Implementing the Residue Logarithmic Number System Using Interpolation and Cotransformation

The Residue Logarithmic Number System (RLNS) offers fast multiplication and division, but poses challenges for implementing addition and subtraction because the underlying integer Residue Number System (RNS) has slow sign detection. The conventional Binary Logarithmic Number Systems (BLNS) has benefited from interpolation and cotransformation. We propose a dual-path ALU that speculates about the sign detection to adapt interpolation and cotransformation to the limitations of RLNS. Synthesis shows for the same precision and technology, the area of the proposed RLNS circuit is similar to BLNS and much smaller than prior RLNS methods. We also compare against Floating Point (FP).