How to Detect Integer Overflow in Java with Built‑in Math Methods

# Problem

When solving practice problems, you may need to determine whether adding two int values overflows and, if so, return Integer.MAX_VALUE.

# Solution

JDK 8 already implements overflow‑checking methods in Math; the following examples were found on StackOverflow.

Addition

public static int addExact(int x, int y) {
    int r = x + y;
    // HD 2-12 Overflow iff both arguments have the opposite sign of the result
    if (((x ^ r) & (y ^ r)) < 0) {
        throw new ArithmeticException("integer overflow");
    }
    return r;
}

Subtraction

public static int subtractExact(int x, int y) {
    int r = x - y;
    // HD 2-12 Overflow iff the arguments have different signs and the sign of the result is different than the sign of x
    if (((x ^ y) & (x ^ r)) < 0) {
        throw new ArithmeticException("integer overflow");
    }
    return r;
}

Multiplication (int)

public static int multiplyExact(int x, int y) {
    long r = (long) x * (long) y;
    if ((int) r != r) {
        throw new ArithmeticException("integer overflow");
    }
    return (int) r;
}

Note that long and int behave differently; an overload for long multiplication is also provided.

Multiplication (long)

public static long multiplyExact(long x, long y) {
    long r = x * y;
    long ax = Math.abs(x);
    long ay = Math.abs(y);
    if (((ax | ay) >>> 31) != 0) {
        // Some bits greater than 2^31 that might cause overflow
        // Check the result using division and handle the special case Long.MIN_VALUE * -1
        if ((y != 0 && r / y != x) || (x == Long.MIN_VALUE && y == -1)) {
            throw new ArithmeticException("long overflow");
        }
    }
    return r;
}

Directly calling these methods is the most convenient approach, but for performance‑critical code you may want to avoid the relatively expensive exception handling.

The purpose of this note is to summarize the built‑in overflow‑checking functions that Java already provides, making it easier to share with others.