Optimal Time and Minimum Space-Time Product for Reversing a Certain Class of Programs

Abstract : This report concerns time/space trade-offs for the reverse mode of automatic differentiation on the straight-line programs with nested loops class of programs. In the first part we consider the problem of reversing a finite sequence given by $u_{n+1}=3Df(u_n)$, which can mode lize a certain class of finite loops. We show an optimal time strategy for this problem, the number of available registers being fixed, and a lower bound on the time-space product equal to $\frac{p (\ln p)^2}{(\ln 4)^2}$. We then present an optimal strategy on nested loops with the objective of taking care of the program structure. Finally we consider an application of this storage/recomputation strategy to compute in reverse mode the derivatives of a function represented as a {\sc fortran} program.
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RR-2794, INRIA. 1996
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José Grimm, Loïc Pottier, Nicole Rostaing-Schmidt. Optimal Time and Minimum Space-Time Product for Reversing a Certain Class of Programs. RR-2794, INRIA. 1996. 〈inria-00073896〉

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