Modulus and Remainder operations (Was Re: Help with a bit of C code)

["David A. Cobb" <COBB@V22BZ.NPT.NUWC.NAVY.MIL>]

X-In-Reply-To: Mon, 26 Sep 1994 14:35:11 EDT <bruce@AIS.COM>

<quote>
    Strictly speaking, the % operator in C is a REMAINDER operator, not a
    MODULUS operator.  This often seems to be a confusing point for a lot
    of people, but the results are different for negative numbers (Try it
    with, eg, PL/I, which uses the modulus function rather than the remainder
    function).  For example, these 3 languages give the following results:
</quote>

Ada, the language everyone loves to hate, has both but has the
decency to give both clear definitions.  I assume the designers
talked to a mathamagician:

<quote>
    A = (A/B)*B + (A rem B) where (A rem B) <e>has the sign of A</e>
and an absolute value less than B. ....

    A = B*N + (A mod B), for some signed integer N, where (A mod B)
<e>has the sign of B</e> and an absolute value less than the
absolute value of B.
</quote>

Thus:
<pre>
    A        B        A/B      A rem B   A mod B
    12        5         2         2         2
   -12        5        -2        -2         3
    12       -5        -2         2        -3
   -12       -5        -2        -2        -2
</pre>