An Optimizing ESN Implementation

Dave Benson

$\begin{section}{ABSTRACT} We extend Al Barr's ESN preprocessor implementation to... ... do the computation in phases, to reduce the number of multiplies. \end{section}$

$\begin{section}{Motivation} The original ESN implementation simply loops over al... ...e computational cost varies with the actual ranges of the indices. \end{section}$

$\begin{section}{Notation} In order to write more simply, we introduce a notation... ...m} = [ {}_{im} b_{ik} [ {}_{km} c_{kl} d_{lm} ] ].\end{displaymath}\end{section}$

$\begin{section}{Algebra} This section contains mundane details about manipulatin... ...doesn't appear in the brackets, we can drop it, and just get $il$. \end{section}$

$\begin{section}{The Cost of Evaluation} In order to optimize, we have to estimat... ...um variables if they only appear in a context-free subexpression). \end{section}$

$\begin{section}{Dynamic Programming Problem} Now, suppose we have some very long... ... can accumulate those in a recursive function. \par\end{subsection}\end{section}$

$\begin{section}{An Implementation} ... \end{section}$

$\begin{section}{Implementation Availability} ... \end{section}$

$\begin{section}{Implementation Shortcomings} ... \end{section}$

$\begin{section}{Future Work} ... \end{section}$

About this document ...

d 2002-12-19