EXP08-J. Be aware of integer promotions in binary operators

When using binary operators with mixed operand sizes, be aware that some of the narrower operands may be promoted to a wider type, to match the type of the other operand. For example in the expression 'a' == 42, the field 'a' will be promoted to an int before the comparison is carried out.

According to [[JLS 05]]:

If an integer operator other than a shift operator has at least one operand of type long, then the operation is carried out using 64-bit precision, and the result of the numerical operator is of type long. If the other operand is not long, it is first widened (§5.1.5) to type long by numeric promotion (§5.6). Otherwise, the operation is carried out using 32-bit precision, and the result of the numerical operator is of type int. If either operand is not an int, it is first widened to type int by numeric promotion.

The Java Language Specification [[JLS 05]] section 5.6 "Numeric Promotions" describes numeric promotion as:

1. If any of the operands is of a reference type, unboxing conversion is performed. Then:
2. If either operand is of type double, the other is converted to double.
3. Otherwise, if either operand is of type float, the other is converted to float.
4. Otherwise, if either operand is of type long, the other is converted to long.
5. Otherwise, both operands are converted to type int.

Widening conversions resulting from integer promotions preserve the overall magnitude of the number. However, promotions in which the operands are converted from a numeric type such as an integer to a float or a long to a double, are particularly pernicious (see INT33-J. Be careful while casting numeric types to wider floating-point types for more details). These implicit casts can lead to an undesirable loss in precision.

These conversions can happen with the following operators : multiplicative operators (%, *, /), additive operators (+, -), comparison operators (<, >, <=, >=) and equality (==, !=) and the integer bitwise operators (&, |, ^).

In the following example, a is promoted to a double before the + operator is applied.

int a = some_value;
double b = some_other_value;
double c = a + b;

As another example, consider:

int a = some_value;
char b = some_character;

if((a + b) == 0.0f) {
  //do something
}

Here, b is first converted to int so that the + operator can be applied to operands of the same type. The result of (a+b) is then converted to a float, and the comparison operator is finally applied.

Noncompliant Code Example

Here is an example of what could happen.

class Test{
  public static void main(String[] args){
    int big = 1999999999;
    double big_float = big;
    float one = 1.0f;
    System.out.println(big*one);
    System.out.println(big_float);
  }
}

The output is
2.0E9
1.999999999E9
while the expected output is :
2.0E9
2.0E9.
big is first converted to a float, and loses some precision, which explains the 2.0E9. However, big_float doesn't lose any precision since it's a wider type than float, this is why the two output are different.

Compliant solution

In that particular case, it would be sufficient to use a double instead of a float :

class Test{
  public static void main(String[] args){
    int big = 1999999999;
    double big_float = big;
    double one = 1.0d;
    System.out.println(big*one);
    System.out.println(big_float);
  }
}

the output is what is expected :
1.999999999E9
1.999999999E9,
because this time, one is a double and doesn't lose precision.

Note : these output were generated on a Java Hotspot(TM) 64-bit server VM (version 1.5.0), and compiled with javac, version 1.5.0.

Risk assessment

Failing to consider integer promotions while dealing with floating point and integer operands together, can result in loss of precision.

References

[[JLS 05]] 4.2.2 "Integer Operations" and 5.6 "Numeric Promotions"