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Advanced Computer Arithmetic Design

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    Prefacep. xi
    Acknowledgmentsp. xiii
    Notationp. xv
    Integer Additionp. 1
    Backgroundp. 1
    Ripple Adders; Manchester Carry Chainp. 2
    Carry Skip Adders; Multilevel Carry Skipp. 2
    Carry-Select and Conditional-Sum Addersp. 3
    Carry Lookahead Adders; Canonic Addersp. 4
    Ling Addersp. 6
    Adder Implementationsp. 7
    An ECL Ling Adderp. 10
    Group Generatesp. 10
    Lookahead Networkp. 10
    Final Sump. 13
    Critical Pathp. 14
    Implementationp. 14
    A CMOS Ling Adderp. 14
    Group Generatesp. 16
    Lookahead Networkp. 17
    Final Sump. 18
    Critical Pathp. 119
    Implementationp. 20
    Conclusionp. 21
    Floating-Point Additionp. 23
    Improved Algorithms for High-Speed FP Additionp. 23
    A Brief Review of FP Addition Algorithms (A1 and A2)p. 24
    A New Algorithm: A3 (Two Path with Integrated Rounding)p. 27
    Summaryp. 33
    Variable-Latency FP Additionp. 33
    Variable-Latency Algorithmp. 34
    Two-Cycle Algorithmp. 34
    One-Cycle Algorithmp. 36
    Performance Resultsp. 38
    Conclusionp. 42
    Multiplication with Partially Redundant Multiplesp. 43
    Introductionp. 43
    Backgroundp. 43
    Add and Shiftp. 43
    Dot Diagramsp. 45
    Booth's Algorithmp. 46
    Booth 3p. 47
    Booth 4 and Higherp. 50
    Redundant Boothp. 50
    Booth 3 with Fully Redundant Partial Productsp. 50
    Booth 3 with Partially Redundant Partial Productsp. 52
    Dealing with Negative Partial Productsp. 52
    Booth with Biasp. 53
    Choosing the Right Constantp. 55
    Producing the Multiplesp. 57
    Redundant Booth 3p. 57
    Redundant Booth 4p. 58
    Choosing the Adder Lengthp. 63
    Conclusionp. 63
    Multiplier Topologiesp. 65
    Review of Issues in Partial-Product Summationp. 66
    Regular Topologiesp. 68
    Array Topologiesp. 69
    Tree Topologiesp. 75
    Effects of the Number of Tracks per Channelp. 85
    Irregular Topologiesp. 89
    Wallace Treep. 89
    Algorithmic Generationp. 89
    Conclusionp. 99
    Technology Scaling Effects on Multipliersp. 101
    Effects of Smaller Feature Sizesp. 101
    Wire Effectsp. 102
    Binary Trees vs Procedural Layoutsp. 106
    Scaling Effects on Encoding Schemesp. 109
    Topologyp. 110
    Area [times] Time Productp. 112
    Pipeliningp. 113
    Powerp. 114
    Encoding Schemesp. 115
    Topologyp. 115
    Conclusionp. 116
    Design Issues in Divisionp. 117
    Introductionp. 117
    System Level Studyp. 118
    Instrumentationp. 118
    Method of Analysisp. 119
    Resultsp. 120
    Instruction Mixp. 120
    Compiler Effectsp. 120
    Performance and Area Tradeoffsp. 122
    Shared-Multiplier Effectsp. 125
    Shared Square Rootp. 127
    On-the-Fly Rounding and Conversionp. 128
    Consumers of Division Resultsp. 129
    Conclusionp. 130
    Minimizing the Complexity of SRT Tablesp. 133
    Theory of SRT Divisionp. 134
    Recurrencep. 134
    Choice of Radixp. 135
    Choice of Quotient Digit-Setp. 135
    Implementing SRT Tablesp. 138
    Divisor and Partial-Remainder Estimatesp. 138
    Uncertainty Regionsp. 139
    Reducing Table Complexityp. 140
    Experimental Methodologyp. 143
    TableGenp. 143
    Table Synthesisp. 145
    Resultsp. 145
    Same-Radix Tradeoffsp. 145
    Higher Radicesp. 147
    Conclusionp. 150
    Very High-Radix Divisionp. 153
    Taylor Series Expansionp. 153
    Algorithm Ap. 154
    Number of Accurate Bits per Iterationp. 157
    Representing X Using Redundancyp. 161
    Algorithm Bp. 162
    Number of Accurate Bits per Iterationp. 164
    Representing X Using Redundancyp. 170
    Algorithm Cp. 171
    Theoryp. 171
    Lookup-Table Constructionp. 173
    Booth Recodingp. 173
    Error Analysisp. 175
    Optimization Techniquesp. 175
    Discussionp. 178
    Related Algorithmsp. 179
    Cyrix Short-Reciprocal Algorithmp. 179
    Comparison with the Newton-Raphson Methodp. 179
    Comparison with the IBM RISC System/6000p. 181
    Comparison with MacLaurin Seriesp. 181
    Conclusionp. 182
    Using a Multiplier for Function Approximationp. 183
    Proposed Method: Implementationp. 183
    Partial-Product Arrayp. 183
    Related Workp. 186
    Implementationp. 187
    Summary of Implementationp. 192
    Proposed Method: Derivationp. 192
    Algorithm 1: Describing an Operation as a Signed PPAp. 192
    Algorithm 2: Adapting the Signed PPA to the Multiplier's PPAp. 200
    Performance and Comparisonsp. 203
    Summary of Derivationp. 207
    Reciprocal, Division, and Square Rootp. 207
    Reciprocal Operationp. 208
    Division Operationp. 213
    Square-Root Operationp. 220
    Conclusionp. 230
    FUPAp. 235
    Introductionp. 235
    Backgroundp. 237
    Components of FUPAp. 237
    Technology Scalingp. 238
    Latency Component of FUPAp. 239
    Derivation of Delay Scale Factorp. 239
    Area Component of FUPAp. 240
    Derivation of Area Scale Factorp. 240
    Relationship between Area, Operating Frequency, and Powerp. 241
    Application Profilingp. 242
    Computation of FUPAp. 243
    Microprocessor FPU Comparisonsp. 244
    Effective and Normalized Effective Latency of Microprocessor FPUsp. 244
    Die-Area and Normalized-Die-Area Usage of Microprocessor FPUsp. 246
    FUPA of Microprocessor FPUsp. 247
    Limitations of FUPAp. 249
    Conclusionp. 249
    High-Speed Clocking Using Wave Pipeliningp. 251
    Backgroundp. 251
    Pipelining and Wave Pipeliningp. 252
    Wave Pipeline Researchp. 253
    Theoryp. 254
    Minimum Clock Period for Traditional Pipelinesp. 254
    Minimum Clock Period for Wave Pipelinesp. 256
    Device Technologies: Applicability and Performancep. 259
    Performance Limits of Wave Pipeliningp. 260
    Path-Length Imbalancep. 261
    Data Dependencesp. 261
    Fabrication Processp. 262
    Environmental Variationp. 263
    CMOS Process and Environmental Performance Limitsp. 264
    Design Optimizationsp. 265
    Rough Tuningp. 266
    Fine Tuningp. 266
    CMOS Delay Compensationp. 270
    SNAP Wave-Pipeline Demonstration VLSIp. 273
    Bipolar Population Counterp. 273
    CMOS Multipler Circuitp. 273
    CMOS VLSI Vector Unitp. 274
    Conclusionp. 283
    Rational Arithmeticp. 285
    Introductionp. 285
    Continued Fractionsp. 287
    The M-log-Fraction Transformationp. 290
    The Signed-Digit M-log Fractionp. 292
    A Rational-Arithmetic Unitp. 293
    Linear Fractional Transformationp. 297
    Quadratic Transformationsp. 298
    A Shift-and-Add-Based Rational-Arithmetic Unitp. 298
    Implementing the Bilinear Function (ax + b)/(cx + d)p. 299
    VLSI Implementation of Rational Arithmetic Unitsp. 301
    Higher-Radix Rational Arithmeticp. 302
    Related Workp. 304
    Conclusionsp. 306
    Historical Notes on Continued Fractions in Arithmeticp. 306
    Bibliographyp. 309
    Indexp. 321
    Table of Contents provided by Syndetics. All Rights Reserved.

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    This volume presents the results of a decade's research in innovative and progressive design techniques. Covering all the most important research topics in the field, Advanced Computer Arithmetic Design is the most up-to-date and comprehensive treatment of new research currently available.

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    Flynn, M. J./ Oberman, Stuart F./ Flynn, Michael J [Àú] ½ÅÀ۾˸² SMS½Åû
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