Fredrik Johansson

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Contact: fredrik.johansson@gmail.com

I'm a junior researcher (chargé de recherche) in the Canari team at Inria and Institut de Mathématiques de Bordeaux (my office). I work on computer algebra, mainly on efficient algorithms for arbitrary-precision arithmetic and rigorous computation with real and complex numbers.

News

My blog features semi-regular updates. For more frequent updates, follow me on Mastodon. Current events I'm attending:

Software

Check my GitHub profile for more projects.

Publications

This list is available (possibly out of date) in BibTeX format (txt file). I also have a Google Scholar profile.

  1. Fast multiple precision exp(x) with precomputations
    With Joris van der Hoeven. Preprint, 2024. [HAL]
  2. Computing elementary functions using multi-prime argument reduction
    Preprint, 2022. [arXiv] [HAL]
  3. Rapid computation of special values of Dirichlet L-functions
    Preprint, 2021. [arXiv] [HAL]
  4. Arbitrary-precision computation of the gamma function
    Maple Transactions, Vol 3 No 1, 2023. [arXiv] [HAL] [DOI]
  5. Computing isolated coefficients of the j-function
    Preprint, 2020. [arXiv] [HAL]
  6. On a fast and nearly division-free algorithm for the characteristic polynomial
    Technical report, 2020. [arXiv] [HAL]
  7. Calcium: computing in exact real and complex fields
    ISSAC '21. [arXiv] [HAL] [DOI]
  8. The minimal Fried average entropy for higher-rank Cartan actions
    With Eduardo Friedman and Gabriel Ramirez-Raposo. Mathematics of Computation, 90 (2021), 973-978. [HAL] [DOI]
  9. Calculer avec les nombres réels (published French translation by Xavier Caruso) / Computing with real numbers (original English manuscript)
    Informatique Mathématique - Une photographie en 2020 edited by Sébastien Labbé, Vincent Penelle. CNRS Éditions, 2020, pp. 115-147.
  10. FunGrim: a symbolic library for special functions
    ICMS 2020: Mathematical Software, pp 315-323, Springer LNCS, 2020. [arXiv] [HAL] [DOI]
  11. Faster arbitrary-precision dot product and matrix multiplication
    26th IEEE Symposium on Computer Arithmetic (ARITH26), 2019. [arXiv] [HAL] [DOI]
  12. Numerical evaluation of elliptic functions, elliptic integrals and modular forms
    Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Springer, 2019, pp. 269-293. [arXiv] [HAL] [DOI]
  13. Computing Stieltjes constants using complex integration
    With Iaroslav V. Blagouchine. Mathematics of Computation, vol 88, 2019, pp. 1829-1850. [arXiv] [HAL] [DOI]
  14. Numerical integration in arbitrary-precision ball arithmetic
    Mathematical Software - ICMS 2018, Springer LNCS, 2018, pp. 255-263. [arXiv] [HAL] [DOI]
  15. Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights
    With Marc Mezzarobba. SIAM Journal on Scientific Computing 40(6), 2018, pp. C726-C747. [arXiv] [HAL] [DOI]
  16. Computing the Lambert W function in arbitrary-precision complex interval arithmetic
    Numerical Algorithms vol 83, pages 221-242 (2020). [arXiv] [HAL] [DOI]
  17. Nemo/Hecke: computer algebra and number theory packages for the Julia programming language
    With Claus Fieker, William Hart and Tommy Hofmann. 42nd International Symposium on Symbolic and Algebraic Computation (ISSAC'17), 2017, pp. 157-164. [arXiv] [HAL]
  18. Arb: efficient arbitrary-precision midpoint-radius interval arithmetic
    IEEE Transactions on Computers, vol 66, issue 8, 2017, pp. 1281-1292. [DOI] [PDF] [arXiv] [HAL]
  19. Short addition sequences for theta functions
    With Andreas Enge and William Hart. Journal of Integer Sequences, vol 21, 2018, article 18.2.4. [arXiv] [HAL]
  20. Computing hypergeometric functions rigorously
    ACM Transactions on Mathematical Software, vol 45, issue 3, 2019, pages 1–26. [PDF] [arXiv] [HAL] [DOI]
  21. SymPy: Symbolic computing in Python
    With Aaron Meurer et al. PeerJ Computer Science 3:e103, 2017. [DOI] [HAL]
  22. Efficient implementation of elementary functions in the medium-precision range
    22nd IEEE Symposium on Computer Arithmetic (ARITH22), 2015, pp. 83-89. [PDF] [arXiv] [DOI]
  23. A bound for the error term in the Brent-McMillan algorithm
    With Richard P. Brent. Mathematics of Computation, vol 84, 2015, pp. 2351-2359. [PDF] [arXiv] [DOI]
  24. A fast algorithm for reversion of power series
    Mathematics of Computation, vol 84, 2015, pp. 475-484. [PDF] [arXiv] [DOI] [info]
  25. Fast and rigorous computation of special functions to high precision
    PhD thesis, RISC, Johannes Kepler University, Linz, 2014. [PDF] [info]
  26. Evaluating parametric holonomic sequences using rectangular splitting
    39th International Symposium on Symbolic and Algebraic Computation (ISSAC'14), 2014, pp. 256-263. [PDF] [slides] [arXiv] [DOI] [info]
  27. Using functional equations to enumerate 1324-avoiding permutations
    With Brian Nakamura. Advances in Applied Mathematics, vol 56, 2014, pp. 20-34. [PDF] [arXiv] [DOI] [info]
  28. Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
    Numerical Algorithms, vol 69, issue 2, 2015, pp. 253-270. [PDF] [arXiv] [DOI] [info]
  29. Ore polynomials in Sage
    With Manuel Kauers and Maximilian Jaroschek. Computer Algebra and Polynomials, Springer LNCS, 2015, pp. 105-125. [PDF] [arXiv] [DOI] [info]
  30. Arb: a C library for ball arithmetic
    ACM Communications in Computer Algebra, vol 47, issue 4, December 2013, pp. 166-169. [PDF] [slides] [DOI] [info]
    Note: the 2017 IEEE TC paper largely supersedes this extended abstract.
  31. Finding hyperexponential solutions of linear ODEs by numerical evaluation
    With Manuel Kauers and Marc Mezzarobba. 38th International Symposium on Symbolic and Algebraic Computation (ISSAC'13), 2013, pp. 211-218. [PDF] [arXiv] [DOI] [info]
  32. Efficient implementation of the Hardy-Ramanujan-Rademacher formula
    LMS Journal of Computation and Mathematics, vol 15, 2012, pp. 341-359. [PDF] [arXiv] [DOI] [info]
  33. Simulation of the Maxwell-Dirac and Schrödinger-Poisson systems
    Master's thesis, Chalmers University of Technology, Gothenburg, 2010. [PDF] [slides] [info]

Erdős number

My Erdős number is 3 (0-1, 1-2, 2-3).

Awards

Talks

  1. September 2023: The practical complexity of arbitrary-precision functions, Fundamental Algorithms and Algorithmic Complexity, RTCA 2023, Institut Henri Poincaré, Paris, France
  2. June 2023: FLINT: Fast Library for Number Theory, Mathematical Software and High Performance Algebraic Computing, ENS Lyon, France
  3. May 2023: Computing special functions using integral representations, Certified and Symbolic-Numeric Computation, ENS Lyon, France
  4. March 2023: Faster computation of elementary functions, AriC seminar, ENS Lyon, France, online
  5. January 2023: Faster computation of elementary functions, MATHEXP–Polsys seminar, Inria Saclay, France
  6. September 2022: Faster computation of elementary functions, LFANT seminar, IMB, Bordeaux, France
  7. August 2022: [Video] Real numbers: a computational perspective, ANTS XV, University of Bristol, UK
  8. June 2022: [Video] FLINT: Fast Library for Number Theory, Global Virtual Sage Days 112.358, online
  9. May 2022: Fungrim: a semantic library of mathematical functions, Big Data in Pure Mathematics 2022, online
  10. July 2021: Exact linear algebra over the complex numbers, Applications of Computer Algebra (ACA) 2021, online
  11. July 2021: Calcium: computing in exact real and complex fields, ISSAC 2021, online
  12. April 2021: Calcium: computing in exact real and complex fields, NuSCAP kick-off meeting, France, online
  13. November 2020: Calcium: computing in exact real and complex fields, LFANT seminar, Bordeaux, France, online
  14. July 2020: What's new in Flint (2.6), ICMS 2020, online
  15. July 2020: [Video] FunGrim: a symbolic library for special functions, ICMS 2020, online
  16. July 2020: [Video] Special functions in Fungrim, OPSFOTA virtual seminar series, online
  17. June 2020: Computing with real numbers / Calculer avec les nombres réels (Part 1 + 2), EJCIM 2020, online
  18. December 2019: Numerical and symbolic tools for reliable computing with real numbers, CAPA seminar, Uppsala University, Sweden
  19. October 2019: Reliable real computing, Computational Mathematics and Applications Seminar, University of Oxford, UK
  20. October 2019: Ball arithmetic as a tool in computer algebra, Maple Conference, Waterloo, ON, Canada
  21. September 2019: Fungrim: The Mathematical Functions Grimoire, LFANT seminar, IMB, Bordeaux, France
  22. July 2019: Fungrim: The Mathematical Functions Grimoire, OPSFA 2019, Hagenberg, Austria
  23. June 2019: Faster arbitrary-precision dot product and matrix multiplication, ARITH26, Kyoto Research Park, Kyoto, Japan
  24. May 2019: Fungrim: The Mathematical Functions Grimoire, FastRelax Workshop, ENS Lyon, France
  25. February 2019: Arb demonstration, Free Computational Mathematics, CIRM, Luminy, France
  26. January 2019: Computing with precision, Guilty Spark Tech Talk, X, Mountain View, CA, USA
  27. January 2019: Progress in arbitrary-precision ball arithmetic: numerical integration and faster arithmetic, Scientific Computing and Matrix Computations Seminar, UC Berkeley, CA, USA
  28. November 2018: Faster dot product and matrix multiplication in arbitrary-precision ball arithmetic, MPFR / MPC / iRRAM Workshop, University of Trier, Germany
  29. November 2018: Faster dot product and matrix multiplication in arbitrary-precision ball arithmetic, RAIM 2018, LRI, Gif-sur-Yvette, France
  30. September 2018: Complex integration in Arb, SCAN 2018, Waseda University, Tokyo, Japan
  31. July 2018: Numerical integration in arbitrary-precision ball arithmetic, ICMS 2018, University of Notre Dame, South Bend, IN, USA
  32. June 2018: Numerical integration in arbitrary-precision ball arithmetic, FastRelax meeting, Inria Sophia-Antipolis, France
  33. March 2018: Numerical integration in arbitrary-precision ball arithmetic, AriC seminar, LIP, ENS Lyon, France
  34. February 2018: Fast and rigorous numerical integration, Comite des projet, Inria Bordeaux Sud-Ouest, France
  35. January 2018: Fast and rigorous arbitrary-precision evaluation of Legendre polynomials and Gauss-Legendre quadrature nodes, JNCF 2018, CIRM, Luminy, France
  36. January 2018: Numerical integration in complex interval arithmetic, LFANT seminar, IMB, Bordeaux, France
  37. December 2017: Numerical integration in complex interval arithmetic, MAX seminar, LIX, Ecole Polytechnique, Paris, France
  38. October 2017: Numerics of classical elliptic functions, elliptic integrals and modular forms, Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, DESY, Zeuthen, Germany
  39. October 2017: Numerics of classical elliptic functions, elliptic integrals and modular forms, LFANT seminar, IMB, Bordeaux, France
  40. August 2017: Fundamental algorithms in Arb, OSCAR : Antic workshop, TU Kaiserslautern, Germany
  41. July 2017: Arb: efficient arbitrary-precision midpoint-radius interval arithmetic, ARITH24, Imperial College London, UK
  42. June 2016: Fast reversion of formal power series, RAIM 2016, Banyuls-sur-mer, France
  43. May 2016: Hypergeometric functions in Arb, FastRelax meeting, LAAS-CNRS, Toulouse, France
  44. November 2015: Taking precision to the limit, Unithe ou cafe, INRIA, Bordeaux, France
  45. October 2015: Computing transcendental functions with error bounds, LFANT seminar, IMB, Bordeaux, France
  46. September 2015: Addition sequences and numerical evaluation of modular forms, DK Statusseminar, Strobl, Austria
  47. June 2015: Efficient implementation of elementary functions in the medium-precision range, ARITH22, ENS Lyon, France
  48. June 2015: Fast arbitrary-precision evaluation of special functions in the Arb library, OPSFA13, NIST, Gaithersburg, MD, USA
  49. May 2015: High-precision methods for zeta functions. Part 3: fast evaluation of sequences, UNCG Summer School in Computational Number Theory, Greensboro, NC, USA
  50. May 2015: High-precision methods for zeta functions. Part 2: derivatives, UNCG Summer School in Computational Number Theory, Greensboro, NC, USA
  51. May 2015: High-precision methods for zeta functions. Part 1: functions, formulas, UNCG Summer School in Computational Number Theory, Greensboro, NC, USA
  52. May 2015: Special functions in arbitrary-precision interval arithmetic, CAPA seminar, Uppsala University, Sweden
  53. March 2015: Special functions in the Arb library, AriC seminar, LIP, ENS Lyon, France
  54. March 2015: Special functions in the Arb library, Pequan seminar, LIP6, UPMC, Paris, France
  55. March 2015: Special functions in the Arb library, SpecFun seminar, INRIA Saclay Ile-de-France, Palaiseau, France
  56. September 2014: Reliable multiprecision arithmetic for number theory, LFANT seminar, IMB, Bordeaux, France
  57. July 2014: Evaluating parametric holonomic sequences using rectangular splitting, ISSAC 2014, Kobe University, Japan
  58. May 2014: Making change for 1020, computer algebra seminar, TU Kaiserslautern, Germany
  59. March 2014: Making change for 1020, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
  60. October 2013: Progress on algorithms for high-precision evaluation of special functions, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
  61. July 2013: Efficient implementation of the Hardy-Ramanujan-Rademacher formula, 2013 SIAM Annual Meeting, San Diego, CA, USA
  62. June 2013: Arb: a C library for ball arithmetic, ISSAC 2013, Boston, MA, USA
  63. June 2013: Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation, ISSAC 2013, Boston, MA, USA
  64. March 2013: Fast, rigorous, arbitrary precision numerics with ball arithmetic, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
  65. November 2012: Algorithms for hyperexponential solutions of differential equations, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
  66. May 2012: Fast special function computations with FLINT, RISC-DESY Workshop, RISC, Hagenberg, Austria
  67. December 2011: Fast combinatorial special functions, Sage Days 35: Algorithms in Number Theory and FLINT, University of Warwick, UK
  68. November 2011: Partitions in the quintillions or Billions of congruences, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
  69. November 2011: Fast reversion of power series, Algorithmic Combinatorics Seminar, RISC, Hagenberg, Austria
  70. July 2010: Computation of special functions in mpmath, Sage Days 24: Symbolic Computation in Differential Algebra and Special Functions, RISC, Hagenberg, Austria
  71. July 2010: Computation of special functions in mpmath, Sage Days 23: Number Theory and Algebra, Lorentz Center, Leiden, Netherlands
  72. May 2009: mpmath: arbitrary-precision floating-point arithmetic and special functions, Sage Days 15, University of Washington, Seattle, WA, USA

Academic history

Other professional activity

Conference organization

Reviewing

I've reviewed papers for a number of journals and conferences, including Mathematics of Computation, Journal of Symbolic Computation, Numerical Algorithms, BIT Numerical Mathematics, Advances in Applied Mathematics, Mathematics, ACM Transactions on Mathematical Software, IEEE Transactions on Circuits and Systems, IEEE Transactions on Computers.

Summers of code

I've taken part in Google Summer of Code once as a student and three times as a mentor:

In summer 2009 and 2010, I worked on Sage and mpmath for William Stein, formally as a contractor for the American Institute of Mathematics.

Unprofessional activity

Sports

I have an account on Strava for tracking running, cycling, hiking activities.

Music

Doom levels

My old Doom maps and related info.