A model implementation of window scaling is as follows, using the notation of RFC-793 [Postel81]:
SND.WND = SEG.WND << Snd.Wind.Scale
(assuming the other conditions of RFC793 are met, and using the "C" notation "<<" for left-shift).
SEG.WND = RCV.WND >> Rcv.Wind.Scale.
TCP determines if a data segment is "old" or "new" by testing whether its sequence number is within 2**31 bytes of the left edge of the window, and if it is not, discarding the data as "old". To insure that new data is never mistakenly considered old and vice- versa, the left edge of the sender's window has to be at most 2**31 away from the right edge of the receiver's window. Similarly with the sender's right edge and receiver's left edge. Since the right and left edges of either the sender's or receiver's window differ by the window size, and since the sender and receiver windows can be out of phase by at most the window size, the above constraints imply that 2 * the max window size must be less than 2**31, or
max window < 2**30
Since the max window is 2**S (where S is the scaling shift count) times at most 2**16 - 1 (the maximum unscaled window), the maximum window is guaranteed to be < 2*30 if S <= 14. Thus, the shift count must be limited to 14 (which allows windows of 2**30 = 1 Gbyte). If a Window Scale option is received with a shift.cnt value exceeding 14, the TCP should log the error but use 14 instead of the specified value.
The scale factor applies only to the Window field as transmitted in the TCP header; each TCP using extended windows will maintain the window values locally as 32-bit numbers. For example, the "congestion window" computed by Slow Start and Congestion Avoidance is not affected by the scale factor, so window scaling will not introduce quantization into the congestion window.