Integer overflow

In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the range that can be represented with a given number of digits – either higher than the maximum or lower than the minimum representable value.

The most common result of an overflow is that the least significant representable digits of the result are stored; the result is said to wrap around the maximum (i.e. modulo a power of the radix, usually two in modern computers, but sometimes ten or other number). On some processors like graphics processing units (GPUs) and digital signal processors (DSPs) which support saturation arithmetic, overflowed results would be clamped, i.e. set to the minimum value in the representable range if the result is below the minimum and set to the maximum value in the representable range if the result is above the maximum, rather than wrapped around.

An overflow condition may give results leading to unintended behavior. In particular, if the possibility has not been anticipated, overflow can compromise a program's reliability and security.

For some applications, such as timers and clocks, wrapping on overflow can be desirable. The C11 standard states that for unsigned integers, modulo wrapping is the defined behavior and the term overflow never applies: "a computation involving unsigned operands can never overflow."^[1]