FFTW 3.2alpha2

FFTW User Manual

Welcome to FFTW, the Fastest Fourier Transform in the West. FFTW is a collection of fast C routines to compute the discrete Fourier transform. This manual documents FFTW version 3.2alpha2.

• Introduction
• Tutorial
• Other Important Topics
• FFTW Reference
• Multi-threaded FFTW
• Distributed-memory FFTW with MPI
• FFTW on the Cell Processor
• Calling FFTW from Fortran
• Upgrading from FFTW version 2
• Installation and Customization
• Acknowledgments
• License and Copyright
• Concept Index
• Library Index

--- The Detailed Node Listing ---

Tutorial

• Complex One-Dimensional DFTs
• Complex Multi-Dimensional DFTs
• One-Dimensional DFTs of Real Data
• Multi-Dimensional DFTs of Real Data
• More DFTs of Real Data

More DFTs of Real Data

• The Halfcomplex-format DFT
• Real even/odd DFTs (cosine/sine transforms)
• The Discrete Hartley Transform

Other Important Topics

• Data Alignment
• Multi-dimensional Array Format
• Words of Wisdom-Saving Plans
• Caveats in Using Wisdom

Data Alignment

• SIMD alignment and fftw_malloc
• Stack alignment on x86

Multi-dimensional Array Format

• Row-major Format
• Column-major Format
• Fixed-size Arrays in C
• Dynamic Arrays in C
• Dynamic Arrays in C-The Wrong Way

FFTW Reference

• Data Types and Files
• Using Plans
• Basic Interface
• Advanced Interface
• Guru Interface
• New-array Execute Functions
• Wisdom
• What FFTW Really Computes

Data Types and Files

• Complex numbers
• Precision
• Memory Allocation

Basic Interface

• Complex DFTs
• Planner Flags
• Real-data DFTs
• Real-data DFT Array Format
• Real-to-Real Transforms
• Real-to-Real Transform Kinds

Advanced Interface

• Advanced Complex DFTs
• Advanced Real-data DFTs
• Advanced Real-to-real Transforms

Guru Interface

• Interleaved and split arrays
• Guru vector and transform sizes
• Guru Complex DFTs
• Guru Real-data DFTs
• Guru Real-to-real Transforms
• 64-bit Guru Interface

Wisdom

• Wisdom Export
• Wisdom Import
• Forgetting Wisdom
• Wisdom Utilities

What FFTW Really Computes

• The 1d Discrete Fourier Transform (DFT)
• The 1d Real-data DFT
• 1d Real-even DFTs (DCTs)
• 1d Real-odd DFTs (DSTs)
• 1d Discrete Hartley Transforms (DHTs)
• Multi-dimensional Transforms

Multi-threaded FFTW

• Installation and Supported Hardware/Software
• Usage of Multi-threaded FFTW
• How Many Threads to Use?
• Thread safety

Distributed-memory FFTW with MPI

• FFTW MPI Installation
• Linking and Initializing MPI FFTW
• Simple MPI example
• MPI data distribution
• Multi-dimensional MPI DFT of Real Data
• Other Multi-dimensional Real-data MPI Transforms
• FFTW MPI Transposes
• FFTW MPI Wisdom
• Avoiding MPI Deadlocks
• FFTW MPI Performance Tips
• Combining MPI and Threads
• FFTW MPI Reference

MPI data distribution

• Basic and advanced distribution interfaces
• Load balancing
• Transposed distributions
• One-dimensional distributions

FFTW MPI Transposes

• Basic distributed-transpose interface
• Advanced distributed-transpose interface
• An improved replacement for MPI_Alltoall

FFTW on the Cell Processor

• Cell Installation
• Cell Caveats
• FFTW Accuracy on Cell

Calling FFTW from Fortran

• Fortran-interface routines
• FFTW Constants in Fortran
• Fortran Examples
• Wisdom of Fortran?

Installation and Customization

• Installation on Unix
• Installation on non-Unix systems
• Cycle Counters
• Generating your own code