Functional evaluation is one of key arithmetic operations in many applications including 3D graphics and stereo. Among various designs of hardware-based function evaluators, piecewise polynomial approximation methods are the most popular which interpolate the piecewise function curve in a sub-interval using polynomials with polynomial coefficients of each sub-interval stored in an entry of a ROM. The conventional piecewise methods usually determine the bit-widths of each ROM entry and multipliers and adders by analyzing the various error sources, including polynomial approximation errors, coefficient quantization errors, truncation errors of arithmetic operations, and the final rounding error. In this thesis, we present a new piecewise function evaluation design by considering all the error sources together. By combining all the error sources during the approximation, quantization, truncation and rounding, we can efficiently reduce the area cost of ROM and the corresponding arithmetic units. The proposed method is applied to piecewise function evaluators of both uniform and non-uniform segmentation.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0830111-144139 |
| Date | 30 August 2011 |
| Creators | Tseng, Yu-ling |
| Contributors | Ming-Chih Chen, Shiann-Rong Kuang, Chen Chung-Ho, Shen-Fu Hsiao, Yun-Nan Chang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0830111-144139 |
| Rights | user_define, Copyright information available at source archive |
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