ncw ncw - 1 month ago 27
Java Question

Java precedence for multiple + and - operators

This is more of a theoretical question to understand Java's evaluation of arithmetic operations. Since

+
and
-
have the same precedence, I don't quite understand how Java evaluates the following expressions (where there are more than one
+
and
-
operators between the two operands).

public static void main(String[] args) {
int a = 1;
int b = 2;
System.out.println(a+-b); // results in -1
System.out.println(a-+b); // results in -1
System.out.println(a+-+b); // results in -1
System.out.println(a-+-b); // results in 3
System.out.println(a-+-+b); // results in 3
System.out.println(a+-+-b); // results in 3
System.out.println(a-+-+-b); // results in -1
System.out.println(a+-+-+b); // results in 3
}


From the Java 8 Language Specification (ยง15.8.2):


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.

[...]

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.


What I also noticed, is that everytime the #operators is even, the result is the same and the order doesn't matter.
But when the #operators is odd, this doesn't necessarily influence the result. E.g. in the following two expressions there is one more
-
than
+
, however the result is different.

System.out.println(a-+-b); // results in 3
System.out.println(a-+-+-b); // results in -1


With all that information I still don't see the pattern or the way how this works.

Answer

In math, how would you evaluate this?

a - + - b   

Adding some brackets helps:

a - (+ (-b))

We can do this, because this doesn't violate the rules of precedence.

Then we can start reducing: + (-b) is really -b, and a - -b is really a + b, so the result is 1 + 2 = 3.

Let's see the second one:

a - + - + - b
a - (+ (- (+ (-b))))
a - (+ (- (-b)))
a - (+ b)
a - b
1 - 2 = -1

So simple rules of math work naturally.