Higher Radix and Redundancy Factor for Floating Point SRT Division

The execution performances of the Sweeney, Robertson, Tocher (SRT) division algorithm depend on two parameters: the radix-r and the redundancy factor p. In this paper, a study of the effect of these parameters on the division performances is presented. At each iteration, the SRT algorithm performs a multiplication by the quotient digit q_i+1. This last can be just a simple shift, if the digit q_{i i +1}is a power of two (q_i+1 = 2^k), otherwise, the SRT iteration needs a multiplier. We propose, in this work, an approach to circumvent this multiplication by decomposing the quotient digit q_i+1 into two or three terms multiples of 2. Then, the multiplication is carried out by simple shifts and a carry save addition. The implementation of this approach on Virtex-II field-programmable gate-array (FPGA) circuits gives best performances than the approach which uses the embedded multipliers 18times18 bits. The iterations delays are operands sizes independent. The reduction tree delays are at most equivalent to the delay of two Virtex-II slices. This approach was tested for the 4, 8, and 16 radixes in the two cases of minimum and maximum redundancy factors. By this study, we conclude that the use of the radix-8 with a maximum redundancy factor gives the best performances by using our approach for the double precision computation of the SRT division.