What does the unary operator ~ do in numpy?

Question

I came across a line of code using Python's numpy that looked like this:

~array([0,1,2,3,4,5,4,3,2,1,0,-1,-2])

And it gave the output:

array([-1, -2, -3, -4, -5, -6, -5, -4, -3, -2, -1,  0,  1])

Does the unary operator (~) take an array and apply A -> -(A+1)

If so, whats the point?

Answer 1

Chris Lutz' comment is correct.

~ is the bitwise negation operator

It looks like it turns A to -(A+1) because on many modern computers, negative numbers are represented as the Two's Complement of the corresponding positive integer, where the number is subtracted from 2^(bit length) (that's "two to the power of bit length", not "two exclusive or bit length"...).

In such a system, -1 would be represented as all ones. Of course, so would the sum of a number and its bitwise negative, so we have the situation where

a + ~a = -1        =>
    ~a = -1 - a    =>
    ~a = -(a + 1)

as you noticed.

Answer 2

http://en.wikipedia.org/wiki/Bitwise_operation#NOT

The reason why you end up with negative numbers is how they are represented in binary form:

http://en.wikipedia.org/wiki/Two%27s_complement