From Newsgroup: comp.lang.forth


A few days ago, I released an experiment on how Forth might adapt to a balanced ternary architecture, with an instruction set emulator and a native FPGA implementation included. In balanced ternary, all numbers are signed with low-level arithmetic being quite elegant, and there are new logic operators to explore. If you like to dive in: https://codeberg.org/Mecrisp/mecrisp-ternary

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From Newsgroup: comp.lang.forth

Matthias Koch <m.cook@gmx.net> writes:
[reformatted to follow line length conventions:]

A few days ago, I released an experiment on how Forth might adapt to
a balanced ternary architecture, with an instruction set emulator and
a native FPGA implementation included. In balanced ternary, all
numbers are signed with low-level arithmetic being quite elegant, and
there are new logic operators to explore. If you like to dive in: >https://codeberg.org/Mecrisp/mecrisp-ternary

Quite interesting.

A note on:

|In balanced ternary, a right shift is exactly the same as symmetric
|division by powers of three, unlike binary in which right-shifting
|negative two-complement numbers to divide by powers of two gives
|rounding artifacts.

Floored division is not any more a rounding artifact than symmetric
division is. Whether to use floored or symmetric division depends on
the application. That's why we have FM/MOD and SM/REM in the
standard. The Forth-83 committee was so strongly in favour of floored
that they broke compatibility with Forth-79 because of that.

Gforth since 0.7 implements / and other division words where Forth-94
allows the system to choose as floored division words. This means
that in Gforth, "2 /" is equivalent to 2/ (which is defined as a shift
right by 1 bit):

-3 2 / . \ prints -2
-3 2/ . \ prints -2

- 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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From Newsgroup: comp.lang.forth

On 26/05/2026 4:10 am, Anton Ertl wrote:

Matthias Koch <m.cook@gmx.net> writes:
...
|In balanced ternary, a right shift is exactly the same as symmetric |division by powers of three, unlike binary in which right-shifting
|negative two-complement numbers to divide by powers of two gives
|rounding artifacts.

Floored division is not any more a rounding artifact than symmetric
division is. Whether to use floored or symmetric division depends on
the application. That's why we have FM/MOD and SM/REM in the
standard. The Forth-83 committee was so strongly in favour of floored
that they broke compatibility with Forth-79 because of that.

Gforth since 0.7 implements / and other division words where Forth-94
allows the system to choose as floored division words. This means
that in Gforth, "2 /" is equivalent to 2/ (which is defined as a shift
right by 1 bit):

-3 2 / . \ prints -2
-3 2/ . \ prints -2

Which is all very nice until beginners ask how that makes any sense ;-)

ANS at least tells you 2* 2/ are bit-shifters with historic, albeit misleading, names.

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From Newsgroup: comp.lang.forth

On 26/05/2026 5:46 pm, Anton Ertl wrote:

dxf <dxforth@gmail.com> writes:

On 26/05/2026 4:10 am, Anton Ertl wrote:

Gforth since 0.7 implements / and other division words where Forth-94
allows the system to choose as floored division words. This means
that in Gforth, "2 /" is equivalent to 2/ (which is defined as a shift
right by 1 bit):

-3 2 / . \ prints -2
-3 2/ . \ prints -2

Which is all very nice until beginners ask how that makes any sense ;-)

They don't (I know because I have been teaching Forth beginners for
three decades). That's because negative dividends are rare, and
negative divisors are even rarer. But in those cases where negative dividends occur, floored division usually makes sense, and users
encountering it don't ask.

In a teaching scenario I wouldn't necessarily expect questions either. Importantly it didn't make sense to forth vendors to make breaking
changes for something that was occasionally useful.

ANS at least tells you 2* 2/ are bit-shifters with historic, albeit misleading,
names.

The name of 2* is not misleading on architectures with 2s-complement arithmetic. I.e., every architecture designed in the last
half-century (the IBM S/360 is actually 62 years old), and everything
that any existing standard system (for any Forth standard) runs on.

And it's on such machines that one finds symmetric hardware division co-existing with arithmetic right shift instructions and coders not
getting freaked out by it.

...

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From Newsgroup: comp.lang.forth

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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From Newsgroup: comp.lang.forth

On 26-05-2026 07:53, dxf wrote:

ANS at least tells you 2* 2/ are bit-shifters with historic, albeit

misleading,

names.

You know I'm a pragmatic guy. Back in the 32 bit era, I tested every
single value with both 2* and "2 *" - no difference. So, 2* essentially
became "2 *".

Very different story with 2/. So, there is a unique opcode 2/ in 4tH -
but not a true 2*. ;-)

Hans Bezemer
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From Newsgroup: comp.lang.forth

On 2/06/2026 7:23 am, Hans Bezemer wrote:

On 26-05-2026 07:53, dxf wrote:

ANS at least tells you 2* 2/ are bit-shifters with historic, albeit misleading,
names.

You know I'm a pragmatic guy. Back in the 32 bit era, I tested every single value with both 2* and "2 *" - no difference. So, 2* essentially became "2 *".

Very different story with 2/. So, there is a unique opcode 2/ in 4tH - but not a true 2*. ;-)

In eForth one finds:

: 2* 2 * ;
: 2/ 2 / ;

which rather defeats the purpose of the functions which is 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 ...

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From Newsgroup: comp.lang.forth

On 03-06-2026 05:30, dxf wrote:

On 2/06/2026 7:23 am, Hans Bezemer wrote:

On 26-05-2026 07:53, dxf wrote:

ANS at least tells you 2* 2/ are bit-shifters with historic, albeit misleading,
names.

You know I'm a pragmatic guy. Back in the 32 bit era, I tested every single value with both 2* and "2 *" - no difference. So, 2* essentially became "2 *".

Very different story with 2/. So, there is a unique opcode 2/ in 4tH - but not a true 2*. ;-)

In eForth one finds:

: 2* 2 * ;
: 2/ 2 / ;

which rather defeats the purpose of the functions which is 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 ...

True. "2 /" is twice as slow. I needed about a billion iterations to
reliably measure that.

Small detail - first I thought "2 /" was faster. That was because the optimizer was able to fold the value and consequently create a constant.

Sooo -- in some cases "2 /" will actually be faster (in 4tH) because of
that. Given that you will need millions of iterations to get *any*
measurable benefit of 2/ and 2* I think I made the right trade-off.

The more since hardware 1's complement and signed-magnitude are so rare
(as integer system) that I can safely ignore them. I've long given up
catering for such systems.

And - the reason for this all - tokens are a precious resource in 4tH.
I'd rather use it for something else.

Hans Bezemer
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From Newsgroup: comp.lang.forth

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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From Newsgroup: comp.lang.forth

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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