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I've allready replied to the question posted some days before. Montgomery multiplication is another way to perform modular multiplication in the residue system representation. The operation induced is in fact a group morphism. In GF(p), p prime, or in the multiplicative group $Z/nZ$, the transformation allows to perform modular multiplication without ...
The confusion comes from the choice of representation. I'd a quick look to the referenced paper, where the autors use a 2-radix representation. Then you shoud initialise $e=\frac{m+15}{w}$ instead of $e=\frac{m+1}{w}$ as you use a 16 bit adder! The best is to read again the seminal paper of P.L. ...