A class of stored-transfer representations for redundant number systems

Redundant representations play an important role in highspeed computer arithmetic. One key reason is that such representations support carry free addition; i.e., addition in a small, constant time, independent of operand widths. We explore the implications of stored-transfer or transfer-save representation of digit sets for redundant number systems on the speed and cost of arithmetic algorithms and show that our methods lead to some of the fastest, most efficient implementations of carry free arithmetic reported thus far. The speed/efficiency arises from storing or saving, instead of combining through addition, the transfer values generated during carry free arithmetic.