Architectural Exploration of Function Computation Based on Cubic Polynomial Interpolation with Application in Deep Neural Networks

Computation of function values is widely used in applications of computer vision, communication, and artificial neural networks. Piecewise polynomial approximation (PPA) with lookup tables (LUT) assisted by arithmetic units is usually adopted in hardware implementation. In high-precision requirements, the degree of per-segment polynomial is usually increased in order to reduce the size of LUT, but the cost of arithmetic units usually dominates the entire design. This paper analyzes different architectural designs of function computation units based on degree-three polynomial interpolation where the arithmetic units include truncated multipliers, squaring unit (squarer), and cubic unit (cuber). Significant savings in area and power are achieved by selecting architectures without cuber. Furthermore, we design reconfigurable functional computation units supporting four different precision modes with shared hardware resources. The designs are applied to the computation of several arithmetic functions including some popular activation functions for deep neural networks where the bit-accuracy requirement across network layer might vary.