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Reports Year : 2003

TBR Analysis in Reverse-Mode Automatic Differentiation

Uwe Naumann
  • Function : Author
Valérie Pascual


The automatic generation of adjoints of mathematical models that are implemented as computer programs is receiving a increased attention in the scientific and engineering communities. Reverse-mode Automatic Differentiation (AD) is of particular interest for large-scale optimization problems. It allows for the computation of gradients at a small constant multiple of the cost for evaluating the objective function itself, that is independent of the number of input parameters. Source-to-source transformation tools for AD are available to generate adjoint codes based on the adjoint version of every statement, built by applying simple differentiation rules. A reversal of the control flow of the original program becomes necessary. To guarantee correctness, certain values that are computed and overwritten in the original program must be made available in the adjoint program. They can be determined by performing a static data flow analysis, the so-called TBR analysis. Overestimation of this set must be kept minimal to get efficient adjoint codes.For many real-world applications, this efficiency is compulsory to apply a source-to-source transformation such as AD.
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Dates and versions

inria-00071727 , version 1 (23-05-2006)


  • HAL Id : inria-00071727 , version 1


Laurent Hascoët, Uwe Naumann, Valérie Pascual. TBR Analysis in Reverse-Mode Automatic Differentiation. RR-4856, INRIA. 2003. ⟨inria-00071727⟩
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