Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM '00), pages 73--82. ACM Press, Jan. 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... targeted toward very high level set theoretic languages were investigated by Fong and Ullman (Fong and Ullman, 1976; Fong, 1977; Fong, 1979) More recently, Liu and Stoller have used some extensions of these ideas to optimize array computations (Liu and Stoller, 1998) and recursive programs (Liu and Stoller, 2000). Liu et al. have also shown how such transformations can be applied to derive algorithms for incrementalcomputation problems (i.e. problems in which the goal is to maintain the value of some function F (x) as the input x undergoes small changes) Liu, 1995; Liu and Teitelbaum, 1995a; Liu and ....

Liu, Y. and S. Stoller: 2000, `From Recursion to Iteration: What are the Optimizations ?'. In: Proc. of the 2000 ACM SIGPLAN Workshop on Part. Eval. and Sem.-Based Prog. Manip. New York, NY, pp. 73-82, ACM Press.

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Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Program Manipulation, pages 73-82. ACM, New York, 2000.

....of memoization [22] and tabulation [3] as a result of incremental computation. Third, although the optimization method based on incrementalization has been used successfully to optimize loops, arrays, recursive functions, and recursive data structures [15] and transform recursion to iteration [17], the power of the method in general remains unknown. A similar method has also been used to optimize set and fixed point operations [4, 23, 24] Previously, all these optimizations succeeded in deriving e#cient programs, including well known dynamic programming programs [19, 18] from more ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000.

....forms a triangle shape, rather than a two dimensional array of square shape. It is nontrivial to see that recursive data structures give the same asymptotic speedup as arrays for some examples. Our recent work on transforming recursion into iteration can help eliminate the linear stack space used [36]. There are dynamic programming problems, e.g. 0 1 knapsack, for which the use of an array, with constant time access to elements, helps achieve desired asymptotic speedups. Such situations become evident when doing incrementalization and can be accommodated easily, as will be described in a ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000.

....this optimized version enables one to easily see that an additional array could be used for copying rExt , removing the need to allocate and garbage collect the array for each incremental step. We have preliminary results on transforming recursion into iteration using incrementalization [20]. Detailed study is a future work. When there are multiple minimal increment operations, for example, the longest common subsequence and matrix chain multiplication problems [12, 19] each has two, we found that any one of them may be used, and they may lead to optimized programs with the same ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000.

....this optimized version enables one to easily see that an addtional array could be used for copying rExt , removing the need to allocate and garbage collect the array for each incremental step. We have preliminary results on transforming recursion into iteration using incrementalization [15]. Detailed study is a future work. When there are multiple minimal increment operations, for example, the longest common subsequence and matrix chain multiplication problems [8, 14] each has two, we found that any one of them may be used, and they may lead to optimized programs with the same time ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000 Workshop on Partial Evaluation and Semantics-Based Program Manipulation, pages 73-82. ACM, New York, Jan. 2000.

....graduate courses on related topics. To better integrate existing functionalities in the system, and to facilitate implementation of improvements to these functionalities, we are currently planning on a redesign and cleanup of the system. This should also allow us to easily add new extensions [51,53]. ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000 Workshop on Partial Evaluation and Semantics-Based Program Manipulation, pages 73-82. ACM, New York, Jan. 2000.

....forms a triangle shape, rather than a two dimensional array of square shape. It is nontrivial to see that recursive data structures give the same asymptotic speedup as arrays for some examples. Our recent work on transforming recursion into iteration can help eliminate the linear stack space used [36]. There are dynamic programming problems, e.g. 0 1 knapsack, for which the use of an array, with constant time access to elements, helps achieve desired asymptotic speedups. Such situations become evident when doing incrementalization and can be accommodated easily, as will be described in a ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000 Workshop on Partial Evaluation and Semantics-Based Program Manipulation, pages 73-82. ACM, New York, Jan. 2000.

....this transformed program only if this indeed yields speedups. For example, for factorial, this amounts to replacing n ( n Gamma 1) n Gamma 2) by (n (n Gamma 1) n Gamma 2) but the latter might be slower due to multiplying bigger numbers; this effect is indeed true in real measurements [34]. For list reversal, this amounts to replacing append(append(x;y) z) by append(x;append(y; z) which clearly produces a speedup, since append takes time proportional to the size of its first argument. 3 4. MULTIPLE BASE CASES Consider a recursive function f on x with one or more base ....

....iteration, exploring special properties or being in the context of other studies. Associativity allows a kind of reversal of the order of computation and is used by many in transforming recursion to iteration [4; 41; 9] but none addresses possible slowdown, as we found for the factorial function [34]. We consider it as a separate optimization, and a simple analysis is used to guarantee performance improvement. Waters [53] studied transforming series expressions into loops in the context of their program synthesis project. Its underlying idea 8 is the same as incrementalization, but series ....

Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? Technical Report TR 527, Computer Science Department, Indiana University, Bloomington, Indiana, July 1999.

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Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN Workshop on Partial Evaluation and Semantics-Based Program Manipulation (PEPM '00), pages 73--82. ACM Press, Jan. 2000.

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Y. A. Liu and S. D. Stoller. From recursion to iteration: what are the optimizations? In Proceedings of the ACM SIGPLAN 2000.

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