What is the Overflow Behavior of Signed and Unsigned Integers in C ?

Overflow Behavior for Signed Integers in C

In C , signed integer overflow, like in C, is undefined behavior. This means that the result of an expression that overflows is not specified by the standard, and the compiler is free to handle it in an implementation-defined manner. However, C 11 introduced the concept of "integer with fixed width" types, such as int8_t, int16_t, int32_t, and int64_t.

Integer Types with Fixed Width

These types guarantee that negative numbers are represented using 2's complement representation. This suggests that arithmetic operations on these types might behave as modulo 2^n, where n is the width of the integer. However, this is not the case.

Overflow Behavior for Fixed Width Types

Even for fixed width types, signed integer overflow remains undefined behavior. The C 11 standard (paragraph 5/4) explicitly states that if an expression results in a mathematically undefined or unrepresentable value, the behavior is undefined.

Unsigned Integer Overflow

In contrast to signed integer overflow, unsigned integer overflow is explicitly defined for fixed width types. According to paragraph 3.9.1/4 of the C 11 standard, unsigned arithmetic obeys the laws of arithmetic modulo 2^n. Footnote 46 clarifies that unsigned integer operations do not overflow as the result is reduced modulo the maximum representable value.

Conclusion

Despite using 2's complement representation for fixed width types, signed integer overflow remains undefined behavior. On the other hand, unsigned integer overflow is well-defined and follows modulo arithmetic. This difference highlights the fundamental distinction between signed and unsigned integer types in C .

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