[COFF] Pointers for maths routines in "assembly"

[COFF] Pointers for maths routines in "assembly"

[wkt]

Hi all, I have a strange question and I'm looking for pointers.

Assume that you can multiply two 8-bit values in hardware and get a 16-bit
result (e.g. ROM lookup table). It's straightforward to use this to multiply
two 16-bit values:

        AABB *
        CCDD
        ----
        PPPP = BB*DD
      QQQQ00 = BB*CC
      RRRR00 = AA*DD
    SSSS0000 = AA*CC
    --------
 32-bit result

But if the hardware can only provide the low eight bits of the 8-bit by
8-bit multiply, is it still possible to do a 16-bit by 16-bit multiply?

Next question, is it possible to do 16-bit division when the hardware
can only do 8-bit divided by 8-bit. Ditto 16-bit modulo with only 8-bit
modulo?

Yes, I could sit down and nut it all out from scratch, but I assume that
somewhere this has already been done and I could use the results.

Thanks in advance for any pointers.
	Warren

** Back story. I'm designing an 8-bit TTL CPU which has 8-bit multiply, divide
and modulo in a ROM table. I'd like to write subroutines to do 16-bit and
32-bit integer maths.

[COFF] Pointers for maths routines in "assembly"

[ralph]

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Hi Warren,

> Assume that you can multiply two 8-bit values in hardware and get a
> 16-bit result (e.g. ROM lookup table). It's straightforward to use
> this to multiply two 16-bit values:
...
> But if the hardware can only provide the low eight bits of the 8-bit
> by 8-bit multiply, is it still possible to do a 16-bit by 16-bit
> multiply?

Yes.  Given hex 8-b numbers ab and cd, use your 8×8=8 hardware multiply
to work out

    b × d = BD
    a × d = AD
    b × c = BC
    a × c = AC

and then shift and add:

    BD + (AD << 4) + (BC << 4) + (AC << 8)

> ** Back story. I'm designing an 8-bit TTL CPU which has 8-bit
> multiply, divide and modulo in a ROM table. I'd like to write
> subroutines to do 16-bit and 32-bit integer maths.

That's quite an unusual mix.  Eight-bit CPUs I can think of either have
no hardware multiply of which to take advantage,
e.g. http://6502org.wikidot.com/software-math-intmul, or have a 8×8=16.

-- 
Cheers, Ralph.

[COFF] Pointers for maths routines in "assembly"

[dfawcus+lists-coff]

On Mon, May 25, 2020 at 02:27:26PM +1000, Warren Toomey wrote:
> 
> Next question, is it possible to do 16-bit division when the hardware
> can only do 8-bit divided by 8-bit. Ditto 16-bit modulo with only 8-bit
> modulo?

I believe so.

I've seen code for a 68000 to do division of 32 bit values when the chip
only provides for division of 16 bit values.  So the same approach should
apply for extending an 8 bit divide to provide 16 bit division.

The book I have this in attributes the algorith to a Dr. Arthur Norman.

See https://archive.org/stream/Programming_The_M68000_1983_Adn-Wesley_Publishing_Company/Programming_The_M68000_1983_Addison-Wesley_Publishing_Company_djvu.txt

Section 5.8 & 5.9, page 99 in the actual printed book.

DF