From mboxrd@z Thu Jan  1 00:00:00 1970
From: erik quanstrom <quanstro@quanstro.net>
To: 9fans@cse.psu.edu, Jack Johnson <knapjack@gmail.com>
References: <6e35c0620512152004n37c06ff5wd250424db50d874d@mail.gmail.com>
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In-Reply-To: <6e35c0620512152004n37c06ff5wd250424db50d874d@mail.gmail.com>
Subject: [9fans] More Microsoft bashing
Message-Id: <20051216045306.126521B12F3@dexter-peak.quanstro.net>
Date: Thu, 15 Dec 2005 22:53:06 -0600
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these can be shown to be the same:

Jack Johnson <knapjack@gmail.com> writes

| result  = value1 MOD value2 satisfies the following conditions:
| result = value1 - value2 * (value1 DIV value2), and
| 0 <= |result| < |value2|, and
| sign(result) = sign(value1)

but subsituting with wirth's eqn:
	
	r = x MOD y
thus
	(x MOD y) = x - y*(x DIV y)
so
	x = (x DIV y) + (x MOD y)

| 
| Please note that this definition of DIV and MOD differs from the
| definition given in [M. Reiser, N. Wirth. Programming in Oberon. p.
| 36]:
| x  = (x DIV y) * y + (x MOD y), and
| 0 <= (x MOD y) < y
| 
| ( from http://www.bluebottle.ethz.ch/oberon.net/faq.html#ad_DivMod )

| 
| ------
| 
| I kind of collect random, older computer science texts, so I cracked
| open The Nature of Computation by Pohl and Shaw, which yields:
| 
|   "x MOD y = x - (x ÷ y) * y, where ÷ indicates integer division (i.e.
| fractions are disregarded; equivalently, the result of the division is
| truncated)."

uh, if you replace ÷ with DIV (since the definition is the same),

	x MOD y = x - (x DIV y)*y
thus
	x  = (x DIV y) * y + (x MOD y)

| 
| So, what *is* -5 MOD 3?
| 

-2