Operators - Precedence and Associativity

Java has well-defined rules for specifying the order in which the operators in an expression are evaluated when the expression has several operators. For example, multiplication and division have a higher precedence than addition and subtraction. Precedence rules can be overridden by explicit parentheses.

Precedence Order

When two operators share an operand the operator with the higher precedence goes first. For example, 1 + 2 * 3 is treated as 1 + (2 * 3), whereas 1 * 2 + 3 is treated as (1 * 2) + 3 since multiplication has a higher precedence than addition.

Associativity

When two operators with the same precendence the expression is evaluated according to its associativity. For example x = y = z = 17 is treated as x = (y = (z = 17)), leaving all three variables with the value 17, since the = operator has right-to-left associativty (and an assignment statement evaluates to the value on the right hand side). On the other hand, 72 / 2 / 3 is treated as (72 / 2) / 3 since the / operator has left-to-right associativity.

Precedence and associativity of Java operators

The table below shows all Java operators from highest to lowest precedence, along with their associativity. Most programmers do not memorize them all, and even those that do still use parentheses for clarity.

Operator	Description	Level	Associativity
[] . () ++ --	access array element access object member invoke a method post-increment post-decrement	1	left to right
++ -- + - ! ~	pre-increment pre-decrement unary plus unary minus logical NOT bitwise NOT	2	right to left
() new	cast object creation	3	right to left
* / %	multiplicative	4	left to right
+ - +	additive string concatenation	5	left to right
<< >> >>>	shift	6	left to right
<  <= >  >= instanceof	relational type comparison	7	left to right
== !=	equality	8	left to right
&	bitwise AND	9	left to right
^	bitwise XOR	10	left to right
|	bitwise OR	11	left to right
&&	conditional AND	12	left to right
||	conditional OR	13	left to right
?:	conditional	14	right to left
=   +=   -=  *=   /=   %=  &=   ^=   |= <<=  >>= >>>=	assignment	15	right to left

Caveats

There is no explicit operator precedence table in the Java Language Specification and different tables on the Web and in textbooks disagree in some minor ways.

Order of evaluation

In Java, the left operand is always evaluated before the right operand. Also applies to function arguments. Short circuiting. When using the conditional AND and OR operators (&& and ||), Java does not evaluate the second operand unless it is necessary to resolve the result. Allows statements like if (s != null && s.length() < 10) to work reliably. Programmers rarely use the non short-circuiting versions (& and |) with boolean expressions.

Precedence order gone awry

Sometimes the precedence order defined in a language do not conform with mathematical norms. For example, in Microsoft Excel, -a^b is interpreted as (-a)^b instead of -(a^b). So -1^2 is equal to 1 instead of -1, which is the values most mathematicians would expect. Microsoft acknowledges this quirkas a "design choice". One wonders whether the programmer was relying on the C precedence order in which unary operators have higher precedence than binary operators. This rule agrees with mathematical conventions for all C operators, but fails with the addition of the exponentiation operator. Once the order was established in Microsoft Excel 2.0, it could not easily be changed without breaking backward compatability.