Genetic programming in FPGA implementation of addition as a part of the convolution

In FPGAs, an addition should be carried out in the standard way employing ripple-carry adders (rather than carry-save adders), which complicates search for an optimal adder structure as routing order has a substantial influence on the addition cost. Further, complex parameters of inputs to the adder block have been considered e.g. correlation between inputs. These parameters are specified in different ways for different convolver architectures. Consequently optimisation of the adder tree is a key issue addressed in this paper. Simulated Annealing and Genetic Programming have been proposed, and obtained results compared with the Greedy Algorithm (GrA) and the Exhaustive Search (ES). As a result, the GrA is the best solution when computation time is of great importance. Otherwise, the Simulated Annealing should be employed for the number of addition inputs N>8, and the ES is recommended for N⩽8. Employing the Simulated Annealing gives about 10-20% area reduction in comparison to the GrA