The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function I : R" ~ Rm. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution. Automatic Differentiation of FORtran (ADIFOR) is a source transformation tool that accepts Fortran 77 code for the computation of a function and writes portable Fortran 77 code for the computation of the derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a source transformation problem. ADIFOR employs the data analysis capabilities of the ParaScope Parallel Programming Environment, which enable us to handle arbitrary Fortran 77 codes and to exploit the computational context in the computation of derivatives. Experimental results show that ADIFOR can handle real-life codes and that ADIFOR-generated codes are competitive with divided-difference approximations of derivatives. In addition, studies suggest that the source transformation approach to automatic differentiation may improve the time to compute derivatives by orders of magnitude.

Cover Cover art by George Kitrinos, a derivative of "Circuit board elements background" from freedesignfile.com, used under Creative Commons Attribution 3.0. Equations from a far-field approximation of the Green's function solution to the acoustic analogy equation with thermoacoustic sources.

No abstract

No abstract

Message passing via MPI is widely used in singleprogram, multiple-data (SPMD) parallel programs. Existing data-flow frameworks do not model the semantics of message-passing SPMD programs, which can result in less precise and even incorrect analysis results. We present a data-flow analysis framework for performing interprocedural analysis of message-passing SPMD programs. The framework is based on the MPI-ICFG representation, which is an interprocedural control-flow graph (ICFG) augmented with communication edges between possible send and receive pairs and partial context sensitivity.We show how to formulate nonseparable data-flow analyses within our framework using reaching constants as a canonical example. We also formulate and provide experimental results for the nonseparable analysis, activity analysis. Activity analysis is a domain-specific analysis used to reduce the computation and storage requirements for automatically differentiated MPI programs. Automatic differentiation is important for application domains such as climate modeling, electronic device simulation, oil reservoir simulation, medical treatment planning and computational economics to name a few. Our experimental results show that using the MPI-ICFG data-flow analysis framework improves the precision of activity analysis and as a result significantly reduces memory requirements for the automatically differentiated versions of a set of parallel benchmarks, including some of the NAS Parallel Benchmarks.