Elementary function generators for neural-network emulators

Piecewise first- and second-order approximations are employed to design commonly used elementary function generators for neural-network emulators. Three novel schemes are proposed for the first-order approximations. The first scheme requires one multiplication, one addition, and a 28-byte lookup table. The second scheme requires one addition, a 14-byte lookup table, and no multiplication. The third scheme needs a 16-byte lookup table, no multiplication, and no addition. A second-order approximation approach provides better function precision; it requires more hardware and involves the computation of one multiplication and two additions and access to a 28-byte lookup table. We consider bit serial implementations of the schemes to reduce the hardware cost. The maximum delay for the four schemes ranges from 24- to 32-bit serial machine cycles; the second-order approximation approach has the largest delay. The proposed approach can be applied to compute other elementary function with proper considerations.