FFTW 3.0

Table of Contents

• FFTW User Manual
• 1 Introduction
• 2 Tutorial
  • 2.1 Complex One-Dimensional DFTs
  • 2.2 Complex Multi-Dimensional DFTs
  • 2.3 One-Dimensional DFTs of Real Data
  • 2.4 Multi-Dimensional DFTs of Real Data
  • 2.5 More DFTs of Real Data
    • 2.5.1 The Halfcomplex-format DFT
    • 2.5.2 Real even/odd DFTs (cosine/sine transforms)
    • 2.5.3 The Discrete Hartley Transform
• 3 Other Important Topics
  • 3.1 Data Alignment
    • 3.1.1 SIMD alignment and fftw_malloc
    • 3.1.2 Stack alignment on x86
  • 3.2 Multi-dimensional Array Format
    • 3.2.1 Row-major Format
    • 3.2.2 Column-major Format
    • 3.2.3 Static Arrays in C
    • 3.2.4 Dynamic Arrays in C
    • 3.2.5 Dynamic Arrays in C--The Wrong Way
  • 3.3 Words of Wisdom--Saving Plans
  • 3.4 Caveats in Using Wisdom
• 4 FFTW Reference
  • 4.1 Data Types and Files
    • 4.1.1 Complex numbers
    • 4.1.2 Precision
    • 4.1.3 Memory Allocation
  • 4.2 Using Plans
  • 4.3 Basic Interface
    • 4.3.1 Complex DFTs
    • 4.3.2 Planner Flags
    • 4.3.3 Real-data DFTs
    • 4.3.4 Real-data DFT Array Format
    • 4.3.5 Real-to-Real Transforms
    • 4.3.6 Real-to-Real Transform Kinds
  • 4.4 Advanced Interface
    • 4.4.1 Advanced Complex DFTs
    • 4.4.2 Advanced Real-data DFTs
    • 4.4.3 Advanced Real-to-real Transforms
  • 4.5 Guru Interface
    • 4.5.1 Interleaved and split arrays
    • 4.5.2 Guru vector and transform sizes
    • 4.5.3 Guru Complex DFTs
    • 4.5.4 Guru Real-data DFTs
    • 4.5.5 Guru Real-to-real Transforms
    • 4.5.6 Guru Execution of Plans
  • 4.6 Wisdom
    • 4.6.1 Wisdom Export
    • 4.6.2 Wisdom Import
    • 4.6.3 Forgetting Wisdom
    • 4.6.4 Wisdom Utilities
  • 4.7 What FFTW Really Computes
    • 4.7.1 The 1d Discrete Fourier Transform (DFT)
    • 4.7.2 The 1d Real-data DFT
    • 4.7.3 1d Real-even DFTs (DCTs)
    • 4.7.4 1d Real-odd DFTs (DSTs)
    • 4.7.5 1d Discrete Hartley Transforms (DHTs)
    • 4.7.6 Multi-dimensional Transforms
• 5 Parallel FFTW
  • 5.1 Multi-threaded FFTW
    • 5.1.1 Installation and Supported Hardware/Software
    • 5.1.2 Usage of Multi-threaded FFTW
    • 5.1.3 How Many Threads to Use?
  • 5.2 Thread safety
• 6 Calling FFTW from Fortran
  • 6.1 Fortran-interface routines
  • 6.2 FFTW Constants in Fortran
  • 6.3 Fortran Examples
  • 6.4 Wisdom of Fortran?
• 7 Upgrading from FFTW version 2
• 8 Installation and Customization
  • 8.1 Installation on Unix
  • 8.2 Installation on non-Unix systems
  • 8.3 Cycle Counters
  • 8.4 Generating your own code
• 9 Acknowledgments
• 10 License and Copyright
• 11 Concept Index
• 12 Library Index

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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 3.0.

• Introduction:
• Tutorial:
• Other Important Topics:
• FFTW Reference:
• Parallel FFTW:
• 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:
• Static 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:
• 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:
• Guru Execution of Plans:

  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:

  Parallel FFTW

• Multi-threaded FFTW:
• Thread safety:

  Multi-threaded FFTW

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

  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: