On automatic derivation of fast Hadamard transform using genetic programming

Automatic generation of fast Hadamard transform (FHT) algorithms through genetic programming is studied. The design of FHT algorithms is viewed as a search in the space of linear algorithms employing restricted types of coefficients. A generic circuit that can realize all algorithms belonging to this space is proposed. The goal is to automatically find an algorithm that can perform Hadamard transform properly using a specified number of multiply/add operations. It is shown that genetic programming is able to discover a 4-point FHT that requires only 7 multiply/add operations.