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Fredrik Johansson's blog

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Posts

Optimizing multiprecision LLL in FLINT

Palaiseau FLINT workshop report

Further optimizing bigfloat matrix multiplication

Complex floats and some big root-finding speedups

Faster, vector-friendly bigfloats in FLINT

Faster crypto-sized residue ring arithmetic in FLINT

Bordeaux FLINT workshop report

What's new in FLINT 3.1

The reciprocal Fibonacci constant

Kaiserslautern FLINT meeting report

FLINT furnished with faster FFT

Generics in FLINT

Arb 2.23 released

Multithreaded elementary functions

Parallelizing Arb for fun and profit

Things I would like to see in a computer algebra system

Arb is 10

Long-term development of some mathematical software projects

Computing the Lerch transcendent

A series complexity problem

Computing special functions using numerical integration

Optimizing erf in arbitrary precision

Computing classical combinatorial numbers

Floating-point wrappers in Arb

Citing papers in software

Bringing Calcium to Julia

Calcium development update

Printing algebraic numbers

Computing with metavalues

The symbolic formula language in Calcium and Fungrim

Developing mathematical software in C

Infinity in Calcium and Fungrim

Flat-packed symbolic expressions

Exact matrix functions in Calcium

Benchmarking exact DFT computation

Calcium 0.1

Grim symbolic computation

Arb 2.17 released

Fungrim ♥ OEIS

What is the most common real number?

New logos: Fungrim, FLINT, mpmath

A grimoire of functions

Eigenvalues in Arb

Announcing Python-FLINT 0.2

Accelerated arithmetic in Arb 2.15

High-precision linear algebra in Julia: BigFloat vs Arb

Arb 2.14 released

Interesting interference integrals

The Arb matrix revolutions

The Arb matrix reloaded

New color functions

Arb 2.13.0 released, and more on integration

Arb 2.12 released

New rigorous numerical integration in Arb

mpmath 1.0, and a ten-year retrospective

Faster exp, sin and cos at high precision

Arb 2.11 is available

Arb 2.10.0 released

Arb 2.9.0 released

Dirichlet L-functions in Arb

The Riemann-Siegel formula in Arb

Additional results

Taking the error out of the error function

Phaseful plots

Arb 2.8.0 released

Airy in the library

The 2F1 bites the dust

Finding Nemo

Computing Bell numbers

What's new in Arb 2.7.0

Tio taktlösa trubadurer (tretton timmar till Tunis)

Arb 2.5.0 released

Arb and FLINT in Python

Faster high-precision arctangents

Arb 2.4.0

Hypergeometric functions in Arb

Theta functions and elliptic functions in Arb

Modular forms in Arb

Wrapping up FLINT's Summer of Code 2014

Arb 2.3.0 with faster elementary functions

Thirty times faster arctangents

Easy hypergeometric series at unity

Arb 2.1 released

Arb 2.0 available

Arb 2.0 preview: intervals at the speed of points

Arb 1.1 released, 2.0 right around the corner

Embettered polynomial multiplication

New partition function record: p(10^20) computed

Blog simplified

FLINT 2.4 and Arb 1.0

Tradeoffs in ball arithmetic

Rigorous numerical integration

Arb example programs, rigorous calculus

Parallelism and scaling

Arb 0.7: getting serious with power series

More digits of zetazero(1)

Computing 100,000 digits of zetazero(1)

Numerical power series reversion

Numerically stable fast polynomial arithmetic

Testing Li’s criterion

Arb 0.5

Coping with a big argument

Machin-like formulas for logarithms

An even speedier gamma function

Precise computation of roots of unity

Timings for the complex gamma function in Arb

Arb 0.4

Arb 0.3, with complex numbers

Automatic hypergeometric series

Ball linear algebra

Sometimes faster is worse

Implementing log-gamma using the Stirling series

Karatsuba’s algorithm for the gamma function

Code rewrite, and Fibonacci numbers

What’s new in FLINT 2.3

Experiments with low-level ball arithmetic

Logarithms as well

Revisiting transcendental functions

Algorithm selection for zeta(n)

High-precision ball arithmetic

Partitions into the quintillions

Factorials mod n and Wilson’s theorem

Blog moved

Some FLINT 2.2 highlights

100 mpmath one-liners for pi

A FLINT example: Lambert W function power series

Announcing mpmath 0.16

Again, mpmath in Sage is about to get faster

Fast combinatorial and number-theoretic functions with FLINT 2

Euler-Maclaurin summation of hypergeometric series

Post Sage Days 24 report

Sage Days 23, and Bessel function zeros

Symbolic infinite series

Incomplete elliptic integrals complete

Assorted special functions update

Announcing mpmath 0.15

Hypergeneralization

Computing large zeta zeros with mpmath

Speedups of elementary functions

Numerical multidimensional infinite series

A new gamma function implementation

Mpmath 0.14 released

mpmath in Sage to become 3x faster

Using Sage numbers in mpmath

Zeta evaluation with the Riemann-Siegel expansion

YAMDU (yet another mpmath development update)

Accurate hypergeometric functions for large parameters

Analytic continuation of 3F2, 4F3 and higher functions

Python floats and other unusual things spotted in mpmath

Released: mpmath 0.13

Torture testing special functions

3D visualization of complex functions with matplotlib

Coulomb wave functions and orthogonal polynomials

Hurwitz zeta function, Dirichlet L-series, Appell F1

Another Mathematica bug

Improved incomplete gamma and exponential integrals; Clausen functions

Meijer G, more hypergeometric functions, fractional differentiation

Massive hypergeometric update

Hypergeometric 2F1, incomplete beta, exponential integrals

Mpmath 0.12 released

Cython mpmath performance, part 2

Cython mpmath performance

Report from Sage Days 15

Computing (generalized) Bell numbers

How (not) to compute harmonic numbers

Python 3.1 twice as fast as 3.0

Approximate prime counting

Galerkin’s method in SymPy

Fun with zeta functions

Mpmath 0.11 released

Jacobi theta function fractals

A spiralling little tune

ANN: mpmath 0.10

Mpmath’s first birthday

Fun with the digamma function

Wrapping it up

Division: the sequel (with bonus material)

Making division in Python faster

Hypergeometric series with SymPy

Faster pi, more integrals and complex numbers