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108
The design and implementation of FFTW3
 Proceedings of the IEEE
, 2005
"... FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with handoptimized libraries, and describes the software structure that makes our cu ..."
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Cited by 393 (3 self)
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FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with handoptimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for realdata DFTs of prime size, a new way of implementing DFTs by means of machinespecific singleinstruction, multipledata (SIMD) instructions, and how a specialpurpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm. Keywords—Adaptive software, cosine transform, fast Fourier transform (FFT), Fourier transform, Hartley transform, I/O tensor.
Automated empirical optimizations of software and the ATLAS project
 PARALLEL COMPUTING
, 2001
"... This paper describes the automatically tuned linear algebra software (ATLAS) project, as well as the fundamental principles that underly it. ATLAS is an instantiation of a new paradigm in high performance library production and maintenance, which we term automated empirical optimization of software ..."
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Cited by 289 (36 self)
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This paper describes the automatically tuned linear algebra software (ATLAS) project, as well as the fundamental principles that underly it. ATLAS is an instantiation of a new paradigm in high performance library production and maintenance, which we term automated empirical optimization of software (AEOS); this style of library management has been created in order to allow software to keep pace with the incredible rate of hardware advancement inherent in Moore's Law. ATLAS is the application of this new paradigm to linear algebra software, with the present emphasis on the basic linear algebra subprograms (BLAS), a widely used, performancecritical,
SPIRAL: Code Generation for DSP Transforms
 PROCEEDINGS OF THE IEEE SPECIAL ISSUE ON PROGRAM GENERATION, OPTIMIZATION, AND ADAPTATION
, 2005
"... Abstract — Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performancecritical domain of linear digital sig ..."
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Cited by 140 (31 self)
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Abstract — Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performancecritical domain of linear digital signal processing (DSP) transforms. For a specified transform, SPIRAL automatically generates high performance code that is tuned to the given platform. SPIRAL formulates the tuning as an optimization problem, and exploits the domainspecific mathematical structure of transform algorithms to implement a feedbackdriven optimizer. Similar to a human expert, for a specified transform, SPIRAL “intelligently ” generates and explores algorithmic and implementation choices to find the best match to the computer’s microarchitecture. The “intelligence” is provided by search and learning techniques that exploit the structure of the algorithm and implementation space to guide the exploration and optimization. SPIRAL generates high performance code for a broad set of DSP transforms including the discrete Fourier transform, other trigonometric transforms, filter transforms, and discrete wavelet transforms. Experimental results show that the code generated by SPIRAL competes with, and sometimes outperforms, the best available human tuned transform library code. Index Terms — library generation, code optimization, adaptation, automatic performance tuning, high performance computing, linear signal transform, discrete Fourier transform, FFT, discrete cosine transform, wavelet, filter, search, learning, genetic and evolutionary algorithm, Markov decision process I.
Cacheoblivious Btrees
, 2000
"... Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of me ..."
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Cited by 134 (22 self)
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Abstract. This paper presents two dynamic search trees attaining nearoptimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the blocktransfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary blocktransfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of Θ(1+logB+1 N) memory transfers. This bound is also achieved by the classic Btree data structure on a twolevel memory hierarchy with a known blocktransfer size B. The first search tree supports insertions and deletions in Θ(1 + logB+1 N) amortized memory transfers, which matches the Btree’s worstcase bounds. The second search tree supports scanning S consecutive elements optimally in Θ(1 + S/B) memory transfers and supports insertions and deletions in Θ(1 + logB+1 N + log2 N) amortized memory transfers, matching the performance of the Btree for B = B Ω(log N log log N).
Sequoia: Programming the Memory Hierarchy
, 2006
"... We present Sequoia, a programming language designed to facilitate the development of memory hierarchy aware parallel programs that remain portable across modern machines featuring different memory hierarchy configurations. Sequoia abstractly exposes hierarchical memory in the programming model and p ..."
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Cited by 97 (7 self)
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We present Sequoia, a programming language designed to facilitate the development of memory hierarchy aware parallel programs that remain portable across modern machines featuring different memory hierarchy configurations. Sequoia abstractly exposes hierarchical memory in the programming model and provides language mechanisms to describe communication vertically through the machine and to localize computation to particular memory locations within it. We have implemented a complete programming system, including a compiler and runtime systems for Cell processorbased blade systems and distributed memory clusters, and demonstrate efficient performance running Sequoia programs on both of these platforms.
SPL: A Language and Compiler for DSP Algorithms
, 2001
"... We discuss the design and implementation of a compiler that translates formulas representing signal processing transforms into ecient C or Fortran programs. The formulas are represented in a language that we call SPL, an acronym from Signal Processing Language. The compiler is a component of the SPI ..."
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Cited by 80 (11 self)
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We discuss the design and implementation of a compiler that translates formulas representing signal processing transforms into ecient C or Fortran programs. The formulas are represented in a language that we call SPL, an acronym from Signal Processing Language. The compiler is a component of the SPIRAL system which makes use of formula transformations and intelligent search strategies to automatically generate optimized digital signal processing (DSP) libraries. After a discussion of the translation and optimization techniques implemented in the compiler, we use SPL formulations of the fast Fourier transform (FFT) to evaluate the compiler. Our results show that SPIRAL, which can be used to implement many classes of algorithms, produces programs that perform as well as \hardwired" systems like FFTW.
CacheOblivious Algorithms
, 1999
"... This thesis presents "cacheoblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cac ..."
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Cited by 78 (1 self)
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This thesis presents "cacheoblivious" algorithms that use asymptotically optimal amounts of work, and move data asymptotically optimally among multiple levels of cache. An algorithm is cache oblivious if no program variables dependent on hardware configuration parameters, such as cache size and cacheline length need to be tuned to minimize the number of cache misses. We show that the ordinary algorithms for matrix transposition, matrix multiplication, sorting, and Jacobistyle multipass filtering are not cache optimal. We present algorithms for rectangular matrix transposition, FFT, sorting, and multipass filters, which are asymptotically optimal on computers with multiple levels of caches. For a cache with size Z and cacheline length L, where Z =# (L 2 ), the number of cache misses for an m × n matrix transpose is #(1 + mn=L). The number of cache misses for either an npoint FFT or the sorting of n numbers is #(1 + (n=L)(1 + log Z n)). The cache complexity of computing n ...
SPIRAL: A Generator for PlatformAdapted Libraries of Signal Processing Algorithms
 Journal of High Performance Computing and Applications
, 2004
"... SPIRAL is a generator for libraries of fast software implementations of linear signal processing transforms. These libraries are adapted to the computing platform and can be reoptimized as the hardware is upgraded or replaced. This paper describes the main components of SPIRAL: the mathematical fra ..."
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Cited by 71 (20 self)
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SPIRAL is a generator for libraries of fast software implementations of linear signal processing transforms. These libraries are adapted to the computing platform and can be reoptimized as the hardware is upgraded or replaced. This paper describes the main components of SPIRAL: the mathematical framework that concisely describes signal transforms and their fast algorithms; the formula generator that captures at the algorithmic level the degrees of freedom in expressing a particular signal processing transform; the formula translator that encapsulates the compilation degrees of freedom when translating a specific algorithm into an actual code implementation; and, finally, an intelligent search engine that finds within the large space of alternative formulas and implementations
Optimizing the performance of sparse matrixvector multiplication
, 2000
"... Copyright 2000 by EunJin Im ..."
Telescoping languages: A strategy for automatic generation of scientific problemsolving systems from annotated libraries. www.netlib.org/utk/people/JackDongarra/PAPERS/ Telescope.pdf
, 2000
"... As machines and programs have become more complex, the process of programming applications that can exploit the power of highperformance systems has become more difficult and correspondingly more laborintensive. This has substantially widened the software gap the discrepancy between the need for n ..."
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Cited by 46 (7 self)
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As machines and programs have become more complex, the process of programming applications that can exploit the power of highperformance systems has become more difficult and correspondingly more laborintensive. This has substantially widened the software gap the discrepancy between the need for new software and the aggregate capacity of the workforce to produce it. This problem has been compounded by the slow growth of programming productivity, especially for highperformance programs, over the past two decades. One way to bridge this gap is to make it possible for end users to develop programs in highlevel domainspecific programming systems. In the past, a major impediment to the acceptance of such systems has been the poor performance of the resulting applications. To address this problem, we are developing a new compilerbased infrastructure, called