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Signed integer overflow is undefined behavior 36. Consequently, implementations have considerable latitude in how they deal with signed integer overflow (see MSC15-C. Do not depend on undefined behavior). An implementation that defines signed integer types as being modulo, for example, need not detect integer overflow. Implementations may also trap on signed arithmetic overflows, or simply assume that overflows will never happen and generate object code accordingly.  It is also possible for the same conforming implementation to emit code that exhibits different behavior in different contexts. For example, an implementation may determine that a signed integer loop control variable declared in a local scope cannot overflow and may emit efficient code on the basis of that determination, while the same implementation may determine that a global variable used in as a similar context will wrap.

For these reasons, it is important to ensure that operations on signed integers do no not result in overflow. Of particular importance are operations on signed integer values that originate from a tainted source and are used as:

• integer Integer operands of any pointer arithmetic, including array indexing;
• the The assignment expression for the declaration of a variable length array;
• the The postfix expression preceding square brackets [] or the expression in square brackets [] of a subscripted designation of an element of an array object; and
• function Function arguments of type size_t or rsize_t (for example, an argument to a memory allocation function).

Most integer operations can result in overflow if the resulting value cannot be represented by the underlying representation of the integer. The following table indicates which operators operations can result in overflow:.

The following sections examine specific operations that are susceptible to integer overflow. When operating on small integer types (smaller 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 see INT02-C. Understand integer conversion rules).)

Implementation Details

GNU GCC invoked with the -fwrapv command-line option defines the same modulo arithmetic for both unsigned and signed integers.

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The C Standard defines the behavior of arithmetic on atomic signed integer types to use two's complement representation with silent wraparound on overflow; there are no undefined results. However, although Although defined, these results may be unexpected and therefore carry similar risks to unsigned integer wrapping (see INT30-C. Ensure that unsigned integer operations do not wrap). Consequently, signed integer overflow of atomic integer types should also be prevented or detected. 

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Addition is between two operands of arithmetic type or between a pointer to an object type and an integer type. This rule only applies to addition between two operands of arithmetic type . See (see ARR37-C. Do not add or subtract an integer to a pointer to a non-array object and ARR30-C. Do not form or use out-of-bounds pointers or array subscripts).

Incrementing is equivalent to adding 1.

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This noncompliant code example may can result in a signed integer overflow during the addition of the signed operands si_a and si_b. :

void func(signed int si_a, signed int si_b) {
  signed int sum = si_a + si_b;
  /* ... */
}

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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 only applies to subtraction between two operands of arithmetic type .  See (see ARR36-C. Do not subtract or compare two pointers that do not refer to the same array, ARR37-C. Do not add or subtract an integer to a pointer to a non-array object, and ARR30-C. Do not form or use out-of-bounds pointers or array subscripts for information about pointer subtraction).

Decrementing is equivalent to subtracting 1.

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This noncompliant code example can result in a signed integer overflow during the subtraction of the signed operands si_a and si_b.:

void func(signed int si_a, signed int si_b) {
  signed int diff = si_a - si_b;
  /* ... */
}

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This noncompliant code example can result in a signed integer overflow during the multiplication of the signed operands si_a and si_b.:

void func(signed int si_a, signed int si_b) {
  signed int result = si_a * si_b;
  /* ... */
}

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The product of two operands can always be represented using twice the number of bits than exist in the precision of the larger of the two operands. This compliant solution eliminates signed overflow on systems where long long is at least twice the width precision of int:

#include <stddef.h>
#include <assert.h>
#include <limits.h>
#include <inttypes.h>
 
extern size_t popcount(uintmax_t);
#define PRECISION(umax_value) popcount(umax_value) 
  
void func(signed int si_a, signed int si_b) {
  signed int result;
  signed long long tmp;
  assert(PRECISION(ULLONG_MAX) >= 2 * PRECISION(UINT_MAX));
  tmp = (signed long long)si_a * (signed long long)si_b;
 
  /*
   * If the product cannot be represented as a 32-bit integer,
   * handle as an error condition.
   */
  if ((tmp > INT_MAX) || (tmp < INT_MIN)) {
    /* Handle error */
  } else {
    result = (int)tmp;
  }
  /* ... */
}

The assertion fails if long long has less than twice the width precision of int. The  PRECISION() macro and popcount() function are explained in INT35-C. Use correct integer precisions. 

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The following portable compliant solution can be used for on with any conforming implementation, including those that do not have an integer type that is at least twice as big as int.the precision of int:

#include <limits.h>
 
void func(signed int si_a, signed int si_b) {
  signed int result;  
  if (si_a > 0) {  /* si_a is positive */
    if (si_b > 0) {  /* si_a and si_b are positive */
      if (si_a > (INT_MAX / si_b)) {
        /* Handle error */
      }
    } else { /* si_a positive, si_b nonpositive */
      if (si_b < (INT_MIN / si_a)) {
        /* Handle error */
      }
    } /* si_a positive, si_b nonpositive */
  } else { /* si_a is nonpositive */
    if (si_b > 0) { /* si_a is nonpositive, si_b is positive */
      if (si_a < (INT_MIN / si_b)) {
        /* Handle error */
      }
    } else { /* si_a and si_b are nonpositive */
      if ( (si_a != 0) && (si_b < (INT_MAX / si_a))) {
        /* Handle error */
      }
    } /* End if si_a and si_b are nonpositive */
  } /* End if si_a is nonpositive */

  result = si_a * si_b;
}

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Division is between two operands of arithmetic type. Overflow can occur during two's complement signed integer division when the dividend is equal to the minimum (negative) value for the signed integer type and the divisor is equal to −1. Division operations are also susceptible to divide-by-zero errors . (See see INT33-C. Ensure that division and remainder operations do not result in divide-by-zero errors).)

Noncompliant Code Example

This noncompliant code example prevents divide-by-zero errors in compliance with  INT33-C. Ensure that division and remainder operations do not result in divide-by-zero errors but does not prevent a signed integer overflow error on twosin two's-complement platforms. 

void func(signed long s_a, signed long s_b) {
  signed long result;
  if (s_b == 0) {
    /* Handle error */
  } else {
    result = s_a / s_b;
  }
  /* ... */
}

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The remainder operator provides the remainder when two operands of integer type are divided. Because many platforms implement remainder and division in the same instruction, the remainder operator is also susceptible to arithmetic overflow and division by 0.  (See see INT33-C. Ensure that division and remainder operations do not result in divide-by-zero errors).)

Noncompliant Code Example

Many hardware architectures implement remainder as part of the division operator, which can overflow. Overflow can occur during a remainder operation when the dividend is equal to the minimum (negative) value for the signed integer type and the divisor is equal to −1. This occurs even though the result of such a remainder operation is mathematically 0.  This noncompliant code example prevents divide-by-zero errors in compliance with  INT33-C. Ensure that division and remainder operations do not result in divide-by-zero errors but does not prevent integer overflow.:

void func(signed long s_a, signed long s_b) {
  signed long result;
  if (s_b == 0) {
    /* Handle error */
  } else {
    result = s_a % s_b;
  }
  /* ... */
}

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#include <limits.h>
 
void func(signed long s_a, signed long s_b) {
  signed long result;
  if ((s_b == 0 ) || ((s_a == LONG_MIN) && (s_b == -1))) {
    /* Handle error */
  } else {
    result = s_a % s_b;
  }
  
  /* ... */
}

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The left-shift operator takes two operands of integer type. The result of E1 << E2 is E1 left-shifted E2 bit positions; vacated bits are filled with zeros. 

The C Standard, 6.5.7, paragraph 4 [ISO/IEC 9899:2011], states

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In almost every case, an attempt to shift by a negative number of bits or by more bits than exist in the operand indicates a bug ( logic error). These issues are covered by INT34-C. 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.

Noncompliant Code Example

This noncompliant code example performs a left shift, after verifying that the number being shifted is not negative, and the number of bits to shift is valid.  The PRECISION() macro and popcount() function are explained in INT35-C. Use correct integer precisions. However, because this code does no overflow check, it can result in an unrepresentable value. 

#include <limits.h>
#include <stddef.h>
#include <inttypes.h>
 
extern size_t popcount(uintmax_t);
#define PRECISION(umax_value) popcount(umax_value) 

void func(signed long si_a, signed long si_b) {
  signed long result;
  if ((si_a < 0) || (si_b < 0) ||
      (si_b >= PRECISION(ULONG_MAX)) {
    /* Handle error */
  } else {
    result = si_a << si_b;
  }
 
  /* ... */
}

Compliant Solution

This compliant solution eliminates the possibility of overflow resulting from a left-shift operation:

#include <limits.h>
#include <stddef.h>
#include <inttypes.h>
 
extern size_t popcount(uintmax_t);
#define PRECISION(umax_value) popcount(umax_value) 

void func(signed long si_a, signed long si_b) {
  signed long result;
  if ((si_a < 0) || (si_b < 0) ||
      (si_b >= PRECISION(ULONG_MAX)) ||
      (si_a > (LONG_MAX >> si_b))) {
    /* Handle error */
  } else {
    result = si_a << si_b;
  }
 
  /* ... */
}

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void func(signed long s_a) {
  signed long result = -s_a;

  /* ... */
}

Compliant Solution

This compliant solution tests the suspect negation operation to guarantee there is no possibility of signed overflow:

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Bibliography

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