Efficient Function Evaluations with Lookup Tables for Structured Matrix Operations

Sobti, K.; Deng, Lanping; Chakrabarti, C.; Pitsianis, Nikos P.; Sun, Xiaobai; Kim, J.; Mangalagiri, Prasanth; Irick, Kevin; Kandemir, Mahmut; Narayanan, V.

doi:10.1109/sips.2007.4387592

Cited by 11 publications

(11 citation statements)

References 3 publications

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“…The work in [3] supports a larger set of functions with small-order polynomial, including sine, cosine, exponential, Gamma and Bessel functions, but for fixed-point data. In particular, the Taylor expansion polynomial is employed in the following literature, [1], [2], [5], [7], [8], [9], and [10]. Takagi [5] presents an optimization method for power function x p by utilizing one multiplier, while Cody et al [7] extend the work to exponential, central Bessel and Gamma functions with consideration of truncation error.…”

Section: Related Workmentioning

confidence: 99%

A special-purpose compiler for look-up table and code generation for function evaluation

Zhang¹,

Deng²,

Yedlapalli³

et al. 2010

2010 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE 2010)

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Abstract-Elementary functions are extensively used in computer graphics, signal and image processing, and communication systems. This paper presents a special-purpose compiler that automatically generates customized look-up tables and implementations for elementary functions under user given constraints. The generated implementations include a C/C++ code that can be used directly by applications running on multicores, as well as a MATLAB-like code that can be translated directly to a hardware module on FPGA platforms. The experimental results show that our solutions for function evaluation bring significant performance improvements to applications on multicores as well as significant resource savings to designs on FPGAs.

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Section: Related Workmentioning

confidence: 99%

A special-purpose compiler for look-up table and code generation for function evaluation

Zhang¹,

Deng²,

Yedlapalli³

et al. 2010

2010 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE 2010)

View full text Add to dashboard Cite

show abstract

“…This LUT approach has been used for evaluating trigonometric functions, square-root extraction, logarithmic and exponential function, and more complex functions such as the Bessel functions. Details can be found in [31].…”

Section: Algorithm Optimizermentioning

confidence: 99%

“…For general N-body simulations, the change in particle coordinates with time is incremental, and re-partitioning is not done until the particles travel beyond the tile boundaries. Details for GT have been provided in our earlier paper [31]. Figure 4 shows the numerical ranges of the input samples in each tile after applying PT and GT.…”

Section: Interaction Matrix Tilingmentioning

confidence: 99%

“…When tiled intelligently, this can result in good performance with respect to accuracy while reducing the hardware resource requirement. Additional details are included in [31], [32].…”

Section: Data Traversalmentioning

confidence: 99%

“…With GT, the dynamic range of the numerical values in each tile is restricted and thus only one segment of the table needs to be loaded for processing a tile. In contrast, if PT is used, each tile exhibits roughly the entire dynamic range and thus the complete table would have to be available [31].…”

Section: Examplesmentioning

confidence: 99%

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An Automated Framework for Accelerating Numerical Algorithms on Reconfigurable Platforms Using Algorithmic/Architectural Optimization

Kim

Deng

Mangalagiri

et al. 2009

IEEE Trans. Comput.

Self Cite

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Abstract-This paper describes TANOR, an automated framework for designing hardware accelerators for numerical computation on reconfigurable platforms. Applications utilizing numerical algorithms on large-size data sets require high-throughput computation platforms. The focus is on N-body interaction problems which have a wide range of applications spanning from astrophysics to molecular dynamics. The TANOR design flow starts with a MATLAB description of a particular interaction function, its parameters, and certain architectural constraints specified through a graphical user interface. Subsequently, TANOR automatically generates a configuration bitstream for a target FPGA along with associated drivers and control software necessary to direct the application from a host PC. Architectural exploration is facilitated through support for fully custom fixed-point and floating point representations in addition to standard number representations such as single precision floating point. Moreover, TANOR enables joint exploration of algorithmic and architectural variations in realizing efficient hardware accelerators. TANOR's capabilities have been demonstrated for three different N-body interaction applications: the calculation of gravitational potential in astrophysics, the diffusion or convolution with Gaussian kernel common in image processing applications, and the force calculation with vector-valued kernel function in molecular dynamics simulation. Experimental results show that TANOR-generated hardware accelerators achieve lower resource utilization without compromising numerical accuracy, in comparison to other existing custom accelerators.

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An optimization‐based approach to lookup table program transformations

Wilcox

Strout

Bieman

2013

J Software Evolu Process

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Scientific programmers can improve the performance of function evaluation by precomputing and storing results in a lookup table (LUT), thereby replacing costly evaluation code with an inexpensive memory access. A code transformation that replaces computation with LUT code can improve performance; however, accuracy is reduced because of error inherent in reconstructing values from LUT data. LUTs are commonly used to approximate expensive elementary functions. The current practice is for software developers to: (i) manually identify expressions that can benefit from an LUT; (ii) modify the code by hand to implement the LUT transformation; and (iii) run experiments to determine if the resulting error is within application requirements. This approach reduces productivity, obfuscates code, and limits programmer control over accuracy and performance. We propose source code analysis and program transformation to substantially automate LUT transformations. Our approach uses a novel optimization algorithm that selects Pareto optimal sets of expressions that benefit most from an LUT, on the basis of the error and performance estimates. We demonstrate our methodology with the Mesa tool, which achieves speedups of 1.4–6.8× on scientific codes with an acceptable loss of accuracy. Our tool makes the programmer more productive and facilitates finding effective LUT transformations. Copyright © 2013 John Wiley & Sons, Ltd.

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Efficient Function Evaluations with Lookup Tables for Structured Matrix Operations

Cited by 11 publications

References 3 publications

A special-purpose compiler for look-up table and code generation for function evaluation

A special-purpose compiler for look-up table and code generation for function evaluation

An Automated Framework for Accelerating Numerical Algorithms on Reconfigurable Platforms Using Algorithmic/Architectural Optimization

An optimization‐based approach to lookup table program transformations

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