Overflow
TLDR: Overflow occurs when a computational operation results in a value exceeding the maximum representable range of a data type or system. This phenomenon is common in integer arithmetic and floating-point arithmetic, where fixed-size storage limits the range of values. Overflow can lead to unexpected results, such as wrapping around to a minimum value (in integer operations) or producing special values like infinity (in floating-point systems as defined by IEEE 754 in 1985).
https://en.wikipedia.org/wiki/Arithmetic_overflow
In integer operations, overflow typically results in modular arithmetic behavior, where values wrap around to the opposite end of the range. For example, adding 1 to the maximum value of a 32-bit signed integer (2,147,483,647) results in -2,147,483,648. In floating-point arithmetic, overflow leads to results like positive infinity or negative infinity when the computed value exceeds the representable range. Programming languages like Java and Python offer mechanisms to detect overflow or handle overflow, although behavior may vary depending on the language design.
https://docs.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html
Handling overflow is critical in ensuring the computational reliability and correctness of software systems. Developers use techniques such as type promotion, range checks, or libraries like BigInteger in Java to manage calculations involving large numbers. Modern processors and compilers may include hardware and software-level detection for overflow events, generating exceptions or warnings to alert developers to potential issues. By addressing overflow during development, software can avoid critical errors in domains like financial modeling, cryptography, and scientific computing.
https://www.gnu.org/software/libc/manual/html_node/Integer-Overflow.html