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See the following example:

Noncompliant Code Example

 In we have the following simple method the result could overflow

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Addition

Addition (and all operations) in Java are performed in signed numbers as Java does not support unsigned numbers

Noncompliant Code Example

In this example the addition could result in overflow

public int do_operation(int a,int b)
{
   int temp = a + b;
//Could result in overflow
//do other processing
   return temp;
}

Compliant Solution (Bounds Checking)

A solution would be to explicitly check the range of each arithmetic operation and throw an ArithmeticException on overflow, otherwise downcast the value to an integer. For arithmetical operations on  really big numbers one should always use the BigInteger Class

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By using the BigInteger class there is no chance to overflow (see section on BigInteger class) but the performance is degraded so it should be used only on really large operations

Subtraction

Care must be taken in subtraction operations as well as these can overflow as well.

Noncompliant Code Example

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

Compliant Code Example

The appropriate way is to check explicitely the range before doing the subtraction

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public bool underflow(int a, int b)
{
    java.math.BigInteger ba = new java.math.BigInteger(String.valueOf(a));
    java.math.BigInteger bb = new java.math.BigInteger(String.valueOf(b));
    java.math.BigInteger br = ba.subtract(bb);
    if(br.compareTo(java.math.BigInteger.valueOf(Integer.MAX_VALUE)) == 1
              || br.compareTo(java.math.BigInteger.valueOf(Integer.MIN_VALUE))== -1)
        return true;//We have underflow
    //Can proceed
   return false
}

public int do_operation(int a, int b) throws ArithmeticException
{
      if(undeflow(a,b))
         throw ArithmeticException;
      else //we are within range safely perform the addition
}

Multiplication

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

Noncompliant Code Example

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

Compliant Code Example

Since in this platform the size of type long (64 bits) is twice the size of type int (32 bits) we should perform the multiplication in terms of long and if the product is in the integer range we downcast the result to int

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

Division

Although Java throws a java.lang.ArithmeticException: / by zero exception for division by zero, there is the same issue as in C\C++ when dividing the Integer.MIN_VALUE with -1. It produces Integer.MIN_VALUE unexpectedly

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A non-compliant example is:

Noncompliant Code Example

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

Compliant Code Example

if(a == Integer.MIN_VALUE && b == -1)
throw ArithmeticException;//May be Integer.MIN_VALUE again????
else
result = a/b;//safe operation

Division

For modulo operator the only problem is if we take the modulo of Integer.MIN_VALUE with -1. The result is always 0 in JAVA so we are back to the previous rule (for division)

Unary Negation

If we negate Integer.MIN_VALUE we get Integer.MIN_VALUE. So we explicitely check the range

if(a == Integer.MIN_VALUE)
throw ArithmeticException;
else
result = --a;

SHIFTING

The shift in java is quite different than in C\C++.

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if(shift_value > 31 or shift_value <0)if(shift_value > 31 or shift_value <0)
  throw ArithmeticException;
else
int val = 2 << shift_value;
  throw ArithmeticException;
else
int val = 2 << shift_value;

Unsigned Right shifting >>>

It is identical to the right-shift operator if the shifted value is positive. If it is negative the sign value can
change because the left-operand high-order bit is not retained and the sign value can change; Excerpt
from JLS:
"if n is negative, the result is equal to that of the expression (n>>s)(2<<~s) if the type of the left-hand operand is int, and to the result of the expression (n>>s)(2L<<~s) if the type of the left-hand operand is long. The added term (2<<~s) or (2L<<~s) cancels out the propagated sign bit. (Note that, because of the implicit masking of the right-hand operand of a shift operator, ~s as a shift distance is equivalent to 31-s when shifting an int value and to 63-s when shifting a longvalue.)"

 For example: -32 >>> 2 = (-32 >> 2 ) + ( 2 << ~2 ) = 1073741816

Operations Requiring Really Long Numbers

For these operations the BigInteger class should be used. According to SUN BigInteger Class:

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For instance operations on long are operations on 64 bits. For example addition:

Compliant Code Example

java.math.BigInteger big_long_max = new java.math.BigInteger(String.valueOf(Long.MAX_VALUE));
System.out.println("big_long="+big_long_max);
big_long_max = big_long_max.add(java.math.BigInteger.valueOf(1));//same as ++big_long_max
System.out.println("big_long="+big_long_max);
These print
big_long=9223372036854775807
big_long=9223372036854775808//exceeds the maximum range of long, no problem

java.math.BigInteger big_long_min = new java.math.BigInteger(String.valueOf(Long.MIN_VALUE));
System.out.println("big_long_min="+big_long_min);
big_long_min = big_long_min.subtract(java.math.BigInteger.valueOf(1));//same as --big_long_min
System.out.println("big_long_min="+big_long_min);//goes bellow minimum range of long, no problem

These print:
big_long_min=-9223372036854775808
big_long_min=-9223372036854775809
if(big_long < Long.MAX_VALUE && big_long > Long.MIN_VALUE)//value within range can go to the primitive type
long value = big_log.longValue();//get primitive type
else
//Perform error handling. We can not downcast since the value can not be represented as a long

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