Static Analysis for Automatic Differentiation

Differentiation is the single most important numerical operation inscientific computing. Creating derivative functions manually or byusing finite differencing is error-prone, time-consuming andpotentially inaccurate. Automatic differentiation (AD) holds great promisefor overcoming these problems, but it has not caught on beyond ahandful of research laboratories because the naive approaches used areinefficient. Sophisticated static analysis of source code is requiredto overcome these inefficiencies. Such tools are difficult andexpensive to produce. GrammaTech has a fifteen-year investment inadvanced general-purpose static analysis tools which can be targetedtowards this problem. Our dependence-graph technology is capable ofproviding exactly the right kinds of analysis needed to help createefficient derivatives. We propose to build a system for AD that willuse our dependence-graph technology to provide exactly the right kindsof analysis needed to help create efficient derivatives.