1. A specialized functional block for use in a programmable logic device, said specialized functional block comprising: a plurality of block inputs; a plurality of dedicated multiplier circuits having multiplier inputs connected to said block inputs, and having multiplier outputs; a plurality of first-level dedicated adder circuits having first-level adder inputs and first-level adder outputs; and programmable connections between said multiplier outputs and said first-level adder inputs whereby said specialized functional block is configurable to add together in said first-level adders products output by said dedicated multiplier circuits; wherein: said programmable connections include respective programmable bit-shifting circuitry associated with each respective one of said dedicated multiplier circuits, for programmably shifting, to more significant bits, bits of said product output by said respective one of said dedicated multiplier circuits, said respective programmable bit shifting circuitry comprising bit diversion circuitry for diverting bits of lesser significance, in a respective product output by said respective one of said dedicated multiplier circuits, from said first-level adder inputs.