[Tutor] x%2

[Steven D'Aprano]

bob gailer wrote:
> On 1/10/2012 1:47 PM, Noah Hall wrote:
>> a % b is the remainder operator. It returns what's "left" after 
>> dividing a by b. 
> Not to beat a dead horse- but % is the modulo operator.

That depends on how you define "remainder" and "modulo". There is no 
definition agreed on by all people, and so we get into terminology disputes.

To a mathematician, "modulo operator" is meaningless. Modulo is a modifier to 
a statement, not an operator, and is written "mod" as in:

1 = 5*3 mod 7


> It returns the residue class of the 2 operands. When a is positive this 
> is the same as remainder, but not so for negative a.

"Remainder" is ambiguous for negative values. -7/5 could be given as -1 with 
-2 remainder, or as -2 with 3 remainder. One might define a remainder 
operation as returning a result:

- which is always positive
- with the sign of the divisor
- with the sign of the dividend
- which is closest to zero
- which is furthest away from zero

The last two require further variations, depending on how you resolve ties.

One might also define i%0 to be i, or as undefined. So by my count, there are 
at least 18 consistent ways to define a remainder/modulo operator.

A very few languages define two operators, or functions, e.g. Ada defines a 
rem operator which returns the remainder with the sign of the dividend and a 
mod operator which returns the remainder with the sign of the operator.


-- 
Steven