@inproceedings{vdHoevenJohansson2024, title = {Fast multiple precision $\exp(x)$ with precomputations}, url = {http://dx.doi.org/10.1109/ARITH61463.2024.00023}, DOI = {10.1109/arith61463.2024.00023}, booktitle = {2024 IEEE 31st Symposium on Computer Arithmetic (ARITH)}, publisher = {IEEE}, author = {Joris van der Hoeven and Fredrik Johansson}, year = {2024}, month = jun, pages = {80–87} } @article{Johansson2023, title = {Arbitrary-precision computation of the gamma function}, volume = {3}, ISSN = {2564-3029}, url = {http://dx.doi.org/10.5206/mt.v3i1.14591}, DOI = {10.5206/mt.v3i1.14591}, number = {1}, journal = {Maple Transactions}, publisher = {University of Western Ontario, Western Libraries}, author = {Fredrik Johansson}, year = {2023}, month = feb } @inproceedings{Johansson2021, series = {ISSAC '21}, title = {Calcium: Computing in Exact Real and Complex Fields}, url = {http://dx.doi.org/10.1145/3452143.3465513}, DOI = {10.1145/3452143.3465513}, booktitle = {Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation}, publisher = {ACM}, author = {Fredrik Johansson}, year = {2021}, month = jul, pages = {225–232}, collection = {ISSAC ’21} } @incollection{Johansson2020fungrim, doi = {10.1007/978-3-030-52200-1_31}, url = {https://doi.org/10.1007/978-3-030-52200-1_31}, year = {2020}, publisher = {Springer}, pages = {315--323}, author = {Fredrik Johansson}, title = {{FunGrim}: a symbolic library for special functions}, booktitle = {Mathematical Software -- ICMS 2020} } @misc{Johansson2020lambertw, title={Computing the {L}ambert {W} function in arbitrary-precision complex interval arithmetic}, author={Fredrik Johansson}, journal={Numerical Algorithms}, volume={83}, pages={221--242}, year={2020}, publisher={Springer}, note = {\url{https://arxiv.org/abs/1705.03266}}, } @inproceedings{Johansson2019faster, doi = {10.1109/arith.2019.00012}, url = {https://doi.org/10.1109/arith.2019.00012}, year = {2019}, month = jun, publisher = {{IEEE}}, author = {Fredrik Johansson}, title = {Faster arbitrary-precision dot product and matrix multiplication}, booktitle = {2019 {IEEE} 26th Symposium on Computer Arithmetic ({ARITH})} } @incollection{Johansson2019elliptic, title={Numerical evaluation of elliptic functions, elliptic integrals and modular forms}, author={Fredrik Johansson}, booktitle={Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}, pages={269--293}, year={2019}, publisher={Springer}, note = {\url{https://arxiv.org/abs/1806.06725}} } @article{JohanssonBlagouchine2018stieltjes, title={Computing {S}tieltjes constants using complex integration}, author={Fredrik Johansson and Iaroslav Blagouchine}, journal={Mathematics of Computation}, volume={88}, number={318}, pages={1829--1850}, year={2019}, note = {\url{https://arxiv.org/abs/1804.01679}}, } @inproceedings{Johansson2018numerical, author = {Fredrik Johansson}, title = {Numerical integration in arbitrary-precision ball arithmetic}, year = {2018}, booktitle = {Mathematical Software -- ICMS 2018}, publisher = {Springer Lecture Notes in Computer Science}, pages = {255--263}, doi = {10.1007/978-3-319-96418-8_30}, note = {\url{https://doi.org/10.1007/978-3-319-96418-8_30}, \url{https://arxiv.org/abs/1802.07942}}, } @article{JohanssonMezzarobba2018fast, author = {Fredrik Johansson and Marc Mezzarobba}, title = {Fast and rigorous arbitrary-precision computation of {G}auss-{L}egendre quadrature nodes and weights}, year = {2018}, journal = {SIAM Journal on Scientific Computing}, pages = {C726--C747}, volume = {40}, issue = {6}, doi = {10.1137/18M1170133}, note = {\url{http://arxiv.org/abs/1802.03948}}, } @inproceedings{Fieker2017nemo, author = {Claus Fieker and William Hart and Tommy Hofmann and Fredrik Johansson}, title = {{Nemo/Hecke}: computer algebra and number theory packages for the {J}ulia programming language}, booktitle = {Proceedings of the 42nd International Symposium on Symbolic and Algebraic Computation}, series = {ISSAC '17}, pages = {1--1}, publisher = {ACM}, address = {Kaiserslautern, Germany}, year = {2017}, } @misc{Johansson2019hypergeometric, title={Computing hypergeometric functions rigorously}, author={Fredrik Johansson}, journal={ACM Transactions on Mathematical Software (TOMS)}, volume={45}, number={3}, pages={1--26}, year={2019}, publisher={ACM New York, NY, USA}, note = {\url{http://arxiv.org/abs/1606.06977}}, } @article{Johansson2017arb, author = {Fredrik Johansson}, title = {Arb: efficient arbitrary-precision midpoint-radius interval arithmetic}, journal = {IEEE Transactions on Computers}, year = {2017}, volume = {66}, issue = {8}, pages = {1281--1292}, doi = {10.1109/TC.2017.2690633}, note = {\url{https://doi.org/10.1109/TC.2017.2690633}, \url{https://arxiv.org/abs/1611.02831}} } @article{Meurer2017sympy, title = {{SymPy}: symbolic computing in {P}ython}, author = {Aaron Meurer et al.}, year = 2017, volume = 3, pages = {e103}, journal = {PeerJ Computer Science}, issn = {2376-5992}, url = {}, note={\url{https://doi.org/10.7717/peerj-cs.103}, \url{https://hal.inria.fr/hal-01404156}}, doi = {10.7717/peerj-cs.103} } @article{Enge2016addseq, author = {Andreas Enge and William Hart and Fredrik Johansson}, title = {Short addition sequences for theta functions}, year = {2018}, journal = {Journal of Integer Sequences}, volume = {21}, issue = {2}, pages = {18.2.4}, } @inproceedings{Johansson2015elementary, title={Efficient implementation of elementary functions in the medium-precision range}, author={Fredrik Johansson}, booktitle={22nd IEEE Symposium on Computer Arithmetic}, series={ARITH22}, doi={10.1109/ARITH.2015.16}, note={\url{http://dx.doi.org/10.1109/ARITH.2015.16}, \url{http://arxiv.org/abs/1410.7176}}, pages={83--89}, year={2015}, location={Lyon, France}, } @article{BrentJohansson2015bound, title={A bound for the error term in the {B}rent-{M}c{M}illan algorithm}, author={Richard P. Brent and Fredrik Johansson}, journal={Mathematics of Computation}, volume={84}, pages={2351--2359}, doi={10.1090/S0025-5718-2015-02931-7}, note={\url{http://dx.doi.org/10.1090/S0025-5718-2015-02931-7}, \url{http://arxiv.org/abs/1312.0039}}, year={2015}, } @article{Johansson2015reversion, title={A fast algorithm for reversion of power series}, author={Fredrik Johansson}, journal={Mathematics of Computation}, volume={84}, pages={475--484}, year={2015}, doi={10.1090/S0025-5718-2014-02857-3}, note={\url{http://dx.doi.org/10.1090/S0025-5718-2014-02857-3}, \url{http://arxiv.org/abs/1108.4772}}, } @phdthesis{Johansson2014thesis, title={Fast and rigorous computation of special functions to high precision}, author={Fredrik Johansson}, school={RISC, Johannes Kepler University}, year={2014}, address={Linz}, note={\url{http://fredrikj.net/thesis/}} } @inproceedings{Johansson2014rectangular, author={Fredrik Johansson}, title={Evaluating parametric holonomic sequences using rectangular splitting}, booktitle={Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation}, series={ISSAC '14}, year={2014}, isbn={978-1-4503-2501-1}, location={Kobe, Japan}, pages={256--263}, publisher={ACM}, address={New York, NY, USA}, note={\url{http://dx.doi.org/10.1145/2608628.2608629}, \url{http://arxiv.org/abs/1310.3741}}, doi={10.1145/2608628.2608629}, } @article{JohanssonNakamura2014functional, author = {Fredrik Johansson and Brian Nakamura}, title = {Using functional equations to enumerate 1324-avoiding permutations}, journal = {Advances in Applied Mathematics}, volume = {56}, year = {2014}, pages = {20--34}, note={\url{http://dx.doi.org/10.1016/j.aam.2014.01.006}, \url{http://arxiv.org/abs/1309.7117}}, doi={10.1016/j.aam.2014.01.006}, } @article{Johansson2014hurwitz, title={Rigorous high-precision computation of the {H}urwitz zeta function and its derivatives}, author={Fredrik Johansson}, journal={Numerical Algorithms}, year={2015}, volume={69}, issue={2}, pages={253--270}, doi={10.1007/s11075-014-9893-1}, note={\url{http://dx.doi.org/10.1007/s11075-014-9893-1}, \url{http://arxiv.org/abs/1309.2877}}, } @incollection{KauersJaroschekJohansson2015ore, title={{O}re polynomials in {S}age}, author={Manuel Kauers and Maximilian Jaroschek and Fredrik Johansson}, booktitle={Computer Algebra and Polynomials}, year={2015}, publisher={Springer Lecture Notes in Computer Science}, pages={105--125}, doi={10.1007/978-3-319-15081-9_6}, note={\url{http://dx.doi.org/10.1007/978-3-319-15081-9_6}, \url{http://arxiv.org/abs/1306.4263}}, } @article{Johansson2013arb, title={{A}rb: a {C} library for ball arithmetic}, author={Fredrik Johansson}, journal={ACM Communications in Computer Algebra}, volume={47}, number={4}, pages={166--169}, year={2013}, publisher={ACM}, doi={10.1145/2576802.2576828}, note={\url{http://dx.doi.org/10.1145/2576802.2576828}}, } @inproceedings{JohanssonKauersMezzarobba2013hyperexponential, author={Fredrik Johansson and Manuel Kauers and Marc Mezzarobba}, title={Finding hyperexponential solutions of linear {ODE}s by numerical evaluation}, journal={Advances in Applied Mathematics}, booktitle={Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation}, series={ISSAC '13}, year={2013}, location={Boston, USA}, pages={211--218}, publisher={ACM}, address={New York, NY, USA}, doi={10.1145/2465506.2465513}, note={\url{http://dx.doi.org/10.1145/2465506.2465513}, \url{http://arxiv.org/abs/1301.2486}}, } @article{Johansson2012hrr, author={Fredrik Johansson}, title={Efficient implementation of the {H}ardy-{R}amanujan-{R}ademacher formula}, journal={LMS Journal of Computation and Mathematics}, volume={15}, year={2012}, pages={341--359}, doi={10.1112/S1461157012001088}, note={\url{http://dx.doi.org/10.1112/S1461157012001088}, \url{http://arxiv.org/abs/1205.5991}}, } @mastersthesis{Johansson2010, author={Fredrik Johansson}, title={Simulation of the Maxwell-Dirac and Schr\"{o}dinger-Poisson systems}, publisher={Chalmers University of Technology}, place={G\"{o}teborg}, year={2010}, }