Common use of Background and Implementation Clause in Contracts

Background and Implementation. Koç et al. [11] proposed Coarsely Integrated Operate Operand Scanning (CIOS) and Finely Integrated Operate Operand Scanning (FIOS) algorithms as an optimization for Xxxxxxxxxx multiplication targeting word size processors or multiplication units. The CIOS algorithm, as shown in Algorithm 1 computes one entire partial product, lines 2– 6, before performing a reduction, lines 8–12. FIOS on the other hand, computes the multiplication of a word of each input, lines 2 and 6, and then proceeds with the reduction, lines 4, 7 and 9. While the CIOS algorithm operates directly on partial products, the iterative word-based structure of the FIOS algorithm allows for a design with two parallel units, one doing the multiplication, line 6, and the other one the reduction, line 7. In the proposed implementations, the IGLOO 2 FPGA family from Microsemi is targeted. These FPGAs include Algorithm 1 CIOS Xxxxxxxxxx multiplication algo- rithm [11] ≤ Require: a, b 2n, r = 2()()log2 (n)+2¶/word size)¶·word size), − [ | n′ = n—1 (mod r), w = 2word size, l = log2(r/w) · Ensure: o = a b/r (mod n) ←