跳到主要內容

臺灣博碩士論文加值系統

(18.97.14.90) 您好!臺灣時間:2025/01/14 00:30
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:陳亮安
研究生(外文):Liang-An Chen
論文名稱:快速浮點數乘加單元的電路設計與效能評估
論文名稱(外文):Circuit Design and performance analysis of a Fast Floating-Point Multiplication-Add Fused Unit
指導教授:陳啟鏘
學位類別:碩士
校院名稱:逢甲大學
系所名稱:資訊工程所
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:2002
畢業學年度:90
語文別:中文
論文頁數:110
中文關鍵詞:倍精密度格式有號數字系統浮點數乘加法融合運算器數系轉換加法器管線結構兩階段的正規化方式
外文關鍵詞:VerilogDouble-precisionPipelineTwo-step normalizationFloating-pointSigned-digit additionMultiplication-add fused
相關次數:
  • 被引用被引用:0
  • 點閱點閱:382
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0

  本論文依據IEEE 754倍精密度格式輸出入標準,以帶號位元(Signed-digit)數字系統所提供的加法器,設計一個快速浮點數乘法與加法融合(MAC)的運算單元。此乘加運算單元分成三個階層的管線結構,第一階層為實現指數差值對齊假數的動作、並完成帶號位元數字系統乘法與加法運算,第二階層為正負號的決定與假數的正規化,第三階層為假數的SD-to-SM數系轉換與捨位運算,使運算誤差表現符合IEEE 7 54標準的規定。我們採用無進位傳遞特性的帶號位元數字系統運算,故在第一階層中可快速完成絕大部分的帶號位元數字系統之乘與加法運作。帶號位元數字系統的運算具有快速特性,但最終仍須將結果轉換成標準輸出入格式的數字。為加速數系轉換的速度,提出的電路架構直接在帶號位元數字格式下執行正規化及捨位運算,使得浮點數乘加器所需的SD-to-SM數系轉換器長度由162-digit縮短成54-digit。再搭配「兩階段的正規化」電路架構,使得所需前置零位元偵測電路長度由162-digit縮短成110-digit。提出的新架構之浮點乘加融合單元以Verilog 硬體描述語言設計電路,在個人電腦的Xilinx 輔助軟體及大型工作站中的Verilog-XL 模擬軟體進行輸出入功能驗證,並經Synopsys 軟體驗證晶片製作的可行性。經由Gate-level的電路分析,提出的改良式浮點數乘加器的正規化、數系轉換及捨位運算階段之運算速度,相較於傳統型浮點數乘加器,效能提昇了28%。


This thesis presents a design of an IEEE floating-point (FLP) multiplication-and-addition fused (MAF) unit by using signed digit (SD) adders. This unit is divided into three pipeline stages. The function of the first pipeline stage includes the alignment of the exponents, the mantissa multiplication and addition. The second stage performs the mantissa normalization. In the third stages, SD-to-SM conversion of the SD mantissa and its rounding are performed. Because of the usage of SD multiplier and SD adders, which are carry-propagation-free, the speed of the first stage can be very fast. Different from conventional MAF unit design, the mantissa normalization in the second stages is performed in SD format. In this way, the width of the SD-to-SM conversion can be only one single word, which is much smaller than the three-word-length carry-propagation adder in a conventional MAF unit.
The adoption of the so-called “two-step normalization” enables the reduction of the word length of the leading-zero detection from 162-digits into only 110 digits. We have designed the proposed FLP MAF unit in verilog HDL. The designed unit has been verified by simulations on Xilinx and Verilog-XL CAD tools. Through Synopsis synthesis and gate-level analysis, the speed improvement of the proposed unit over conventional unit can be up to 28% in the normalization and rounding circuits.


摘要i
Abstractii
目錄iii
圖目錄v
表目錄vi
第一章 簡介1
第一節 研究動機與問題的描述1
第二節 論文架構5
第二章 帶號位元數字系統6
第一節 帶號位元數系算術(signed-digit arithmetic ; SD)的定義6
第二節 Signed-magnitude與Signed-digit數字系統之間的轉換9
第三節 帶號位元(signed-digit)數字系的無進位傳遞加法器(carry-propagation-free adder)介紹12
第三章 乘法器架構探究16
第一節 Booth-recoding對乘法器影響之探討16
第二節 以CSA或SD加法器組成二元樹狀結構乘法器優劣分析18
第三節 帶號位元數字格式部分積產生原理21
第四節 乘法器電路設計23
第3.4.1小節 二元樹狀結構乘法器電路設計23
第3.4.2小節 帶號位元數字格式部分積產生電路設計26
第四章 傳統浮點數乘加器架構探究30
第一節 IEEE 浮點數標準格式30
第二節 浮點數之乘法原理32
第三節 浮點數之加法原理33
第四節 浮點數之乘加器探究及架構探討37
第五章 二階段正規化之浮點數乘加器架構探究42
第一節 二階段正規化浮點數乘加器整體架構說明42
第二節 分析加法運算指數差值對齊(Alignment)原理45
第三節 First-step normalization步驟的介紹47
第四節 浮點數乘加器捨位方式介紹48
第六章 改良後之浮點數乘加器的架構51
第一節 乘法與加法階段(Stage1)之說明53
第二節 數值正負號決定與帶號位元數字正規化(Stage 2)之說明55
第三節 SD-to-SM數系轉換與捨位處理階段(Stage3)之說明57
第七章 數系轉換及正規化電路設計59
第一節 Signed-digit加法器/乘法器的設計59
第二節 LZA電路設計60
第7.2.1小節 LZA電路原理60
第7.2.2小節 110-digit LZA電路設計64
第三節 LZA 1-bit預測誤差的偵測及補償電路66
第7.3.1小節 預測誤差偵測電路69
第7.3.2小節 預測誤差補償電路72
第四節 帶號位元數字捨位方式75
第五節 帶號位元數字尾端1序列預測電路80
第六節 Sign-detector電路設計86
第七節 SD-to-SM減法器的設計89
第八章 模擬結果及效能評估95
第九章 結論100
參考文獻101


[1] Oehler, R.R., Blasgen, M.W., “IBM RISC System/6000: Architecture and Performance,” IEEE Micro Volume: 11 3 , June 1991 , Page(s): 14 -17, 56-62.[2] White, S.W., Hester, P.D., Kemp, J.W. and McWilliams, G.J., ”How Does Processor MHz Relate to End-User Performance? I. Pipelines and Functional Units,“ IEEE Micro Volume: 13 4 , Aug. 1993 , Page(s): 8 -16[3] White, S.W., Hester, P.D., Kemp, J.W. and McWilliams, G.J., ”How Does Processor MHz Relate to End-User Performance? II. Memory Subsystem and Instruction Set,“ IEEE Micro Volume: 13 5, Oct. 1993, Page(s): 79 —89.[4] Beaumont-Smith, A.; Burgess, N.; Lefrere, S.; Lim, C.C., “Reduced latency IEEE floating-point standard adder architectures,” Computer Arithmetic, 1999. Proceedings. 14th IEEE Symposium on, Page(s): 35 -42[5] Jessani, R.M. and Putrino, M., “Comparison of Single- and Dual-pass Multiply-Add Fused Floating Point Units,” Computers, IEEE Transactions on Volume: 47 9, Sept. 1998, Page(s): 927 —937.[6] Santoro, M.R.; Bewick, G.; Horowitz, M.A., “Rounding algorithms for IEEE multipliers,” Computer Arithmetic, 1989, Proceedings of 9th Symposium on, Page(s): 176 -183[7] Beaumont-Smith, A.; Lim, C.-C., “Parallel prefix adder design,” Computer Arithmetic, 2001. Proceedings. 15th IEEE Symposium on, Page(s): 218 -225[8] Naofumi Takagi, Hiroto Yasuura and Shuzo Yajima, “High-Speed VLSI Multiplication Algorithm with a Redundant Binary Addition Tree,” IEEE Transactions on Computer Volume, C-34, no. 9, Sept. 1985, Page(s): 789 - 796.[9] Y. HARATA et al., ”A High-Speed Multiplier Using a Redundant Binary Adder Tree,” IEEE Journal of Solid-State Circuit, vol. SC-22, Feb. 1987, Page(s): 28-33.[10] Suzuki, H., orinaka, H., akino, H., Nakase, Y., Mashiko, K. and Sumi, T., “Leading-Zero Anticipatory Logic for High-Speed Floating Point Addition,” Solid-State Circuits, IEEE Journal of Volume: 31 8, Aug. 1996 , Page(s): 1157 —1164.[11] Bruguera, J.D., Lang, T., “Leading-one prediction with concurrent position correction,” Computers, IEEE Transactions on, Volume: 48 Issue: 10, Oct. 1999, Page(s): 1083 -1097[12] Stouraitis, T. and Chen, C., ”Fast digit-parallel conversion of signed digit into conventional representations,” Electronics Letters Volume: 27 11, 23 May 1991, Page(s): 964 —965.[13] Chichyang Chen; Liang-An Chen; Jih-Ren Cheng, “Architectural design of a fast floating-point multiplication-add fused unit using signed-digit addition,” Digital Systems, Design, 2001. Proceedings. Euromicro Symposium on, Page(s): 346 -353[14] Neil Burgess, “The Flagged Prefix adder for Dual Additions,” in Proc. SPIC ASPAAI-7, volume 3461, San Diego, Jul. 1998, pages 567-575[15] Behrooz Parhami, Computer Arithmetic Algorithms and Hardware Designs, New York, Oxford, 2000.[16] Israel Koren, Computer Arithmetic Algorithm, Eaglewood Cliffs, New York, 1993.[17] Makino, H.; Nakase, Y., Suzuki, H., Morinaka, H., Shinohara, H., Mashiko, K., “An 8.8-ns 54x54-Bit Multiplier with High Speed Redundant Binary Architecture,” Solid-State Circuits, IEEE, Volume: 31 Issue: 6, June 1996, Page(s): 773 -783[18] IEEE standard for binary floating-point arithmetic, ANSI/IEEE 754-1985, also in Computer 14(Mar. 1981), 51-62.[19] Kayed, S.I.; Ragaie, H.F. “A new efficient design of the 2-to-1 multiplexer,” International Conference on Microelectronics, 1995, pages 817-822

QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top