The C Standard, 6.2.5, paragraph 9 [ISO/IEC 9899:2011], states
A computation involving unsigned operands can never overflow, because a result that cannot be represented by the resulting unsigned integer type is reduced modulo the number that is one greater than the largest value that can be represented by the resulting type.
This behavior is more informally called unsigned integer wrapping. Unsigned integer operations can wrap if the resulting value cannot be represented by the underlying representation of the integer. The following table indicates which operators can result in wrapping:
Operator  Wrap  Operator  Wrap  Operator  Wrap  Operator  Wrap 

Yes  Yes  Yes 
 No  
Yes  Yes 
 No 
 No  
Yes 
 No 
 No 
 No  
 No 
 No 
 No 
 No 
 No  Yes 
 No 
 No  
 Yes 
 No 
 No 
 No 
 Yes 
 No 
 No 
 No 
 No 
 No 
 No 
 No 
Yes 
 No 
 Yes 
 No 
The following sections examine specific operations that are susceptible to unsigned integer wrap. When operating on integer types with less precision than int
, integer promotions are applied. The usual arithmetic conversions may also be applied to (implicitly) convert operands to equivalent types before arithmetic operations are performed. Programmers should understand integer conversion rules before trying to implement secure arithmetic operations. (See INT02C. Understand integer conversion rules.)
Integer values must not be allowed to wrap, especially if they are used in any of the following ways:
[]
or the expression in square brackets []
of a subscripted designation of an element of an array objectsize_t
or rsize_t
(for example, an argument to a memory allocation function)The C Standard defines arithmetic on atomic integer types as readmodifywrite operations with the same representation as regular integer types. As a result, wrapping of atomic unsigned integers is identical to regular unsigned integers and should also be prevented or detected.
Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. This rule applies only to addition between two operands of arithmetic type. (See ARR37C. Do not add or subtract an integer to a pointer to a nonarray object and ARR30C. Do not form or use outofbounds pointers or array subscripts.)
Incrementing is equivalent to adding 1.
This noncompliant code example can result in an unsigned integer wrap during the addition of the unsigned operands ui_a
and ui_b
. If this behavior is unexpected, the resulting value may be used to allocate insufficient memory for a subsequent operation or in some other manner that can lead to an exploitable vulnerability.
void func(unsigned int ui_a, unsigned int ui_b) { unsigned int usum = ui_a + ui_b; /* ... */ } 
This compliant solution performs a precondition test of the operands of the addition to guarantee there is no possibility of unsigned wrap:
#include <limits.h> void func(unsigned int ui_a, unsigned int ui_b) { unsigned int usum; if (UINT_MAX  ui_a < ui_b) { /* Handle error */ } else { usum = ui_a + ui_b; } /* ... */ } 
This compliant solution performs a postcondition test to ensure that the result of the unsigned addition operation usum
is not less than the first operand:
void func(unsigned int ui_a, unsigned int ui_b) { unsigned int usum = ui_a + ui_b; if (usum < ui_a) { /* Handle error */ } /* ... */ } 
Subtraction is between two operands of arithmetic type, two pointers to qualified or unqualified versions of compatible object types, or a pointer to an object type and an integer type. This rule applies only to subtraction between two operands of arithmetic type. (See ARR36C. Do not subtract or compare two pointers that do not refer to the same array, ARR37C. Do not add or subtract an integer to a pointer to a nonarray object, and ARR30C. Do not form or use outofbounds pointers or array subscripts for information about pointer subtraction.)
Decrementing is equivalent to subtracting 1.
This noncompliant code example can result in an unsigned integer wrap during the subtraction of the unsigned operands ui_a
and ui_b
. If this behavior is unanticipated, it may lead to an exploitable vulnerability.
void func(unsigned int ui_a, unsigned int ui_b) { unsigned int udiff = ui_a  ui_b; /* ... */ } 
This compliant solution performs a precondition test of the unsigned operands of the subtraction operation to guarantee there is no possibility of unsigned wrap:
void func(unsigned int ui_a, unsigned int ui_b) { unsigned int udiff; if (ui_a < ui_b){ /* Handle error */ } else { udiff = ui_a  ui_b; } /* ... */ } 
This compliant solution performs a postcondition test that the result of the unsigned subtraction operation udiff
is not greater than the minuend:
void func(unsigned int ui_a, unsigned int ui_b) { unsigned int udiff = ui_a  ui_b; if (udiff > ui_a) { /* Handle error */ } /* ... */ } 
Multiplication is between two operands of arithmetic type.
The Mozilla Foundation Security Advisory 200701 describes a heap buffer overflow vulnerability in the Mozilla Scalable Vector Graphics (SVG) viewer resulting from an unsigned integer wrap during the multiplication of the signed int
value pen>num_vertices
and the size_t
value sizeof(cairo_pen_vertex_t)
[VU#551436]. The signed int
operand is converted to size_t
prior to the multiplication operation so that the multiplication takes place between two size_t
integers, which are unsigned. (See INT02C. Understand integer conversion rules.)
pen>num_vertices = _cairo_pen_vertices_needed( gstate>tolerance, radius, &gstate>ctm ); pen>vertices = malloc( pen>num_vertices * sizeof(cairo_pen_vertex_t) ); 
The unsigned integer wrap can result in allocating memory of insufficient size.
This compliant solution tests the operands of the multiplication to guarantee that there is no unsigned integer wrap:
pen>num_vertices = _cairo_pen_vertices_needed( gstate>tolerance, radius, &gstate>ctm ); if (pen>num_vertices > SIZE_MAX / sizeof(cairo_pen_vertex_t)) { /* Handle error */ } pen>vertices = malloc( pen>num_vertices * sizeof(cairo_pen_vertex_t) ); 
INT30CEX1: Unsigned integers can exhibit modulo behavior (wrapping) when necessary for the proper execution of the program. It is recommended that the variable declaration be clearly commented as supporting modulo behavior and that each operation on that integer also be clearly commented as supporting modulo behavior.
INT30CEX2: Checks for wraparound can be omitted when it can be determined at compile time that wraparound will not occur. As such, the following operations on unsigned integers require no validation:
unsigned int
may safely be subtracted from UINT_MAX
UINT_MAX >> x
is valid as long as 0 <= x < 32
(assuming that the precision of unsigned int
is 32 bits)INT30CEX3. The leftshift operator takes two operands of integer type. Unsigned left shift <<
can exhibit modulo behavior (wrapping). This exception is provided because of common usage, because this behavior is usually expected by the programmer, and because the behavior is well defined. For examples of usage of the leftshift operator, see INT34C. Do not shift an expression by a negative number of bits or by greater than or equal to the number of bits that exist in the operand.
Integer wrap can lead to buffer overflows and the execution of arbitrary code by an attacker.
Rule  Severity  Likelihood  Remediation Cost  Priority  Level 

INT30C  High  Likely  High  P9  L2 
Tool  Version  Checker  Description 

CodeSonar  ALLOC.SIZE.ADDOFLOW  Addition overflow of allocation size  
Compass/ROSE 

 Can detect violations of this rule by ensuring that operations are checked for overflow before being performed (Be mindful of exception INT30EX2 because it excuses many operations from requiring validation, including all the operations that would validate a potentially dangerous operation. For instance, adding two 
Coverity  6.5  INTEGER_OVERFLOW  Implemented 
Klocwork  NUM.OVERFLOW CWARN.NOEFFECT.OUTOFRANGE  
LDRA tool suite  493 S, 494 S  Partially implemented  
Polyspace Bug Finder  R2016a  Unsigned integer overflow  Overflow from operation between unsigned integers 
PRQA QAC  2910 (C)  Partially implemented 
CVE20091385 results from a violation of this rule. The value performs an unchecked subtraction on the length
of a buffer and then adds those many bytes of data to another buffer [xorl 2009]. This can cause a buffer overflow, which allows an attacker to execute arbitrary code.
A Linux Kernel vmsplice exploit, described by Rafal Wojtczuk [Wojtczuk 2008], documents a vulnerability and exploit arising from a buffer overflow (caused by unsigned integer wrapping).
Don Bailey [Bailey 2014] describes an unsigned integer wrap vulnerability in the LZO compression algorithm, which can be exploited in some implementations.
CVE20144377 describes a vulnerability in iOS 7.1 resulting from a multiplication operation that wraps, producing an insufficiently small value to pass to a memory allocation routine, which is subsequently overflowed.
Search for vulnerabilities resulting from the violation of this rule on the CERT website.
[Bailey 2014]  Raising Lazarus  The 20 Year Old Bug that Went to Mars 
[Dowd 2006]  Chapter 6, "C Language Issues" ("Arithmetic Boundary Conditions," pp. 211–223) 
[ISO/IEC 9899:2011]  Subclause 6.2.5, "Types" 
[Seacord 2013b]  Chapter 5, "Integer Security" 
[Viega 2005]  Section 5.2.7, "Integer Overflow" 
[VU#551436]  
[Warren 2002]  Chapter 2, "Basics" 
[Wojtczuk 2008]  
[xorl 2009]  "CVE20091385: Linux Kernel E1000 Integer Underflow" 