This manual documents version 3.3.5 of FFTW, the cannam@127: Fastest Fourier Transform in the West. FFTW is a comprehensive cannam@127: collection of fast C routines for computing the discrete Fourier cannam@127: transform (DFT) and various special cases thereof. cannam@127: cannam@127: cannam@127:
We assume herein that you are familiar with the properties and uses of cannam@127: the DFT that are relevant to your application. Otherwise, see cannam@127: e.g. The Fast Fourier Transform and Its Applications by E. O. Brigham cannam@127: (Prentice-Hall, Englewood Cliffs, NJ, 1988). cannam@127: Our web page also has links to FFT-related cannam@127: information online. cannam@127: cannam@127:
cannam@127: cannam@127:In order to use FFTW effectively, you need to learn one basic concept cannam@127: of FFTW’s internal structure: FFTW does not use a fixed algorithm for cannam@127: computing the transform, but instead it adapts the DFT algorithm to cannam@127: details of the underlying hardware in order to maximize performance. cannam@127: Hence, the computation of the transform is split into two phases. cannam@127: First, FFTW’s planner “learns” the fastest way to compute the cannam@127: transform on your machine. The planner cannam@127: cannam@127: produces a data structure called a plan that contains this cannam@127: cannam@127: information. Subsequently, the plan is executed cannam@127: cannam@127: to transform the array of input data as dictated by the plan. The cannam@127: plan can be reused as many times as needed. In typical cannam@127: high-performance applications, many transforms of the same size are cannam@127: computed and, consequently, a relatively expensive initialization of cannam@127: this sort is acceptable. On the other hand, if you need a single cannam@127: transform of a given size, the one-time cost of the planner becomes cannam@127: significant. For this case, FFTW provides fast planners based on cannam@127: heuristics or on previously computed plans. cannam@127:
cannam@127:FFTW supports transforms of data with arbitrary length, rank, cannam@127: multiplicity, and a general memory layout. In simple cases, however, cannam@127: this generality may be unnecessary and confusing. Consequently, we cannam@127: organized the interface to FFTW into three levels of increasing cannam@127: generality. cannam@127:
We expect that most users will be best served by the basic interface, cannam@127: whereas the guru interface requires careful attention to the cannam@127: documentation to avoid problems. cannam@127: cannam@127: cannam@127: cannam@127:
cannam@127: cannam@127:Besides the automatic performance adaptation performed by the planner, cannam@127: it is also possible for advanced users to customize FFTW manually. For cannam@127: example, if code space is a concern, we provide a tool that links only cannam@127: the subset of FFTW needed by your application. Conversely, you may need cannam@127: to extend FFTW because the standard distribution is not sufficient for cannam@127: your needs. For example, the standard FFTW distribution works most cannam@127: efficiently for arrays whose size can be factored into small primes cannam@127: (2, 3, 5, and 7), and otherwise it uses a cannam@127: slower general-purpose routine. If you need efficient transforms of cannam@127: other sizes, you can use FFTW’s code generator, which produces fast C cannam@127: programs (“codelets”) for any particular array size you may care cannam@127: about. cannam@127: cannam@127: cannam@127: For example, if you need transforms of size cannam@127: 513 = 19*33,you can customize FFTW to support the factor 19 efficiently. cannam@127:
cannam@127:For more information regarding FFTW, see the paper, “The Design and cannam@127: Implementation of FFTW3,” by M. Frigo and S. G. Johnson, which was an cannam@127: invited paper in Proc. IEEE 93 (2), p. 216 (2005). The cannam@127: code generator is described in the paper “A fast Fourier transform cannam@127: compiler”, cannam@127: cannam@127: by M. Frigo, in the Proceedings of the 1999 ACM SIGPLAN Conference cannam@127: on Programming Language Design and Implementation (PLDI), Atlanta, cannam@127: Georgia, May 1999. These papers, along with the latest version of cannam@127: FFTW, the FAQ, benchmarks, and other links, are available at cannam@127: the FFTW home page. cannam@127:
cannam@127:The current version of FFTW incorporates many good ideas from the past cannam@127: thirty years of FFT literature. In one way or another, FFTW uses the cannam@127: Cooley-Tukey algorithm, the prime factor algorithm, Rader’s algorithm cannam@127: for prime sizes, and a split-radix algorithm (with a cannam@127: “conjugate-pair” variation pointed out to us by Dan Bernstein). cannam@127: FFTW’s code generator also produces new algorithms that we do not cannam@127: completely understand. cannam@127: cannam@127: The reader is referred to the cited papers for the appropriate cannam@127: references. cannam@127:
cannam@127:The rest of this manual is organized as follows. We first discuss the cannam@127: sequential (single-processor) implementation. We start by describing cannam@127: the basic interface/features of FFTW in Tutorial. cannam@127: Next, Other Important Topics discusses data alignment cannam@127: (see SIMD alignment and fftw_malloc), cannam@127: the storage scheme of multi-dimensional arrays cannam@127: (see Multi-dimensional Array Format), and FFTW’s mechanism for cannam@127: storing plans on disk (see Words of Wisdom-Saving Plans). Next, cannam@127: FFTW Reference provides comprehensive documentation of all cannam@127: FFTW’s features. Parallel transforms are discussed in their own cannam@127: chapters: Multi-threaded FFTW and Distributed-memory FFTW with MPI. Fortran programmers can also use FFTW, as described in cannam@127: Calling FFTW from Legacy Fortran and Calling FFTW from Modern Fortran. Installation and Customization explains how to cannam@127: install FFTW in your computer system and how to adapt FFTW to your cannam@127: needs. License and copyright information is given in License and Copyright. Finally, we thank all the people who helped us in cannam@127: Acknowledgments. cannam@127:
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