On the implementation of dynamic evaluation

Broadbery, Peter; Gómez-Díaz, Teresa; Watt, Stephen M.

doi:10.1145/220346.220356

Cited by 6 publications

(2 citation statements)

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“…Early implementations simply handled splittings by redoing the entire computation under stricter constraints [13]. Unnecessary recomputations can be avoided through the use of high-level control structures such as continuations [4]. Unfortunately, efficient implementations of such control structures are rarely available for common programming languages.…”

Section: Previous Workmentioning

confidence: 99%

“…Early implementations of dynamic evaluation were therefore naive [13], the computation tree essentially being reevaluated for every separate case: see subsection 4.3.1. In theory, using SCHEME-style continuations or UNIX-style forking, it is possible to factor out many common computations between the different cases; see [4]. We analyze these approaches from a complexity point of view in section 4.3.2.…”

Section: Comparison With Previous Workmentioning

confidence: 99%

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Directed evaluation

Hoeven

Lecerf

2020

Journal of Complexity

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Let be a fixed effective field. The most straightforward approach to compute with an element in the algebraic closure of is to compute modulo its minimal polynomial. The determination of a minimal polynomial from an arbitrary annihilator requires an algorithm for polynomial factorization over. Unfortunately, such algorithms do not exist over generic effective fields. They do exist over fields that are explicitly generated over their prime sub-field, but they are often expensive. The dynamic evaluation paradigm, introduced by Duval and collaborators in the eighties, offers an alternative algorithmic solution for computations in the algebraic closure of. This approach does not require an algorithm for polynomial factorization, but it still suffers from a non-trivial overhead due to suboptimal recomputations. For the first time, we design another paradigm, called directed evaluation, which combines the conceptual advantages of dynamic evaluation with a good worst case complexity bound.

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Section: Previous Workmentioning

confidence: 99%

Section: Comparison With Previous Workmentioning

confidence: 99%