This 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 2x-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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Shinobu NAGAYAMA, Tsutomu SASAO, Jon T. BUTLER, "Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method" in IEICE TRANSACTIONS on Fundamentals,
vol. E89-A, no. 12, pp. 3510-3518, December 2006, doi: 10.1093/ietfec/e89-a.12.3510.
Abstract: This 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 2x-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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.12.3510/_p
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@ARTICLE{e89-a_12_3510,
author={Shinobu NAGAYAMA, Tsutomu SASAO, Jon T. BUTLER, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method},
year={2006},
volume={E89-A},
number={12},
pages={3510-3518},
abstract={This 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 2x-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.},
keywords={},
doi={10.1093/ietfec/e89-a.12.3510},
ISSN={1745-1337},
month={December},}
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TY - JOUR
TI - Compact Numerical Function Generators Based on Quadratic Approximation: Architecture and Synthesis Method
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 3510
EP - 3518
AU - Shinobu NAGAYAMA
AU - Tsutomu SASAO
AU - Jon T. BUTLER
PY - 2006
DO - 10.1093/ietfec/e89-a.12.3510
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2006
AB - This 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 2x-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.
ER -