A parallel method for fast and practical high-order newton interpolation

Eğecioǧlu, Ömer; Gallopoulos, Efstratios; Koç, Çetin Kaya

doi:10.1007/bf02017348

Cited by 13 publications

(4 citation statements)

References 15 publications

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“…As a consequence, we currently use a method inspired from [14] where most of the calculation is done in parallel with fully independent kernels, and the rest is made of prefix operations that can be computed in a logarithmic parallel approach. Such operations have been used for polynomial interpolation [15] or even stream compaction [16], and are good candidates for parallelization. If we consider a binary operator * , then the (inclusive) prefix operation of * on a vector…”

Section: Data-dependent Parallelismmentioning

confidence: 99%

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

Chrétien

Escande

Kheddar

2016

IEEE Trans. Parallel Distrib. Syst.

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We propose a many-core GPU implementation of robotic motion planning formulated as a semi-infinite optimization program. Our approach computes the constraints and their gradients in parallel, and feeds the result to a nonlinear optimization solver running on the CPU. To ensure the continuous satisfaction of our constraints, we use polynomial approximations over time intervals. Because each constraint and its gradient can be evaluated independently for each time interval, we end up with a highly parallelizable problem that can take advantage of many-core architectures. Classic robotic computations (geometry, kinematics, and dynamics) can also benefit from parallel processors, and we carefully study their implementation in our context. This results in having a full constraint evaluator running on the GPU. We present several optimization examples with a humanoid robot. They reveal substantial improvements in terms of computation performance compared to a parallel CPU version.

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Section: Data-dependent Parallelismmentioning

confidence: 99%

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

Chrétien

Escande

Kheddar

2016

IEEE Trans. Parallel Distrib. Syst.

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“…Stream compaction [2,16] Int + Sorting algorithms [16,30] Int + Polynomial interpolation [13] Float * a Line-of-sight calculation [4] Int max Binary addition [22] pairs-of-bits carry operator…”

Section: Data-type Operatormentioning

confidence: 99%

A sound and complete abstraction for reasoning about parallel prefix sums

2014

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Prefix sums are key building blocks in the implementation of many concurrent software applications, and recently much work has gone into efficiently implementing prefix sums to run on massively parallel graphics processing units (GPUs). Because they lie at the heart of many GPU-accelerated applications, the correctness of prefix sum implementations is of prime importance. We introduce a novel abstraction, the interval of summations, that allows scalable reasoning about implementations of prefix sums. We present this abstraction as a monoid, and prove a soundness and completeness result showing that a generic sequential prefix sum implementation is correct for an array of length $n$ if and only if it computes the correct result for a specific test case when instantiated with the interval of summations monoid. This allows correctness to be established by running a single test where the input and result require O(n lg(n)) space. This improves upon an existing result by Sheeran where the input requires O(n lg(n)) space and the result O(n 2 \lg(n)) space, and is more feasible for large n than a method by Voigtlaender that uses O(n) space for the input and result but requires running O(n 2 ) tests. We then extend our abstraction and results to the context of data-parallel programs, developing an automated verification method for GPU implementations of prefix sums. Our method uses static verification to prove that a generic prefix sum implementation is data race-free, after which functional correctness of the implementation can be determined by running a single test case under the interval of summations abstraction. We present an experimental evaluation using four different prefix sum algorithms, showing that our method is highly automatic, scales to large thread counts, and significantly outperforms Voigtlaender's method when applied to large arrays.

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“…The cumulative sum problem generalizes to any associative operator; in this Julia function, the argument + specifies the operator of interest, allowing the same code to be Application Operator Addition Poisson random variates [35] sequence lengths Minimal coverings [40] joining 2D regions Stream reduction [26] counting records Maximization Line of sight [7] height String alignment [24,14] substring length Multiplication Binary addition [47] Boolean matrices Polynomial interpolation [19] scalars Sorting [24,6] permutations Tridiagonal equations [36] matrices Function composition Finite state automata [34,24] reused for other operators like multiplication (*), maximization (max) [46], or even string concatenation 2 . The !…”

Section: The Scan Algorithmmentioning

confidence: 99%

Parallel Prefix Polymorphism Permits Parallelization, Presentation &amp; Proof

Edelman

2014

2014 First Workshop for High Performance Technical Computing in Dynamic Languages

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Polymorphism in programming languages enables code reuse. Here, we show that polymorphism has broad applicability far beyond computations for technical computing: parallelism in distributed computing, presentation of visualizations of runtime data flow, and proofs for formal verification of correctness. The ability to reuse a single codebase for all these purposes provides new ways to understand and verify parallel programs.

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A parallel method for fast and practical high-order newton interpolation

Cited by 13 publications

References 15 publications

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

A sound and complete abstraction for reasoning about parallel prefix sums

Parallel Prefix Polymorphism Permits Parallelization, Presentation &amp; Proof

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A parallel method for fast and practical high-order newton interpolation

Cited by 13 publications

References 15 publications

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

GPU Robot Motion Planning Using Semi-Infinite Nonlinear Programming

A sound and complete abstraction for reasoning about parallel prefix sums

Parallel Prefix Polymorphism Permits Parallelization, Presentation &amp;amp; Proof

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Parallel Prefix Polymorphism Permits Parallelization, Presentation & Proof