Zig Zag Decoding

Question

In the google protocol buffers encoding overview, they introduce something called "Zig Zag Encoding", this takes signed numbers, which have a small magnitude, and creates a series of unsigned numbers which have a small magnitude.

For example

Encoded => Plain
0 => 0
1 => -1
2 => 1
3 => -2
4 => 2
5 => -3
6 => 3

And so on. The encoding function they give for this is rather clever, it's:

(n << 1) ^ (n >> 31) //for a 32 bit integer

I understand how this works, however, I cannot for the life of me figure out how to reverse this and decode it back into signed 32 bit integers

Answer 1

Try this one:

(n >> 1) ^ (-(n & 1))

Edit:

I'm posting some sample code for verification:

#include <stdio.h>

int main()
{
  unsigned int n;
  int r;

  for(n = 0; n < 10; n++) {
    r = (n >> 1) ^ (-(n & 1));
    printf("%u => %d\n", n, r);
  }

  return 0;
}

I get following results:

0 => 0
1 => -1
2 => 1
3 => -2
4 => 2
5 => -3
6 => 3
7 => -4
8 => 4
9 => -5