This manual documents version 3.3.8 of FFTW, the cannam@167: Fastest Fourier Transform in the West. FFTW is a comprehensive cannam@167: collection of fast C routines for computing the discrete Fourier cannam@167: transform (DFT) and various special cases thereof. cannam@167: cannam@167: cannam@167:
We assume herein that you are familiar with the properties and uses of cannam@167: the DFT that are relevant to your application. Otherwise, see cannam@167: e.g. The Fast Fourier Transform and Its Applications by E. O. Brigham cannam@167: (Prentice-Hall, Englewood Cliffs, NJ, 1988). cannam@167: Our web page also has links to FFT-related cannam@167: information online. cannam@167: cannam@167:
cannam@167: cannam@167:In order to use FFTW effectively, you need to learn one basic concept cannam@167: of FFTW’s internal structure: FFTW does not use a fixed algorithm for cannam@167: computing the transform, but instead it adapts the DFT algorithm to cannam@167: details of the underlying hardware in order to maximize performance. cannam@167: Hence, the computation of the transform is split into two phases. cannam@167: First, FFTW’s planner “learns” the fastest way to compute the cannam@167: transform on your machine. The planner cannam@167: cannam@167: produces a data structure called a plan that contains this cannam@167: cannam@167: information. Subsequently, the plan is executed cannam@167: cannam@167: to transform the array of input data as dictated by the plan. The cannam@167: plan can be reused as many times as needed. In typical cannam@167: high-performance applications, many transforms of the same size are cannam@167: computed and, consequently, a relatively expensive initialization of cannam@167: this sort is acceptable. On the other hand, if you need a single cannam@167: transform of a given size, the one-time cost of the planner becomes cannam@167: significant. For this case, FFTW provides fast planners based on cannam@167: heuristics or on previously computed plans. cannam@167:
cannam@167:FFTW supports transforms of data with arbitrary length, rank, cannam@167: multiplicity, and a general memory layout. In simple cases, however, cannam@167: this generality may be unnecessary and confusing. Consequently, we cannam@167: organized the interface to FFTW into three levels of increasing cannam@167: generality. cannam@167:
We expect that most users will be best served by the basic interface, cannam@167: whereas the guru interface requires careful attention to the cannam@167: documentation to avoid problems. cannam@167: cannam@167: cannam@167: cannam@167:
cannam@167: cannam@167:Besides the automatic performance adaptation performed by the planner, cannam@167: it is also possible for advanced users to customize FFTW manually. For cannam@167: example, if code space is a concern, we provide a tool that links only cannam@167: the subset of FFTW needed by your application. Conversely, you may need cannam@167: to extend FFTW because the standard distribution is not sufficient for cannam@167: your needs. For example, the standard FFTW distribution works most cannam@167: efficiently for arrays whose size can be factored into small primes cannam@167: (2, 3, 5, and 7), and otherwise it uses a cannam@167: slower general-purpose routine. If you need efficient transforms of cannam@167: other sizes, you can use FFTW’s code generator, which produces fast C cannam@167: programs (“codelets”) for any particular array size you may care cannam@167: about. cannam@167: cannam@167: cannam@167: For example, if you need transforms of size cannam@167: 513 = 19*33, cannam@167: you can customize FFTW to support the factor 19 efficiently. cannam@167:
cannam@167:For more information regarding FFTW, see the paper, “The Design and cannam@167: Implementation of FFTW3,” by M. Frigo and S. G. Johnson, which was an cannam@167: invited paper in Proc. IEEE 93 (2), p. 216 (2005). The cannam@167: code generator is described in the paper “A fast Fourier transform cannam@167: compiler”, cannam@167: cannam@167: by M. Frigo, in the Proceedings of the 1999 ACM SIGPLAN Conference cannam@167: on Programming Language Design and Implementation (PLDI), Atlanta, cannam@167: Georgia, May 1999. These papers, along with the latest version of cannam@167: FFTW, the FAQ, benchmarks, and other links, are available at cannam@167: the FFTW home page. cannam@167:
cannam@167:The current version of FFTW incorporates many good ideas from the past cannam@167: thirty years of FFT literature. In one way or another, FFTW uses the cannam@167: Cooley-Tukey algorithm, the prime factor algorithm, Rader’s algorithm cannam@167: for prime sizes, and a split-radix algorithm (with a cannam@167: “conjugate-pair” variation pointed out to us by Dan Bernstein). cannam@167: FFTW’s code generator also produces new algorithms that we do not cannam@167: completely understand. cannam@167: cannam@167: The reader is referred to the cited papers for the appropriate cannam@167: references. cannam@167:
cannam@167:The rest of this manual is organized as follows. We first discuss the cannam@167: sequential (single-processor) implementation. We start by describing cannam@167: the basic interface/features of FFTW in Tutorial. cannam@167: Next, Other Important Topics discusses data alignment cannam@167: (see SIMD alignment and fftw_malloc), cannam@167: the storage scheme of multi-dimensional arrays cannam@167: (see Multi-dimensional Array Format), and FFTW’s mechanism for cannam@167: storing plans on disk (see Words of Wisdom-Saving Plans). Next, cannam@167: FFTW Reference provides comprehensive documentation of all cannam@167: FFTW’s features. Parallel transforms are discussed in their own cannam@167: chapters: Multi-threaded FFTW and Distributed-memory FFTW with MPI. Fortran programmers can also use FFTW, as described in cannam@167: Calling FFTW from Legacy Fortran and Calling FFTW from Modern Fortran. Installation and Customization explains how to cannam@167: install FFTW in your computer system and how to adapt FFTW to your cannam@167: needs. License and copyright information is given in License and Copyright. Finally, we thank all the people who helped us in cannam@167: Acknowledgments. cannam@167:
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