How Do I Handle Negative Modulo Operations Correctly?

Navigating the Challenges of Negative Modulo

The modulo operator (%) can be tricky when dealing with negative numbers. While it smoothly returns the remainder for positive integers, its behavior with negative numbers often leads to confusion. This operator provides the remainder after division.

The Issue with Negative Modulo

Consider an array with a length of 3:

<code>i % 3 =
4 -> 1
3 -> 0
2 -> 2
1 -> 1
0 -> 0
-1 -> -1
-2 -> -2
-3 -> 0
-4 -> -1</code>

Notice how negative remainders remain negative, unlike their positive counterparts which cycle through the positive range.

A Solution for Negative Modulo

To ensure negative numbers behave as expected (wrapping around), a custom function is needed:

<code class="language-c++">int GetArrayIndex(int i, int arrayLength) {
    int r = i % arrayLength;
    return (r < 0) ? (r + arrayLength) : r;
}</code>

How it Works

This function cleverly adds arrayLength to the remainder (r) only if r is negative. This "wraps" the negative remainder into the positive range, mimicking the desired modulo behavior.

Practical Application

Let's test the function with our 3-element array:

GetArrayIndex( 4, 3) -> 1 GetArrayIndex( 3, 3) -> 0 GetArrayIndex( 2, 3) -> 2 GetArrayIndex( 1, 3) -> 1 GetArrayIndex( 0, 3) -> 0 GetArrayIndex(-1, 3) -> 2 GetArrayIndex(-2, 3) -> 1 GetArrayIndex(-3, 3) -> 0 GetArrayIndex(-4, 3) -> 2

This custom function effectively handles negative modulo operations, providing consistent and predictable results. Now you can confidently work with negative modulo without encountering unexpected behavior.

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