Programmable Numerical Function Generators for Two-Variable Functions

Nagayama, Shinobu; Butler, Jon T.; Sasao, Tsutomu

doi:10.1109/dsd.2008.27

Cited by 4 publications

(3 citation statements)

References 18 publications

(15 reference statements)

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“…Since the comparator and multiplexers operate in parallel with the segment index encoder, there is no speed penalty due to these additional circuits. Table 1 compares the number of segments needed for the bilinear interpolation method with that for the tangent plane approximation 1 [9] for various functions. For those functions that are symmetric, Table 1 shows the number of symmetric segments.…”

Section: Theorem 1 the Segmentation Of A Symmetric Function Produced mentioning

confidence: 99%

“…Consider the design of the LUT cascade and adders in Fig. 2(b), given the segmentation produced by the algorithm in [9]. We begin by representing the segment index function using a multi-terminal BDD (MTBDD) [1].…”

Section: Segmentsmentioning

confidence: 99%

“…Thus, effective segmentation algorithms are needed to achieve fast and compact NFGs. We use a recursive planar segmentation algorithm [9] (based on bilinear interpolation).…”

Section: Polynomial Approximation Using Bilinear Interpolationmentioning

confidence: 99%

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Numerical function generators using bilinear interpolation

Nagayama

Sasao

Butler

2008

2008 International Conference on Field Programmable Logic and Applications

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Two-variable numerical functions are widely used in various applications, such as computer graphics and digital signal processing. Fast and compact hardware implementations are required. This paper introduces the bilinear interpolation method to produce fast and compact numerical function generators (NFGs) for two-variable functions. This paper also introduces a design method for symmetric two-variable functions. This method can reduce the memory size needed for symmetric functions by nearly half with small speed penalty. Experimental results show that the bilinear interpolation method can significantly reduce the memory size needed for two-variable functions, and the speed of NFGs based on the bilinear method is comparable to that of NFGs based on tangent plane approximation. For a complicated function, our NFG is faster and more compact than a circuit designed using a one-variable NFG.

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Section: Theorem 1 the Segmentation Of A Symmetric Function Produced mentioning

confidence: 99%

Section: Segmentsmentioning

confidence: 99%

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Numerical function generators using bilinear interpolation

Nagayama

Sasao

Butler

2008

2008 International Conference on Field Programmable Logic and Applications

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A Design Method for Programmable Two-Variable Discrete Function Generators Using Spline and Bilinear Interpolations

Nakano¹,

Wakaba

Nagayama

et al. 2011

2011 14th Euromicro Conference on Digital System Design

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Numeric Function Generators

Butler¹,

Sasao

Nagayama

2009

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We show the architecture and design of a numeric function generator that realizes, at high speed, arithmetic functions, like log x, sin x, 1 x , etc.. This approach is general; different circuits are not needed for different functions. Further, composite functions, like log (sin (1 x)) can be realized as easily as individual functions. A tutorial description of the method is presented, followed by descriptions of the design considerations that must be made. For example, we discuss how circuit complexity increases as the desired approximation error decreases. Also, we discuss enhancements of the basic numeric function generator approach, including higher order polynomial approximations, floating point, and multi-variable implementations. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Programmable Numerical Function Generators for Two-Variable Functions

Cited by 4 publications

References 18 publications

Numerical function generators using bilinear interpolation

Numerical function generators using bilinear interpolation

A Design Method for Programmable Two-Variable Discrete Function Generators Using Spline and Bilinear Interpolations

Numeric Function Generators

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