Approximating elementary functions with symmetric bipartite tables

Schulte, Michael; Stine, James E.

doi:10.1109/12.795125

Cited by 140 publications

(112 citation statements)

References 24 publications

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“…3 from the EVMDD. Since our NFG directly realizes the function table, it is more accurate than existing NFGs using polynomial approximation [7], [16], [25], [30], [31].…”

Section: Design Methods For Nfgs Using Evmddsmentioning

confidence: 99%

“…Various design methods for numeric function generators (NFGs) have been developed [18]. However, most existing methods are intended for one-variable numeric functions [7], [16], [21], [25], [29]- [31], and only a few methods have been reported for specific multi-variable numeric functions [9], [10], [34]. Thus, different numeric functions require different methods.…”

Section: Introductionmentioning

confidence: 99%

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A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Nagayama

Sasao

Butler

2010

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edgevalued multiple-valued decision diagram (EVMDD), and shows a systematic design method based on the EVMDD. To achieve a design, we characterize a numeric function f by the values of l and p for which f is an l-restricted Mp-monotone increasing function. Here, l is a measure of subfunctions of f and p is a measure of the rate at which f increases with an increase in the dependent variable. For the special case of an EVMDD, the EVBDD, we show an upper bound on the number of nodes needed to realize an l-restricted Mp-monotone increasing function. Experimental results show that all of the two-variable numeric functions considered in this paper can be converted into an l-restricted Mp-monotone increasing function with p = 1 or 3. Thus, they can be compactly realized by EVBDDs. Since EVMDDs have shorter paths and smaller memory size than EVBDDs, EVMDDs can produce fast and compact NFGs. key words: two-variable numeric function generators (NFGs), edgevalued multiple-valued decision diagrams (EVMDDs), edge-valued binary decision diagrams (EVBDDs), graph-based representation of numeric functions, programmable memory-based architecture

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“…3 from the EVMDD. Since our NFG directly realizes the function table, it is more accurate than existing NFGs using polynomial approximation [7], [16], [25], [30], [31].…”

Section: Design Methods For Nfgs Using Evmddsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Nagayama

Sasao

Butler

2010

IEICE Trans. Inf. & Syst.

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“…In hardware implementation of polynomial approximations, the size of the multipliers is a major concern. Several solutions have been investigated to limit their size: argument reduction and series expansions in [1], small table and a modified multiplication in [2], or the multipartite tables method [3,4].…”

Section: Hardware Operators For Function Evaluation Using Sparse-coefmentioning

confidence: 99%

Hardware operators for function evaluation using sparse-coefficient polynomials

et al. 2006

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“…For piecewise polynomial approximations, in many cases, the domain is partitioned into uniform segments [2]- [4], [21], [22]. Such methods are simple and fast, but for some kinds of numerical functions, too many segments are required, resulting in large memory.…”

Section: Piecewise Quadratic Approximationmentioning

confidence: 99%

“…To reduce the memory size, polynomial approximations have been used [9], [10], [21], [22]. These methods approximate the given numerical functions by piecewise polynomials, and realize the polynomials with hardware.…”

Section: Introductionmentioning

confidence: 99%

Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

Nagayama¹,

Sasao²,

Butler³

2006

IEICE Transactions on Fundamentals of Electronics, Communicatio

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SUMMARYThis paper presents an architecture and a synthesis method for compact numerical function generators (NFGs) for trigonometric, logarithmic, square root, reciprocal, and combinations of these functions. Our NFG partitions a given domain of the function into non-uniform segments using an LUT cascade, and approximates the given function by a quadratic polynomial for each segment. Thus, we can implement fast and compact NFGs for a wide range of functions. Experimental results show that: 1) our NFGs require, on average, only 4% of the memory needed by NFGs based on the linear approximation with non-uniform segmentation; 2) our NFG for 2 x − 1 requires only 22% of the memory needed by the NFG based on a 5th-order approximation with uniform segmentation; and 3) our NFGs achieve about 70% of the throughput of the existing table-based NFGs using only a few percent of the memory. Thus, our NFGs can be implemented with more compact FPGAs than needed for the existing NFGs. Our automatic synthesis system generates such compact NFGs quickly.

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Approximating elementary functions with symmetric bipartite tables

Cited by 140 publications

References 24 publications

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

A Systematic Design Method for Two-Variable Numeric Function Generators Using Multiple-Valued Decision Diagrams

Hardware operators for function evaluation using sparse-coefficient polynomials

Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method

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