Modulo a negative number

I'm quite surprised to found that MOD with -ve dividend number is NOT THE SAME as MOD with +ve dividend number.

What is modulo (MOD)?
It's a operation/function which returns the remainder of a division by two integers. It's like division, except it returns the remainder. E.g. 9/4=2.25, 9 MOD 4 = 1 (since 2x4+1=9).

For +ve dividend number, x MOD n means = x - (floor(x/n) * n)
But for -ve dividend number, x MOD n means =

1. x + ( floor(-x/n)+1 ) * n, or
2. -(-x MOD n) + n

Literally, the solution is like this : do as normal MOD, but add the remainder (negative number) with the divisor. E.g. -8 MOD 3, frankly return -2, but then add -2 with 3 = 1. Also in the above formulae, floor() is a function which return the answer rounded up towards bottom integer value e.g. 8.4 = 8, 11.9 = 11 etc. (always take the low integer).

Example:

x = 11, n = 3

11 MOD 3, use x - (floor(x/n) * n);
= 11 - ( floor(11/3) * 3)
= 11 - (3 * 3)
= 2

but if x = -11, n = 3

-11 MOD 3, use x + ( floor(-x/n)+1 ) * n;
= -11 + ( floor(11/3) + 1) * 3
= -11 + (3 + 1) * 3
= -11 + 12
= 1

or

-11 MOD 3, use -(-x MOD n) + n
= -(-(-11) MOD 3) + 3
= -(11 MOD 3) + 3
= -2 + 3
= 1

but, what if -11 MOD -3?
Hmmm...

Links:
http://en.wikipedia.org/wiki/Modulo_operation


p/s: if u still wondering what is 'dividend' : if a/b = c, a is dividend, b is divisor and c is quotient.

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A blunder ... can compiler help?

Yesterday, as i was writing another code, i made this simple mistake, illustrated by the following example (example only, don't do this!):

int foo(int i)
{

int j = 2;
if(i > 0)
return i; /* here should be j*/
else
return 0;

}

ok, this is not a good example (it is rubbish), yet clarify my point. It is not simply a typo (which can possibly be another blunder, duh!). I wrote 'return i' instead of 'return j' because i thought it should be 'i'. This is called semantical error. It is not syntactical error, nor grammatical error. It is simply a blunder, and worse, it can't be detected by a compiler.

Is it only about logic?

What programming is all about? I mean the philosophy beneath. Is it only about logical thinking, or pure imagination (creative) or something that combined both? Hmmm... i'm still curious ...

However, i believe that both thinking are involved (other than the fact both are the functions of our brain). Since at certain levels, we have to use our abstract, creative imagination as to think about a any possible solutions. Whereas during the level where we are going to form the solution, we must use our logical thinking.

... ?

Snippet - a release from wholeday coding

Two friends, Ritchie and Ben (not real names), are heading back after losing their football match that they had just played. As this lost was so embarrassing that they lose to underdog team, they decided to hid their identities from locals.

The next morning, Ritchie went out in disguise. On his path, he met with an old woman. Suddenly as he's passing her by, she said to him, 'hi Ritchie!'. What a shocking it was to Ritchie, as he thought no one would recognize him. So frustrated and worried, then hurriedly he went back, thinking about other disguise.

The next morning, he went out again, but now with a different disguised. And there, again, he met with the same old woman that he met yesterday. 'We'll see if you can catch me again!' as he said to himself. Then, another shock readied upon him as he is came so close to the old women, she said 'Hi Ritchie!'. Ritchie was shocked. 'How on earth did she knows it is me?!!!' Ritchie never met with this woman before.

'How come did you know it's me?' he asked.

'Shh... it's me, Ben!'