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From: anton@mips.complang.tuwien.ac.at (Anton Ertl)
Newsgroups: comp.lang.forth
Subject: Re: FP number syntax
Date: Fri, 03 Jan 2025 09:59:20 GMT
Organization: Institut fuer Computersprachen, Technische Universitaet Wien
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dxf <dxforth@gmail.com> writes:
>Well, I consider mixed-math to be genius :)  Was it a Forth first -
>or it pre-existed in some language/system?

I am not aware of any other non-assembly language that supports
mixed-width math.  Some other programming languages have multiple
integer or FP widths, but they tend to define their operations as
first converting to a common width, and then producing a result of the
same width.  This can be used to specify widening operations, e.g., as
follows (in C):

int64_t widening_mul(int32_t a, int32_t b)
{
   return a * (int64_t)b;
}

but the compiler has to do extra work to recognize that this is a
widening multiplication (rather than first sign-extending the operands
and then performing a 64bit*64bit->64bit multiplication).

And for division there is no way to specify the likes of UM/MOD or
SM/REM in C such that it can be implemented with just the DIV or IDIV
instruction (plus maybe register-register moves) of IA-32 or AMD64.

Mixed-width multiplication and division is a natural outcome of
implementing multiplication and division using repeated addition,
subtraction and shifting, and of course the first PDP-11
implementation, the 8086, 68000 and MIPS R2000, which implemented
these operations internally in that way, provide mixed-width
instructions for them.

More recent CPUs use different implementation techniques, so recent
architectures tend not to provide mixed-width division instructions.
They tend to have support for mixed-width multiplication (but usually
split that into two instructions), probably because it's important for
implementing wide multiplication, which is important for cryptography.

- anton
-- 
M. Anton Ertl  http://www.complang.tuwien.ac.at/anton/home.html
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