## Why Does Java\'s Modulus Operator (%) Return Negative Results for Negative Numbers?

Modulus Calculations in Java: Handling Negative Numbers

In Java, performing modulus operations on negative numbers often yields unexpected results. When applying the modulus operator (%) on a negative number, one might expect to obtain a positive value, but in some cases, it returns a negative result. To understand this behavior, it is essential to delve into the inner workings of modulus calculations.

The modulus operator calculates the remainder when dividing one number by another. For positive numbers, the remainder is consistently positive. However, when dealing with negative numbers, there are two possible definitions of modulus:

1. Floored Modulus: This definition rounds down the remainder to the nearest integer towards negative infinity.
2. Truncating Modulus: This definition rounds down the remainder to zero (i.e., it discards any fractional part).

Java employs the truncating modulus definition. Consequently, when dividing a negative number by a positive number, the remainder is always negative. For instance, -13 % 64 evaluates to -13 in Java because -13 is divided by 64 without any fractional component.

If one desires a positive remainder for negative inputs, the following code snippet can be employed:

<code class="java">int r = x % n;
if (r > 0 && x < 0) {
    r -= n;
}</code>

Conversely, if one prefers a negative remainder for negative inputs, the following code snippet can be used:

<code class="java">int r = x % n;
if (r < 0) {
    r += n;
}</code>

Understanding the varying definitions of modulus is crucial when working with negative numbers in different programming languages. By comprehending the distinctions between floored and truncating modulus, developers can ensure that their code behaves as intended, especially when dealing with negative inputs.

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