Integer operations must result in an integer value within the range of the integer type (that is, the resulting value is the same as the result produced by unlimited-range integers). Frequently, the range is more restrictive depending on the use of the integer value, for example, as an index. Integer values can be verified by code review or by static analysis.

Integer overflow is undefined behavior, so a compiled program can do anything, including go off to play the Game of Life. Furthermore, a compiler may perform optimizations that assume an overflow will never occur, which can easily yield unexpected results. Compilers can optimize away if statements that check whether an overflow occurred. See MSC15-C. Do not depend on undefined behavior for an example.

Verifiably in-range operations are often preferable to treating out-of-range values as an error condition because the handling of these errors has been repeatedly shown to cause denial-of-service problems in actual applications. The quintessential example is the failure of the Ariane 5 launcher, which occurred because of an improperly handled conversion error that resulted in the processor being shut down [Lions 1996].

A program that detects an integer overflow to be imminent may do one of two things: (1) signal some sort of error condition or (2) produce an integer result that is within the range of representable integers on that system. Some situations can be handled by an error condition, where an overflow causes a change in control flow (such as the system complaining about bad input and requesting alternative input from the user). Others are better handled by the latter option because it allows the computation to proceed and generate an integer result, thereby avoiding a denial-of-service attack. However, when continuing to produce an integer result in the face of overflow, the question of what integer result to return to the user must be considered.

The saturation and modwrap algorithms and the technique of restricted range usage, defined in the following subsections, produce integer results that are always within a defined range. This range is between the integer values MIN and MAX (inclusive), where MIN and MAX are two representable integers with MIN < MAX.

Saturation Semantics

For saturation semantics, assume that the mathematical result of the computation is result. The value actually returned to the user is set out in the following table:

Modwrap Semantics

In modwrap semantics (also called modulo arithmetic), integer values "wrap round." That is, adding 1 to MAX produces MIN. This is the defined behavior for unsigned integers in the C Standard, subclause 6.2.5, paragraph 9. It is frequently the behavior of signed integers, as well. However, it is more sensible in many applications to use saturation semantics instead of modwrap semantics. For example, in the computation of a size (using unsigned integers), it is often better for the size to stay at the maximum value in the event of overflow rather than to suddenly become a very small value.

Restricted Range Usage

Another technique for avoiding integer overflow is to use only half the range of signed integers. For example, when using an int, use only the range [INT_MIN/2, INT_MAX/2]. This practice has been a trick of the trade in Fortran for some time, and now that optimizing C compilers are more sophisticated, it can be valuable in C.

Consider subtraction. If the user types the expression a - b, where both a and b are in the range [INT_MIN/2, INT_MAX/2], the result will be in the range (INT_MIN, INT_MAX] for a typical two's complement machine.

Now, if the user types a < b, an implicit subtraction often occurs. On a machine without condition codes, the compiler may simply issue a subtract instruction and check whether the result is negative. This behavior is allowed because the compiler is allowed to assume there is no overflow. If all explicitly user-generated values are kept in the range [INT_MIN/2, INT_MAX/2], then comparisons will always work even if the compiler performs this optimization on such hardware.

Noncompliant Code Example

In this noncompliant example, i + 1 will overflow on a 16-bit machine. The C Standard allows signed integers to overflow and produce incorrect results. Compilers can take advantage of this to produce faster code by assuming an overflow will not occur. As a result, the if statement that is intended to catch an overflow might be optimized away.

int i = /* Expression that evaluates to the value 32767 */;
/* ... */
if (i + 1 <= i) {
  /* Handle overflow */
}
/* Expression involving i + 1 */

Compliant Solution

Using a long instead of an int is guaranteed to accommodate the computed value:

long i = /* Expression that evaluates to the value 32767 */;
/* ... */
/* No test is necessary; i is known not to overflow */
/* Expression involving i + 1 */

Risk Assessment

Out-of-range integer values can result in reading from or writing to arbitrary memory locations and the execution of arbitrary code.

Automated Detection

Tool	Version	Checker	Description
Astrée		integer-overflow	Fully checked
Axivion Bauhaus Suite		CertC-INT08
CodeSonar		ALLOC.SIZE.ADDOFLOW ALLOC.SIZE.IOFLOW ALLOC.SIZE.MULOFLOW ALLOC.SIZE.SUBUFLOW MISC.MEM.SIZE.ADDOFLOW MISC.MEM.SIZE.BAD MISC.MEM.SIZE.MULOFLOW MISC.MEM.SIZE.SUBUFLOW	Addition Overflow of Allocation Size Integer Overflow of Allocation Size Multiplication Overflow of Allocation Size Subtraction Underflow of Allocation Size Addition Overflow of Size Unreasonable Size Argument Multiplication Overflow of Size Subtraction Underflow of Size
Compass/ROSE			Could detect violations of this recommendation by flagging any comparison expression involving addition that could potentially overflow. For example, instead of comparing a + b < c (where b and c are compile-time constants) and b > c, the code should compare a < c - b. (This assumes a, b, c are unsigned ints. Usually b is small and c is an upper bound such as INT_MAX.)
Helix QAC		C2800,  C2910 DF2801, DF2802, DF2803, DF2911, DF2912, DF2913
LDRA tool suite		488 S, 493 S, 493 S	Partially implemented
Parasoft C/C++test		CERT_C-INT08-a CERT_C-INT08-b CERT_C-INT08-c CERT_C-INT08-d	Avoid data loss when converting between integer types Avoid signed integer overflows Avoid value change when converting between integer types Avoid wraparounds when performing arithmetic integer operations
PC-lint Plus		648, 650, 679, 680, 776, 952, 2704	Partially supported
Polyspace Bug Finder		CERT C: Rec. INT08-C	Checks for integer overflow or integer constant overflow (rec. fully covered)

Related Vulnerabilities

Search for vulnerabilities resulting from the violation of this rule on the CERT website.

Related Guidelines

Bibliography