A plurality of specialized processing blocks in a programmable logic device, including multipliers and circuitry for adding results of those multipliers, can be configured as a larger multiplier by adding to the specialized processing blocks selectable circuitry for shifting multiplier results before adding. In one embodiment, this allows all but the final addition to take place in specialized processing blocks, with the final addition occurring in programmable logic. In another embodiment, additional compression and adding circuitry allows even the final addition to occur in the specialized processing blocks. Circuitry that controls when an input is signed or unsigned facilitates complex arithmetic.