Some properties of the absolute value function are as follows.

1. |a| = 0 <==> a = 0; 2. |a| = |-a| 3. |a * b| = |a| * |b| 4. |a| <= b <==> a <= b or a <= -b <==> -b <= a <= b 5. |a| >= b <==> a >=b or a <= -b

Properties 1 and 2 are quite obvious.

Property number 3 can be useful when optimizing programs. ABS(x) * ABS(y) is in fact slower than ABS(x*y).

Properties 4 and 5 are interesting because they can replace two tests with a single test.