Buch, Englisch, 263 Seiten, Format (B × H): 145 mm x 210 mm
Zugl. Diss.
Buch, Englisch, 263 Seiten, Format (B × H): 145 mm x 210 mm
ISBN: 978-3-89722-556-5
Verlag: Logos
The thesis of this dissertation is that an effective exploitation of the inherent parallelism in algorithms is possible at the highlevel of functional programming. Parallelism is a promising concept for achieving a high acceleration of computations, but most parallel programming languages and tools of today address mainly experts in parallel computing. This limits the use of massive parallelism by the average programmer.
Our approach to overcome this limit are skeletons, also called combinators or templates. They are polymorphic programschemata that have an efficient, possibly parallel, implementation. Skeletons are embedded into a functional source languageand receive a special treatment in the compilation of the program to target code. We distinguish two views of a skeleton: theuser's view and the implementer's view. A skeleton appears in the program as a single function call which is specialized bythe user with problem-specific customizing functions. We focus on skeletons for the divide-and-conquer (DC) paradigm,because DC algorithms provide a high potential for parallelism. In DC, two of the customizing functions describe how theproblem is divided into subproblems and how the partial solutions are combined. Starting from a skeleton that represents ageneral kind of DC, we derive, successively, special cases which lead to an efficient parallel implementation. The functionaldefinitions of the skeletons and the programs which use them are denoted in the language Haskell.
The implementer views a skeleton as an additional module of the compiler, which generates, for every skeleton application, anappropriate, optimized implementation in the target language. Thus, know-how of a problem domain, e.g., DC, can be added tothe compiler. The straight-forward way to parallelize DC, by simply spawning independent tasks, can cause a serious loadimbalance. Load balance can be established by an appropriate mapping of operations to time steps and processors. For themore specialized skeletons, this can be done completely at compile time. Otherwise, the space-time mapping can beexpressed in dependence of run-time information. We transform the recursive definition of each of the DC skeletonspresented to an index-based form in order to apply a space-time mapping to the set of operations. A transformation consistsof a sequence of semantics-preserving rule applications. The power of recursion motivates the introduction of a computationalmodel which is more sophisticated than the polytope model used for nested loops. The new model supports a potentiallyunbounded dimensionality of the index space.
A subset of the functional language Haskell, called HDC, is used for experiments with example programs. Contrary to Haskell,HDC is strict. This is necessary to guarantee that the space-time mapping made at compile-time is respected by theexecution. We present compilation techniques that transform polymorphic, higher-order functional programs into functionalprograms which can easily be compiled into C and linked together with the skeleton implementations.
Experimental results are presented for Karatsuba's polynomial multiplication, the n queens problem, the maximum independentset problem, the convex hull computation and sorting. It turns out that significant speedups can be achieved for realisticapplications, but under special conditions on the algorithmic structure. Some of the skeletons enforce these conditions byconstruction. For the others, there is still a high potential for optimization left for the future.
Herrmann
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Our approach to overcome this limit are skeletons, also called combinators or templates. They are polymorphic programschemata that have an efficient, possibly parallel, implementation. Skeletons are embedded into a functional source languageand receive a special treatment in the compilation of the program to target code. We distinguish two views of a skeleton: theuser's view and the implementer's view. A skeleton appears in the program as a single function call which is specialized bythe user with problem-specific customizing functions. We focus on skeletons for the divide-and-conquer (DC) paradigm,because DC algorithms provide a high potential for parallelism. In DC, two of the customizing functions describe how theproblem is divided into subproblems and how the partial solutions are combined. Starting from a skeleton that represents ageneral kind of DC, we derive, successively, special cases which lead to an efficient parallel implementation. The functionaldefinitions of the skeletons and the programs which use them are denoted in the language Haskell.
The implementer views a skeleton as an additional module of the compiler, which generates, for every skeleton application, anappropriate, optimized implementation in the target language. Thus, know-how of a problem domain, e.g., DC, can be added tothe compiler. The straight-forward way to parallelize DC, by simply spawning independent tasks, can cause a serious loadimbalance. Load balance can be established by an appropriate mapping of operations to time steps and processors. For themore specialized skeletons, this can be done completely at compile time. Otherwise, the space-time mapping can beexpressed in dependence of run-time information. We transform the recursive definition of each of the DC skeletonspresented to an index-based form in order to apply a space-time mapping to the set of operations. A transformation consistsof a sequence of semantics-preserving rule applications. The power of recursion motivates the introduction of a computationalmodel which is more sophisticated than the polytope model used for nested loops. The new model supports a potentiallyunbounded dimensionality of the index space.
A subset of the functional language Haskell, called HDC, is used for experiments with example programs. Contrary to Haskell,HDC is strict. This is necessary to guarantee that the space-time mapping made at compile-time is respected by theexecution. We present compilation techniques that transform polymorphic, higher-order functional programs into functionalprograms which can easily be compiled into C and linked together with the skeleton implementations.
Experimental results are presented for Karatsuba's polynomial multiplication, the n queens problem, the maximum independentset problem, the convex hull computation and sorting. It turns out that significant speedups can be achieved for realisticapplications, but under special conditions on the algorithmic structure. Some of the skeletons enforce these conditions byconstruction. For the others, there is still a high potential for optimization left for the future.
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