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From: ForthNet@willett.pgh.pa.us (ForthNet articles from GEnie)
Newsgroups: comp.lang.forth
Subject: PYGMY Forth
Message-ID: <1609.UUL1.3#5129@willett.pgh.pa.us>
Date: 27 Aug 90 03:30:44 GMT
Organization: String, Scotch tape, and Paperclips.  (in Pgh, PA)
Lines: 62

Category 1,  Topic 45
Message 38        Sun Aug 26, 1990
R.BERKEY [Robert]            at 14:57 PDT
 
  Frank Sergeant writes, 90-08-19:

   >       I've recently been pouring over Knuth's book and Roedy
   >  Green's assembly listing on division and thinking about and
   >  worrying over division.

I got out and brought up most of Roedy Green's division code in the middle of
last month.  Just needs eighteen assembler labels, and a 43K file, with the
end result a floored */ with an intermediate 64-bit result.  Whew.  Of course,
most of his file is documentation, and the key code implements a 64-bit
divided by a 32-bit UM/MOD for the 80x8n.



   >      In working over some higher precision division words, I was
   > prepared to try flooring.

I'm curious as to which ones.  I've tried implementing a signed version of
MU/MOD ( d n -- rem d ) built with truncated-to-zero division, and another
version built with floored division.  In each case the code at first seemed to
work, but actually contained subtle bugs.



   >  I think my applications involving negative numbers are much more
   >  likely to concern negative dollars or positive dollars divided by
   >  a positive number.  In such a case, I think it is unfair
   >  discrimination  (I fully support accurate, just discrimination) to
   >  treat the numbers on one side of a balance sheet as different from
   >  those on the other side.  So, I want  -1000 3 / to give -333 with a
   >  -1 left to be dealt with and  1000 3 / to give +333 with a +1 left
   >  to be dealt with.

Those "to be dealt with" remainders make a difference.

(1) If they are being discarded, then we're talking about the numerals shown,
i.e., unrounded truncated-to-zero quotients.  (2) If the remainders are used
to adjust the quotient, that's rounded-to-nearest division, and the numerals
shown are temporary intermediates. (3) A report with both values, such as the
split-up of the partnership, is not one I'm familiar with.  Conceptually it
makes sense, but how a programmer gets involved with it isn't apparent to me.


   >      I hear you need floored with negative operands in order to
   > control stepper motors without them jerking.  This makes no sense
   > to me.  Drive 'em from a table; drive 'em always with either +1
   > or -1 till a feedback switch goes true; scale the   -10 -9 -8 ...
   > -1 0 +1 +2 ... +9 +10  up to 0 1 2 3 ...  18 19 20   - so what's
   > the problem?

   Yes, without having the code from application examples it is difficult to
verify what the problem is.

 Robert

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