Integer overflow: Difference between revisions

Revision as of 18:39, 22 February 2017

Revision as of 08:06, 23 February 2017

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[[Image:Odometer rollover.jpg|thumb|250px|[[Odometer]] rollover, a mechanical form of integer overflow. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit to change to a 1, so the counter resets to zero. This is ''wrapping'' in contrast to ''saturating''.]]

In [[computer programming]], an '''integer overflow''' occurs when an [[arithmetic]] operation attempts to create a numeric value that is outside of the range that can be represented withinwith thea availablegiven storagenumber spaceof bits - either larger than the maximum representable value, or lower than the minimum representable value.

The most common result of an overflow is that the least significant representable bits of the result are stored; the result is said to ''wrap''. On some processors like [[graphics processing unit]]s (GPUs) and [[digital signal processor]]s (DSPs), the result [[saturation arithmetic|saturates]]; that is, once the maximum value is reached, any attempt to increase it always returns the maximum integer value.

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* 128 bits: maximum representable value 2¹²⁸ − 1 = 340,282,366,920,938,463,463,374,607,431,768,211,455

When an arithmetic operation produces a result larger than the maximum above, an integer overflow reduces the result to [[modulo operation|modulo]] of the maximum possible value, retaining only the least significant bits and effectively causing a ''wrap around'';.

Multiplying or adding two integers may result in a value that is unexpectedly small, and subtracting from a small valueinteger may also cause a wrap to a large positive value (for example, 8-bit integer addition 255 + 1 results in 0, which is {{math|256 mod 255}}, and similarly subtraction 0 - 1 results in 255, a [[two's complement]] representation of -1).

{{anchor|Security ramifications}}

MultiplyingSuch orwrap adding two integersaround may resultcause insecurity aproblems value- thatif isan unexpectedlyoverflown small. If this numbervalue is used as the number of bytes to allocate for a buffer, the buffer will be allocated unexpectedly small, leading to a potential buffer overflow and arbitrary code execution.

If the variable has a [[Signed number representations|signed integer]] type, a program may make the assumption that a variable always contains a positive value. An integer overflow can cause the value to wrap and become negative, which violates the program's assumption and may lead to unexpected behavior (for example, 8-bit integer addition of 127 + 1 results in -128, a two's complement of 128).

If the variable has a [[Signed number representations|signed integer]] type, a program may make the assumption that a variable always contains a positive value. An integer overflow can cause the value to wrap and become negative, which violates the program's assumption and may lead to unexpected behavior (for example, 8-bit integer addition of 127 + 1 results in -128, a two's complement of 128).

Multiplying or adding two integers may result in a value that is unexpectedly small. If this number is used as the number of bytes to allocate for a buffer, the buffer will be allocated unexpectedly small, leading to a potential buffer overflow.

==Methods to mitigate integer overflow problems==