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

I have found a solution, unfortunately it's not the one line beauty I was hoping for:

uint signMask = u << 31;
int iSign = *((Int32*)&signMask);
iSign >>= 31;
signMask = *((UInt32*)&iSign);

UInt32 a = (u >> 1) ^ signMask;
return *((Int32*)&a);

Answer 2

I'm sure there's some super-efficient bitwise operations that do this faster, but the function is straightforward. Here's a python implementation:

def decode(n):
  if (n < 0):
    return (2 * abs(n)) - 1
  else:
    return 2 * n

>>> [decode(n) for n in [0,-1,1,-2,2,-3,3,-4,4]]
[0, 1, 2, 3, 4, 5, 6, 7, 8]

Answer 3

How about

(n>>1) - (n&1)*n

Answer 4

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