1. A logic element for a programmable integrated circuit device, said logic element comprising: a logic stage; an adder; and an output stage; wherein said logic stage comprises: logic units, a first logic stage selector having as inputs (a) a first output of said logic units, and (b) a first logic unit output of another said logic element, said first logic stage selector selectably outputting to an input of said adder at least (a) said first output of said logic units, or (b) said first logic unit output of said another said logic element, and a second logic stage selector having as inputs (a) a second output of said logic units, and (b) an output of said adder, said second logic stage selector selectably outputting to said output stage (a) said second output of said logic units, or (b) said output of said adder.