Self Crossing

You are given an array x of n positive numbers. You start at point (0,0) and moves x[0] metres to the north, then x[1] metres to the west, x[2] metres to the south, x[3] metres to the east and so on. In other words, after each move your direction changes counter-clockwise.
Write a one-pass algorithm with O(1) extra space to determine, if your path crosses itself, or not.
Example 1:
1. Given x = [2, 1, 1, 2],
2. ┌───┐
3. │ │
4. └───┼──>
5. │
6. 7. Return true (self crossing)

Example 2:
1. Given x = [1, 2, 3, 4],
2. ┌──────┐
3. │ │
4. │
5. │
6. └────────────>
7. 8. Return false (not self crossing)

Example 3:
1. Given x = [1, 1, 1, 1],
2. ┌───┐
3. │ │
4. └───┼>
5. 6. Return true (self crossing)