Fast Fourier transform algorithms for parallel computers
Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used for many applications in engineering, science, and...
| Main Author: | Takahashi, Daisuke, 1961- |
|---|---|
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Singapore :
Springer,
2019.
|
| Physical Description: |
1 online resource (ix, 114 pages) : illustrations. |
| Series: |
High-performance computing series ;
v. 2. |
| Subjects: |
| Summary: |
Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used for many applications in engineering, science, and mathematics. Presenting many algorithms in pseudo-code and a complexity analysis, this book offers a valuable reference guide for graduate students, engineers, and scientists in the field who wish to apply FFT to large-scale problems. Parallel computation is becoming indispensable in solving the large-scale problems increasingly arising in a wide range of applications. The performance of parallel supercomputers is steadily improving, and it is expected that a massively parallel system with hundreds of thousands of compute nodes equipped with multi-core processors and accelerators will be available in the near future. Accordingly, the book also provides up-to-date computational techniques relevant to the FFT in state-of-the-art parallel computers. Following the introductory chapter, Chapter 2 introduces readers to the DFT and the basic idea of the FFT. Chapter 3 explains mixed-radix FFT algorithms, while Chapter 4 describes split-radix FFT algorithms. Chapter 5 explains multi-dimensional FFT algorithms, Chapter 6 presents high-performance FFT algorithms, and Chapter 7 addresses parallel FFT algorithms for shared-memory parallel computers. In closing, Chapter 8 describes parallel FFT algorithms for distributed-memory parallel computers. |
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| Item Description: |
Includes bibliographical references and index. Intro; Preface; Contents; 1 Introduction; References; 2 Fast Fourier Transform; 2.1 Definitions of DFT; 2.2 Basic Idea of FFT; 2.3 Cooley-Tukey FFT Algorithm; 2.4 Bit-Reversal Permutation; 2.5 Stockham FFT Algorithm; 2.6 FFT Algorithm for Real Data; 2.6.1 FFT of Two Real Data Simultaneously; 2.6.2 n-Point Real FFT Using n/2-Point Complex FFT; References; 3 Mixed-Radix FFT Algorithms; 3.1 Two-Dimensional Formulation of DFT; 3.2 Radix-3 FFT Algorithm; 3.3 Radix-4 FFT Algorithm; 3.4 Radix-5 FFT Algorithm; 3.5 Radix-8 FFT Algorithm; References; 4 Split-Radix FFT Algorithms. 4.1 Split-Radix FFT Algorithm; 4.2 Extended Split-Radix FFT Algorithm; References; 5 Multidimensional FFT Algorithms; 5.1 Definition of Two-Dimensional DFT; 5.2 Two-Dimensional FFT Algorithm; 5.3 Definition of Three-Dimensional DFT; 5.4 Three-Dimensional FFT Algorithm; Reference; 6 High-Performance FFT Algorithms; 6.1 Four-Step FFT Algorithm; 6.2 Five-Step FFT Algorithm; 6.3 Six-Step FFT Algorithm; 6.4 Blocked Six-Step FFT Algorithm; 6.5 Nine-Step FFT Algorithm; 6.6 Recursive Six-Step FFT Algorithm; 6.7 Blocked Multidimensional FFT Algorithms; 6.7.1 Blocked Two-Dimensional FFT Algorithm. 6.7.2 Blocked Three-Dimensional FFT Algorithm; 6.8 FFT Algorithms Suitable for Fused Multiply-Add (FMA) Instructions; 6.8.1 Introduction; 6.8.2 FFT Kernel; 6.8.3 Goedecker's Technique; 6.8.4 Radix-16 FFT Algorithm; 6.8.5 Radix-16 FFT Algorithm Suitable for Fused Multiply-Add Instructions; 6.8.6 Evaluation; 6.9 FFT Algorithms for SIMD Instructions; 6.9.1 Introduction; 6.9.2 Vectorization of FFT Kernels Using Intel SSE3 Instructions; 6.9.3 Vectorization of FFT Kernels Using Intel AVX-512 Instructions; References; 7 Parallel FFT Algorithms for Shared-Memory Parallel Computers. 7.1 Implementation of Parallel One-Dimensional FFT on Shared-Memory Parallel Computers; 7.1.1 Introduction; 7.1.2 A Recursive Three-Step FFT Algorithm; 7.1.3 Parallelization of Recursive Three-Step FFT; 7.2 Optimizing Parallel FFTs for Manycore Processors; 7.2.1 Introduction; 7.2.2 Parallelization of Six-Step FFT; 7.2.3 Performance Results; References; 8 Parallel FFT Algorithms for Distributed-Memory Parallel Computers; 8.1 Implementation of Parallel FFTs in Distributed-Memory Parallel Computers; 8.1.1 Parallel One-Dimensional FFT Using Block Distribution. 8.1.2 Parallel One-Dimensional FFT Using Cyclic Distribution; 8.1.3 Parallel Two-Dimensional FFT in Distributed-Memory Parallel Computers; 8.1.4 Parallel Three-Dimensional FFT in Distributed-Memory Parallel Computers; 8.2 Computation-Communication Overlap for Parallel One-Dimensional FFT; 8.2.1 Introduction; 8.2.2 Computation-Communication Overlap; 8.2.3 Automatic Tuning of Parallel One-Dimensional FFT; 8.2.4 Performance Results; 8.3 Parallel Three-Dimensional FFT Using Two-Dimensional Decomposition; 8.3.1 Introduction. Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used for many applications in engineering, science, and mathematics. Presenting many algorithms in pseudo-code and a complexity analysis, this book offers a valuable reference guide for graduate students, engineers, and scientists in the field who wish to apply FFT to large-scale problems. Parallel computation is becoming indispensable in solving the large-scale problems increasingly arising in a wide range of applications. The performance of parallel supercomputers is steadily improving, and it is expected that a massively parallel system with hundreds of thousands of compute nodes equipped with multi-core processors and accelerators will be available in the near future. Accordingly, the book also provides up-to-date computational techniques relevant to the FFT in state-of-the-art parallel computers. Following the introductory chapter, Chapter 2 introduces readers to the DFT and the basic idea of the FFT. Chapter 3 explains mixed-radix FFT algorithms, while Chapter 4 describes split-radix FFT algorithms. Chapter 5 explains multi-dimensional FFT algorithms, Chapter 6 presents high-performance FFT algorithms, and Chapter 7 addresses parallel FFT algorithms for shared-memory parallel computers. In closing, Chapter 8 describes parallel FFT algorithms for distributed-memory parallel computers. |
| Physical Description: |
1 online resource (ix, 114 pages) : illustrations. |
| Bibliography: |
Includes bibliographical references and index. |
| ISBN: |
9789811399657 9811399654 9811399646 9789811399640 9789811399664 9811399662 9789811399671 9811399670 |
| ISSN: |
2662-3420 ; |