現今CMOS製程與三維繪圖技術快速發展，三維圖形處理器（3-D GPU）已漸漸被廣泛使用於手持式裝置上。然而，此應用需要較複雜的運算才得以完成，而且這些運算都需要消耗大量的電力，這對於電池容量有限的手持式裝置是一項嚴峻的考驗。此外，電池製造技術的發展速度無法像IC製程技術這麼快速，其蓄電量無法長時間供給手持式裝置運作。如果想要有效利用電池所提供的有限能源，省電模式設計就必須被加入三維圖形應用中。
本論文提出一個適用於三維圖形處理器的特殊函數指令精確度分配系統，提供的特殊函數運算包含倒數、倒數開根號、對數與指數，每種運算都能依照需求動態地選擇不同的精確度模式執行。藉由此方式，我們不但可以省下一些功率消耗，而且圖形的輸出品質也能夠被接受。
本論文首先介紹一個符合IEEE-754單精度浮點數標準的多重精確度函數插補器，並且將其架構套用於三維圖形處理器之模擬器的特殊函數運算中。此多重精確度函數插補器提供了四種精確度模式，藉由降低特殊函數運算的輸出精確度來減少功率的消耗。接著，我們以仿射算術為基礎來建立誤差模型。此誤差模型顯示出每個特殊函數運算可使用的不同精確度模式與最終輸出結果的關連性。藉由上述的多重精確度函數插補器與基於仿射算術之誤差模型，我們發展一個快速的禁忌搜尋（TS）演算法，根據使用者所需的圖形輸出品質來分配每個特殊函數運算的精確度模式。

Today COMS process and 3-D graphics technology are quickly developed, and 3-D graphics processing units (3-D GPU) have already been used in the handheld devices. However, this application requires many complex operations which consume a lot of power. This is a severe challenge for handheld devices with limited battery capacity. Furthermore, the development of battery manufacturing technology is slower than the IC process technology. As a result, the power storage of handheld devices cannot supply for a long time of operation. If we want to effectively use the limited battery capacity, the power-saving mode must be added to the application.
In this thesis, we propose a low-power precision assignment for special function instructions in 3-D GPU. Its special function operations include reciprocal, reciprocal square root, logarithm and exponential. Each operation is able to perform one of four different precision modes dynamically in demand. In this way, not only some power consumptions can be saved, but also the quality of graphics is able to be accepted by users.
This paper first introduces a multi-precision function interpolator which is compliant with the IEEE-754 single precision floating point standard, and this function interpolator is used for special function operations in 3-D GPU. This multi-precision function interpolator provides four precision modes to trade power consumption with output accuracy of special function operations. Subsequently, affine arithmetic is modified to build the error model of special function. This error model indicates the relationship between the precision mode of each special function operation and the final output. Based on this multi-precision function interpolator and the modified affine arithmetic error model, a fast tabu search (TS) algorithm is developed to assign the precision modes of each special function operation. Besides, the necessary graphics output quality can be provided, according to the requirements of the users.

第一章 概論 . . . . . . . . . . . . . . . . . 1
1.1 研究動機 . . . . . . . . . . . . . . . . . 1
1.2 論文大綱 . . . . . . . . . . . . . . . . . 2
第二章 研究背景 . . . . . . . . . . . . . . . . . 3
2.1 OpenGL ES繪圖流程 . . . . . . . . . . . . . . . . . 3
2.1.1 OpenGL ES 1.x . . . . . . . . . . . . . . . . . 3
2.1.2 OpenGL ES 2.0 . . . . . . . . . . . . . . . . . 6
2.2 ATTILA 3-D Graphics Processing Unit Simulator . . . . . . . . . . . . . . . . . 7
2.2.1 ATTILA模擬器驗證流程 . . . . . . . . . . . . . . . . . 7
2.2.2 模擬器架構 . . . . . . . . . . . . . . . . . 9
2.3多重精確度函數插補器 . . . . . . . . . . . . . . . . . 13
2.3.1 多項式逼近法 . . . . . . . . . . . . . . . . . 13
2.3.2 多重精確度函數插補器架構 . . . . . . . . . . . . . . . . . 15
第三章 低功率特殊函數指令精確度分配系統 . . . . . . . . . . . . . . . . . 19
3.1指令精確度分配流程 . . . . . . . . . . . . . . . . . 20
3.2 ATTILA模擬器的調整與修改 . . . . . . . . . . . . . . . . . 21
3.3 指令精確度分配系統 . . . . . . . . . . . . . . . . . 24
3.3.1 資料非循環圖 . . . . . . . . . . . . . . . . . 25
3.3.2 基於仿射算術誤差模型 . . . . . . . . . . . . . . . . . 28
3.3.3誤差與功率表格 . . . . . . . . . . . . . . . . . 35
3.3.4禁忌搜尋演算法 . . . . . . . . . . . . . . . . . 38
第四章 實驗結果 . . . . . . . . . . . . . . . . . 42
4.1 實驗步驟與方法 . . . . . . . . . . . . . . . . . 42
4.2 實驗數據 . . . . . . . . . . . . . . . . . 42
第五章 結論與未來研究方向 . . . . . . . . . . . . . . . . . 54
5.1 結論 . . . . . . . . . . . . . . . . . 54
5.2 未來研究方向 . . . . . . . . . . . . . . . . . 54
參考文獻 . . . . . . . . . . . . . . . . . 56

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