Determine Rank of a Node

Rank(T,x) $\;\;\;\;\;$ $\;\;\;\;\;$ $\;\;\;\;\;$; return rank of node x
1 $\;\;\;\;\;$rank = size(left(x)) + 1
2 $\;\;\;\;\;$while x $\neq$ root(T)
3 $\;\;\;\;\;$ $\;\;\;\;\;$if x = right(parent(x))
4 $\;\;\;\;\;$ $\;\;\;\;\;$then rank = rank + size(left(parent(x))) + 1
5 $\;\;\;\;\;$ $\;\;\;\;\;$x = parent(x)
6 $\;\;\;\;\;$return rank

T(n) is approximately equal to height of tree = O(lg n)