overflowunderflow

Overflow and underflow are terms used to describe situations in numeric computing where a calculation yields a value outside the range that a given numeric type can represent. They are most commonly discussed in fixed-width integer arithmetic and in floating-point arithmetic, where different rules apply for how values are stored and manipulated.

Integer overflow occurs when a result lies beyond the maximum or below the minimum value that a fixed-width integer can represent. In two’s complement machines, this often manifests as wrap-around, where the value cycles back into the opposite end of the range. Some languages define overflow for signed integers as undefined behavior, while unsigned integers typically wrap around in a well-defined way. Floating-point overflow, by contrast, occurs when a result exceeds the largest finite value; many systems represent this as infinity and may raise an exception or flag an error.

Floating-point underflow refers to magnitudes that are smaller than the smallest normalized positive value. In IEEE 754 arithmetic, such results may become subnormal (denormals), allowing gradual underflow, or may underflow to zero. Integer underflow is less commonly treated as a separate category; it is usually described as overflow in the negative direction, with wrap-around behavior on two’s complement systems or as undefined behavior in some languages.

The effects of overflow and underflow can range from harmless to severe, including incorrect calculations, program crashes, or security vulnerabilities. Preventive approaches include using larger or arbitrary-precision types, performing range checks before operations, employing saturating arithmetic, and relying on language- or library-supported exceptions or flags to detect and handle exceptional results.