CHAPTER 15: Expressions

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15.17 Additive Operators

The operators + and - are called the additive operators. They have the same precedence and are syntactically left-associative (they group left-to-right).

AdditiveExpression:

	MultiplicativeExpression

	AdditiveExpression + MultiplicativeExpression

	AdditiveExpression - MultiplicativeExpression

If the type of either operand of a + operator is String , then the operation is string concatenation.

Otherwise, the type of each of the operands of the + operator must be a primitive numeric type, or a compile-time error occurs.

In every case, the type of each of the operands of the binary - operator must be a primitive numeric type, or a compile-time error occurs.

15.17.1 String Concatenation Operator +

If only one operand expression is of type String , then string conversion is performed on the other operand to produce a string at run time. The result is a reference to a newly created String object that is the concatenation of the two operand strings. The characters of the left-hand operand precede the characters of the right-hand operand in the newly created string.

15.17.1.1 String Conversion

Any type may be converted to type String by string conversion.

A value x of primitive type T is first converted to a reference value as if by giving it as an argument to an appropriate class instance creation expression:

• If T is boolean , then use new Boolean( x) (S20.4).
• If T is char , then use new Character( x) (S20.5).
• If T is byte , short , or int , then use new Integer( x) (S20.7).
• If T is long , then use new Long( x) (S20.8).
• If T is float , then use new Float( x) (S20.9).
• If T is double , then use new Double( x) (S20.10).

This reference value is then converted to type String by string conversion.

Now only reference values need to be considered. If the reference is null , it is converted to the string "null " (four ASCII characters n , u , l , l ). Otherwise, the conversion is performed as if by an invocation of the toString method of the referenced object with no arguments; but if the result of invoking the toString method is null , then the string "null " is used instead. The toString method (S20.1.2) is defined by the primordial class Object (S20.1); many classes override it, notably Boolean , Character , Integer , Long , Float , Double, and String .

15.17.1.2 Optimization of String Concatenation

An implementation may choose to perform conversion and concatenation in one step to avoid creating and then discarding an intermediate String object. To increase the performance of repeated string concatenation, a Java compiler may use the StringBuffer class (S20.13) or a similar technique to reduce the number of intermediate String objects that are created by evaluation of an expression.

For primitive objects, an implementation may also optimize away the creation of a wrapper object by converting directly from a primitive type to a string.

15.17.1.3 Examples of String Concatenation

The example expression:

"The square root of 2 is " + Math.sqrt(2)

produces the result:

"The square root of 2 is 1.4142135623730952"

The + operator is syntactically left-associative, no matter whether it is later determined by type analysis to represent string concatenation or addition. In some cases care is required to get the desired result. For example, the expression:

a + b + c

is always regarded as meaning:

(a + b) + c

Therefore the result of the expression:

1 + 2 + " fiddlers"

is:

"3 fiddlers"

but the result of:

"fiddlers " + 1 + 2

is:

"fiddlers 12"

In this jocular little example:

class Bottles {

	static void printSong(Object stuff, int n) {
		String plural = "s";
		loop: while (true) {
			System.out.println(n + " bottle" + plural
				+ " of " + stuff + " on the wall,");
			System.out.println(n + " bottle" + plural
				+ " of " + stuff + ";");
			System.out.println("You take one down "
				+ "and pass it around:");
			--n;
			plural = (n == 1) ? "" : "s";
			if (n == 0)
				break loop;
			System.out.println(n + " bottle" + plural
				+ " of " + stuff + " on the wall!");
			System.out.println();
		}
		System.out.println("No bottles of " +
								stuff + " on the wall!");
	}

}

the method printSong will print a version of a children's song. Popular values for stuff include "pop" and "beer" ; the most popular value for n is 100 . Here is the output that results from Bottles.printSong("slime", 3) :

3 bottles of slime on the wall,
3 bottles of slime;
You take one down and pass it around:
2 bottles of slime on the wall!

2 bottles of slime on the wall,
2 bottles of slime;
You take one down and pass it around:
1 bottle of slime on the wall!

1 bottle of slime on the wall,
1 bottle of slime;
You take one down and pass it around:
No bottles of slime on the wall!

In the code, note the careful conditional generation of the singular "bottle " when appropriate rather than the plural "bottles "; note also how the string concatenation operator was used to break the long constant string:

"You take one down and pass it around:"

into two pieces to avoid an inconveniently long line in the source code.

15.17.2 Additive Operators (+ and -) for Numeric Types

The binary + operator performs addition when applied to two operands of numeric type, producing the sum of the operands. The binary - operator performs subtraction, producing the difference of two numeric operands.

Binary numeric promotion is performed on the operands (S5.6.2). The type of an additive expression on numeric operands is the promoted type of its operands. If this promoted type is int or long , then integer arithmetic is performed; if this promoted type is float or double , then floating-point arithmetic is performed.

Addition is a commutative operation if the operand expressions have no side effects. Integer addition is associative when the operands are all of the same type, but floating-point addition is not associative.

If an integer addition overflows, then the result is the low-order bits of the mathematical sum as represented in some sufficiently large two's-complement format. If overflow occurs, then the sign of the result is not the same as the sign of the mathematical sum of the two operand values.

The result of a floating-point addition is determined using the following rules of IEEE arithmetic:

• If either operand is NaN, the result is NaN.
• The sum of two infinities of opposite sign is NaN.
• The sum of two infinities of the same sign is the infinity of that sign.
• The sum of an infinity and a finite value is equal to the infinite operand.
• The sum of two zeros of opposite sign is positive zero.
• The sum of two zeros of the same sign is the zero of that sign.
• The sum of a zero and a nonzero finite value is equal to the nonzero operand.
• The sum of two nonzero finite values of the same magnitude and opposite sign is positive zero.
• In the remaining cases, where neither an infinity, nor a zero, nor NaN is involved, and the operands have the same sign or have different magnitudes, the sum is computed. If the magnitude of the sum is too large to represent, we say the operation overflows; the result is then an infinity of appropriate sign. If the magnitude is too small to represent, we say the operation underflows; the result is then a zero of appropriate sign. Otherwise, the sum is rounded to the nearest representable value using IEEE 754 round-to-nearest mode. The Java language requires support of gradual underflow as defined by IEEE 754 (S4.2.4).

The binary - operator performs subtraction when applied to two operands of numeric type producing the difference of its operands; the left-hand operand is the minuend and the right-hand operand is the subtrahend. For both integer and floating-point subtraction, it is always the case that a-b produces the same result as a+(-b) . Note that, for integer values, subtraction from zero is the same as negation. However, for floating-point operands, subtraction from zero is not the same as negation, because if x is +0.0 , then 0.0-x equals +0.0 , but -x equals -0.0 .

Despite the fact that overflow, underflow, or loss of information may occur, evaluation of a numeric additive operator never throws a run-time exception.