Finding a nonzero integer x where x == -x?

Question

In a course on algorithms and data structures at my university, I received this question:

Which integer has the same bit-pattern as his negative value?

Means: x == -x

I know that 0 works, but I suspect that the instructor was looking for some other number x. What x is it? How would you find it?

Answer 1

Integer.MIN_VALUE and Long.MIN_VALUE have no equivalent positive value and when you take the negative value of these, you get the same value.

Negative is the same as flipping all the bits and adding one. i.e.

-x = ~x + 1 

So -0x80000000 = 0x7fffffff + 1 = 0x8000000

Note: Math.abs(Integer.MIN_VALUE) == Integer.MIN_VALUE which is negative. This is outlined in the javadoc for this method.

Technically there are many answers and types

byte x = 0; short x = 0; char x = 0; int x = 0; int x = Integer.MIN_VALUE; float x = 0.0f; float x = -0.0f; long x = 0; long x = Long.MIN_VALUE; double x = 0.0; double x = -0.0; Byte x = 0; Short x = 0; Character x = 0; Integer x = 0; Integer x = Integer.MIN_VALUE; Float x = 0.0f; Float x = -0.0f; Long x = 0L; Long x = Long.MIN_VALUE; Double x = 0.0; Double x = -0.0; 

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A similar Java Puzzler is; when is the following expression true.

x != x + 0 

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EDIT: Floating point has both +0.0 and -0.0. A such you might consider -0.0 a different value to 0.0 although it is the case that -0.0 == -(-0.0)

Note: Double.compare(0.0, -0.0) > 0 Note: