在數位訊號處理過程中，常常會使用到可以運算特定函數的硬體單元，例如：求倒數、開根號、取指數或對數…等運算。一般說來通常採用以查表為主的函數近似方法來實作，如此可避免因為運算繁雜而導致效能不佳，但是隨著精準度提高，表格所占的面積卻將大幅增加。本論文透過非等份切割法，切割表格後再將表格重排，以取得可較節省面積的對應方式，此方法針對函數近似演算法加以改良，可有效減少表格面積及額外的硬體負擔。

In many digital signal processing applications, we often need some special function
units that can compute complicated arithmetic functions such as reciprocal, logarithm, power of 2, trigonometric functions, etc. The most popular designs are based on look-up tables with polynomial approximation. However, the table size will increase significantly in accordance with precision. In this thesis, we propose a method called remapping to reduce the table size by using non-uniform segmentation. When we obtain the coefficients for all segments, we do not store them in order. By sorting the coefficients in the ROM ,we design a efficient hardware mapping. The method can reduce the ROM size with lower extra cost spent in address mapping for non-uniform segmentation.

Chapter 1 導論 8
1.1 研究動機 8
1.2 論文架構 9
Chapter 2 研究背景與相關研究 10
2.1 函數近似方法分類 10
2.2 查表法(Table-lookup Methods) 11
2.3 Bipartite and Multipartite Table Methods 13
2.3.1 Bipartite Methods 13
2.3.2 Multipartite Methods 16
2.4 Table-polynomial Methods 18
2.4.1 Uniform Piecewise Methods 19
2.4.2 Non-uniform Piecewise Methods 24
2.5 Interpolation Methods 29
Chapter 3 Remapping Method 31
3.1 方法概述 31
3.2 架構設計 39
3.3 誤差分析以及bit width最佳化 44
Chapter 4 實驗結果以及比較 49
4.1 演算法之分析比較 49
4.2 面積以及速度之評估 51
Chapter 5 結論及未來展望 60
5.1 結論 60
5.2 未來展望 61
參考文獻 62

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