浮點運算器設計

Abstract

本論文目的在設計一高性能之浮點計算處理器架構, 其可有效的達到 快速及多功能計算, 除了基本的四則浮點運算外, 其將能快速執行多種工 程運用及電腦繪圖幾何座標轉換之基本函數計算, 如三角函數, 超越函 數, 指數函數, 及如上函數之反函數等等. 我們主要是討論 Intel Pentium 處理器中超越函數指令運算, 期能設計出在指令及精確 度上與 X86 相容的浮點運算處理器, 函數計算採用 Table-driven 演算 法. 已建立函數所需的 table, 列於附錄之中. 經由程式模擬的結果, 在 速度與精確度上已有相當不錯的成果. 另外於第四章討論 CORDIC 演算法的旋轉模式, 來計算 sinh(x), cosh( x) 等函數 ,在 Redundant CORDIC 的架構上採用 on-line 比例因數分解 的演算法,藉由快速分解出比例因數的連乘項參數, 而不須保持比例因數 為常數, 並且能快速地作比例因數補償. In this thesis, a high performance floating-point architecture is designed. It can execute multi-functions in a small compatible hardware. The floating-point unit can perform versatile functions such as triangular , hyperbolic ,exponential functions and their inverse functions. The floating-point unit employes table-driven algorithms. It is compatibleto Intel Pentium FPU.The necessary tables of table- driven algorithms have beenestablished. The detail contents of the tables are given in appendix A. Simu-lations of these functions verify the correctness of these functions and theirspeed are comparable to those of the Pentium floating-point unit. In addtion, to compute functions of sinh( x) and cosh(x),an efficient vari-able scale factor compensation for the redundant CORDIC is discussed. By on-line decompositon of the complicated variable scale factor, we can easily do variable scale factor compensation by simply performing shift- and-add opera-tions for the redundant CORDIC.