Here's still another simplification ... very clean, and optimizes the use of internal TC capabilities. It's based on the clause for the first-bar in the SGN formula above.

Plot the following DM-difference as a Custom Indicator:
(H0-H1)*(H0-H1>L1-L0)*(H0>H1) - (L1-L0)*(H0-H1<L1-L0)*(L0<L1)

Now apply the exponential equivalent of Wilders's smoothing to it, as a part of the CI definition:
Exponential Pds = (Wilder Pds * 2) -1 = 14*2 - 1
= 27-day exponential smoothing.

Be sure to check "center zero line" when you plot it.

The resulting plotted line calculates virtually instantaneously (compared to all the other stuff, above).

Any time this line CROSSES ZERO, that's a place where the +DI and -DI lines had a crossover.

If this line is GREATER than zero, there is a BULLISH Directional Movement condition (i.e. the posDI line is above the negDI line), and vice versa for Bearish.

IMHO, this is probably the "final" form necessary, since it provides an exceptionally clean, perfectly accurate, and very fast solution.

Please note two applications that are natural uses of it:
1) SortBy Value and flag for >0 or <0
2) Rewrite for some fixed daysago for backtesting

Jim Dean