當今應用之大量運算，以其硬體技術之革新。運算之繁重，效能優化愈發重要。當今編譯器研究，在消滅冗餘運算，然則時有功敗垂成，譬如部分冗餘消滅(PRE)。其主因在於節點與節點間，編譯信息傳遞練之斷裂。而向量之介入，情勢急轉直下，以其天生之swizzle運算。
當此，於此篇論文，提出PREDAF以當PRE問題。PREDAF且得類同信息於全值分析(GVN)，該以珈吉(Karthik Gargi)之法以營之。於PRE問題，導入資料存取函式(DAF)以經之，且衍其純量型式。當其為符號判讀之際，PREDAF遣DAF以當其運算，而得之以其理。惟PRE之發掘，以上浮移動(Hoist Code Motion)以應之。
PREDAF成之於LLVM 7。以LLVM測試案例檢驗PRE，以疑難雜症證實向量swizzle效應。PRE之測驗，得之以18.37%與7%之程式碼降低，比之於原本，以及New GVN；至於向量，而得之以49.52%與46.19%之程式碼降低，較之與原本，以及New GVN。實驗之結果，驗證PREDAF之有效性。

Modern applications tend to require enormous computations with constant hardware technology breakthrough. With increasing heavier calculation missions on computers, performance issues gains more and more importance. Many researches provide compile-time optimizations to reduce unnecessary instructions, but they sometimes may not work well, e.g., partial redundancy elimination (PRE). Main reason indicates the process of analysis information relay tends to be interrupted after transfer from one basic block to another one. The situation goes wrong during occurrence of vector instructions, which is caused by nature behavior of special vector swizzle operations.

In this thesis, We propose PREDAF to PRE problem. PREDAF runs under the foundation of global value numbering (GVN) to easily access the congruence information for each value. PREDAF adopts Karthik Gargi's GVN work for better accuracy. For PRE analysis, we introduce mathematical analysis of data access functions (DAFs) and deduce scalar version of DAFs. During symbolic evaluation, PREDAF applies DAFs in both forms to formalize engaged instructions and carries out PRE diagnoses which PREDAF utilizes to match PRE pattern. Once pattern matched, PREDAF performs hoist code motion to eliminate the redundancy.

PREDAF is implemented in LLVM 7. We test PRE case with LLVM test suite and vector swizzle effect with complicated examples. The experimental results indicate that PREDAF reduces code size of LLVM IR programs with -18.37% and -7% compared to original programs and New GVN results respectively for LLVM test suite as well as reduces that of IR programs with -49.52% and -46.19% compared to original GVN pass and New GVN pass respectively with selected 20 complicated vector swizzle programs. Such result proves the efficacy of PREDAF.

Contents
Abstract i
Contents iii
List of Figures v
List of Tables vi
1 Introduction 1
1.1 GVN and PRE 2
1.2 GVN and Vector 4
1.3 PREDAF 5
2 Related Work 6
2.1 GVN 7
2.2 DAF 8
2.3 PRE 9
2.4 PREDAF 10
3 PREDAF 11
3.1 GVM Insertion Points 12
3.2 Introduction of DAF 14
3.3 PRE Optimization 15
4 16
4.1 Array Version of DAF 17
4.2 Vector Version of DAF 19
4.3 Scalar Version of DAF 20
5 Design and Implementation 21
5.1 Data Structures, Algorithms, and Implementation 22
6 Experiments 23
6.1 Examples for Vector PRE 24
6.2 Verification to PRE 25
6.3 Verification to Vector Swizzle 27
7 Future Work and Conclusion 30
7.1 Future Work 30
7.2 Conclusion 31
Bibliography 32

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