biblio.bib

@article{adamek_2016,
   title={gevolution: a cosmological N-body code based on General Relativity},
   volume={2016},
   ISSN={1475-7516},
   url={http://dx.doi.org/10.1088/1475-7516/2016/07/053},
   DOI={10.1088/1475-7516/2016/07/053},
   number={07},
   journal={Journal of Cosmology and Astroparticle Physics},
   publisher={IOP Publishing},
   author={Adamek, Julian and Daverio, David and Durrer, Ruth and Kunz, Martin},
   year={2016},
   month={Jul},
   pages={053–053}
}
@article{springel_2020,
      title={Simulating cosmic structure formation with the GADGET-4 code}, 
      author={Volker Springel and Rüdiger Pakmor and Oliver Zier and Martin Reinecke},
      year={2020},
      eprint={2010.03567},
      archivePrefix={arXiv},
      primaryClass={astro-ph.IM}
}
@article{FFTW05,
  author =   {Frigo, Matteo and Johnson, Steven~G.},
  title =    {The Design and Implementation of {FFTW3}},
  journal =      {Proceedings of the IEEE},
  year =     2005,
  volume =   93,
  number =   2,
  pages =    {216--231},
  note =     {Special issue on ``Program Generation, Optimization, and Platform Adaptation''}
}
@article{pippig_13,
    AUTHOR = {Michael Pippig},
    TITLE = {{PFFT} - {A}n Extension of {FFTW} to Massively Parallel Architectures},
    JOURNAL = {SIAM J. Sci. Comput.},
    YEAR = {2013},
    Volume = {35},
    optNumber = {3},
    Pages = {C213 -- C236}
}
@inproceedings{furer07,
author = {F\"{u}rer, Martin},
title = {Faster Integer Multiplication},
year = {2007},
isbn = {9781595936318},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/1250790.1250800},
doi = {10.1145/1250790.1250800},
abstract = {For more than 35 years, the fastest known method for integer multiplication has been the Sch\"{o}nhage-Strassen algorithm running in time O(n log n log log n). Under certain restrictive conditions there is a corresponding Ω(n log n) lower bound. The prevailing conjecture has always been that the complexity of an optimal algorithm is Θ(n log n). We present a major step towards closing the gap from above by presenting an algorithm running in time n log n, 2O(log* n).The main result is for boolean circuits as well as for multitape Turing machines, but it has consequences to other models of computation as well.},
booktitle = {Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing},
pages = {57–66},
numpages = {10},
keywords = {computer arithmetic, discrete Fourier transform, FFT, complexity, integer multiplication},
location = {San Diego, California, USA},
series = {STOC '07}
}

@misc{cufft,
    title = "Cuda Toolkit Documentation: cuFFT",
    howpublished = "\url{docs.nvidia.com/cuda/pdf/CUFFT_Library.pdf}"
}
@misc{boost,
    title = "Boost C++ Libraries",
    howpublished = "\url{www.boost.org}"
}
@misc{boostmath,
    title = "Boost.Math",
    howpublished = "\url{github.com/boostorg/math}"
}
@misc{icpc,
    title = "International Collegiate Programming Contest",
    howpublished = "\url{icpc.global}"
}
@misc{codeforces,
    title = "Codeforces",
    howpublished = "\url{codeforces.com}"
}
@book{stroustrup11,
author = {Stroustrup, Bjarne},
title = {The C++ Programming Language},
year = {2013},
isbn = {0321563840},
publisher = {Addison-Wesley Professional},
edition = {4th},
abstract = {C++11 has arrived: thoroughly master it, with the definitive new guide from C++ creator Bjarne Stroustrup, C++ Programming Language, Fourth Edition! The brand-new edition of the world's most trusted and widely read guide to C++, it has been comprehensively updated for the long-awaited C++11 standard. Extensively rewritten to present the C++11 language, standard library, and key design techniques as an integrated whole, Stroustrup thoroughly addresses changes that make C++11 feel like a whole new language, offering definitive guidance for leveraging its improvements in performance, reliability, and clarity. C++ programmers around the world recognize Bjarne Stoustrup as the go-to expert for the absolutely authoritative and exceptionally useful information they need to write outstanding C++ programs. Now, as C++11 compilers arrive and development organizations migrate to the new standard, they know exactly where to turn once more: Stoustrup's C++ Programming Language, Fourth Edition.}
}
@book{josuttis11,
author = {Josuttis, Nicolai},
title = {The C++ Standard Library},
year = {2012},
isbn = {978-0-321-62321-8},
publisher = {Addison-Wesley},
edition = {2nd},
}
@book{josuttis17,
author = {Josuttis, Nicolai},
title = {C++17 The Complete Guide},
year = {2019},
isbn = {978-3-96730-017-8}
}

@book{lidl97,
   title =     {Applied Abstract Algebra (Second Edition)},
   author =    {Rudolf Lidl, Günter Pilz},
   publisher = {Springer},
   isbn =      {0387982906,9780387982908},
   year =      {1997},
   series =    {},
   edition =   {2nd},
   volume =    {},
   url =       {http://gen.lib.rus.ec/book/index.php?md5=176C3CFD768173A1D04BFB6D99D6341B}}
   
@ARTICLE{rader68,  author={C. M. {Rader}},  journal={Proceedings of the IEEE},
title={Discrete Fourier transforms when the number of data samples is prime},
year={1968},  volume={56},  number={6},  pages={1107-1108},
doi={10.1109/PROC.1968.6477}}

@article{cooley65,
    author={James W. {Cooley} and John W. {Tukey}},
    journal={Math. Comp.},
    pages={297--301},
    volume={19},
    year={1965},
    doi={10.1090/S0025-5718-1965-0178586-1}
}
@article{winograd78,
    author={S. Winograd},
    journal={Mathematics of Computation},
    pages={175--199},
    volume={32},
    number={141},
    year={1978},
    doi={10.1090/S0025-5718-1978-0468306-4}
}
@article{bluestein70,
  author={L. {Bluestein}},
  journal={IEEE Transactions on Audio and Electroacoustics}, 
  title={A linear filtering approach to the computation of discrete Fourier transform}, 
  year={1970},
  volume={18},
  number={4},
  pages={451-455},
  doi={10.1109/TAU.1970.1162132}} 
  
@article{soresen87,  author={H. {Sorensen} and
  D. {Jones} and M. {Heideman} and C. {Burrus}},  journal={IEEE Transactions on
  Acoustics, Speech, and Signal Processing},   title={Real-valued fast Fourier
  transform algorithms},   year={1987},  volume={35},  number={6},
  pages={849-863},  doi={10.1109/TASSP.1987.1165220}}
@article{duhamel1990,
title = {Fast fourier transforms: A tutorial review and a state of the art},
journal = {Signal Processing},
volume = {19},
number = {4},
pages = {259-299},
year = {1990},
issn = {0165-1684},
doi = {https://doi.org/10.1016/0165-1684(90)90158-U},
url = {https://www.sciencedirect.com/science/article/pii/016516849090158U},
author = {P. Duhamel and M. Vetterli},
keywords = {Fourier transforms, fast algorithms, computational complexity},
abstract = {The publication of the Cooley-Tukey fast Fourier transform (FFT) algorithm in 1965 has opened a new area in digital signal processing by reducing the order of complexity of some crucial computational tasks like Fourier transform and convultion from N2 to N log2, where N is the problem size. The development of the major algorithms (Cooley-Tukey and split-radix FFT, prime factor algorithm and Winograd fast Fourier transform) is reviewed. Then, an attempt is made to indicate the state of the art on the subject, showin the standing of researh, open problems and implementations.
Zusammenfassung
Die Publikation von Cooley-Tukey's schnellem Fourier Transformations Algorithmus in 1965 brachte eine neue Area in der digitalen signaverarbeitung weil die Ordnung der Komplexität von gewissen zentralen Berechnungen, wie die Fourier Transformations und die digitale Faltung, von N2 zu Nlog2N reduziert wurden (wo N die Problemgrösse darstellt). Die Entwickflung der wichtigsten Algorithmen (Cooley-Tukey und Split-Radix FFT), Prime Factor Algorithmus und Winograd's schneller Fourier Transformation) ist nachvollzogen. Dann wird, den Stand des Feldes zu beschreiben, um zu zeigen wo die Forschung steht, was für Probleme noch offenstehen, wie zum Beispel in Implementierungen.
Résumé
La publication de l'algorithme de Cooley-Tukey pour la transformation de Fourier rapide a ouvert une nouvelle ère dans traitement numérique des signaux, en résiduisant l'ordre de comlexité de problèmes cruciaux, comme la transformation de Fourier ou la convulution de N2 à Nlog2N (où N est la taille du problème). Le dévelopment des algorithmes principaux (Cooley-Tukey, split-radix FFT, algorithmes des facteurs premiers, et transformée rapidem de Winograd) est déscrit. Ensuite, l'état de l'art est donné, et on parle problémes ouverts et des implantations.}
}