Best way to make Java's modulus behave like it should with negative numbers?

It behaves as it should a % b = a - a / b * b; i.e. it's the remainder.

You can do (a % b + b) % b

This expression works as the result of (a % b) is necessarily lower than b, no matter if a is positive or negative. Adding b takes care of the negative values of a, since (a % b) is a negative value between -b and 0, (a % b + b) is necessarily lower than b and positive. The last modulo is there in case a was positive to begin with, since if a is positive (a % b + b) would become larger than b. Therefore, (a % b + b) % b turns it into smaller than b again (and doesn't affect negative a values).

As of Java 8, you can use Math.floorMod(int x, int y) and Math.floorMod(long x, long y). Both of these methods return the same results as Peter's answer.

Math.floorMod( 2,  3) =  2
Math.floorMod(-2,  3) =  1
Math.floorMod( 2, -3) = -1
Math.floorMod(-2, -3) = -2

For those not using (or not able to use) Java 8 yet, Guava came to the rescue with IntMath.mod(), available since Guava 11.0.

IntMath.mod( 2, 3) = 2
IntMath.mod(-2, 3) = 1

One caveat: unlike Java 8's Math.floorMod(), the divisor (the second parameter) cannot be negative.

In number theory, the result is always positive. I would guess that this is not always the case in computer languages because not all programmers are mathematicians. My two cents, I would consider it a design defect of the language, but you can't change it now.

=MOD(-4,180) = 176 =MOD(176, 180) = 176

because 180 * (-1) + 176 = -4 the same as 180 * 0 + 176 = 176

Using the clock example here, http://mathworld.wolfram.com/Congruence.html you would not say duration_of_time mod cycle_length is -45 minutes, you would say 15 minutes, even though both answers satisfy the base equation.