Programs must not allow mathematical operations to exceed the integer ranges provided by their primitive integer data types. According to The Java Language Specification (JLS), §4.2.2, "Integer Operations" [JLS 2015]:

The built-in integer operators do not indicate overflow or underflow in any way. Integer operators can throw a NullPointerException if unboxing conversion of a null reference is required. Other than that, the only integer operators that can throw an exception are the integer divide operator / and the integer remainder operator %, which throw an ArithmeticException if the right-hand operand is zero, and the increment and decrement operators ++ and -- which can throw an OutOfMemoryError if boxing conversion is required and there is insufficient memory to perform the conversion.

The integral types in Java, representation, and inclusive ranges are shown in the following table taken from the JLS, §4.2.1, "Integral Types and Values" [JLS 2015]:

The following table shows the integer overflow behavior of the integral operators.

Because the ranges of Java types are not symmetric (the negation of each minimum value is one more than each maximum value), even operations such as unary negation can overflow if applied to a minimum value. Because the java.lang.math.abs() method returns the absolute value of any number, it can also overflow if given the minimum int or long as an argument.

When a mathematical operation cannot be represented using the supplied integer types, Java's built-in integer operators silently wrap the result without indicating overflow. The silent wrap can result in incorrect computations and unanticipated outcomes. Failure to account for integer overflow has resulted in failures of real systems, for example, when implementing the compareTo() method. The meaning of the return value of the compareTo() method is defined only in terms of its sign and whether it is zero; the magnitude of the return value is irrelevant. Consequently, an apparent but incorrect optimization would be to subtract the operands and return the result. For operands of opposite signs, this approach can result in integer overflow, consequently violating the compareTo() contract [Bloch 2008].

Comparison of Compliant Techniques

Following are the three main techniques for detecting unintended integer overflow:

• Precondition testing. Check the inputs to each arithmetic operator to ensure that overflow cannot occur. Throw an ArithmeticException when the operation would overflow if it were performed; otherwise, perform the operation.

• Upcasting. Cast the inputs to the next larger primitive integer type and perform the arithmetic in the larger size. Check each intermediate result for overflow of the original smaller type and throw an ArithmeticException if the range check fails. Note that the range check must be performed after each arithmetic operation; larger expressions without per-operation bounds checking can overflow the larger type. Downcast the final result to the original smaller type before assigning to a variable of the original smaller type. This approach cannot be used for type long because long is already the largest primitive integer type.

• BigInteger. Convert the inputs into objects of type BigInteger and perform all arithmetic using BigInteger methods. Type BigInteger is the standard arbitrary-precision integer type provided by the Java standard libraries. The arithmetic operations implemented as methods of this type cannot overflow; instead, they produce the numerically correct result. Consequently, compliant code performs only a single range check just before converting the final result to the original smaller type and throws an ArithmeticException if the final result is outside the range of the original smaller type.

The precondition testing technique requires different precondition tests for each arithmetic operation. This approach can be somewhat more difficult to implement and to audit than either of the other two approaches.

The upcast technique is the preferred approach when applicable. The checks it requires are simpler than those of the previous technique; it is substantially more efficient than using BigInteger. Unfortunately, it cannot be applied to operations involving type long, as there is no bigger type to upcast to.

The BigInteger technique is conceptually the simplest of the three techniques because arithmetic operations on BigInteger cannot overflow. However, it requires the use of method calls for each operation in place of primitive arithmetic operators, which can obscure the intended meaning of the code. Operations on objects of type BigInteger can also be significantly less efficient than operations on the original primitive integer type.

Precondition Testing

The following code example shows the necessary precondition checks required for each arithmetic operation on arguments of type int. The checks for the other integral types are analogous. These methods throw an exception when an integer overflow would otherwise occur; any other conforming error handling is also acceptable. Since ArithmeticException inherits from RuntimeException, we do not need to declare it in a throws clause.

static final int safeAdd(int left, int right) {
  if (right > 0 ? left

The following excerpt is from Sun's Secure Coding Guidelines document \[[SCG 07|AA. Java References#SCG 07]\]:

The (Java) language is type-safe, and the runtime provides automatic memory management and range-checking on arrays. These features also make Java programs immune to the stack-smashing and buffer overflow attacks possible in the C and C++ programming languages, and that have been described as the single most pernicious problem in computer security today.

While this statement is true, arithmetic operations in the Java platform require as much caution as in C and C++. Integer operations can result in overflow because Java does not provide any indication of overflow conditions and silently wraps (Java arithmetic throws an exception only on a division by zero).

The following excerpt is from the Java Language Specification \[[JLS 03|AA. Java References#JLS 03]\] 4.2.2 Integer Operations:

The built-in integer operators do not indicate overflow or underflow in any way. Integer operators can throw a NullPointerException if unboxing conversion of a null reference is required. Other than that, the only integer operators that can throw an exception are the integer divide operator / and the integer remainder operator %, which throw an ArithmeticException if the right-hand operand is zero, and the increment and decrement operators ++ and -- which can throw an OutOfMemoryError if boxing conversion is required and there is not sufficient memory available to perform the conversion.

The table shown below enlists the operators that can lead to overflows:

Addition

Addition (as with all arithmetic operations) in Java is performed on signed numbers only as unsigned numbers are unsupported.

Noncompliant Code Example

In this noncompliant code example, the result of the addition can overflow.

public int do_operation(int a, int b){
  // May result in overflow 
  int temp = a + b;
  return temp;
}

If the result of the addition is greater than the maximum value or less than the minimum value that the int type can store, then the variable temp will contain an erroneous result. Unlike C and C++ integer overflows are harder to exploit in Java. For example, if temp has a negative value as a result of an overflow and is used as an array index, java.lang.ArrayIndexOutOfBoundsException) results whereas this is a more pernicious issue in C and C++ wherein memory regions outside the array bounds can be maliciously altered. In Java, wrapped values typically result in incorrect computations and unanticipated outcomes.

Compliant Solution (Bounds Checking)

Explicitly check the range of each arithmetic operation and throw an ArithmeticException on overflow. When performing operations on values of type int or smaller, the arithmetic can be done using variables of type long. For performing arithmetic operations on numbers of type long, the BigInteger Class must be used.

According to the Java Tutorials \[[Tutorials 08|AA. Java References#Tutorials 08]\], Primitive Data Types:

_ _ -the integer data type is a 32-bit signed two's complement integer. It has a minimum value of -2,147,483,648 and a maximum value of 2,147,483,647 (inclusive).
_ _ - the long data type is a 64-bit signed two's complement integer. It has a minimum value of -9,223,372,036,854,775,808 and a maximum value of 9,223,372,036,854,775,807 (inclusive). Use this data type when you need a range of values wider than those provided by int.

Since a variable of the long type is guaranteed to hold the result of an addition, subtraction or multiplication of values of type int, the result can be assigned to a variable of type long, and if the result is in the integer range, we can simply downcast to a value of type int.

Compliant Solution (Use long and Downcast)

This compliant solution uses a variable of type long to store the result of the addition and proceeds to range check the value. If the value cannot be represented as a value of type int, it throws an ArithmeticException. Otherwise, it downcasts the result to a value of type int.

public int do_operation(int a, int b) throws ArithmeticException {
   long temp = (long)a + (long)b;
   if(temp >Integer.MAX_VALUE || temp < Integer.MIN_VALUE) {
     throw new ArithmeticException();
   }
   return (int)temp; // Value within range can perform the addition
}

Compliant Solution (Bounds Checking)

This compliant solution uses range checking to ensure that the result will not overflow.

public int do_operation(int a, int b) throws ArithmeticException {
  if( b>0 ? a > Integer.MAX_VALUE - b right
                : aleft < Integer.MIN_VALUE - b right) {
    throw new ArithmeticException("Integer overflow");
  }
  return aleft + bright;
}

static final //Value within range can perform the addition
}

Compliant Solution (Use BigInteger Class)

This compliant solution uses the BigInteger class as a wrapper to test for the overflow.

public boolean overflow(long a, long bint safeSubtract(int left, int right) {
  BigIntegerif ba = new java.math.BigInteger(String.valueOf(a));
  BigInteger bb = new java.math.BigInteger(String.valueOf(b));
  BigInteger br = ba.add(bb);
  return (br.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) == 1 ||(right > 0 ? left < Integer.MIN_VALUE + right 
                : left > Integer.MAX_VALUE + right) {
    throw      br.compareTo(BigInteger.valueOf(Long.MIN_VALUE))== -1new ArithmeticException("Integer overflow");
  }

public  long do_operation(long a, long b) throws ArithmeticExceptionreturn left - right;
}

static final int safeMultiply(int left, int right) {
  if(overflow(a,b)) {
    throw new ArithmeticException();
  }
  // Within range; safely perform the addition
  return a + b;
}

With use of the BigInteger class, integer overflows are definitely eliminated. However, due to increased performance costs, it should be used only when other methods are not appropriate.

Subtraction

Care must be taken while performing the subtraction operation as well since overflows (or underflows) are still possible.

Noncompliant Code Example

In this noncompliant code example, the subtraction operation may overflow negatively when a is a negative integer and b is a large positive integer such that their sum is not representable as a value of type int. It can also overflow when a is positive and b is negative and their sum is not representable as a value of type int.

public int do_operation(int a, int b) {
  int temp = a - b;
  // Could result in overflow
  return temp;
}

Compliant Solution (Use Long)

This compliant solution suggests explicit range checking before performing the subtraction.

public int do_operation(int a,int b) {
  long temp = (long)a - (long)b;
  if(temp < Integer.MIN_VALUE || temp > Integer.MAX_VALUE) {
    throw new ArithmeticException();
  }
  return (int) temp;
}

Compliant Solution (Bounds Checking)

This compliant solution uses range checking to ensure that the result will not overflow.

public int do_operation(int a, int b) throws ArithmeticException {
  if( b>0 ? a < Integer.MIN_VALUE + b : a > Integer.MAX_VALUE + b ) {
    throw new ArithmeticException();
  }
  return a - b;  //Value within range can perform the addition
}

Compliant Code Example (Use BigInteger Class)

The BigInteger class can be used as a test-wrapper as shown in this compliant solution.

public boolean underflow(long a, long b) {
  BigInteger ba = new BigInteger(String.valueOf(a));
  BigInteger bb = new BigInteger(String.valueOf(b));
  BigInteger br = ba.subtract(bb);
  return (br.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) == 1 ||
          br.compareTo(BigInteger.valueOf(Long.MIN_VALUE)) == -1);
}

public long do_operation(long a, long b) throws ArithmeticException {
  if(underflow(a,b)) {
    throw new ArithmeticException();
  }
  // Within range; safely perform the subtraction
  return a - b;
}

Multiplication

This noncompliant code example can result in a signed integer overflow during the multiplication of the signed operands a and b. If this behavior is unanticipated, the resulting value may lead to undefined behavior.

Noncompliant Code Example

int a,b,result
//do stuff
result = a*b; // May result in overflow

Compliant Solution

Since the size of the type long (64 bits) is twice the size of the type int (32 bits), the multiplication should be performed using a variable of type long. If the product is in the range of the int type, it can be safely downcast to a value of type int.

int a,b,result;
long temp = (long) a * (long)b;
if(temp > Integer.MAX_VALUE || temp < Integer.MIN_VALUE) {
  throw new ArithmeticException(); // Overflow
}
result = (int) temp; // Value within range, safe to downcast

Division

Although Java throws a java.lang.ArithmeticException for division by zero, the same issue as with C/C++ manifests, while dividing the Integer.MIN_VALUE by -1. It produces Integer.MIN_VALUE unexpectedly (since the result is -(Integer.MIN_VALUE) = Integer.MAX_VALUE + 1)).

Noncompliant Code Example

This noncompliant code example divides a and b without checking the range of the result.

int a,b,result
result = a/b;

Compliant Solution

This compliant solution handles the the special case of Integer.MIN_VALUE and -1 being used as the dividend and divisor, respectively.

if(a == Integer.MIN_VALUE && b == -1) {
  throw new ArithmeticException(); // May be Integer.MIN_VALUE and -1
}
result = a/b; // Safe operation

Remainder Operator

The remainder operation is safer in Java than the corresponding modulo operator in C/C++.

• If the modulo of Integer.MIN_VALUE with -1 is taken the result is always 0 in Java.

• If the right-hand operand is zero, then the integer remainder operator % will throw an ArithmeticException.

• The sign of the remainder is always the same as that of the dividend. For example, -3 % -2 will result in the value -1. As a result its behavior can sometimes be deceptive.

Refer to INT02-J. Do not assume a positive remainder when using the % operator for more details.

Unary Negation

If Integer.MIN_VALUE is negated, the same value Integer.MIN_VALUE is obtained. Range checking is important in this case as well.

Noncompliant Code Example

This noncompliant code example tries to negate the result without checking whether it is Integer.MIN_VALUE.

int temp = -result;

Compliant Solution

This compliant solution explicitly checks whether the input is Integer.MIN_VALUE and throws an exception if it is; otherwise, it negates the result.

if(result == Integer.MIN_VALUE) {
  throw new ArithmeticException();
}
temp = -result;

Absolute Value

A related pitfall is the use of the Math.abs() method that takes a parameter of type int and returns its absolute value. Because of the asymmetry between the representation of negative and positive integer values (there is an extra minimum negative value -128), there is no equivalent positive value (+128) for Integer.MIN_VALUE. As a result, Math.abs(Integer.MIN_VALUE) always returns a non positive Integer.MIN_VALUE.

Shifting

The shift operation in Java is quite different from C/C++,

• The right shift is an arithmetic shift, while in C/C++ it is implementation defined (logical or arithmetic).

• The types boolean, float and double cannot use the bit shifting operators.

• In C/C++ if the value being left shifted is negative or the right-hand operator of the shift operation is negative or greater than or equal to the width of the promoted left operand, there is undefined behavior. This does not extend to Java. If the value to be shifted is of type int, only the five lowest-order bits of the right-hand operand are used as the shift distance. That is, the shift distance is the value of the right-hand operand masked by 31 (0x1F). This results in a value modulo 31, inclusive.

• Wiki Markup
  When the value to be shifted (left-operand) is of type {{long}}, only the last 6 bits of the right-hand operand are used to perform the shift. The shift distance is the value of the right-hand operand masked by 63 (0x3D) \[[JLS 03|AA. Java References#JLS 03]\], i.e., it is always between 0 and 63. (If the shift value is greater than 64, then the shift is {{value % 64}}.)

Refer to INT36-J. Use shift operators correctly for further details about the behavior of the shift operators.

Noncompliant Code Example

In this example, the programmer wishes to shift the value {{i}} of type {{int}} until, after 32 iterations, the value becomes 0. Unfortunately, this loop never terminates as an attempt to shift a value of type {{int}} by 32 bits results in the original value rather than the value 0. \[[Bloch 05|AA. Java References#Bloch 05]\] 

int i = 0;
while ((-1 << i) != 0)
  i++;

Compliant Solution

This compliant solution initially sets the value val to -1 and repeatedly shifts the value by one place on each successive iteration.

for (int val = -1; val != 0; val <<= 1) { /* ... */ }

Risk Assessment

Failure to perform explicit range checking can lead to integer overflows causing unexpected program control flow or unanticipated program behavior.

Automated Detection

TODO

Related Vulnerabilities

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

Other Languages

This rule appears in the C Secure Coding Standard as INT32-C. Ensure that operations on signed integers do not result in overflow.

This rule appears in the C++ Secure Coding Standard as INT32-CPP. Ensure that operations on signed integers do not result in overflow.

References

\[[SCG 07|AA. Java References#SCG 07]\] Introduction
\[[JLS 03|AA. Java References#JLS 03]\] 4.2.2 Integer Operations and 15.22 Bitwise and Logical Operators
\[[Tutorials 08|AA. Java References#Tutorials 08]\] Primitive Data Types
\[[Seacord 05|AA. Java References#Seacord 05]\] Chapter 5. Integers
\[[Bloch 05|AA. Java References#Bloch 05]\] Puzzle 27: Shifty i's
\[[MITRE 09|AA. Java References#MITRE 09]\] [CWE ID 682|http://cwe.mitre.org/data/definitions/682.html] "Incorrect Calculation", [CWE ID 190|http://cwe.mitre.org/data/definitions/190.html] "Integer Overflow or Wraparound", [CWE ID 191|http://cwe.mitre.org/data/definitions/191.html]  "Integer Underflow (Wrap or Wraparound)"

 (right > 0 ? left > Integer.MAX_VALUE/right
                  || left < Integer.MIN_VALUE/right 
                : (right < -1 ? left > Integer.MIN_VALUE/right 
                                || left < Integer.MAX_VALUE/right
                              : right == -1 
                                && left == Integer.MIN_VALUE) ) {
    throw new ArithmeticException("Integer overflow");
  }
  return left * right;
}

static final int safeDivide(int left, int right) {
  if ((left == Integer.MIN_VALUE) && (right == -1)) {
    throw new ArithmeticException("Integer overflow");
  }
  return left / right;
}

static final int safeNegate(int a) {
  if (a == Integer.MIN_VALUE) {
    throw new ArithmeticException("Integer overflow");
  }
  return -a;
}
static final int safeAbs(int a) {
  if (a == Integer.MIN_VALUE) {
    throw new ArithmeticException("Integer overflow");
  }
  return Math.abs(a);
}

These method calls are likely to be inlined by most just-in-time (JIT) systems.

These checks can be simplified when the original type is char. Because the range of type char includes only positive values, all comparisons with negative values may be omitted.

Noncompliant Code Example

Either operation in this noncompliant code example could result in an overflow. When overflow occurs, the result will be incorrect.

public static int multAccum(int oldAcc, int newVal, int scale) {
  // May result in overflow
  return oldAcc + (newVal * scale);
}

Compliant Solution (Precondition Testing)

This compliant solution uses the safeAdd() and safeMultiply() methods defined in the "Precondition Testing" section to perform secure integral operations or throw ArithmeticException on overflow:

public static int multAccum(int oldAcc, int newVal, int scale) {
  return safeAdd(oldAcc, safeMultiply(newVal, scale));
}

Compliant Solution (Java 8, Math.*Exact())

This compliant solution uses the addExact() and multiplyExact() methods defined in the Math class. These methods were added to Java as part of the Java 8 release, and they also either return a mathematically correct value or throw ArithmeticException. The Math class also provides SubtractExact() and negateExact() but does not provide any methods for safe division or absolute value.

public static int multAccum(int oldAcc, int newVal, int scale) {
  return Math.addExact(oldAcc, Math.multiplyExact(newVal, scale));
}

Compliant Solution (Upcasting)

This compliant solution shows the implementation of a method for checking whether a value of type long falls within the representable range of an int using the upcasting technique. The implementations of range checks for the smaller primitive integer types are similar.

public static long intRangeCheck(long value) {
  if ((value < Integer.MIN_VALUE) || (value > Integer.MAX_VALUE)) {
    throw new ArithmeticException("Integer overflow");
  }
  return value;
}

public static int multAccum(int oldAcc, int newVal, int scale) {
  final long res = intRangeCheck(
   ((long) oldAcc) + intRangeCheck((long) newVal * (long) scale)
  );
  return (int) res; // Safe downcast
}

Note that this approach cannot be applied to values of type long because long is the largest primitive integral type. Use the BigInteger technique instead when the original variables are of type long.

Compliant Solution (BigInteger)

This compliant solution uses the BigInteger technique to detect overflow:

private static final BigInteger bigMaxInt = 
  BigInteger.valueOf(Integer.MAX_VALUE);
private static final BigInteger bigMinInt =    
  BigInteger.valueOf(Integer.MIN_VALUE);

public static BigInteger intRangeCheck(BigInteger val) {
  if (val.compareTo(bigMaxInt) == 1 ||
      val.compareTo(bigMinInt) == -1) {
    throw new ArithmeticException("Integer overflow");
  }
  return val;
}

public static int multAccum(int oldAcc, int newVal, int scale) {
  BigInteger product =
    BigInteger.valueOf(newVal).multiply(BigInteger.valueOf(scale));
  BigInteger res = 
    intRangeCheck(BigInteger.valueOf(oldAcc).add(product));
  return res.intValue(); // Safe conversion
}

Noncompliant Code Example (AtomicInteger)

Operations on objects of type AtomicInteger suffer from the same overflow issues as other integer types. The solutions are generally similar to the solutions already presented; however, concurrency issues add additional complications. First, potential issues with time-of-check, time-of-use (TOCTOU) must be avoided (see VNA02-J. Ensure that compound operations on shared variables are atomic for more information). Second, use of an AtomicInteger creates happens-before relationships between the various threads that access it. Consequently, changes to the number of accesses or order of accesses can alter the execution of the overall program. In such cases, you must either choose to accept the altered execution or carefully craft your implementation to preserve the exact number of accesses and order of accesses to the AtomicInteger.

This noncompliant code example uses an AtomicInteger, which is part of the concurrency utilities. The concurrency utilities lack integer overflow checks.

class InventoryManager {
  private final AtomicInteger itemsInInventory = new AtomicInteger(100);

  //...
  public final void nextItem() {
    itemsInInventory.getAndIncrement();
  }
}

Consequently, itemsInInventory can wrap around to Integer.MIN_VALUE when the nextItem() method is invoked when itemsInInventory == Integer.MAX_VALUE.

Compliant Solution (AtomicInteger)

This compliant solution uses the get() and compareAndSet() methods provided by AtomicInteger to guarantee successful manipulation of the shared value of itemsInInventory. This solution has the following characteristics:

• The number and order of accesses to itemsInInventory remain unchanged from the noncompliant code example.
• All operations on the value of itemsInInventory are performed on a temporary local copy of its value.
• The overflow check in this example is performed in inline code rather than encapsulated in a method call. This is an acceptable alternative implementation. The choice of method call versus inline code should be made according to your organization's standards and needs.

class InventoryManager {
  private final AtomicInteger itemsInInventory =
      new AtomicInteger(100);

  public final void nextItem() {
    while (true) {
      int old = itemsInInventory.get();
      if (old == Integer.MAX_VALUE) {
        throw new ArithmeticException("Integer overflow");
      }
      int next = old + 1; // Increment
      if (itemsInInventory.compareAndSet(old, next)) {
        break;
      }
    } // End while
  } // End nextItem()
}

The two arguments to the compareAndSet() method are the expected value of the variable when the method is invoked and the intended new value. The variable's value is updated only when the current value and the expected value are equal [API 2006] (refer to VNA02-J. Ensure that compound operations on shared variables are atomic for more details).

Exceptions

NUM00-J-EX0: Depending on circumstances, integer overflow could be benign. For example, many algorithms for computing hash codes use modular arithmetic, intentionally allowing overflow to occur. Such benign uses must be carefully documented.

NUM00-J-EX1: Prevention of integer overflow is unnecessary for numeric fields that undergo bitwise operations and not arithmetic operations (see NUM01-J. Do not perform bitwise and arithmetic operations on the same data for more information).

Risk Assessment

Failure to perform appropriate range checking can lead to integer overflows, which can cause unexpected program control flow or unanticipated program behavior.

Automated Detection

Automated detection of integer operations that can potentially overflow is straightforward. Automatic determination of which potential overflows are true errors and which are intended by the programmer is infeasible. Heuristic warnings might be helpful.

Related Guidelines

Android Implementation Details

Mezzofanti for Android contained an integer overflow that prevented the use of a big SD card. Mezzofanti contained an expression:

(int) StatFs.getAvailableBlocks() * (int) StatFs.getBlockSize() 

to calculate the available memory in an SD card, which could result in a negative value when the available memory is larger than Integer.MAX_VALUE. Note that these methods are deprecated in API level 18 and replaced by getAvailableBlocksLong() and getBlockSizeLong().

Bibliography

[API 2006]	Class AtomicInteger
[Bloch 2005]	Puzzle 27, "Shifty i's"
[Bloch 2008]	Item 12, "Minimize the Accessibility of Classes and Members"
[Java Tutorials]	Primitive Data Types
[JLS 2015]	§4.2.1, "Integral Types and Values" §4.2.2, "Integer Operations" §15.22, "Bitwise and Logical Operators"
[Seacord 2005]	Chapter 5, "Integers"
[Seacord 2015]	Image Added IDS17-J. Prevent XML External Entity Attacks LiveLesson

...

Image Added Image Added Image AddedINT33-J. Do not cast numeric types to wider floating-point types without range checking      06. Integers (INT)      INT35-J. Do not attempt to store signed values in the char integral type