How Does Unsigned Integer Overflow Work in C/C ?

Unsigned Integer Overflow in C/C

In integer arithmetic, overflow occurs when a result exceeds the representable range of the data type being used. However, in the context of unsigned integer operations, a different behavior is observed.

Explanation

When performing computations involving unsigned integers, the result cannot overflow in the traditional sense. This is because the result is automatically reduced modulo the number one greater than the largest representable value.

In other words, the result "wraps around" within the representable range of the data type. For example, consider the following sequence of operations:

UINT_MAX + 1 == 0
UINT_MAX + 2 == 1
UINT_MAX + 3 == 2

and so on. The result continually cycles back within the range [0, UINT_MAX].

Analogy with Modulo Operation

This behavior is analogous to the modulo operation, which calculates the remainder when a number is divided by a given divisor. For example, the result of 11 % 5 is 1, since dividing 11 by 5 yields a remainder of 1.

Implications

The wraparound behavior of unsigned integer arithmetic can have important implications for security and program correctness. For instance, if a counter or index value exceeds UINT_MAX, it may reset to 0 without causing an error. This can lead to unexpected behavior and potential vulnerabilities.

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