值域傳遞技術是一種追蹤變數值域的分析方法。值域傳遞技術類似常數傳遞，差別是他們傳遞的物件不同：常數傳遞傳遞的是常數，而值域傳遞傳遞的是值域。值域傳遞技術是在靜態編譯環境下執行，分析結果包含值域以及值域所含的比例。此分析技術可用來提升預測分支、確認迴圈界限、暫存器配置以及減少ALU計算量。由於提升執行效能的需求日漸增加，多核心架構亦越來越重要。然而，卻還沒有任何關於值域傳遞技術的是在多核心架構上，因此，我們在這篇論文提出了可以使用在高階多核心架構的增強值域傳遞技術。

Value range propagation is a analysis method to track the range of variables in a static single static form program. It is similar to constant propagation, and the difference between them is the item they propagated during execution: constant propagation propagates constants, and value range
propagation propagates value range. Value range propagation analyzes value ranges of variables in a static-single-assignment-form (SSA-form) program, and each range is with its portion. The results of the analysis can be used
to improve some optimizations such as branch prediction, loop bound check, register allocation and ALU computation reduction. With the increasing requirements of execution performance, the multi-core architecture becomes more and more important. However, there has not been a research of multi-core architecture related to value range propagation. Therefore, in this thesis, we propose an algorithm of enhanced value range propagation, which can be used to analyze programs in the multi-core architecture.

Abstract i
Contents ii
List of Figures iv
List of Tables v
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . 4
2 Background 6
2.1 OpenCL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Static Single Assignment Form . . . . . . . . . . . . . . . . . . 8
2.3 Value Range Propagation . . . . . . . . . . . . . . . . . . . . 11
3 Algorithm 15
3.1 Enhanced Value Range Propagation . . . . . . . . . . . . . . . 15
3.2 Detail of the Algorithm . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Algorithm of Enhanced Value Range Propagation . . . 16
3.2.2 Algorithm of Value Range Evaluation . . . . . . . . . . 19
3.2.3 Algorithm of Conditional Branch Examination . . . . . 21
3.2.4 Rule of Expressions in Enhanced Value Range Propa-
gation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.5 Algorithm Efficiency . . . . . . . . . . . . . . . . . . . 26
3.3 Evaluation of Samples . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Sample 1: With a Branch . . . . . . . . . . . . . . . . 26
3.3.2 Sample 2: With a For-Loop . . . . . . . . . . . . . . . 30
4 Conclusion 33
4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
iii

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