Adaptive Range Reduction for Hardware Function Evaluation
Dong-U Lee, Altaf Abdul Gaffar, Oskar Mencer and Wayne Luk
[IEEE Conference on Field Programmable Technology, Brisbane, Dec. 2004]

abstract.

Function evaluation f(x) typically consists of range reduction
and the actual function evaluation on a small interval.
In this paper, 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, /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 px 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.