. -John]

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Re: Are there different programming languages that are compiled to the same intermediate language? Martin Ward <mwardgkc@gmail.com> - 2023-01-31 14:04 +0000
  Re: Are there different programming languages that are compiled to the same intermediate language? arnold@freefriends.org (Aharon Robbins) - 2023-02-01 08:07 +0000
    Re: Software proofs, was Are there different programming languages that are compiled to the same intermediate language? Spiros Bousbouras <spibou@gmail.com> - 2023-02-05 15:14 +0000
      Re: C arithmetic, was Software proofs, was Are there different Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2023-02-05 16:14 -0800
        Re: C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-06 13:26 -0800
          Re: C arithmetic, was Software proofs, was Are there different Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2023-02-07 14:31 +0100
            Re: C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-08 01:10 -0800
              Re: C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-09 00:26 -0800
                Re: C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-11 00:01 -0800
                Re: C arithmetic, was Software proofs, was Are there different drb@ihatespam.msu.edu (Dennis Boone) - 2023-02-12 04:37 +0000
            Re: C arithmetic, was Software proofs, was Are there different anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2023-02-08 10:19 +0000
              Re: C arithmetic, was Software proofs, was Are there different Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2023-02-10 19:11 +0100
                Re: C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-10 23:47 -0800
                Re: C arithmetic, was Software proofs, was Are there different anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2023-02-11 22:34 +0000
                Re: old floating point, C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-11 22:48 -0800
            Re: C arithmetic, was Software proofs, was Are there different Hans-Peter Diettrich <DrDiettrich1@netscape.net> - 2023-02-08 15:24 +0100
              Re: C arithmetic, was Software proofs, was Are there different gah4 <gah4@u.washington.edu> - 2023-02-09 00:37 -0800

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