Non-uniform Segmentation for Hardware Function Evaluation

Lee, Dong-U; Luk, Wayne; Villasenor, John; Cheung, Peter Y. K.

doi:10.1007/978-3-540-45234-8_77

Cited by 27 publications

(32 citation statements)

References 11 publications

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“…For a given error, non-uniform segmentation of the domain uses fewer segments than uniform segmentation [9], [18]. However, a non-uniform segmentation requires an additional circuit that maps values of x to a segment number.…”

Section: Piecewise Quadratic Approximationmentioning

confidence: 99%

“…Potentially, this is a complex circuit. To simplify the additional circuit, Lee et al [9] have proposed a special non-uniform segmentation for the √ − ln(x) function. Their method produces a simple circuit by restricting the segmentation points, and results in fewer segments as well as faster and more compact NFG than produced by uniform segmentation.…”

Section: Piecewise Quadratic Approximationmentioning

confidence: 99%

“…Although NFGs based on non-uniform segmentation have a smaller coefficients table than those based on uniform segmentation, the size of segment index encoder may have to be considered to provide a fair comparison. In [9], to simplify the segment index encoder, a special non-uniform segmentation is used for √ − ln(x). However, it does not correspond to an optimum segmentation.…”

Section: Architecture For Nfgsmentioning

confidence: 99%

“…To reduce the number of bits for c 2i and c 1i , we use a scaling method [9]. We represent c 2i and c 1i as c 2i × 2 −l 2i × 2 l 2i and c 1i × 2 −l 1i × 2 l 1i , respectively.…”

Section: Reduction Of the Size Of The Multipliermentioning

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%

See 4 more Smart Citations

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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Section: Piecewise Quadratic Approximationmentioning

confidence: 99%

Section: Piecewise Quadratic Approximationmentioning

confidence: 99%

Section: Architecture For Nfgsmentioning

confidence: 99%

“…To reduce the number of bits for c 2i and c 1i , we use a scaling method [9]. We represent c 2i and c 1i as c 2i × 2 −l 2i × 2 l 2i and c 1i × 2 −l 1i × 2 l 1i , respectively.…”

Section: Reduction Of the Size Of The Multipliermentioning

confidence: 99%