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Forth for a balanced ternary machine

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  Forth for a balanced ternary machine Matthias Koch <m.cook@gmx.net> - 2026-05-25 14:58 +0200
    Re: Forth for a balanced ternary machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-25 18:10 +0000
      Re: Forth for a balanced ternary machine dxf <dxforth@gmail.com> - 2026-05-26 15:53 +1000
        Re: Forth for a balanced ternary machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-26 07:46 +0000
          Re: Forth for a balanced ternary machine dxf <dxforth@gmail.com> - 2026-05-27 00:52 +1000
            Teaching Scenarios [Re: Forth for a balanced ternary machine] Buzz McCool <buzz_mccool@yahoo.com> - 2026-05-26 08:52 -0700
              Re: Teaching Scenarios [Re: Forth for a balanced ternary machine] dxf <dxforth@gmail.com> - 2026-05-28 21:03 +1000
              Re: Teaching Scenarios [Re: Forth for a balanced ternary machine] anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-30 20:16 +0000
                Re: Teaching Scenarios [Re: Forth for a balanced ternary machine] minforth <minforth@gmx.net> - 2026-05-31 11:02 +0200
                  Re: Teaching Scenarios [Re: Forth for a balanced ternary machine] anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-31 14:13 +0000
            Division (was: Forth for a balanced ternary machine) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-30 18:23 +0000
              Re: Division dxf <dxforth@gmail.com> - 2026-05-31 12:49 +1000
                Re: Division anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-31 14:20 +0000
                  Re: Division dxf <dxforth@gmail.com> - 2026-06-01 12:47 +1000
                arithmetic shift right (was: Division) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-05-31 14:43 +0000
                  Re: arithmetic shift right dxf <dxforth@gmail.com> - 2026-06-01 18:18 +1000
        Re: Forth for a balanced ternary machine Hans Bezemer <the.beez.speaks@gmail.com> - 2026-06-01 23:23 +0200
          Re: Forth for a balanced ternary machine dxf <dxforth@gmail.com> - 2026-06-03 13:30 +1000
            Re: Forth for a balanced ternary machine Hans Bezemer <the.beez.speaks@gmail.com> - 2026-06-04 11:59 +0200
              Re: Forth for a balanced ternary machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-06-04 12:15 +0000
            Re: Forth for a balanced ternary machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-06-04 12:08 +0000
              Re: Forth for a balanced ternary machine dxf <dxforth@gmail.com> - 2026-06-05 17:37 +1000
                Re: Forth for a balanced ternary machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-06-05 09:22 +0000
      Re: Forth for a balanced ternary machine Matthias Koch <m.cook@gmx.net> - 2026-05-28 13:36 +0200

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#135126

dxf <dxforth@gmail.com> writes:
>On 2/06/2026 7:23 am, Hans Bezemer wrote:
>In eForth one finds:
>
>  : 2*  2 * ;
>  : 2/  2 / ;
>
>which rather defeats the purpose of the functions which is speed.

But eForth's purpose is not speed.

>As to what is returned by a bit-shifting 2/ depends on the hardware.
>For 2's complement it's floored.  For 1's complement it's symmetric.
>For signed-magnitude it's ...

For sign-magnitude an arithmetic interpretation is that, for positive
numbers, it's division by 2, while for negative numbers, it's the
average between the number and -2^(n-1) (where n is the number of bits
in a cell).  It's not very useful for sign-magnitude, but given that
sign-magnitude and ones-complement have died out long ago and never
had Forth systems, who cares.

- anton
-- 
M. Anton Ertl  http://www.complang.tuwien.ac.at/anton/home.html
comp.lang.forth FAQs: http://www.complang.tuwien.ac.at/forth/faq/toc.html
     New standard: https://forth-standard.org/
EuroForth 2025 proceedings: http://www.euroforth.org/ef25/papers/

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#135130

On 4/06/2026 10:08 pm, Anton Ertl wrote:
> dxf <dxforth@gmail.com> writes:
>> On 2/06/2026 7:23 am, Hans Bezemer wrote:
>> In eForth one finds:
>>
>>  : 2*  2 * ;
>>  : 2/  2 / ;
>>
>> which rather defeats the purpose of the functions which is speed.
> 
> But eForth's purpose is not speed.

Wondering if there was a rationale for eForth, I found this from Bill
Muench's old webpage:

  "I wrote eForth so that it would be easier for me to develop Forth 
   systems for many processors. Processors included 56000, 6502, 68332, 
   68HC11, 8051, 8080, 80C166, 80C196, 80x86, RTX2000, RTX2001, RTX2010, 
   SC32, StrongARM, TMS320, Z80, and I may have forgotten some.

   eForth allows me to make a complete Forth system with about 30 very 
   simple machine code routines. With so few words to code, I could do 
   the coding by hand, that is, without the need to write an assembler 
   first. After this simple model is running, it is desirable to code 
   much of the rest in assembly."

That "30" figure perhaps explains why  1+ 1- 2+ 2- 2* 2/  were excluded
from the kernel and provided as high-level definitions.  The idea being
users would eventually 'code' them.

> 
>> As to what is returned by a bit-shifting 2/ depends on the hardware.
>> For 2's complement it's floored.  For 1's complement it's symmetric.
>> For signed-magnitude it's ...
> 
> For sign-magnitude an arithmetic interpretation is that, for positive
> numbers, it's division by 2, while for negative numbers, it's the
> average between the number and -2^(n-1) (where n is the number of bits
> in a cell).  It's not very useful for sign-magnitude, but given that
> sign-magnitude and ones-complement have died out long ago and never
> had Forth systems, who cares.

Thanks.  Not dead enough for Forth-94 which was the first standard to
expressly mention and support them.  For that reason I was curious what
2/ would do on these.  As the effect does vary, I would expect '94 to
have documented it.  But then the same happened with other words.

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#135131

dxf <dxforth@gmail.com> writes:
>On 4/06/2026 10:08 pm, Anton Ertl wrote:
[On 2/:]
>> It's not very useful for sign-magnitude, but given that
>> sign-magnitude and ones-complement have died out long ago and never
>> had Forth systems, who cares.
>
>Thanks.  Not dead enough for Forth-94 which was the first standard to
>expressly mention and support them.

I think that's a reaction to the fact that Forth-83 limited itself to
16-bit cells and 8-bit chars.  They wanted to lift those limitations,
and while they were at it, they apparently also wanted to eliminate
the limitation to 2s-complement representation of negative numbers.
Of these three, their cell size answer turned out to be right on spot,
while the char size answer turned out to be the wrong one (but it's in
the same spirit as the Windows NT (1993) and Java (1995) answers to
the same issue, so it's excusable that they did not see the right
answer in 1994. OTOH, the X/Open committee XoJIG, Dave Prosser and
Ken Thompson saw in 1992 that this answer was not the right one, and
designed UTF-8 in 1992.)

As for sign-magnitude and ones-complement, these are basically
remnants from the 1950s and 1960s, and I am not aware of a new
sign-magnitude or ones-complement architecture designed after the
1960s, except for followons to machines from the 1950s and 1960s.
These machines were in decline by the 1970s and the decline had
progressed pretty far by the time Forth-94 was developed.

Forth-94 gives lip service to these other representations, but does
not support them properly, especially not in a backwards-compatible
way.  E.g., with ones complement code that uses 0= on the results of
comparisons (a common-usage way to negate the result) would not work
as intended.

And the treatment of 2/ is similar:

>For that reason I was curious what
>2/ would do on these.  As the effect does vary, I would expect '94 to
>have documented it.

The effect of 2/ on the bits is documented.  Given the different
results when applied to negative numbers, the use as arithmetic
operation on negative numbers is obviously not Forth-94 conforming.

All this is fixed by standardizing 2s-complent (already accepted into
the upcoming standard).

- anton
-- 
M. Anton Ertl  http://www.complang.tuwien.ac.at/anton/home.html
comp.lang.forth FAQs: http://www.complang.tuwien.ac.at/forth/faq/toc.html
     New standard: https://forth-standard.org/
EuroForth 2025 proceedings: http://www.euroforth.org/ef25/papers/

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#135104

Thank you for the insight into the symmetric vs. floored decision!

I changed my documentation accordingly:

In balanced ternary, a right shift is the same as symmetric division
by powers of three, whereas in two-complement binary an arithmetic
right shift is equivalent to floored division by powers of two.

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