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Published in:
2006 | OriginalPaper | Chapter
The Adjoint Data-Flow Analyses: Formalization, Properties, and Applications
Authors : Laurent Hascoëet, Mauricio Araya-Polo
Published in: Automatic Differentiation: Applications, Theory, and Implementations
Publisher: Springer Berlin Heidelberg
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Automatic Differentiation (AD) is a program transformation that yields derivatives. Building efficient derivative programs requires complex and specific static analysis algorithms to reduce run time and memory usage. Focusing on the
reverse mode
of AD, which computes
adjoint programs
, we specify jointly the central static analyses that are required to generate an efficient adjoint code. We use a set-based formalization from classical data-flow analysis to specify
Adjoint Liveness, Adjoint Write
, and
To Be Recorded
analyses, and their mutual influences, taking into account the specific structure of adjoint programs. We give illustrations on examples taken from real numerical programs, that we differentiate with our AD tool tapenade, which implements these analyses.