Adaptive range reduction for hardware function evaluation

Function evaluation f(x) typically consists of range reduction and the actual function evaluation on a small interval. We investigate optimization of range reduction given the range and precision of x and f(x). For every function evaluation there exists a convenient interval such as [0, π/2) for sin(x). The adaptive range reduction method, which we propose in this work, involves deciding whether range reduction can be used effectively for a particular design. The decision depends on the function being evaluated, precision, and optimization metrics such as area, latency and throughput. In addition, the input and output range has an impact on the preferable function evaluation method such as polynomial, table-based, or combinations of the two. We explore this vast design space of adaptive range reduction for fixed-point sin(x), log(x) and √(x) accurate to one unit in the last place using MATLAB and ASC, A Stream Compiler. These tools enable us to study over 1000 designs resulting in over 40 million Xilinx equivalent circuit gates, in a few hours´ time. The final objective is to progress towards a fully automated library that provides optimal function evaluation hardware units given input/output range and precision.