204 research outputs found
Parallel Integer Polynomial Multiplication
We propose a new algorithm for multiplying dense polynomials with integer
coefficients in a parallel fashion, targeting multi-core processor
architectures. Complexity estimates and experimental comparisons demonstrate
the advantages of this new approach
Parallel Finger Search Structures
In this paper we present two versions of a parallel finger structure FS on p processors that supports searches, insertions and deletions, and has a finger at each end. This is to our knowledge the first implementation of a parallel search structure that is work-optimal with respect to the finger bound and yet has very good parallelism (within a factor of O(log p)^2) of optimal). We utilize an extended implicit batching framework that transparently facilitates the use of FS by any parallel program P that is modelled by a dynamically generated DAG D where each node is either a unit-time instruction or a call to FS.
The work done by FS is bounded by the finger bound F_L (for some linearization L of D), i.e. each operation on an item with distance r from a finger takes O(log r+1) amortized work. Running P using the simpler version takes O((T_1+F_L)/p + T_infty + d * ((log p)^2 + log n)) time on a greedy scheduler, where T_1, T_infty are the size and span of D respectively, and n is the maximum number of items in FS, and d is the maximum number of calls to FS along any path in D. Using the faster version, this is reduced to O((T_1+F_L)/p + T_infty + d *(log p)^2 + s_L) time, where s_L is the weighted span of D where each call to FS is weighted by its cost according to F_L. FS can be extended to a fixed number of movable fingers.
The data structures in our paper fit into the dynamic multithreading paradigm, and their performance bounds are directly composable with other data structures given in the same paradigm. Also, the results can be translated to practical implementations using work-stealing schedulers
Optimal (Randomized) Parallel Algorithms in the Binary-Forking Model
In this paper we develop optimal algorithms in the binary-forking model for a
variety of fundamental problems, including sorting, semisorting, list ranking,
tree contraction, range minima, and ordered set union, intersection and
difference. In the binary-forking model, tasks can only fork into two child
tasks, but can do so recursively and asynchronously. The tasks share memory,
supporting reads, writes and test-and-sets. Costs are measured in terms of work
(total number of instructions), and span (longest dependence chain).
The binary-forking model is meant to capture both algorithm performance and
algorithm-design considerations on many existing multithreaded languages, which
are also asynchronous and rely on binary forks either explicitly or under the
covers. In contrast to the widely studied PRAM model, it does not assume
arbitrary-way forks nor synchronous operations, both of which are hard to
implement in modern hardware. While optimal PRAM algorithms are known for the
problems studied herein, it turns out that arbitrary-way forking and strict
synchronization are powerful, if unrealistic, capabilities. Natural simulations
of these PRAM algorithms in the binary-forking model (i.e., implementations in
existing parallel languages) incur an overhead in span. This
paper explores techniques for designing optimal algorithms when limited to
binary forking and assuming asynchrony. All algorithms described in this paper
are the first algorithms with optimal work and span in the binary-forking
model. Most of the algorithms are simple. Many are randomized
Towards Comprehensive Parametric Code Generation Targeting Graphics Processing Units in Support of Scientific Computation
The most popular multithreaded languages based on the fork-join concurrency model (CIlkPlus, OpenMP) are currently being extended to support other forms of parallelism (vectorization, pipelining and single-instruction-multiple-data (SIMD)). In the SIMD case, the objective is to execute the corresponding code on a many-core device, like a GPGPU, for which the CUDA language is a natural choice. Since the programming concepts of CilkPlus and OpenMP are very different from those of CUDA, it is desirable to automatically generate optimized CUDA-like code from CilkPlus or OpenMP.
In this thesis, we propose an accelerator model for annotated C/C++ code together with an implementation that allows the automatic generation of CUDA code. One of the key features of this CUDA code generator is that it supports the generation of CUDA kernel code where program parameters (like number of threads per block) and machine parameters (like shared memory size) are treated as unknown symbols. Hence, these parameters need not to be known at code-generation-time: machine parameters and program parameters can be respectively determined when the generated code is installed on the target machine. In addition, we show how these parametric CUDA programs can be optimized at compile-time in the form of a case discussion, where cases depend on the values of machine parameters (e.g. hardware resource limits) and program parameters (e.g. dimension sizes of thread-blocks). This generation of parametric CUDA kernels requires to deal with non-linear polynomial expressions during the dependence analysis and tiling phase. To achieve these algebraic calculations, we take advantage of techniques from computer algebra, in particular in the RegularChains library of Maple. Various illustrative examples are provided together with performance evaluation
Hardware Acceleration Technologies in Computer Algebra: Challenges and Impact
The objective of high performance computing (HPC) is to ensure that the computational power of hardware resources is well utilized to solve a problem. Various techniques are usually employed to achieve this goal. Improvement of algorithm to reduce the number of arithmetic operations, modifications in accessing data or rearrangement of data in order to reduce memory traffic, code optimization at all levels, designing parallel algorithms to reduce span are some of the attractive areas that HPC researchers are working on. In this thesis, we investigate HPC techniques for the implementation of basic routines in computer algebra targeting hardware acceleration technologies. We start with a sorting algorithm and its application to sparse matrix-vector multiplication for which we focus on work on cache complexity issues. Since basic routines in computer algebra often provide a lot of fine grain parallelism, we then turn our attention to manycore architectures on which we consider dense polynomial and matrix operations ranging from plain to fast arithmetic. Most of these operations are combined within a bivariate system solver running entirely on a graphics processing unit (GPU)
Data Oblivious Algorithms for Multicores
As secure processors such as Intel SGX (with hyperthreading) become widely adopted, there is a growing appetite for private analytics on big data. Most prior works on data-oblivious algorithms adopt the classical PRAM model to capture parallelism. However, it is widely understood that PRAM does not best capture realistic multicore processors, nor does it reflect
parallel programming models adopted in practice.
In this paper, we initiate the study of parallel data oblivious algorithms on realistic multicores, best captured by the binary fork-join model of computation. We first show that data-oblivious sorting can be accomplished by a binary fork-join algorithm with optimal total work and optimal (cache-oblivious) cache complexity, and in O(log n log log n) span (i.e., parallel time) that matches the best-known insecure algorithm. Using our sorting algorithm as a core primitive, we show how to data-obliviously simulate general PRAM algorithms in the binary fork-join model with non-trivial efficiency. We also present results for several applications including list ranking, Euler tour, tree contraction, connected components, and minimum spanning forest. For a subset of these applications, our data-oblivious algorithms asymptotically outperform the best known insecure algorithms. For other applications, we show data oblivious algorithms whose performance bounds match the best known insecure algorithms.
Complementing these asymptotically efficient results, we present a practical variant of our sorting algorithm that is self-contained and potentially implementable. It has optimal caching cost, and it is only a log log n factor off from optimal work and about a log n factor off in terms of span; moreover, it achieves small constant factors in its bounds
Efficient parallel processing with optical interconnections
With the advances in VLSI technology, it is now possible to build chips which can each contain thousands of processors. The efficiency of such chips in executing parallel algorithms heavily depends on the interconnection topology of the processors. It is not possible to build a fully interconnected network of processors with constant fan-in/fan-out using electrical interconnections. Free space optics is a remedy to this limitation. Qualities exclusive to the optical medium are its ability to be directed for propagation in free space and the property that optical channels can cross in space without any interference. In this thesis, we present an electro-optical interconnected architecture named Optical Reconfigurable Mesh (ORM). It is based on an existing optical model of computation. There are two layers in the architecture. The processing layer is a reconfigurable mesh and the deflecting layer contains optical devices to deflect light beams. ORM provides three types of communication mechanisms. The first is for arbitrary planar connections among sets of locally connected processors using the reconfigurable mesh. The second is for arbitrary connections among N of the processors using the electrical buses on the processing layer and N2 fixed passive deflecting units on the deflection layer. The third is for arbitrary connections among any of the N2 processors using the N2 mechanically reconfigurable deflectors in the deflection layer. The third type of communication mechanisms is significantly slower than the other two. Therefore, it is desirable to avoid reconfiguring this type of communication during the execution of the algorithms. Instead, the optical reconfiguration can be done before the execution of each algorithm begins. Determining a right configuration that would be suitable for the entire configuration of a task execution is studied in this thesis. The basic data movements for each of the mechanisms are studied. Finally, to show the power of ORM, we use all three types of communication mechanisms in the first O(logN) time algorithm for finding the convex hulls of all figures in an N x N binary image presented in this thesis
The Parallel Persistent Memory Model
We consider a parallel computational model that consists of processors,
each with a fast local ephemeral memory of limited size, and sharing a large
persistent memory. The model allows for each processor to fault with bounded
probability, and possibly restart. On faulting all processor state and local
ephemeral memory are lost, but the persistent memory remains. This model is
motivated by upcoming non-volatile memories that are as fast as existing random
access memory, are accessible at the granularity of cache lines, and have the
capability of surviving power outages. It is further motivated by the
observation that in large parallel systems, failure of processors and their
caches is not unusual.
Within the model we develop a framework for developing locality efficient
parallel algorithms that are resilient to failures. There are several
challenges, including the need to recover from failures, the desire to do this
in an asynchronous setting (i.e., not blocking other processors when one
fails), and the need for synchronization primitives that are robust to
failures. We describe approaches to solve these challenges based on breaking
computations into what we call capsules, which have certain properties, and
developing a work-stealing scheduler that functions properly within the context
of failures. The scheduler guarantees a time bound of in expectation, where and are the work and
depth of the computation (in the absence of failures), is the average
number of processors available during the computation, and is the
probability that a capsule fails. Within the model and using the proposed
methods, we develop efficient algorithms for parallel sorting and other
primitives.Comment: This paper is the full version of a paper at SPAA 2018 with the same
nam
- …