Integer overflow
Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single instruction per operation.
An immediately following add with carry or subtract with borrow operation would use the contents of this flag to modify a register or a memory location that contains the higher part of a multi-word value.
This indicates that an overflow has occurred and the signed result represented in two's complement form would not fit in the given number of bits.
Even when the available space or the fixed data types provided by a programming language or environment are too limited to allow for variables to be defensively allocated with generous sizes, by carefully ordering operations and checking operands in advance, it is often possible to ensure a priori that the result will never be larger than can be stored.
Static analysis tools, formal verification and design by contract techniques can be used to more confidently and robustly ensure that an overflow cannot accidentally result.
CPUs generally have a way to detect this to support addition of numbers larger than their register size, typically using a status bit.
Programming languages implement various mitigation methods against an accidental overflow: Ada, Seed7, and certain variants of functional languages trigger an exception condition on overflow, while Python (since 2.4) seamlessly converts internal representation of the number to match its growth, eventually representing it as long – whose ability is only limited by the available memory.
[14] In languages with native support for arbitrary-precision arithmetic and type safety (such as Python, Smalltalk, or Common Lisp), numbers are promoted to a larger size automatically when overflows occur, or exceptions thrown (conditions signaled) when a range constraint exists.
In the case of Common Lisp, this is possible by using an explicit declaration to type-annotate a variable to a machine-size word (fixnum)[15] and lower the type safety level to zero[16] for a particular code block.
In Rust, while use of basic mathematic operators naturally lacks such flexibility, users can alternatively perform calculations via a set of methods provided by each of the integer primitive types.
Such overflow bugs may be hard to discover and diagnose because they may manifest themselves only for very large input data sets, which are less likely to be used in validation tests.
[22] An unhandled arithmetic overflow in the engine steering software was the primary cause of the crash of the 1996 maiden flight of the Ariane 5 rocket.
[23] The software had been considered bug-free since it had been used in many previous flights, but those used smaller rockets which generated lower acceleration than Ariane 5.
Further, the true cause of the failure was a flaw in the engineering specification of how the software dealt with the overflow when it was detected: it did a diagnostic dump to its bus, which would have been connected to test equipment during software testing during development but was connected to the rocket steering motors during flight; the data dump drove the engine nozzle hard to one side which put the rocket out of aerodynamic control and precipitated its rapid breakup in the air.
[24] On 30 April 2015, the U.S. Federal Aviation Administration announced it will order Boeing 787 operators to reset its electrical system periodically, to avoid an integer overflow which could lead to loss of electrical power and ram air turbine deployment, and Boeing deployed a software update in the fourth quarter.
This is caused by the game's data overflow that was an error of programming as the developers may not have thought said number of lives would be reasonably earned in a full playthrough.
[citation needed] In the arcade game Donkey Kong, it is impossible to advance past level 22 due to an integer overflow in its time/bonus.
IBM–Microsoft Macro Assembler (MASM) version 1.00, and likely all other programs built by the same Pascal compiler, had an integer overflow and signedness error in the stack setup code, which prevented them from running on newer DOS machines or emulators under some common configurations with more than 512 KiB of memory.
The casino refused to pay this amount, calling it a malfunction, using in their defense that the machine clearly stated that the maximum payout was $10,000, so any prize exceeding that had to be the result of a programming bug.
