@techreport{oai:ipsj.ixsq.nii.ac.jp:00027073,
 author = {永山, 忍 and 笹尾, 勤 and JonT．Butler and Shinobu, NAGAYAMA and TsutomuSASAO and JonT.BUTLER},
 issue = {4(2006-SLDM-123)},
 month = {Jan},
 note = {本稿は，三角関数，対数関数，平方根演算，逆数演算などの関数を計算する数値計算回路の構成とその自動合成法を提案する．本数値計算回路は，LUT（Look-UpTable）カスケードを用いて，与えられた定義域を不等区間に分割し，数値関数を各区間毎に二次多項式で近似する．不等区間分割，LUTカスケード，そして二次近似法を用いることで，変化の激しい多様な関数に対しても，従来法よりコンパクトに実現できる．実験により以下を示す：1）本数値計算回路は，線形近似法（不等区間分割）に基づく数値計算回路の4％のメモリ量で実現できる．2）本数値計算回路は，5次近似法（等区間分割）に基づく数値計算回路の22％のメモリ量で実現できる．3）本合成法では，高精度（24ビット精度）数値計算回路を従来法より小規模なFPGAで実現できる．, This paper presents an architecture and a synthesis method for programmable numerical function generators (NFGs) for trigonometric, logarithmic, square root, and reciprocal 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. By using non-uniform segmentation, LUT cascade, and quadratic approximation, we can implement more compact NFGs than the existing methods for a wide range of functions. Implementation results on an FPGA show that: 1) our NFGs require only 49To of the memory needed by NFGs based on the linear approximation with non-uniform segmentation; 2) our NFGs require only 22% of the memory needed by NFGs based on the 5th-order approximation with uniform segmentation; and 3) our high-precision NFGs can be implemented with a compact and low-cost FPGA. Our automatic synthesis system generates such compact NFGs quickly.},
 title = {二次近似法に基づくプログラマブル数値計算回路の構成とその合成法},
 year = {2006}
}