Compilers
Principles, Techniques, & Tools
Second Edition
Alfred V. Abo
Columbia University
Monica S. Lam
Stanford University
Ravi Sethi
Avaya
Jeffrey D. Ullman
Stanford University
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Preface
In the time since the 1986 edition of this book, the world of compiler design has changed significantly. Programming languages have evolved to present new compilation problems. Computer architectures offer a variety of resources of which the compiler designer must take advantage. Perhaps most interestingly, the venerable technology of code optimization has found use outside compilers. It is now used in tools that find bugs in software, and most importantly, find security holes in existing code. And much of the "front-end" technology — grammars, regular expressions, parsers, and syntax-directed translators — are still in wide use.
Thus, our philosophy from previous versions of the book has not changed. We recognize that few readers will build, or even maintain, a compiler for a major programming language. Yet the models, theory, and algorithms associated with a compiler can be applied to a wide range of problems in software design and software development. We therefore emphasize problems that are most commonly encountered in designing a language processor, regardless of the source language or target machine.
Use of the Book
It takes at least two quarters or even two semesters to cover all or most of the material in this book. It is common to cover the first half in an undergraduate course and the second half of the book — stressing code optimization — in a second course at the graduate or mezzanine level. Here is an outline of the chapters:
Chapter 1 contains motivational material and also presents some background issues in computer architecture and programming-language principles.
Chapter 2 develops a miniature compiler and introduces many of the important concepts, which are then developed in later chapters. The compiler itself appears in the appendix.
Chapter 3 covers lexical analysis, regular expressions, finite-state machines, and scanner-generator tools. This material is fundamental to text-processing of all sorts.
Chapter 4 covers the major parsing methods, top-down (recursive-descent, LL) and bottom-up (LR and its variants).
Chapter 5 introduces the principal ideas in syntax-directed definitions and syntax-directed translations.
Chapter 6 takes the theory of Chapter 5 and shows how to use it to generate intermediate code for a typical programming language.
Chapter 7 covers run-time environments, especially management of the run-time stack and garbage collection.
Chapter 8 is on object-code generation. It covers construction of basic blocks, generation of code from expressions and basic blocks, and register-allocation techniques.
Chapter 9 introduces the technology of code optimization, including flow graphs, data-flow frameworks, and iterative algorithms for solving these frameworks.
Chapter 10 covers instruction-level optimization. The emphasis is on the extraction of parallelism from small sequences of instructions and scheduling them on single processors that can do more than one thing at once.
Chapter 11 talks about larger-scale parallelism detection and exploitation. Here, the emphasis is on numeric codes that have many tight loops that range over multidimensional arrays.
Chapter 12 is on interprocedural analysis. It covers pointer analysis, aliasing, and data-flow analysis that takes into account the sequence of procedure calls that reach a given point in the code.
Courses from material in this book have been taught at Columbia, Harvard, and Stanford. At Columbia, a senior/first-year graduate course on programming languages and translators has been regularly offered using material from the first eight chapters. A highlight of this course is a semester-long project in which students work in small teams to create and implement a little language of their own design. The student-created languages have covered diverse application domains including quantum computation, music synthesis, computer graphics, gaming, matrix operations and many other areas. Students use compiler-component generators such as ANTLR, Lex, and Yacc and the syntax- directed translation techniques discussed in chapters two and five to build their compilers. A follow-on graduate course has focused on material in Chapters 9 through 12, emphasizing code generation and optimization for contemporary machines including network processors and multiprocessor architectures.
At Stanford, a one-quarter introductory course covers roughly the material in Chapters 1 through 8, although there is an introduction to global code optimization from Chapter 9. The second compiler course covers Chapters 9 through 12, plus the more advanced material on garbage collection from Chapter 7. Students use a locally developed, Java-based system called Joeq for implementing data-flow analysis algorithms.
Prerequisites
The reader should possess some "computer-science sophistication," including at least a second course on programming, and courses in data structures and discrete mathematics. Knowledge of several different programming languages is useful.
Exercises
The book contains extensive exercises, with some for almost every section. We indicate harder exercises or parts of exercises with an exclamation point. The hardest exercises have a double exclamation point.
Gradiance On-Line Homeworks
A feature of the new edition is that there is an accompanying set of on-line homeworks using a technology developed by Gradiance Corp. Instructors may assign these homeworks to their class, or students not enrolled in a class may enroll in an "omnibus class" that allows them to do the homeworks as a tutorial (without an instructor-created class). Gradiance questions look like ordinary questions, but your solutions are sampled. If you make an incorrect choice you are given specific advice or feedback to help you correct your solution. If your instructor permits, you are allowed to try again, until you get a perfect score.
A subscription to the Gradiance service is offered with all new copies of this text sold in North America. For more information, visit the Addison-Wesley web site www.aw.com/gradiance or send email to [email protected].
Support on the World Wide Web
The book's home page is
dragonbook.Stanford.edu
Here, you will find errata as we learn of them, and backup materials. We hope to make available the notes for each offering of compiler-related courses as we teach them, including homeworks, solutions, and exams. We also plan to post descriptions of important compilers written by their implementers.
Acknowledgements
Cover art is by S. D. Ullman of Strange Tonic Productions.
Jon Bentley gave us extensive comments on a number of chapters of an earlier draft of this book. Helpful comments and errata were received from:
Domenico Bianculli, Peter Bosch, Marcio Buss, Marc Eaddy, Stephen Edwards, Vibhav Garg, Kim Hazelwood, Gaurav Kc, Wei Li, Mike Smith, Art Stamness, Krysta Svore, Olivier Tardieu, and Jia Zeng. The help of all these people is gratefully acknowledged. Remaining errors are ours, of course.
In addition, Monica would like to thank her colleagues on the SUIF compiler team for an 18-year lesson on compiling: Gerald Aigner, Dzintars Avots, Saman Amarasinghe, Jennifer Anderson, Michael Carbin, Gerald Cheong, Amer Diwan, Robert French, Anwar Ghuloum, Mary Hall, John Hennessy, David , Heine, Shih-Wei Liao, Amy Lim, Benjamin Livshits, Michael Martin, Dror Maydan, Todd Mowry, Brian Murphy, Jeffrey Oplinger, Karen Pieper, Martin Rinard, Olatunji Ruwase, Constantine Sapuntzakis, Patrick Sathyanathan, Michael Smith, Steven Tjiang, Chau-Wen Tseng, Christopher Unkel, John Whaley, Robert Wilson, Christopher Wilson, and Michael Wolf.
A. V. A., Chatham NJ M. S. L., Menlo Park CA R. S., Far Hills NJ J. D. U., Stanford CA June, 2006
Table of Contents
1 Introduction 1
1.1 Language Processors............................................................................................ 1
1.1.1 Exercises for Section 1.1..................................................................... 3
1.2 The Structure of a Compiler............................................................................... 4
1.2.1 Lexical Analysis .............................................................................. 5
1.2.2 Syntax Analysis .................................................................................... 8
1.2.3 Semantic Analysis........................................................................... 8
1.2.4 Intermediate Code Generation .................................................... 9
1.2.5 Code Optimization........................................................................... 10
1.2.6 Code Generation............................................................................... 10
1.2.7 Symbol-Table Management........................................................... 11
1.2.8 The Grouping of Phases into Passes................................................ 11
1.2.9 Compiler-Construction Tools............................................................ 12
1.3 The Evolution of Programming Languages................................................... 12
1.3.1 The Move to Higher-level Languages............................................... 13
1.3.2 Impacts on Compilers..................................................................... 14
1.3.3 Exercises for Section 1.3..................................................................... 14
1.4 The Science of Building a Compiler................................................................ 15
1.4.1 Modeling in Compiler Design and Implementation .... 15
1.4.2 The Science of Code Optimization................................................ 15
1.5 Applications of Compiler Technology............................................................. 17
1.5.1 Implementation of High-Level Programming Languages . 17
1.5.2 Optimizations for Computer Architectures................................ 19
1.5.3 Design of New Computer Architectures .................................... 21
1.5.4 Program Translations......................................................................... 22
1.5.5 Software Productivity Tools........................................................... 23
1.6 Programming Language Basics....................................................................... 25
1.6.1 The Static/Dynamic Distinction.................................................... 25
1.6.2 Environments and States ................................................................ 26
1.6.3 Static Scope and Block Structure..................................................... 28
1.6.4 Explicit Access Control....................................................................... 31
1.6.5 Dynamic Scope...................................................................................... 31
1.6.6 Parameter Passing Mechanisms...................................................... 33
1.6.7 Aliasing................................................................................. 35
1.6.8 Exercises for Section 1.6.................................................................... 35
1.7 Summary of Chapter 1.................................................................................... 36
1.8 References for Chapter 1............................................................................... 38
2 A Simple Syntax-Directed Translator 39
2.1 Introduction......................................................................................................... 40
2.2 Syntax Definition............................................................................................... 42
2.2.1 Definition of Grammars...................................................................... 42
2.2.2 Derivations............................................................................................. 44
2.2.3 Parse Trees............................................................................................ 45
2.2.4 Ambiguity............................................................................................... 47
2.2.5 Associativity of Operators.................................................................. 48
2.2.6 Precedence of Operators...................................................................... 48
2.2.7 Exercises for Section 2.2 ................................................................... 51
2.3 Syntax-Directed Translation . ....................................................................... 52
2.3.1 Postfix Notation............................................................................ . 53
2.3.2 Synthesized Attributes................................................................... 54
2.3.3 Simple Syntax-Directed Definitions................................................ 56
2.3.4 Tree Traversals................................................................................. 56
2.3.5 Translation Schemes........................................................................... 57
2.3.6 Exercises for Section 2.3..................................................................... 60
2.4 Parsing ............................................................................................................ 60
2.4.1 Top-Down Parsing................................................................................ 61
2.4.2 Predictive Parsing . . . 64
2.4.3 When to Use c-Productions................................................................. 65
2.4.4 Designing a Predictive Parser 66
2.4.5 Left Recursion.................................................................................... 67
2.4.6 Exercises for Section 2.4..................................................................... 68
2.5 A Translator for Simple Expressions............................................................ 68
2.5.1 Abstract and Concrete Syntax........................................................... 69
2.5.2 Adapting the Translation Scheme................................................ 70
2.5.3 Procedures for the Nonterminals ................................................ 72
2.5.4 Simplifying the Translator............................................................. 73
2.5.5 The Complete Program.................................................................... 74
2.6 Lexical Analysis ............................................................................................... 76
2.6.1 Removal of White Space and Comments....................... 77
2.6.2 Reading Ahead...................................................................................... 78
2.6.3 Constants........................................................................................... 78
2.6.4 Recognizing Keywords and Identifiers............................................. 79
2.6.5 A Lexical Analyzer............................................................................... 81
2.6.6 Exercises for Section 2.6 . 84
2.7 Symbol Tables .................................................................................................. 85
2.7.1 Symbol Table Per Scope...................................................................... 86
2.7.2 The Use of Symbol Tables.................................................................. 89
2.8 Intermediate Code Generation ...................................................................... 91
2.8.1 Two Kinds of Intermediate Representations................... 91
2.8.2 Construction of Syntax Trees................................................ 92
2.8.3 Static Checking........................................................................ 97
2.8.4 Three-Address Code . .......................................................... 99
2.8.5 Exercises for Section 2.8..................................................... 105
2.9 Summary of Chapter 2....................................................................................... 105
3 Lexical Analysis
3.1 The Role of the Lexical Analyzer................................................................... 109
3.1.1 Lexical Analysis Versus Parsing...................................... 110
3.1.2 Tokens, Patterns, and Lexemes........................................ 111
3.1.3 Attributes for Tokens......................................................... 112
3.1.4 Lexical Errors....................................................................... 113
3.1.5 Exercises for Section 3.1..................................................... 114
3.2 Input Buffering.................................................................................................. 115
3.2.1 Buffer Pairs........................................................................... 115
3.2.2 Sentinels................................................................................ 116
3.3 Specification of Tokens.................................................................................... 116
3.3.1 Strings and Languages....................................................... 117
3.3.2 Operations on Languages................................................... 119
3.3.3 Regular Expressions........................................................... 120
3.3.4 Regular Definitions............................................................. 123
3.3.5 Extensions of Regular Expressions................................. 124
3.3.6 Exercises for Section 3.3..................................................... 125
3.4 Recognition of Tokens...................................................................................... 128
3.4.1 Transition Diagrams........................................................... 130
3.4.2 Recognition of Reserved Words and Identifiers .......... 132
3.4.3 Completion of the Running Example.............................. 133
3.4.4 Architecture of a Transition-Diagram-Based Lexical Analyzer 134
3.4.5 Exercises for Section 3.4 . . . . 136
3.5 The Lexical-Analyzer Generator Lex........................................................... 140
3.5.1 Use of Lex............................................................................. 140
3.5.2 Structure of Lex Programs . 141
3.5.3 Conflict Resolution in Lex................................................. 144
3.5.4 The Lookahead Operator.................................................... 144
3.5.5 Exercises for Section 3.5..................................................... 146
3.6 Finite Automata............................................................................................... 147
3.6.1 Nondeterministic Finite Automata................................. 147
3.6.2 Transition Tables................................................................ 148
3.6.3 Acceptance of Input Strings by Automata..................... 149
3.6.4 Deterministic Finite Automata........................................ 149
3.6.5 Exercises for Section 3.6..................................................... 151
3.7 From Regular Expressions to Automata.................................................... 152
3.7.1 Conversion of an NFA to a DFA...................................................... 152
3.7.2 Simulation of an NFA....................................................................... 156
3.7.3 Efficiency of NFA Simulation.......................................................... 157
3.7.4 Construction of an NFA from a Regular Expression . . . 159
3.7.5 Efficiency of String-Processing Algorithms.................................. 163
3.7.6 Exercises for Section 3.7................................................................... 166
3.8 Design of a Lexical-Analyzer Generator .................................................... 166
3.8.1 The Structure ofthe Generated Analyzer...................................... 167
3.8.2 Pattern Matching Based on NFA's................................................. 168
3.8.3 DFA's for Lexical Analyzers............................................................. 170
3.8.4 Implementing the Lookahead Operator . 171
3.8.5 Exercises for Section 3.8................................................................... 172
3.9 Optimization of DFA-Based Pattern Matchers......................................... 173
3.9.1 Important States of an NFA............................................................ 173
3.9.2 Functions Computed From the Syntax Tree................................ 175
3.9.3 Computing nullable, firstpos, and lastpos...................................... 176
3.9.4 Computing followpos.......................................................................... 177
3.9.5 Converting a Regular Expression Directly to a DFA . . ■ 179
3.9.6 Minimizing the Number of States of a DFA................................. 180
3.9.7 State Minimization in Lexical Analyzers................................ .. 184
3.9.8 Trading Time for Space in DFA Simulation................................. 185
3.9.9 Exercises for Section 3.9 186
3.10 Summary of Chapter 3.................................................................................... 187
3.11 References for Chapter 3................................................................................. 189
4 Syntax Analysis 191
4.1 Introduction....................................................................................................... 192
4.1.1 The Role of the Parser....................................................................... 192
4.1.2 Representative Grammars............................................................... 193
4.1.3 Syntax Error Handling...................................................................... 194
4.1.4 Error-Recovery Strategies.................................................................. 195
4.2 Context-Free Grammars................................................................................ 197
4.2.1 The Formal Definition of a Context-Free Grammar . • • • 197
4.2.2 Notational Conventions.................................................................... 198
4.2.3 Derivations........................................................................................... 199
4.2.4 Parse Trees and Derivations............................................................... 201
4.2.5 Ambiguity............................................................................................ 203
4.2.6 Verifying the Language Generated by a Grammar . ... 204
4.2.7 Context-Free Grammars Versus Regular Expressions . . . 205
4.2.8 Exercises for Section 4.2................................................................... 206
4.3 Writing a Grammar........................................................................................... 209
4.3.1 Lexical Versus Syntactic Analysis................................................... 209
4.3.2 Eliminating Ambiguity........................................................................ 210
4.3.3 Elimination of Left Recursion............................................................ 212
4.3.4 Left Factoring .................................................................................... 214
4.3.5 Non-Context-Free Language Constructs...................................... 215
4.3.6 Exercises for Section 4.3...................................................................... 216
4.4 Top-Down Parsing............................................................................................... 217
4.4.1 Recursive-Descent Parsing ................................................................ 219
4.4.2 FIRST and FOLLOW ........................................................................ 220
4.4.3 LL( l) Grammars................................................................................... 222
4.4.4 Nonrecursive Predictive Parsing ................................................... 226
4.4.5 Error Recovery in Predictive Parsing............................................. 228
4.4.6 Exercises for Section 4.4................................................................... 231
4.5 Bottom-Up Parsing.......................................................................................... 233
4.5.1 Reductions........................................................................................... 234
4.5.2 Handle Pruning................................................................................... 235
4.5.3 Shift-Reduce Parsing......................................................................... 236
4.5.4 Conflicts During Shift-Reduce Parsing......................................... 238
4.5.5 Exercises for Section 4.5................................................................... 240
4.6 Introduction to LR Parsing: Simple LR....................................................... 241
4.6.1 Why LR Parsers?................................................................................ 241
4.6.2 Items and the LR( O) Automaton................................................... 242
4.6.3 The LR-Parsing Algorithm............................................................... 248
4.6.4 Constructing SLR-Parsing Tables................................................. 252
4.6.5 Viable Prefixes................................................................................... 256
4.6.6 Exercises for Section 4.6................................................................... 257
4.7 More Powerful LR Parsers.............................................................................. 259
4.7.1 Canonical LR(l) Items . . 260
4.7.2 Constructing LR (l) Sets of Items................................................... 261
4.7.3 Canonical LR(l) Parsing Tables .................................................... 265
4.7.4 Constructing LALR Parsing Tables . . 266
4.7.5 Efficient Construction of LALR Parsing Tables......................... 270
4.7.6 Compaction of LR Parsing Tables . 275
4.7.7 Exercises for Section 4.7 ........................................... . 277
4.8 Using Ambiguous Grammars........................................................................ 278
4.8.1 Precedence and Associativity to Resolve Conflicts .... 279
4.8.2 The "Dangling-Else" Ambiguity .................................................... 281
4.8.3 Error Recovery in LR Parsing.......................................................... 283
4.8.4 Exercises for Section 4.8 . . . 285
4.9 Parser Generators .......................................................................................... 287
4.9.1 The Parser Generator Yacc............................................................. 287
4.9.2 Using Yacc with Ambiguous Grammars..................................... 291
4.9.3 Creating Yacc Lexical Analyzers with Lex................................. 294
4.9.4 Error Recovery in Yacc..................................................................... 295
4.9.5 Exercises for Section 4.9................................................................... 297
4.10 Summary of Chapter 4.................................................................................... 297
4.11 References for Chapter 4................................................................................. 300
5 Syntax-Directed Translation 303
5.1 Syntax-Directed Definitions........................................................................... 304
5.1.1 Inherited and Synthesized Attributes........................................... 304
5.1.2 Evaluating an SDD at the Nodes of a Parse Tree....................... 306
5.1.3 Exercises for Section 5.1................................................................... 309
5.2 Evaluation Orders for SDD's ........................................................................ 310
5.2.1 Dependency Graphs............................................................................ 310
5.2.2 Ordering the Evaluation of Attributes.......................................... 312
5.2.3 S-Attributed Definitions................................................................... 312
5.2.4 L-Attributed Definitions................................................................... 313
5.2.5 Semantic Rules with Controlled Side Effects.............................. 314
5.2.6 Exercises for Section 5.2................................................................... 317
5.3 Applications of Syntax-Directed Translation............................................. 318
5.3.1 Construction of Syntax Trees........................................................... 318
5.3.2 The Structure of a Type..................................................................... 321
5.3.3 Exercises for Section 5.3................................................................... 323
5.4 Syntax-Directed Translation Schemes........................................................ 324
5.4.1 Postfix Translation Schemes........................................................... 324
5.4.2 Parser-Stack Implementation of Postfix SDT's ........................ 325
5.4.3 SDT's With Actions Inside Productions........................................ 327
5.4.4 Eliminating Left Recursion From SDT's....................................... 328
5.4.5 SDT's for L-Attributed Definitions................................................. 331
5.4.6 Exercises for Section 5.4................................................................... 336
5.5 Implementing L-Attributed SDD's............................................................... 337
5.5.1 Translation During Recursive-Descent Parsing ........................ 338
5.5.2 On-The-Fly Code Generation........................................................... 340
5.5.3 L-Attributed SDD's and LL Parsing.............................................. 343
5.5.4 Bottom-Up Parsing of L-Attributed SDD's ................................ 348
5.5.5 Exercises for Section 5.5................................................................... 352
5.6 Summary of Chapter 5.................................................................................... 353
5.7 References for Chapter 5................................................................................. 354
6 Intermediate-Code Generation 357
6.1 Variants of Syntax Trees................................................................................ 358
6.1.1 Directed Acyclic Graphs for Expressions.............................. 359
6.1.2 The Value-Number Method for Constructing DAG's ... 360
6.1.3 Exercises for Section 6.1................................................................... 362
6.2 Three-Address Code......................................................................................... 363
6.2.1 Addresses and Instructions............................................................. 364
6.2.2 Quadruples........................................................................................... 366
6.2.3 Triples................................................................................................... 367
6.2.4 Static Single-Assignment Form...................................................... 369
6.2.5 Exercises for Section 6.2................................................................... 370
6.3 Types and Declarations................................................................................... 370
6.3.1 Type Expressions.................................................................................... 371
6.3.2 Type Equivalence................................................................................... 372
6.3.3 Declarations............................................................................................ 373
6.3.4 Storage Layout for Local Names....................................................... 373
6.3.5 Sequences of Declarations................................................................... 376
6.3.6 Fields in Records and Classes........................................................... 376
6.3.7 Exercises for Section 6.3...................................................................... 378
6.4 Translation of Expressions............................................................................... 378
6.4.1 Operations Within Expressions...................................................... 378
6.4.2 Incremental Translation...................................................................... 380
6.4.3 Addressing Array Elements............................................................. 381
6.4.4 Translation of Array References..................................................... 383
6.4.5 Exercises for Section 6.4................................................................... 384
6.5 Type Checking................................................................................................... 386
6.5.1 Rules for Type Checking.................................................................... 387
6.5.2 Type Conversions ............................................................................. 388
6.5.3 Overloading of Functions and Operators...................................... 390
6.5.4 Type Inference and Polymorphic Functions.................................. 391
6.5.5 An Algorithm for Unification........................................................... 395
6.5.6 Exercises for Section 6.5................................................................... 398
6.6 Control Flow...................................................................................................... 399
6.6.1 Boolean Expressions.......................................................................... 399
6.6.2 Short-Circuit Code............................................................................. 400
6.6.3 Flow-of-Control Statements............................................................ 401
6.6.4 Control-Flow Translation of Boolean Expressions..................... 403
6.6.5 Avoiding Redundant Gotos............................................................... 405
6.6.6 Boolean Values and Jumping Code................................................ 408
6.6.7 Exercises for Section 6.6 ............................................................... . 408
6.7 Backpatching..................................................................................................... 410
6.7.1 One-Pass Code Generation Using Backpatching........................ 410
6.7.2 Backpatching for Boolean Expressions ....................................... 411
6.7.3 Flow-of-Control Statements............................................................ 413
6.7.4 Break-, Continue-, and Goto-Statements..................................... 416
6.7.5 Exercises for Section 6.7................................................................... 417
6.8 Switch-Statements ...................................................................................... . 418
6.8.1 Translation of Switch-Statements................................................. 419
6.8.2 Syntax-Directed Translation of Switch-Statements . . . . 420
6.8.3 Exercises for Section 6.8................................................................... 421
6.9 Intermediate Code for Procedures................................................................ 422
6.10 Summary of Chapter 6.................................................................................... 424
6.11 References for Chapter 6..................................................................... 425 7 Run-Time Environments 427
7.1 Storage Organization...................................................................................... 427
7.1.1 Static Versus Dynamic Storage Allocation .... ..... 429
7.2 Stack Allocation of Space....................................................................... 430
7.2.1 Activation Trees.................................................................................. 430
7.2.2 Activation Records............................................................................. 433
7.2.3 Calling Sequences ............................................................................ 436
7.2.4 Variable-Length Data on the Stack............................................... 438
7.2.5 Exercises for Section 7.2................................................................... 440
7.3 Access to Nonlocal Data on the Stack......................................................... 441
7.3.1 Data Access Without Nested Procedures..................................... 442
7.3.2 Issues With Nested Procedures...................................................... 442
7.3.3 A Language With Nested Procedure Declarations...................... 443
7.3.4 Nesting Depth..................................................................................... 443
7.3.5 Access Links........................................................................................ 445
7.3.6 Manipulating Access Links.............................................................. 447
7.3.7 Access Links for Procedure Parameters ...................................... 448
7.3.8 Displays................................................................................................ 449
7.3.9 Exercises for Section 7.3................................................................... 451
7.4 Heap Management........................................................................................... 452
7.4.1 The Memory Manager . . . 453
7.4.2 The Memory Hierarchy of a Computer........................................... 454
7.4.3 Locality in Programs.......................................................................... 455
7.4.4 Reducing Fragmentation.................................................................. 457
7.4.5 Manual Deallocation Requests . 460
7.4.6 Exercises for Section 7.4................................................................... 463
7.5 Introduction to Garbage Collection.............................................................. 463
7.5.1 Design Goals for Garbage Collectors............................................. 464
7.5.2 Reachability........................................................................................ 466
7.5.3 Reference Counting Garbage Collectors........................................ 468
7.5.4 Exercises for Section 7.5................................................................... 470
7.6 Introduction to Trace-Based Collection...................................................... 470
7.6.1 A Basic Mark-and-Sweep Collector............................................... 471
7.6.2 Basic Abstraction ............................................................................. 473
7.6.3 Optimizing Mark-and-Sweep.......................................................... 475
7.6.4 Mark-and-Compact Garbage Collectors . 476
7.6.5 Copying collectors............................................................................... 478
7.6.6 Comparing Costs................................................................................ 482
7.6.7 Exercises for Section 7.6 . . 482
7.7 Short-Pause Garbage Collection . . 483
7.7.1 Incremental Garbage Collection..................................................... 483
7.7.2 Incremental Reachability Analysis . 485
7.7.3 Partial-Collection Basics.................................................................. 487
7.7.4 Generational Garbage Collection................................................... 488
7.7.5 The Train Algorithm.................. 490 7.7.6 Exercises for Section 7.7 493
7.8 Advanced Topics in Garbage Collection.......................................................... 494
7.8.1 Parallel and Concurrent Garbage Collection.................................. 495
7.8.2 Partial Object Relocation.................................................................... 497
7.8.3 Conservative Collection for Unsafe Languages........................... 498
7.8.4 Weak References................................................................................. 498
7.8.5 Exercises for Section 7.8................................................................... 499
7.9 Summary of Chapter 7.................................................................................... 500
7.10 References for Chapter 7................................................................................. 502
8 Code Generation 505
8.1 Issues in the Design of a Code Generator . 506
8.1.1 Input to the Code Generator............................................................ 507
8.1.2 The Target Program........................................................................... 507
8.1.3 Instruction Selection . 508
8.1.4 Register Allocation............................................................................. 510
8.1.5 Evaluation Order................................................................................ 511
8.2 The Target Language ..................................................................................... 512
8.2.1 A Simple Target Machine Model.................................................... 512
8.2.2 Program and Instruction Costs . 515
8.2.3 Exercises for Section 8.2................................................................... 516
8.3 Addresses in the Target Code........................................................................ 518
8.3.1 Static Allocation ............ . 518
8.3.2 Stack Allocation ............................................................................. . 520
8.3.3 Run-Time Addresses for Names . . 522
8.3.4 Exercises for Section 8.3 . 524
8.4 Basic Blocks and Flow Graphs...................................................................... 525
8.4.1 Basic Blocks ...................................................................................... 526
8.4.2 Next-Use Information....................................................................... 528
8.4.3 Flow Graphs .................... . 529
8.4.4 Representation of Flow Graphs . 530
8.4.5 Loops ................................................................................................. . 531
8.4.6 Exercises for Section 8.4................................................................... 531
8.5 Optimization of Basic Blocks ................. . 533
8.5.1 The DAG Representation of Basic Blocks . 533
8.5.2 Finding Local Common Subexpressions . 534
8.5.3 Dead Code Elimination ................................................................ . 535
8.5.4 The Use of Algebraic Identities...................................................... 536
8.5.5 Representation of Array References . . . . 537
8.5.6 Pointer Assignments and Procedure Calls . 539
8.5.7 Reassembling Basic Blocks From DAG's...................................... 539
8.5.8 Exercises for Section 8.5 ................... . 541
8.6 A Simple Code Generator............................................................................... 542
8.6.1 Register and Address Descriptors . . 543
8.6.2 The Code-Generation Algorithm..................................................... 544
8.6.3 Design of the Function getReg............................................... 547
8.6. ................................... 548
8.7 Peephole Optimization.................................................................................... 549
8.7.1 Eliminating Redundant Loads and Stores..................... 550
8.7.2 Eliminating Unreachable Code....................................... 550
8.7.3 Flow-of-Control Optimizations......................................... 551
8.7.4 Algebraic Simplification and Reduction in Strength . . . . 552
8.7.5 Use of Machine Idioms........................................................ 552
8.7. Exercises for Section 8.7..................................................... 553
8.8 Register Allocation and Assignment........................................................... 553
8.8.1 Global Register Allocation................................................. 553
8.8.2 Usage Counts........................................................................ 554
8.8.3 Register Assignment for Outer Loops ............................ 556
8.8.4 Register Allocation by Graph Coloring............................ 556
8.8.5 Exercises for Section 8.8..................................................... 557
8.9 Instruction Selection by Tree Rewriting ... . .................................... 558
8.9.1 Tree-Translation Schemes................................................. 558
8.9.2 Code Generation by Tiling an Input Tree........................ 560
8.9.3 Pattern Matching by Parsing............................................. 563
8.9.4 Routines for Semantic Checking ..................................... 565
8.9.5 General Tree Matching........................................................ 565
8.9.6 Exercises for Section 8.9.................................................. .567
8.10 Optimal Code Generatipn for Expressions................................................ 567
8.10.1 Ershov Numbers................................................................. 567
8.10.2 Generating Code From Labeled Expression Trees....... 568
8.10.3 Evaluating Expressions with an Insufficient Supply of Registers 570
8.10.4 Exercises for Section 8.10................................................... 572
8.11 Dynamic Programming Code-Generation................................................... 573
8.11.1 Contiguous Evaluation........................................................ 574
8.11.2 The Dynamic Programming Algorithm............................ 575
8.11.3 Exercises for Section 8.11................................................... 577
8.12 Summary of Chapter 8............................... .................................................. 578
8.13 References for Chapter 8................................................................................. 579
9 Machine-Independent Optimizations 583
9.1 The Principal Sources of Optimization........................................................... 584
9.1.1 Causes of Redundancy......................................................... 584
9.1.2 A Running Example: Quicksort......................................... 585
9.1.3 Semantics-Preserving Transformations......................... 586
9.1.4 Global Common Subexpressions .................................... 588
9.1.5 Copy Propagation................................................................. 590
9.1.6 Dead-Code Elimination...................................................... 591
9.1.7 Code Motion........................................................................... 592
9.1.8 Induction Variables and Reduction in Strength............ 592
9.1.9 Exercises for Section 9.1......................................................... 596
9.2 Introduction to Data-Flow Analysis ........................................................... 597
9.2.1 The Data-Flow Abstraction............................................... 597
9.2.2 The Data-Flow Analysis Schema..................................... 599
9.2.3 Data-Flow Schemas on Basic Blocks............................... 600
9.2.4 Reaching Definitions . ............................ 601
9.2.5 Live-Variable Analysis....................................................... 608
9.2.6 Available Expressions........................................................ 610
9.2.7 Summary................................................................................ 614
9.2.8 Exercises for Section 9.2..................................................... 615
9.3 Foundations of Data-Flow Analysis............................................................. 618
9.3.1 Semilattices.......................................................................... 618
9.3.2 Transfer Functions............................................................... 623
9.3.3 The Iterative Algorithm for General Frameworks........ 626
9.3.4 Meaning of a Data-Flow Solution..................................... 628
9.3.5 Exercises for Section 9.3..................................................... 631
9.4 Constant Propagation..................................................................................... 632
9.4.1 Data-Flow Values for the Constant-Propagation Framework 633
9.4.2 The Meet for the Constant-Propagation Framework . . . 633
9.4.3 Transfer Functions for the Constant-Propagation Framework 634
9.4.4 Monotonicity ofthe Constant-Propagation Framework . . 635
9.4.5 Nondistributivity of the Constant-Propagation Framework 635
9.4.6 Interpretation of the Results ........................................... 637
9.4.7 Exercises for Section 9.4 . . . . 637
9.5 Partial-Redundancy Elimination.................................................................. 639
9.5.1 The Sources of Redundancy . . 639
9.5.2 Can All Redundancy Be Eliminated?.............................. 642
9.5.3 The Lazy-Code-Motion Problem . . 644
9.5.4 Anticipation of Expressions ............. . 645
9.5.5 The Lazy-Code-Motion Algorithm . 646
9.5.6 Exercises for Section 9.5 . 655
9.6 Loops in Flow Graphs .............. . 655
9.6.1 Dominators............................................................................ 656
9.6.2 Depth-First Ordering ......................................................... 660
9.6.3 Edges in a Depth-First Spanning Tree............................ 661
9.6.4 Back Edges and Reducibility . 662
9.6.5 Depth of a Flow Graph .................................................................... . 665
9.6.6 Natural Loops ..................................................................... 665
9.6.7 Speed of Convergence of Iterative Data-Flow Algorithms . 667
9.6.8 Exercises for Section 9.6 . 669
9.7 Region-Based Analysis ........................................................... . 672
9.7.1 Regions................................................................................... 672
9.7.2 Region Hierarchies for Reducible Flow Graphs . 673
9.7.3 Overview of a Region-Based Analysis ............................ 676
9.7.4 Necessary Assumptions About Transfer Functions . ... 678
9.7.5 An Algorithm for Region-Based Analysis ..................... 680
9.7.6 Handling Nonreducible Flow Graphs............................... 684
9.7.7 Exercises for Section 9.7...................................................... 686
9.8 Symbolic Analysis............................................................................. 686
9.8.1 Affine Expressions of Reference Variables ................... 687
9.8.2 Data-Flow Problem Formulation .................................... 689
9.8.3 Region-Based Symbolic Analysis . 694
9.8.4 Exercises for Section 9.8 . ................................................. 699
9.9 Summary of Chapter 9.................................................................................... 700
9.10 References for Chapter 9................................................................................. 703
10 Instruction-Level- Parallelism 707
10.1 Processor Architectures ................................................................................. 708
10.1.1 Instruction Pipelines and Branch Delays........................ 708
10.1.2 Pipelined Execution.............................................................. 709
10.1.3 Multiple Instruction Issue.................................................. 710
10.2 Code-Scheduling Constraints........................................................................ 710
10.2.1 Data Dependence.................................................................. 711
10.2.2 Finding Dependences Among Memory Accesses............ 712
10.2.3 Tradeoff Between Register Usage and Parallelism..... 713
10.2.4 Phase Ordering Between Register Allocation and Code Scheduling 716
10.2.5 Control Dependence............................................................. 716
10.2.6 Speculative Execution Support.......................................... 717
10.2.7 A Basic Machine Model . . 719
10.2.8 Exercises for Section 10.2 . 720
10.3 Basic-Block Scheduling................................................................................... 721
10.3.1 Data-Dependence Graphs................................................... 722
10.3.2 List Scheduling of Basic Blocks ....................................... 723
10.3.3 Prioritized Topological Orders ................................. 725
10.3.4 Exercises for Section 10.3................................................... 726
10.4 Global Code Scheduling.................................................................................. 727
10.4.1 Primitive Code Motion ....................................................... 728
10.4.2 Upward Code Motion ......................................................... 730
10.4.3 Downward Code Motion....................................................... 731
10.4.4 Updating Data Dependences.............................................. 732
10.4.5 Global Scheduling Algorithms . ....................................... 732
10.4.6 Advanced Code Motion Techniques.................................. 736
10.4.7 Interaction with Dynamic Schedulers . . 737
10.4.8 Exercises for Section lOA........................... ....................... 737
10.5 Software Pipelining.......................................................................................... 738
10.5.1 Introduction .......................................................................... 738
10.5.2 Software Pipelining of Loops................................................... . 740
10.5.3 Register Allocation and Code Generation....................................... 743
10.5.4 Do-Across Loops..................................................................................... 743
10.5.5 Goals and Constraints of Software Pipelining . 745
10.5.6 A Software-Pipelining Algorithm...................................................... 749
10.5.7 Scheduling Acyclic Data-Dependence Graphs . 749
10.5.8 Scheduling Cyclic Dependence Graphs . . . . 751
10.5.9 Improvements to the Pipelining Algorithms................................ 758
10.5.10 Modular Variable Expansion........................................................... 758
10.5.11 Conditional Statements................................................................... 761
10.5.12 Hardware Support for Software Pipelining.................................. 762
10.5.13 Exercises for Section 10.5................................................................. 763
10.6 Summary of Chapter 10.................................................................................. 765
10.7 References for Chapter 10.............................................................................. 766
11 Optimizing for Parallelism and Locality 769
11.1 Basic Concepts.................................................................................................. 771
11.1.1 Multiprocessors................................................................................... 772
11.1.2 Parallelism in Applications............................................................. 773
11.1.3 Loop-Level Parallelism..................................................................... 775
11.1.4 Data Locality ......................... . 777
11.1.5 Introduction to Affine Transform Theory .................................... 778
11.2 Matrix Multiply: An In-Depth Example...................................................... 782
11.2.1 The Matrix-Multiplication Algorithm . 782
11.2.2 Optimizations..................................................................................... 785
11.2.3 Cache Interference .......................................................................... . 788
11.2.4 Exercises for Section 11.2................................................................. 788
11.3 Iteration Spaces................................................................................................ 788
11.3.1 Constructing Iteration Spaces from Loop Nests......................... 788
11.3.2 Execution Order for Loop Nests .................................................... 791
11.3.3 Matrix Formulation of Inequalities............................................... 791
11.3.4 Incorporating Symbolic Constants................................................. 793
11.3.5 Controlling the Order of Execution................................................. 793
11.3.6 Changing Axes..................................................................................... 798
11.3.7 Exercises for Section 11.3................................................................. 799
11.4 Affine Array Indexes........................................................................................ 801
11.4.1 Affine Accesses.................................................................................... 802
11.4.2 Affine and Nonaffine Accesses in Practice.................................... 803
11.4.3 Exercises for Section 11.4................................................................. 804
11.5 Data Reuse ................... . 804
11.5.1 Types of Reuse..................................................................................... 805
11.5.2 Self Reuse............................................................................................. 806
11.5.3 Self-Spatial Reuse . 809
11.5.4 Group Reuse . . . . 811
11.5.5 Exercises for Section 11.5................................................................. 814
11.6 Array Data-Dependence Analysis................................................................ 815
11.6.1 Definition of Data Dependence of Array Accesses....................... 816
11.6.2 Integer Linear Programming ......................................................... 817
11.6.3 The GCD Test...................................................................................... 818
11.6.4 Heuristics for Solving Integer Linear Programs.......................... 820
11.6.5 Solving General Integer Linear Programs .................................. 823
11.6.6 Summary.............................................................................................. 825
11.6.7 Exercises for Section 11.6................................................................. 826
11.7 Finding Synchronization-Free Parallelism .............................................. 828
11.7.1 An Introductory Example................................................................. 828
11.7.2 Affine Space Partitions..................................................................... 830
11.7.3 Space-Partition Constraints............................................................ 831
11.7.4 Solving Space-Partition Constraints............................................. 835
11.7.5 A Simple Code-Generation Algorithm........................................... 838
11.7.6 Eliminating Empty Iterations........................................................ 841
11.7.7 Eliminating Tests from Innermost Loops.................................... 844
11.7.8 Source-Code Transforms................................................................... 846
11.7.9 Exercises for Section 11.7................................................................. 851
11.8 Synchronization Between Parallel Loops................................................... 853
11.8.1 A Constant Number of Synchronizations..................................... 853
11.8.2 Program-Dependence Graphs.......................................................... 854
11.8.3 Hierarchical Time ............................................................................. 857
11.8.4 The Parallelization Algorithm........................................................ 859
11.8.5 Exercises for Section 11.8................................................................. 860
11.9 Pipelining........................................................................................................... 861
11.9.1 What is Pipelining?............................................................................ 861
11.9.2 Successive Over-Relaxation (SOR): An Example........................ 863
11.9.3 Fully Permutable Loops.................................................................... 864
11.9.4 Pipelining Fully Permutable Loops................................................ 864
11.9.5 General Theory.................................................................................... 867
11.9.6 Time-Partition Constraints............................................................. 868
11.9.7 Solving Time-Partition Constraints by Farkas' Lemma • . 872
11.9.8 Code Transformations....................................................................... 875
11.9.9 Parallelism With Minimum Synchronization.............................. 880
11.9.10 Exercises for Section 11.9................................................................. 882
11.10 Locality Optimizations.................................................................................. 884
11.10.1Temporal Locality of Computed Data........................................... 885
11.10.2Array Contraction.................................................................................. 885
11.10.3Partition Interleaving ......................................................................... 887
11.10.4Putting it All Together .................................................................... 890
11.10.5Exercises for Section 11.10 ............................................................. 892
11.11 Other Uses of Affine Transforms.................................................................... 893
11.11.1Distributed memory machines........................................................... 894
11.11.2 Multi-Instruction-Issue Processors............................................... 895
11.11.3Vector and SIMD Instructions ....................................................... 895
11.11.4 Prefetching.......................................................................................... 896
11.12 Summary of Chapter 11................................................................................ 897
11.13 References for Chapter 11 . . 899
12 Interprocedural Analysis 903
12.1 Basic Concepts.................................................................................................. 904
12.1.1 Call Graphs......................................................................................... 904
12.1.2 Context Sensitivity . . 906
12.1.3 Call Strings ..................................................................................... . 908
12.1.4 Cloning-Based Context-Sensitive Analysis . 910
12.1.5 Summary-Based Context-Sensitive Analysis............................. 911
12.1.6 Exercises for Section 12.1............................................................... ' 914
12.2 Why Interprocedural Analysis?..................................................................... 916
12.2.1 Virtual Method Invocation............................................................... 916
12.2.2 Pointer Alias Analysis...................................................................... 917
12.2.3 Parallelization .................................................................................. 917
12.2.4 Detection of Software Errors and Vulnerabilities .................... 917
12.2.5 SQL Injection...................................................................................... 918
12.2.6 Buffer Overflow................................................................................... 920
12.3 A Logical Representation of Data Flow . . 921
12.3.1 Introduction to Datalog.................................................................... 921
12.3.2 Datalog Rules .................................. . 922
12.3.3 Intensional and Extensional Predicates . . 924
12.3.4 Execution of Datalog Programs .................................................. . 927
12.3.5 Incremental Evaluation of Datalog Programs............................ 928
12.3.6 Problematic Datalog Rules.............................................................. 930
12.3.7 Exercises for Section 12.3................................................................ 932
12.4 A Simple Pointer-Analysis Algorithm......................................................... 933
12.4.1 Why is Pointer Analysis Difficult................................................... 934
12.4.2 A Model for Pointers and References . . 935
12.4.3 Flow Insensitivity ............................................................................ 936
12.4.4 The Formulation in Datalog............................................................ 937
12.4.5 Using Type Information................................................................... 938
12.4.6 Exercises for Section 12.4 . . . 939
12.5 Context-Insensitive Interprocedural Analysis.......................................... 941
12.5.1 Effects of a Method Invocation........................................................ 941
12.5.2 Call Graph Discovery in Datalog.................................................... 943
12.5.3 Dynamic Loading and Reflection.................................................... 944
12.5.4 Exercises for Section 12.5................................................................ 945
12.6 Context-Sensitive Pointer Analysis ........................................................... 945
12.6.1 Contexts and Call Strings............................................................... 946
12.6.2 Adding Context to Datalog Rules................................................... 949
12.6.3 Additional Observations About Sensitivity................................ 949
12.6.4 Exercises for Section 12.6................................................................ 950
12.7 Datalog Implementation by BDD's.............................................................. 951
12.7.1 Binary Decision Diagrams................................................................. 951
12.7.2 Transformations on BDD's ............................................................ 953
12.7.3 Representing Relations by BDD's.................................................. 954
12.7.4 Relational Operations as BDD Operations................................. 954
12.7.5 Using BDD's for Points-to Analysis ............................................. 957
12.7.6 Exercises for Section 12.7................................................................ 958
12.8 Summary of Chapter 12.................................................................................. 958
12.9 References for Chapter 12.............................................................................. 961
A A Complete Front End 965
A.l The Source Language ......................................................................................... 965
A.2 Main....................................................................................................................... 966
A.3 Lexical Analyzer.................................................................................................. 967
A.4 Symbol Tables and Types................................................................................. 970
A.5 Intermediate Code for Expressions................................................................ 971
A.6 Jumping Code for Boolean Expressions ....................................................... 974
A.7 Intermediate Code for Statements ............................................................... 978
A.8 Parser..................................................................................................................... 981
A.9 Creating the Front End...................................................................................... 986
B Finding Linearly Independent Solutions 989
Index 993
Chapter 1
Introduction
Programming languages are notations for describing computations to people and to machines. The world as we know it depends on programming languages, because all the software running on all the computers was written in some programming language. But, before a program can be run, it first must be translated into a form in which it can be executed by a computer.
The software systems that do this translation are called compilers.
This book is about how to design and implement compilers. We shall discover that a few basic ideas can be used to construct translators for a wide variety of languages and machines. Besides compilers, the principles and techniques for compiler design are applicable to so many other domains that they are likely to be reused many times in the career of a computer scientist. The study of compiler writing touches upon programming languages, machine architecture, language theory, algorithms, and software engineering.
In this preliminary chapter, we introduce the different forms of language translators, give a high level overview of the structure of a typical compiler, and discuss the trends in programming languages and machine architecture that are shaping compilers. We include some observations on the relationship between compiler design and computer-science theory and an outline of the applications of compiler technology that go beyond compilation. We end with a brief outline of key programming-language concepts that will be needed for our study of compilers.
1.1 Language Processors
Simply stated, a compiler is a program that can read a program in one language — the source language — and translate it into an equivalent program in another language — the target language; see Fig. 1.1. An important role of the compiler is to report any errors in the source program that it detects during the translation process.
If the target program is an executable machine-language program, it can then be called by the user to process inputs and produce outputs; see Fig. 1.2.
An interpreter is another common kind of language processor. Instead of producing a target program as a translation, an interpreter appears to directly execute the operations specified in the source program on inputs supplied by the user, as shown in Fig. 1.3.
The machine-language target program produced by a compiler is usually much faster than an interpreter at mapping inputs to outputs . An interpreter, however, can usually give better error diagnostics than a compiler, because it executes the source program statement by statement.
Example 1.1: Java language processors combine compilation and interpretation, as shown in Fig. 1.4. A Java source program may first be compiled into an intermediate form called bytecodes. The bytecodes are then interpreted by a virtual machine. A benefit of this arrangement is that bytecodes compiled on one machine can be interpreted on another machine, perhaps across a network.
In order to achieve faster processing of inputs to outputs, some Java compilers, called just-in-time compilers, translate the bytecodes into machine language immediately before they run the intermediate program to process the input. □
In addition to a compiler, several other programs may be required to create an executable target program, as shown in Fig. 1.5. A source program may be divided into modules stored in separate files. The task of collecting the source program is sometimes entrusted to a separate program, called a preprocessor. The preprocessor may also expand shorthands, called macros, into source language statements.
The modified source program is then fed to a compiler. The compiler may produce an assembly-language program as its output, because assembly language is easier to produce as output and is easier to debug. The assembly language is then processed by a program called an assembler that produces relocatable machine code as its output.
Large programs are often compiled in pieces, so the relocatable machine code may have to be linked together with other relocatable object files and library files into the code that actually runs on the machine. The linker resolves external memory addresses, where the code in one file may refer to a location in another file. The loader then puts together all of the executable object files into memory for execution.
1.1.1 Exercises for Section 1.1
Exercise 1.1.1: What is the difference between a compiler and an interpreter?
Exercise 1.1.2 : What are the advantages of (a) a compiler over an interpreter (b) an interpreter over a compiler?
Exercise 1.1.3 : What advantages are there to a language-processing system in which the compiler produces assembly language rather than machine language?
Exercise 1.1.4: A compiler that translates a high-level language into another high-level language is called a source-to-source translator. What advantages are there to using C as a target language for a compiler?
Exercise 1.1.5: Describe some of the tasks that an assembler needs to perform.
1.2 The Structure of a Compiler
Up to this point we have treated a compiler as a single box that maps a source program into a semantically equivalent target program. If we open up this box a little, we see that there are two parts to this mapping: analysis and synthesis.
The analysis part breaks up the source program into constituent pieces and imposes a grammatical structure on them. It then uses this structure to create an intermediate representation of the source program. If the analysis part detects that the source program is either syntactically ill formed or semanti- cally unsound, then it must provide informative messages, so the user can take corrective action. The analysis part also collects information about the source program and stores it in a data structure called a symbol table, which is passed along with the intermediate representation to the synthesis part.
The synthesis part constructs the desired target program from the intermediate representation and the information in the symbol table. The analysis part is often called the front end of the compiler; the synthesis part is the back end.
If we examine the compilation process in more detail, we see that it operates as a sequence of phases, each of which transforms one representation of the source program to another. A typical decomposition of a compiler into phases is shown in Fig. 1.6. In practice, several phases may be grouped together, and the intermediate representations between the grouped phases need not be constructed explicitly. The symbol table, which stores information about the
entire source program, is used by all phases of the compiler.
Some compilers have a machine-independent optimization phase between the front end and the back end. The purpose of this optimization phase is to perform transformations on the intermediate representation, so that the back end can produce a better target program than it would have otherwise produced from an unoptimized intermediate representation. Since optimization is optional, one or the other of the two optimization phases shown in Fig. 1.6 may be missing.
1.2.1 Lexical Analysis
The first phase of a compiler is called lexical analysis or scanning. The lexical analyzer reads the stream of characters making up the source program
and groups the characters into meaningful sequences called lexemes. For each lexeme, the lexical analyzer produces as output a token of the form
{token-name, attribute-value)
that it passes on to the subsequent phase, syntax analysis. In the token, the first component token-name is an abstract symbol that is used during syntax analysis, and the second component attribute-value points to an entry in the symbol table for this token. Information from the symbol-table entry'is needed for semantic analysis and code generation.
For example, suppose a source program contains the assignment statement
position = initial + rate * 60 (1.1)
The characters in this assignment could be grouped into the following lexemes and mapped into the following tokens passed on to the syntax analyzer:
- position is a lexeme that would be mapped into a token {id, 1), where id is an abstract symbol standing for identifier and 1 points to the symbol- table entry for position. The symbol-table entry for an identifier holds information about the identifier, such as its name and type.
- The assignment symbol = is a lexeme that is mapped into the token {=). Since this token needs no attribute-value, we have omitted the second component. We could have used any abstract symbol such as assign for the token-name, but for notational convenience we have chosen to use the lexeme itself as the name of the abstract symbol.
- initial is a lexeme that is mapped into the token (id, 2), where 2 points to the symbol-table entry for initial.
- + is a lexeme that is mapped into the token (+).
- rate is a lexeme that is mapped into the token (id, 3), where 3 points to the symbol-table entry for rate.
- * is a lexeme that is mapped into the token (*) .
- 60 is a lexeme that is mapped into the token (60).[1]
Blanks separating the lexemes would be discarded by the lexical analyzer.
Figure 1.7 shows the representation of the assignment statement (1.1) after lexical analysis as the sequence of tokens
(id,l) (=) (id, 2) (+) (id,3) (*) (60) (1.2)
In this representation, the token names =, +, and * are abstract symbols for the assignment, addition, and multiplication operators, respectively.
1.2.2 Syntax Analysis
The second phase of the compiler is syntax analysis or parsing. The parser uses the first components of the tokens produced by the lexical analyzer to create a tree-like intermediate representation that depicts the grammatical structure of the token stream. A typical representation is a syntax tree in which each interior node represents an operation and the children of the node represent the arguments of the operation. A syntax tree for the token stream (1.2) is shown as the output of the syntactic analyzer in Fig. 1.7.
This tree shows the order in which the operations in the assignment
position = initial + rate * 60
are to be performed. The tree has an interior node labeled * with (id, 3) as its left child and the integer 60 as its right child. The node (id, 3) represents the identifier rate. The node labeled * makes it explicit that we must first multiply the value of rate by 60. The node labeled + indicates that we must add the result of this multiplication to the value of initial. The root of the tree, labeled =, indicates that we must store the result of this addition into the location for the identifier position. This ordering of operations is consistent with the usual conventions of arithmetic which tell us that multiplication has higher precedence than addition, and hence that the multiplication is to be performed before the addition.
The subsequent phases of the compiler use the grammatical structure to help analyze the source program and generate the target program. In Chapter 4 we shall use context-free grammars to specify the grammatical structure of programming languages and discuss algorithms for constructing efficient syntax analyzers automatically from certain classes of grammars. In Chapters 2 and 5 we shall see that syntax-directed definitions can help specify the translation of programming language constructs.
1.2.3 Semantic Analysis
The semantic analyzer uses the syntax tree and the information in the symbol table to check the source program for semantic consistency with the language definition. It also gathers type information and saves it in either the syntax tree or the symbol table, for subsequent use during intermediate-code generation.
I An important part of semantic analysis is type checking,Iwhere the compiler checks that each operator has matching operands. For example, many programming language definitions require an array index to be an integer; the compiler must report an error if a floating-point number is used to index an array.
The language specification may permit some type conversions called coercions. For example, a binary arithmetic operator may be applied to either a pair of integers or to a pair of floating-point numbers. If the operator is applied to a floating-point number and an integer, the compiler may convert or coerce the integer into a floating-point number.
Such a coercion appears in Fig. 1.7. Suppose that position, initial, and rate have been declared to be floating-point numbers, and that the lexeme 60 by itself forms an integer. The type checker in the semantic analyzer in Fig. 1.7 discovers that the operator * is applied to a floating-point number rate and an integer 60. In this case, the integer may be converted into a floating-point number. In Fig. 1.7, notice that the output of the semantic analyzer has an extra node for the operator inttofloat, which explicitly converts its integer argument into a floating-point number. Type checking and semantic analysis are discussed in Chapter 6.
1.2.4 Intermediate Code Generation
In the process of translating a source program into target code, a compiler may construct one or more intermediate representations, which can have a variety of forms. Syntax trees are a form of intermediate representation; they are commonly used during syntax and semantic analysis.
After syntax and semantic analysis of the source program, many compilers generate an explicit low-level or machine-like intermediate representation, which we can think of as a program for an abstract machine. This intermediate representation should have two important properties: it should be easy to produce and it should be easy to translate into the target machine.
In Chapter 6, we consider an intermediate form called three-address code, which consists of a sequence of assembly-like instructions with three operands per instruction. Each operand can act like a register. The output of the intermediate code generator in Fig. 1.7 consists of the three-address code sequence
tl = inttofloat(60) t2 = id3 * tl
t3 = id2 + t2 ( )
idl = t3
There are several points worth noting about three-address instructions. First, each three-address assignment instruction has at most one operator on the right side. Thus, these instructions fix the order in which operations are to be done; the multiplication precedes the addition in the source program (1.1). Second, the compiler must generate a temporary name to hold the value computed by a three-address instruction. Third, some "three-address instructions" like the first and last in the sequence (1.3), above, have fewer than three operands.
In Chapter 6, we cover the principal intermediate representations used in compilers. Chapters 5 introduces techniques for syntax-directed translation that are applied in Chapter 6 to type checking and intermediate-code generation for typical programming language constructs such as expressions, flow-of-control constructs, and procedure calls.
1.2.5 Code Optimization
The machine-independent code-optimization phase attempts to improve the intermediate code so that better target code will result. Usually better meanS faster, but other objectives may be desired, such as shorter code, or target code that consumes less power. For example, a straightforward algorithm generates the intermediate code (1.3), using an instruction for each operator in the tree representation that comes from the semantic analyzer.
| The first operand of each instruction specifies a destination. The F in each instruction tells us that it deals with floating-point numbers. The code in |
A simple intermediate code generation algorithm followed by code optimization is a reasonable way to generate good target code. The optimizer can deduce that the conversion of 60 from integer to floating point can be done once and for all at compile time, so the inttofloat operation can be eliminated by replacing the integer 60 by the floating-point number 60.0. Moreover, t3 is used only once to transmit its value to id1 so the optimizer can transform (1.3) into the shorter sequence
There is a great variation in the amount of code optimization different compilers perform. In those that do the most, the so-called "optimizing compilers," a significant amount of time is spent on this phase. There are simple optimizations that significantly improve the running time of the target program without slowing down compilation too much. The chapters from 8 on discuss machine-independent and machine-dependent optimizations in detail.
1.2.6 Code Generation
The code generator takes as input an intermediate representation of the source program and maps it into the target language. If the target language is machine code, registers Or memory locations are selected for each of the variables used by the program. Then, the intermediate instructions are translated into sequences of machine instructions that perform the same task. A crucial aspect of code generation is the judicious assignment of registers to hold variables.
For example, using registers R1 and R2, the intermediate code in (1.4) might get translated into the machine code
(1.5) loads the contents of address id3 into register R2, then multiplies it with floating-point constant 60.0. The # signifies that 60.0 is to be treated as an immediate constant. The third instruction moves id2 into register Rl and the fourth adds to it the value previously computed in register R2. Finally, the value in register Rl is stored into the address of idl, so the code correctly implements the assignment statement (1.1). Chapter 8 covers code generation.
This discussion of code generation has ignored the important issue of storage allocation for the identifiers in the source program. As we shall see in Chapter 7, the organization of storage at run-time depends on the language being compiled. Storage-allocation decisions are made either during intermediate code generation or during code generation.
1.2.7 Symbol-Table Management
An essential function of a compiler is to record the variable names used in the source program and collect information about various attributes of each name. These attributes may provide information about the storage allocated for a name, its type, its scope (where in the program its value may be used), and in the case of procedure names, such things as the number and types of its arguments, the method of passing each argument (for example, by value or by reference), and the type returned.
The symbol table is a data structure containing a record for each variable name, with fields for the attributes of the name. The data structure should be designed to allow the compiler to find the record for each name quickly and to store or retrieve data from that record quickly. Symbol tables are discussed in Chapter 2.
1.2.8 The Grouping of Phases into Passes
The discussion of phases deals with the logical organization of a compiler. In an implementation, activities from several phases may be grouped together into a pass that reads an input file and writes an output file. For example, the front-end phases of lexical analysis, syntax analysis, semantic analysis, and intermediate code generation might be grouped together into one pass. Code optimization might be an optional pass. Then there could be a back-end pass consisting of code generation for a particular target machine.
Some compiler collections have been created around carefully designed intermediate representations that allow the front end for a particular language to interface with the back end for a certain target machine. With these collections, we can produce compilers for different source languages for one target machine by combining different front ends with the back end for that target machine. Similarly, we can produce compilers for different target machines, by combining a front end with back ends for different target machines.
1.2.9 Compiler-Construction Tools
The compiler writer, like any software developer, can profitably use modern software development environments containing tools such as language editors, debuggers,
[1]TechnicaUy speaking, for the lexeme 60 we should make up a token like (number, 4), where 4 points to the symbol table for the internal representation of integer 60 but we shall defer the discussion of tokens for numbers until Chapter 2. Chapter 3 discusses techniques for building lexical analyzers.