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199
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 hand-optimized libraries, and describes the software structure that makes our cu ..."
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Cited by 726 (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 hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.
SPIRAL: Code Generation for DSP Transforms
- PROCEEDINGS OF THE IEEE SPECIAL ISSUE ON PROGRAM GENERATION, OPTIMIZATION, AND ADAPTATION
"... 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 performance-critical domain of linear digital signal proces ..."
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Cited by 222 (41 self)
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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 performance-critical 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 domain-specific mathematical structure of transform algorithms to implement a feedback-driven 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.
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 156 (9 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 processor-based 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 102 (10 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 \hard-wired" systems like FFTW.
Cache-oblivious algorithms
, 1999
"... requirements for the degree of Master of Science. This thesis presents "cache-oblivious " 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 ..."
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Cited by 85 (1 self)
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requirements for the degree of Master of Science. This thesis presents "cache-oblivious " 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 cache-line length need to be tuned to minimize the number of cache misses. We show that the ordinary algorithms for matrix transposition, matrix multi-plication, sorting, and Jacobi-style multipass filtering are not cache optimal. We present algorithms for rectangular matrix transposition, FFT, sorting, and multi-pass filters, which are asymptotically optimal on computers with multiple levels of caches. For a cache with size Z and cache-line length L, where Z = (L2), the number of cache misses for an m x n matrix transpose is E(1 + mn/L). The number of cache misses for either an n-point FFT or the sorting of n numbers is 0(1 + (n/L)(1 + logzn)). The cache complexity of computing n time steps of a Jacobi-style multipass filter on an array of size n is E(1 + n/L + n2 /ZL). We also give an 8(mnp)-work algorithm to multiply an m x n matrix by an n x p matrix
SPIRAL: A Generator for Platform-Adapted 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 re-optimized as the hardware is upgraded or replaced. This paper describes the main components of SPIRAL: the mathematical fra ..."
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Cited by 85 (21 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 re-optimized 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
Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software
- SIAM REVIEW VOL. 46, NO. 1, PP. 3–45
, 2004
"... Matrix computations are both fundamental and ubiquitous in computational science and its vast application areas. Along with the development of more advanced computer systems with complex memory hierarchies, there is a continuing demand for new algorithms and library software that efficiently utilize ..."
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Cited by 81 (6 self)
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Matrix computations are both fundamental and ubiquitous in computational science and its vast application areas. Along with the development of more advanced computer systems with complex memory hierarchies, there is a continuing demand for new algorithms and library software that efficiently utilize and adapt to new architecture features. This article reviews and details some of the recent advances made by applying the paradigm of recursion to dense matrix computations on today’s memory-tiered computer systems. Recursion allows for efficient utilization of a memory hierarchy and generalizes existing fixed blocking by introducing automatic variable blocking that has the potential of matching every level of a deep memory hierarchy. Novel recursive blocked algorithms offer new ways to compute factorizations such as Cholesky and QR and to solve matrix equations. In fact, the whole gamut of existing dense linear algebra factorization is beginning to be reexamined in view of the recursive paradigm. Use of recursion has led to using new hybrid data structures and optimized superscalar kernels. The results we survey include new algorithms and library software implementations for level 3 kernels, matrix factorizations, and the solution of general systems of linear equations and several common matrix equations. The software implementations we survey are robust and show impressive performance on today’s high performance computing systems.
Optimizing the performance of sparse matrix-vector multiplication
, 2000
"... Copyright 2000 by Eun-Jin Im ..."
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Combining models and guided empirical search to optimize for multiple levels of the memory hierarchy
- In International Symposium on Code Generation and Optimization
, 2005
"... This paper describes an algorithm for simultaneously optimizing across multiple levels of the memory hier-archy for dense-matrix computations. Our approach combines compiler models and heuristics with guided empirical search to take advantage of their comple-mentary strengths. The models and heurist ..."
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Cited by 56 (10 self)
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This paper describes an algorithm for simultaneously optimizing across multiple levels of the memory hier-archy for dense-matrix computations. Our approach combines compiler models and heuristics with guided empirical search to take advantage of their comple-mentary strengths. The models and heuristics limit the search to a small number of candidate implementa-tions, and the empirical results provide the most accu-rate information to the compiler to select among can-didates and tune optimization parameter values. We have developed an initial implementation and applied this approach to two case studies, Matrix Multiply and Jacobi Relaxation. For Matrix Multiply, our results on two architectures, SGI R10000 and Sun UltraSparc IIe, outperform the native compiler, and either outper-form or achieve comparable performance as the ATLAS self-tuning library and the hand-tuned vendor BLAS li-brary. Jacobi results also substantially outperform the native compilers. 1
