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Re: Double multiplication

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David Meyer <papa@sdf.org> writes:
>This newbie may be missing something obvious, but Gforth has no words for 
>multiplying two double-precision integers, nor does it appear that anyone 
>on the Internet has any interest in doing so with Gforth or any other 
>Forth implementations. Is it really such a useless thing to do?

It's needed rarely.

>I hope a little more 
>fiddling will show me how to multiply signed doubles, too.

If you (like everyone else) uses 2s-complement for signed numbers,
then for n-bit x n-bit -> n-bit multiplication there is no difference
between signed and unsigned.  That's why Forth has no U*.  And that's
why UD* is the same as D*.

This hinges on the fact that you can view the negative 2s-complement
number x as being the unsigned number 2^n+x (which is in the range of
unsigned numbers).  If you multiply x with y, you get 2^n*y+x*y, and
2^n*y has only 0 bits in the lowest n bits, so it does not influence
the result.

Concerning the implementation, I'll have a go at it:

: d* { al ah bl bh -- cl ch }
  \ (2^m*ah+al)+(2^m*bh+bl) = 
  \ 2^(2*m)*ah*bh+2^m*(ah*bl+al*bh)+al*bl
  \ take this modulo 2^(2*m), making ah*bh irrelevant
  al bh * ah bl * + 0 swap
  al bl um* d+ ;

- 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: http://www.forth200x.org/forth200x.html
   EuroForth 2013: http://www.euroforth.org/ef13/

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Double multiplication David Meyer <papa@sdf.org> - 2013-11-26 16:06 +0000
  Re: Double multiplication anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2013-11-26 16:13 +0000
    Re: Double multiplication "Alex McDonald" <blog@rivadpm.com> - 2013-11-26 22:59 +0000
    Re: Double multiplication Hans Bezemer <the.beez.speaks@gmail.com> - 2013-11-27 22:34 +0100
      Re: Double multiplication anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2013-11-28 15:51 +0000
  Re: Double multiplication mhx@iae.nl - 2013-11-26 10:14 -0800
    Re: Double multiplication "Ed" <invalid@invalid.com> - 2013-12-01 23:41 +1100
      Re: Double multiplication mhx@iae.nl - 2013-12-02 02:23 -0800
        Re: Double multiplication "Ed" <invalid@invalid.com> - 2013-12-05 22:19 +1100
        Re: Double multiplication Hans Bezemer <the.beez.speaks@gmail.com> - 2013-12-05 13:14 +0100
          Re: Double multiplication Coos Haak <chforth@hccnet.nl> - 2013-12-06 00:16 +0100
          Re: Double multiplication "Rod Pemberton" <dont_use_email@xnohavenotit.cnm> - 2013-12-05 21:24 -0500
  Re: Double multiplication albert@spenarnc.xs4all.nl (Albert van der Horst) - 2013-11-26 20:20 +0000
    Re: Double multiplication "Elizabeth D. Rather" <erather@forth.com> - 2013-11-26 11:43 -1000

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