Modulo of negative numbers [duplicate]

问题

Possible Duplicate:
Mod of negative number is melting my brain!

I was wondering if there was a nicer algorithm for what I'm trying to do:

wrapIndex(-6, 3) = 0
wrapIndex(-5, 3) = 1
wrapIndex(-4, 3) = 2
wrapIndex(-3, 3) = 0
wrapIndex(-2, 3) = 1
wrapIndex(-1, 3) = 2
wrapIndex(0, 3) = 0
wrapIndex(1, 3) = 1
wrapIndex(2, 3) = 2
wrapIndex(3, 3) = 0
wrapIndex(4, 3) = 1
wrapIndex(5, 3) = 2

I came up with

function wrapIndex(i, i_max) {
        if(i > -1)
            return i%i_max;

        var x = i_max + i%i_max;
        if(x == i_max)
            return 0;

        return x;
    }

Is there a nicer way to do this?

回答1:

This solution is branchless, but performs % twice:

function wrapIndex(i, i_max) {
   return ((i % i_max) + i_max) % i_max;
}

It should be said the C#/Java behavior of % is assumed, i.e. the result has the same sign as the dividend. Some languages define the remainder calculation to take the sign of the divisor instead (e.g. mod in Clojure). Some languages have both variants (mod/rem pair in Common Lisp, Haskell, etc). Algol-68 has %x which always returns a non-negative number. C++ left it up to implementation until C++11, now the sign of the remainder is (almost) fully specified according to the dividend sign.

回答2:

The solution with two % operations works, but this is somewhat faster in most languages on most hardware (there are exceptions, however):

int wrapIndex(int i, int i_max) {
    i = i%i_max;
    return i<0 ? i+i_max : i;
}

回答3:

Nicer is a matter of taste, but How about

var x = (i_max + i % i_max) % i_max;

回答4:

You could do this:

function wrapIndex(i, i_max) {
    if (i < 0) i = (i % i_max) + i_max;
    return i % i_max;
}

回答5:

Many users gave good answers, just beware negative numbers, since different languages may behave differently. By example this C snippet writes "-1"

int main ()
{
    printf("%d\n", (-4) % 3);
}

While in python we have a different output value

Python 2.6.4 (r264:75706, Dec  7 2009, 18:43:55) 
[GCC 4.4.1] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> (-4) % 3
2

EDIT: Actually I don't think you'll have negative indexes! However it's good to know that.

来源：https://stackoverflow.com/questions/3417183/modulo-of-negative-numbers

标签

algorithm

math

modulo