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Path: newshost.lanl.gov!tanmoy
From: [e-mail] (Tanmoy Bhattacharya)
Newsgroups: comp.lang.c
Subject: Re: Confusion as to the proper use of MODULAS
Date: 15 Feb 1996 00:26:28 GMT
Organization: Los Alamos National Laboratory
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    <4fthsu$[e-mail]>
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In-reply-to: [e-mail]'s message of 14 Feb 1996 20:49:34 GMT

In article <4fthsu$[e-mail]> [e-mail] (KPN
) writes:
<snip>
   Confusion as to the proper use of MODULAS

That is a funny word. I know of modulus ... guess you must be talking
about the same concept :-) More commonly, the result of % is called
the remainder, and is the basis of a branch of arithmetic called
modular arithmetic.

<snip>
   Modulas operator simply shows:  *** AFTER *** you divide, what is the
   remainder?

Well it couldn't be the remainder, before you divide, could it be?
After all before you can think of something remaining, you have to do
something, right? So, yes, the result of x % y is what remains of x
when you have taken out as many y's as you could out of it. The
precise meaning is in terms of division: it says, that you divide x by
y to get an integral value, multiply the result back by y and subtract
from x. Thus x % y = x - (x/y)*y

   EXAMPLE of this:
       9 % 7 = ?
       9 divided by 7 yields a remainder of 2

Another way of looking at it is that you can take one 7 out of 9, and
after taking it away, you have 2 left over. You cannot take out any
more 7's, so the result is 7.

Of course 9/7 is 1 by the same count. So, 9 % 7 = 9-(9/7)*7 = 2.

       9 % 7 = 2

   1) MODULAS means divide a number and give me the left over number. OK -
   not bad.

Correct. This is always the meaning. x % y = x - (x/y)*y, always (or
rather when x/y is makes sense. Aside for experts: the standard seems
to require no overflow on the rhs ... I had not expected this: maybe I
am misreading the standard in my hurry to finish this post.)

   Next rule:
   If the number to be divided is smaller than the number to divide by,
   the result will always be the number being divided

This is a subcase of the previous rule. If you cannot take any y's out
of x, then what remains is the whole of x, right?

   EXAMPLE of this:

      9 % 12 = ?
      can not divide 9 by a larger number
      9 % 12 = 9
   Now I have rule #2

Yes. But see, you cannot take 12 out of 9: so, what is left over is
9. Doing it the other way, 9/12=0 (i.e. no 12's can be taken out of
9), so 9 % 12 = 9-(9/12)*12 = 9

   2) If the number to be divided is smaller than the nuber to be used as
   a divisor, the result is the original number. OK - again, not bad.

Do you see that this rule is not really needed.

   Here, begin my troubles: using MODULAS in an IF statement.

   I made up a test to see if a number I inputted was a 7. Sample code:

      if (number % 7)
     printf("Not a 7\n");
      else
     printf("First integer was a 7\n");

   So, if the number WAS a 7, the ELSE would take over. OK. But, when I
   enter in a ZERO, it still tells me that the number was a seven?

Well, what does your second rule say? Isn't ZERO less that 7? In that
case shouldn't the answer of number % 7 be number itself? And the
number is ZERO.

Can you see that number % 7 is the same for number being 0, 7, 14, 21
etc.

   Am I going in the right direction? Can someone tell me what IÆm doing

I do not know. I have no idea where you are going ...

   incorrectly, or where IÆm straying? WhatÆs the rule here for using MOD
   in an IF statement?

There is no IF statement, there is an if statement though. C is case
sensitive, so you have to use the correct case. The only rule is that
if the expression controlling the if is zero (of any kind, or a null
pointer), the controlled statement is executed. If the value is
non-zero (or a non-null pointer), the else branch, if any, is executed.

   Thank you for your help,
   kevin

There is only one issue which you have to be careful about. If the
numbers being divided are not positive, x % y = x - (x/y)*y is still
correct, but the meaning of x/y may vary from one machine to another,
and from one compiler to another. Thus (-3) / 2 can be either -1 or
-2, but if (-3)/2 = -1, then (-3) % 2 is -1; whereas if (-3)/2 is -2,
(-3) % 2 is +1.

Cheers
Tanmoy
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