An analytical approach for dynamic range estimation

It has been widely recognized that the dynamic range information of an application can be exploited to reduce the datapath bitwidth of either processors or ASICs, and therefore the overall circuit area, delay and power consumption. While recent proposals of analytical dynamic range estimation methods have shown significant advantages over the traditional profiling-based method in terms of runtime, we argue that the rather simplistic treatment of input correlation may lead to significant error. We instead introduce a new analytical method based on a mathematical tool called Karhunen-Loeve Expansion (KLE), which enables the orthogonal decomposition of random processes. We show that when applied to linear systems, this method can not only lead to much more accurate result than previously possible, thanks to its capability to capture and propagate both spatial and temporal correlation, but also richer information than the value bounds previously produced, which enables the exploration of interesting trade-off between circuit performance and signal-to-noise ratio.