Why Math.abs(Integer.MIN_VALUE) Returns a Negative Value in Java

Problem Overview

When calling Math.abs() on an int value, developers may encounter a surprising negative result. This occurs specifically when the argument is Integer.MIN_VALUE (‑2147483648), because the absolute value cannot be represented within the 32‑bit signed integer range.

Demonstration Code

public static void main(String[] args) {
    int min = Integer.MIN_VALUE;
    int max = Integer.MAX_VALUE;
    System.out.println("Min: " + min);
    System.out.println("Max: " + max);
    int abs = Math.abs(min);
    System.out.println("Abs of Min: " + abs);
}

Running this program prints:

Min: -2147483648
Max: 2147483647
Abs of Min: -2147483648

Why the Negative Result Occurs

The source of the bug lies in the two's‑complement representation of signed integers. In Java, -x is defined as (~x) + 1 (JLS §15.15.4). For Integer.MIN_VALUE the binary pattern is 1000…000 (sign bit 1, all other bits 0). Flipping the bits yields 0111…111 (2147483647), then adding 1 wraps around to 1000…000 again, which is still -2147483648. Because the positive counterpart (2147483648) exceeds Integer.MAX_VALUE, the operation overflows and the original negative value is returned.

Implications

The same issue exists for long values with Long.MIN_VALUE. Developers must guard against this edge case, for example by converting to a larger type (e.g., long) before taking the absolute value, or by handling MIN_VALUE explicitly.