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研究生:黃上峰
研究生(外文):Sang-Feng Huang
論文名稱:可360度旋轉之數位重覆運算CORDIC電路之設計
論文名稱(外文):VLSI Design of Digital-Recurrent CORDIC with Full Rotation Range
指導教授:郭耀煌郭耀煌引用關係
指導教授(外文):Yau-Hwang Kuo
學位類別:碩士
校院名稱:國立成功大學
系所名稱:資訊工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:英文
論文頁數:92
中文關鍵詞:CORDICdouble rotation CORDIC全方位角度線上轉換數字平行輸入依序輸出封包方式輸入與輸出三角函數超大型積體電路
外文關鍵詞:CORDICdouble rotation CORDICfull rotation rangeon-line number translationparallel input and series outputpacket-formatted I/Otrigonometric functionsVLSI
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本篇論文分析3D圖學與虛擬實境的運算需求。依照這些運算需求,我們亦針對多媒體硬體處理器的計算能力進行分析,發現現存媒體器在支援3D圖學及虛擬實境應用仍有不足現象。為了符合3D多媒體的運算需求,我們乃進一步提出一個具有高度集積特性的媒體處理器架構。這個媒體處理器乃基於NSC98微處理器架構修正而來。所以它擁有一個RISC core及多個特殊功能單元。其中用來支援3D運算的主力在於多媒體運算單元及CORDIC運算單元。前者和Intel MMX相容,但另外新增五個指令以提高3D運算效能。CORDIC單元用來執行需要長時間運算的指令,如三角函數的計算等。
在CORDIC單元的電路設計上,我們亦提出若干新技巧,使其效能及成本皆可達到完善。首先我們修正double rotation CORDIC演算法,使其能夠在360度全角度範圍計算三角函數。其次為了增進電路效能與降低電路成本,我們使用了封包方式的輸出與輸入方式。另外為了降低數字表示法轉換的時間,我們使用線上(on-line)方式轉換數字表示法。
所有電路設計都以Verilog語言寫成,並且使用COMPASS 0.35μm元件庫和Synopsys設計輔助工具來合成電路,到目前為止,我們已完成了邏輯電路的合成與時序的模擬,並將送國科會CIC製作。

In this thesis, the computation requirements of 3D graphics and virtual reality are analyzed. According to the computation requirements, some existing architectures of multimedia hardware, for example, the Microsoft Talisman and NSC98 microprocessor, are compared. Obviously, their capability can not sufficiently support 3D graphics computations. To satisfy the computation requirements of 3D multimedia applications, we propose an architecture of highly integrated media processor which is extended from the micro-architecture of NSC98. This architecture consists of a RISC core and some special functional units. In this architecture, most multimedia operations are performed on a Multimedia Functional Unit (MFU), which is Intel MMX compatible. But, to speed up the performance of multimedia computation, we develop another five new instructions to be included into the Intel MMX compatible instruction set. Besides, a CORDIC unit responsible for executing the instructions with long latency is also developed. In this thesis, we focus on the circuit design of CORIDC unit that calculates the triangular functions.
In the design of CORDIC unit, we propose three novel ideas to obtain an excellent solution. First, we modify the double rotation CORDIC algorithm to work on 360-degree full rotation range. It is important for supporting image-based VR computations in a high-performance manner. Second, to enhance performance and reduce circuit cost, the scheme of packed-formatted I/O is adopted. Third, an on-line number translation scheme is applied to reduce number translation time.
In this thesis, the CORDIC unit is modeled by Verilog language, and the COMPASS 0.35μm cell library and Synopsys EDA tool are adopted to synthesize the CORDIC circuit. Until now, we have accomplished logic circuit thesis and timing simulation takes of the CORDIC unit. Then, it will be delivered to Chip Implementation Center at National Science Council for IC prototyping.

LIST OF TABLES
LIST OF FIGURES
CHAPTER 1 INTRODUCTION
1.1 BACKGROUND AND MOTIVATION
1.2 THESIS ORGANIZATION
CHAPTER 2 ARCHITECTURE OF HIGHLY INTEGRATED MEDIA PROCESSOR
2.1 COMPUTATIONAL REQUIREMENTS OF 3D GRAPHICS
2.1.1 Database Traversal
2.1.2 Front-end (Geometric Processing)
2.1.3 Rasterization
2.2 COMPUTATIONAL REQUIREMENTS OF IMAGE-BASED VR
2.3 ANALYSIS OF MEDIA PROCESSORS
2.3.1 Microsoft Talisman Architecture
2.3.2 NSC98 Microprocessor
2.4 THE PROPOSED ARCHITECTURE FOR HIGHLY INTEGRATED MEDIA PROCESSOR
2.4.1 CORDIC Unit
2.4.2 MFU
2.4.3 Enhanced Instruction Set
CHAPTER 3 CORDIC BASED ALGORITHMS
3.1 CORDIC (COORDINATE ROTATION DIGITAL COMPUTER) ALGORITHM
3.2 REDUNDANT CORDIC ALGORITHM
3.3 ON-LINE CORDIC ALGORITHM
3.4 CORRECTING ROTATION CORDIC ALGORITHM
3.5 DOUBLE ROTATION CORDIC ALGORITHM
3.6 OTHER CORDIC ALGORITHMS
CHAPTER 4 ARCHITECTURE DESIGN OF CORDIC CIRCUIT
4.1 MODIFIED DOUBLE ROTATION CORDIC ALGORITHM FOR FULL ROTATION RANGE
4.1.1 Adopting tan-1(2-0) as the starting rotation angle
4.1.2 Moving the starting point to be at 180 degree
4.2 I/O INTERFACE OF THE CORDIC UNIT
4.2.1 Packet-formatted I/O
4.3 ON-LINE NUMBER TRANSLATION
4.4 DETAILED ARCHITECTURE OF THE COMPONENTS IN CORDIC UNIT
4.4.1 Architecture of Preprocessing Sub-unit
4.4.2 Architecture of Residual Angle Computation Sub-unit
4.4.3 Architecture of X & Y Components Computation Sub-unit
4.4.4 Architecture of Post-processing Sub-unit
4.3.5 Controller Sub-unit
CHAPTER 5 MODELING AND IMPLEMENTATION OF CORDIC CIRCUIT
5.1 DESIGN METHODOLOGY
5.2 DESIGN SKILLS
5.2.1 Redundant Number System
5.2.2 Decision the Pair (Pi, Qi)
5.2.3 Z Component Normalization
5.2.4 Redundant Number Adder
5.2.5 Shifter
5.2.6 X and Y Components Normalization
5.2.7 Number Translation
5.3 SYNTHESIS AND SIMULATION RESULTS
CHAPTER 6 CONCLUSION AND FUTURE WORKS
6.1 CONCLUSION
6.2 FUTURE WORKS
REFERENCES
APPENDIX A RTL CODE OF CORDIC UNIT
APPENDIX B SYNTHESIS RESULTS
APPENDIX C SIMULATION RESULTS

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