A Guidebook to Fortran on Supercomputers

Preface1. Introduction 1.1 Conventional Computers 1.2 What's a Supercomputer Anyway? 1.3 Terminology 1.3.1 Scalar 1.3.2 Vector and Stride 1.3.3 Parallel and Concurrent 1.4 Amdahl's Law 1.4.1 Amdahl's Law for Vector Processors 1.4.2 Amdahl's Law for Parallel Processors 1.5 Summary Problems2. Supercomputer Architecture 2.1 Basic Features 2.1.1 Clock Cycle and Performance Measures 2.1.2 Registers 2.1.3 Functional Units 2.1.4 Memory Banks 2.1.5 Memory Caches 2.1.6 Instruction Streams and Data Streams 2.1.7 Summary 2.2 The Vector Processor 2.2.1 Memory-to-Memory Vector Processes 2.2.2 ETA 10 2.2.3 Register-to-Register Vector Processes Problems3. Fortran 3.1 Standard Fortran 3.1.1 Array Layout in Memory 3.2 Compilers 3.2.1 Machine-Independent Optimizations 3.2.2 Machine-Dependent Optimizations 3.3 Vectorization 3.3.1 Explicit Vectorization 3.3.2 Implicit Vectorization Problems4. Vectorization of Fortran Programs 4.1 Obtaining Timing Statistics 4.1.1 Flow Trace 4.1.2 FORGE Timing Facility 4.1.3 How to Use the Timing Statistics 4.2 Discussion of Amdahl's Law 4.3 Modularity and Optimization 4.3.1 Scalar-Valued Routines versus Array-Valued Routines 4.4 A Systematic Approach to Restructuring 4.4.1 Possible Inaccuracies Caused by Vectorization 4.5 Why the Programmer is Needed 4.5.1 Difficulties of Optimizing "Dusty Deck" Fortran 4.6 Candidates For Vectorization 4.7 Vectorization Inhibitors 4.7.1 Compiler Optimization with Incomplete Information 4.8 Effects of Array Access on Performance 4.9 Examples of Restructuring Fortran Loops 4.9.1 Introduction to Examples 4.9.2 Accessing Arrays 4.9.3 Scalar Temporaries (Simple) 4.9.4 Recursion Involving Arrays 4.9.5 Scalar Recursion 4.9.6 More Loop Switching 4.9.7 Loop Unrolling 4.9.8 IF Statements 4.9.9 Subprogram References 4.9.10 I/O Statements 4.9.11 Assigned GO TO Statements 4.9.12 Backward GO TOs 4.10 Summary ProblemsAppendixes A. Abbreviations and Glossary A.1 Common Abbreviations A.2 Glossary of Terms B. Examples of the FORGE Timing Facility B.1 Timing Results from LINPACK Benchmark B.2 Timing Results from HYGRID Program C. Loops for Memory-Access Comparison C.1 Group 1: Indirect Access with Random Index C.2 Group 2: Unitary Stride C.3 Group 3: Direct Access with Stride D. Solutions to ProblemsIndex