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From: firth@sei.cmu.edu (Robert Firth)
Newsgroups: sci.math,comp.lang.modula2
Subject: Re: perpetual calendar (also day of week)
Message-ID: <4179@aw.sei.cmu.edu>
Date: 11 Feb 88 19:54:19 GMT
References: <8802101656.AA08424@decwrl.dec.com> <6413@j.cc.purdue.edu>
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Reply-To: firth@bd.sei.cmu.edu.UUCP (Robert Firth)
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In article <6413@j.cc.purdue.edu] ags@j.cc.purdue.edu.UUCP (Dave Seaman) writes:

]I don't have my copy of the Modula-2 standard available at the moment, but
]I believe that the definition of the MOD operator is similar to Pascal,
]where the standard says:
]
]	A term of the form i mod j shall be an error if j is zero or
]	negative, otherwise the value of i mod j shall be that value of
]	(i-(k*j)) for integral k such that 0 <= i mod j < j.
]
]Therefore the correct value of (-1 MOD 7) is 6, not -1.  In fact, I believe
]that in Modula-2 the result of the MOD operator is type CARDINAL and
]therefore cannot be negative.  It sounds as if you may be stuck with a
]flawed implementation of Modula-2.

Well, I DO have my copy of the reference document [PIM-2, 3rd ed], and it
says no such thing.

Section 8.2 says, in particular

(a) the result of MOD is CARDINAL iff both operands are CARDINAL, and
    otherwise is INTEGER

(b) x MOD y is the remainder after DIV, ie y*(x DIV y) + x MOD y = y

(c) x DIV y is equal to the truncated quotient of x/y

Therefore, the correct value of -1 MOD 7, at least according to Wirth, is -1.