From mboxrd@z Thu Jan  1 00:00:00 1970
From: erik quanstrom <quanstro@quanstro.net>
To: 9fans@cse.psu.edu, Dan Cross <cross@math.psu.edu>
References: <6e35c0620512152004n37c06ff5wd250424db50d874d@mail.gmail.com>
	<20051216045115.GC15067@augusta.math.psu.edu>
	<20051216050214.GD15067@augusta.math.psu.edu>
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Subject: Re: [9fans] More Microsoft bashing
Message-Id: <20051216053346.F1BC41B12F7@dexter-peak.quanstro.net>
Date: Thu, 15 Dec 2005 23:33:46 -0600
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Topicbox-Message-UUID: c9058dac-ead0-11e9-9d60-3106f5b1d025

you've got to take you're math cap off, and put your cs cap on.

the motivation for defining MOD and DIV is so you can do somethign 
like this

	row = size  DIV columns
	col   = size MOD columns

the pseudo-mathematics is applied ex post facto. clearly you have to
get a single value out of the operation but that value is never going to
be a member of Z. it's going to be a n-bit binary integer. also,

; cat > /tmp/fu.c
int main(void){
	int x;

	x = 1 % 0;
}
/tmp/fu.c: In function `main':
/tmp/fu.c:4: warning: division by zero

- erik


Dan Cross <cross@math.psu.edu> writes

| 
| On Thu, Dec 15, 2005 at 11:51:15PM -0500, Dan Cross wrote:
| > On Thu, Dec 15, 2005 at 08:04:02PM -0800, Jack Johnson wrote:
| > > So, what *is* -5 MOD 3?
| > 
| > Well, in general, it depends.
| > 
| > Do you care whether the result a set or an integer?  The definitions due
| > to Wirth et al are the former, while the MS definition appears to be the
| > latter.
| 
| Hmm, I guess on further reflection I ought to explain what I mean by
| this before someone jumps all over me.
| 
| The definition as per Wirth et al gives you a positive generator for an
| equivalence class on Z, whereas the microsoft definition gives you the
| definition of the division function extended to all of Z, which yields
| an integer; the former definition is probably more comfortable for a
| mathematician, and more what one would expect.  The latter is more
| comfortable for someone who just wants to write a program.  In neither
| case does this have much to do with the actual implementation (that is
| to say, it's not like DIV actually gives you back an object
| representing the set of all integers congruent to 0 modulo some integer
| in Pascal), but only how that language interprets the definitions.
| 
| > Regardless, all these definitions are problematic.  No where does it say
| > they're defined only on Z*; what if Y is 0?
| 
| This is still a problem.  You really want a function f: Z x Z* -> Z,
| not f: Z x Z -> Z; that is, for f(x, y) = x div y, y should be non-zero.
| Otherwise, it would be an absurdity.
| 
| 	- Dan C.