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 rho. 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+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 18 x 18 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.
sweeney robertson tocher (srt) division double precision computation high performance design virtex-ii field-programmable gate array (fpga)