Xref: utzoo sci.math:2871 comp.lang.modula2:652
Path: utzoo!mnetor!uunet!mcvax!cernvax!ethz!forty2!claudio
From: claudio@forty2.UUCP (Claudio Nieder)
Newsgroups: sci.math,comp.lang.modula2
Subject: Re: MOD in Modula-2 flawed (was Re: perpetual calendar (also day of week))
Message-ID: <147@forty2.UUCP>
Date: 17 Feb 88 12:04:42 GMT
References: <8802101656.AA08424@decwrl.dec.com> <6413@j.cc.purdue.edu> <4057@xanth.cs.odu.edu>
Reply-To: claudio@forty2.UUCP (Claudio Nieder)
Organization: Exp. Physics University Zuerich
Lines: 40
Keywords: munged

In article <4057@xanth.cs.odu.edu> kent@xanth.UUCP (Kent Paul Dolan) writes:
> ...
>It appears Wirth was too seduced by the beauty of the "identity" x =
>modulus * ( x DIV modulus ) + ( x MOD modulus ) [which is how he
>defines MOD]... 

I think the above mentioned "identity" is quite right, the problem is
how you define x DIV modulus. In PIM3 Wirth defines:

"Integer division is denoted by DIV and truncates the quotient. For
 example ... -15 DIV 4= -3"

but there seems some room for changes. On his compiler for the CERES
(a NS32032 based Workstation built at the ETH) he redefined that, thus
now 

 -15 DIV 4=-4 and -15 MOD 4=1

I have read in some paper that dealt with the proposed BSI Modula-2 standard
that Wirth suggested/considered/approved/wasn't against the following
solution (perhaps somebody who has acces to the BSI papers may tell more 
about that):

 -15 DIV 4=-4, -15 MOD 4=1
 -15  /  4=-3, -15 REM 4=-3

On CERES DIV, MOD and "/" are implemented as mentioned above while "REM"
is not implemented.

The way how you actually implement it may also be influenced by the underlying
Processor. On the NS32032 both definitions of DIV and MOD exist, thus it
is quite easy to provide both.

The MC68000 Processor provides only the "/",REM variant. Therefor on the
M2Amiga compiler, which implements both variants, "/" and REM simply use
the processors DIVS instruction while DIV and MOD generate more complex
code.


				claudio