Wrap around explanation for signed and unsigned variables in C?

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Signed integer variables do not have wrap-around behavior in C language. Signed integer overflow during arithmetic computations produces undefined behavior. Note BTW that GCC compiler you mentioned is known for implementing strict overflow semantics in optimizations, meaning that it takes advantage of the freedom provided by such undefined behavior situations: GCC compiler assumes that signed integer values never wrap around. That means that GCC actually happens to be one of the compilers in which you cannot rely on wrap-around behavior of signed integer types.

For example, GCC compiler can assume that for variable int i the following condition

if (i > 0 && i + 1 > 0)

is equivalent to a mere

if (i > 0)

This is exactly what strict overflow semantics means.

Unsigned integer types implement modulo arithmetic. The modulo is equal 2^N where N is the number of bits in the value representation of the type. For this reason unsigned integer types do indeed appear to wrap around on overflow.

However, C language never performs arithmetic computations in domains smaller than that of int/unsigned int. Type unsigned short int that you mention in your question will typically be promoted to type int in expressions before any computations begin (assuming that the range of unsigned short fits into the range of int). Which means that 1) the computations with unsigned short int will be preformed in the domain of int, with overflow happening when int overflows, 2) overflow during such computations will lead to undefined behavior, not to wrap-around behavior.

For example, this code produces a wrap around

unsigned i = USHRT_MAX;
i *= INT_MAX; /* <- unsigned arithmetic, overflows, wraps around */

while this code

unsigned short i = USHRT_MAX;
i *= INT_MAX; /* <- signed arithmetic, overflows, produces undefined behavior */

leads to undefined behavior.

If no int overflow happens and the result is converted back to an unsigned short int type, it is again reduced by modulo 2^N, which will appear as if the value has wrapped around.

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