"Hierarchical approach to automatic differentiation"

Marco Mancini 
Parallel Computing Laboratory 
Department of Electronics, Computer Science and Systems
University of Calabria
87036 Rende (CS) - Italy

Automatic differentiation (AD) techniques have been investigated since
1980; however, AD technology is still in its infancy. Current tools use
very simple AD algorithms, because most of the development time has been
dedicated to building robust tools instead of implementing more
sophisticated and efficient AD algorithms. 
This talk describes advanced algorithms for generating first-order
derivatives exploiting the program structure of the function to be
differentiated and the associativity of the chain rule, in a global
forward mode approach.
To decrease the complexity of the derivative codes, a hierarchical 
approach to automatic differentiation is used, by exploiting the
interface asymmetries between the number of derivatives to be computed
and the amount of information flowing in or out of a program segment.
The computational results show performance gains of the proposed
techniques compared with existing approaches. We also describe a new
source transformation module for computing first-order derivatives 
and the underlying infrastructure used to create a language-independent
translation tool.