Subclause 6.2.5, paragraph 9, of the C Standard [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 
Although unsigned left shift <<
can result in wrapping, modulo behavior is permitted by this standard because of common usage, because this behavior is usually expected by the programmer, and because the behavior is welldefined.
The following sections examine specific operations that are susceptible to unsigned integer wrap. When operating on small integer types (smaller 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. Make sure you 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 if they are used in any of the following ways:
 As an array index
 In any pointer arithmetic
 As a length or size of an object
 As the bound of an array (for example, a loop counter)
 As an argument to a memory allocation function
 In securitycritical code
Addition
Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. (See ARR37C. Do not add or subtract an integer to a pointer to a nonarray object and ARR38C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array element for information about adding a pointer to an integer.) Incrementing is equivalent to adding 1.
Noncompliant Code Example
This noncompliant code example may 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.
unsigned int ui_a; unsigned int ui_b; unsigned int usum; /* Initialize ui_a and ui_b */ usum = ui_a + ui_b;
Compliant Solution (Precondition Test)
This compliant solution performs a precondition test of the operands of the addition to guarantee there is no possibility of unsigned wrap:
unsigned int ui_a; unsigned int ui_b; unsigned int usum; /* Initialize ui_a and ui_b */ if (UINT_MAX  ui_a < ui_b) { /* handle error condition */ } else { usum = ui_a + ui_b; }
Compliant Solution (Postcondition Test)
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:
unsigned int ui_a; unsigned int ui_b; unsigned int usum; /* Initialize ui_a and ui_b */ usum = ui_a + ui_b; if (usum < ui_a) { /* handle error condition */ }
Subtraction
Subtraction is between two operands of arithmetic type, between two pointers to qualified or unqualified versions of compatible object types, or between a pointer to an object type and an integer 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 ARR38C. Do not add or subtract an integer to a pointer if the resulting value does not refer to a valid array element for information about pointer subtraction. Decrementing is equivalent to subtracting 1.
Noncompliant Code Example
This noncompliant code example may 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.
unsigned int ui_a; unsigned int ui_b; unsigned int udiff; /* Initialize ui_a and ui_b */ udiff = ui_a  ui_b;
Compliant Solution (Precondition Test)
This compliant solution performs a precondition test of the unsigned operands of the subtraction operation to guarantee there is no possibility of unsigned wrap:
unsigned int ui_a; unsigned int ui_b; unsigned int udiff; /* Initialize ui_a and ui_b */ if (ui_a < ui_b){ /* handle error condition */ } else { udiff = ui_a  ui_b; }
Compliant Solution (Postcondition Test)
This compliant solution performs a postcondition test that the result of the unsigned subtraction operation udiff
is not greater than the minuend:
unsigned int ui_a; unsigned int ui_b; unsigned int udiff; /* Initialize ui_a and ui_b */ udiff = ui_a  ui_b; if (udiff > ui_a) { /* handle error condition */ }
Multiplication
Multiplication is between two operands of arithmetic type.
Noncompliant Code Example
The Mozilla Scalable Vector Graphics (SVG) viewer contains a heap buffer overflow vulnerability 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.
Compliant Solution
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 condition */ } pen>vertices = malloc( pen>num_vertices * sizeof(cairo_pen_vertex_t) );
Atomic Integers
The C Standard defines arithmetic on atomic integer types as readmodifywrite operations with the same representation as nonatomic integer types. As a result, wrapping of atomic unsigned integers is identical to nonatomic unsigned integers and should also be prevented or detected.
This section includes an example only for the addition of atomic integer types. For other operations, you can use tests similar to the precondition tests for nonatomic integer types.
Noncompliant Code Example
This noncompliant code example using atomic integers can result in unsigned integer overflow wrapping:
atomic_int i; int ui_a; /* Initialize i, ui_a */ atomic_fetch_add(&i, ui_a);
Compliant Solution
This compliant solution performs a postcondition test to ensure that the result of the unsigned addition operation to i
is not less than the operand ui_a
:
atomic_int i; int ui_a; /* Initialize ui_a, i */ atomic_fetch_add(&i, ui_a); if (atomic_load(&i) < ui_a) { /* handle error condition */ }
Exceptions
INT30EX1. Unsigned integers can exhibit modulo behavior (wrapping) only when this behavior is 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.
INT30EX2. 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:
 Operations on two compiletime constants
 Operations on a variable and 0 (except division by 0, of course)
 Subtracting any variable from its type's maximum. For instance, any
unsigned int
may safely be subtracted fromUINT_MAX
 Multiplying any variable by 1
 Division, as long as the divisor is nonzero
 Rightshifting any type maximum by any number smaller than the type size. For instance,
UINT_MAX >> x
is valid as long as 0 <= x < 32 (assuming that the size ofunsigned int
is 32 bits)  Leftshifting 1 by any number smaller than the type size
Risk Assessment
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 
Automated Detection
Tool  Version  Checker  Description 

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 
Fortify SCA  5.0 
 Can detect violations of this rule with the CERT C Rule Pack 
PRQA QAC  8.1  2910 (C)  Partially implemented 
Related Vulnerabilities
CVE20091385 results from a violation of this rule. The value performs an unchecked subtraction on the length
of a buffer and then adds that 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).
Search for vulnerabilities resulting from the violation of this rule on the CERT website.
Related Guidelines
CERT C++ Secure Coding Standard  INT30CPP. Ensure that unsigned integer operations do not wrap 
ISO/IEC TR 24772:2013  Arithmetic Wraparound Error [FIF] 
MITRE CWE  CWE190, Integer overflow (wrap or wraparound) 
Bibliography
[Dowd 2006]  Chapter 6, "C Language Issues" ("Arithmetic Boundary Conditions," pp. 211–223) 
[ISO/IEC 9899:2011]  Section 6.2.5, "Types" 
[Seacord 2013]  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" 