In a digital signal processing unit, addressing apparatus implements a multiplicity of addressing modes. The addressing modes include a circular buffer memory mode, a frame mode, and a sorting mode. To increase the speed of the address modification, the index, the index in the presence of a positive wrap-around, and the index in the presence of negative wrap-around are determined together. Other apparatus determines the addressing mode and provides control signals for the selection of the correct index. The correct index is combined with the base address to provide the next new address.