LPM_mult : dynamic reduction with signed number

I think I have understood what you are attempting but I'm not 100% sure so here goes...

You may be losing a bit when you convert your unsigned quantity to signed. You should assume your input to be signed rather than actually converting it.

i.e. unsigned range is 0..16383, but if you assume it to be signed as it arrives then you can interpret it to represent -8192..8191 without any form of manipulation.

However, that having been said, 8191 for the B input represents something just short of 1.0 i.e. the range of multiplication is -1.0 <= x < 1.0

This can be corrected by appropriate scaling - google fixed point arithmetic.