# \[ANN\] FundamentalFrequencies.jl: GPU-vectorizable Numerical Analysis of Fundamental Frequencies (NAFF)

**URL:** https://discourse.julialang.org/t/ann-fundamentalfrequencies-jl-gpu-vectorizable-numerical-analysis-of-fundamental-frequencies-naff/136434
**Category:** Package Announcements
**Created:** [March 28, 2026, 11:03am UTC](https://discourse.julialang.org/t/ann-fundamentalfrequencies-jl-gpu-vectorizable-numerical-analysis-of-fundamental-frequencies-naff/136434 "2026-03-28T11:03:46Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![mattsignorelli](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mattsignorelli/32/221502_2.png) [@mattsignorelli](https://discourse.julialang.org/u/mattsignorelli)
#### Post date: [March 28, 2026, 11:03am UTC](https://discourse.julialang.org/t/ann-fundamentalfrequencies-jl-gpu-vectorizable-numerical-analysis-of-fundamental-frequencies-naff/136434/1 "2026-03-28T11:03:46Z")

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> **[GitHub - bmad-sim/FundamentalFrequencies.jl: A GPU-compatible Julia implementation of the...](https://github.com/bmad-sim/FundamentalFrequencies.jl)**
>
> A GPU-compatible Julia implementation of the Numerical Analysis of Fundamental Frequencies (NAFF) method.

This package provides a Julia implementation of the [Numerical Analysis of Fundamental Frequencies (NAFF) method by J. Laskar](https://www.sciencedirect.com/science/article/pii/016727899290028L) to compute fundamental frequencies of quasi-periodic systems to high precision. The evolution of the fundamental frequencies with time can be used to measure chaos. Some papers of interest:

- [The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones](https://www.sciencedirect.com/science/article/pii/001910359090084M)
- [Application of Frequency Map Analysis to the ALS](https://cds.cern.ch/record/301630/files/p183.pdf)

`FundamentalFrequencies.jl` in particular is implemented in a branchless and vectorized way for GPU-accelerated, batched NAFF. With this package, one can do NAFF on e.g. a million particles in parallel on a GPU. While this was initially developed for the [SciBmad accelerator physics code](https://github.com/bmad-sim/SciBmad.jl), the tools developed here may be useful to a much broader nonlinear dynamics audience.