# \[ANN\] AcceleratedDCTs.jl: Device-agnostic 1D/2D/3D DCTs
**URL:** https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274
**Category:** Package Announcements
**Created:** [January 26, 2026, 2:38pm UTC](https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274 "2026-01-26T14:38:08Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)
#### Post date: [January 26, 2026, 2:38pm UTC](https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274/1 "2026-01-26T14:38:08Z")
Hi everyone,
I am excited to announce a new package, **AcceleratedDCTs.jl**.
**Motivation**
To improve the simulation tool of my research group, we require high-performance DCTs up to 3D, especially on GPU. While `Oceananigans.jl` includes a 1D DCT targeting GPU, there was no implementation available that fully supported N-dimensional transforms while remaining device-agnostic.
**Features**
AcceleratedDCTs.jl implements DCT-II and IDCT-II.
- **Dimensions** : Supports 1D, 2D, and 3D arrays.
- **Device Agnostic** : Built with `KernelAbstractions.jl`, so it runs on both CPUs and GPUs.
- **Performance** : Uses Real-to-Complex (R2C) FFTs instead of Complex-to-Complex (C2C) to improve memory usage and speed.
- **Plans** : supports plans and `mul!` interface as in AbstractFFTs.jl.
**Algorithm**
The default implementation follows Makhoul’s algorithm, which utilizes a global pre-processing and post-processing step combined with a simultaneous multi-dimensional FFT. See documentation for more details.
For comparison, I also implemented:
- `dct_batch.jl`: performs batched 1D FFTs along each dimension (labeled “Batched DCT” in benchmarks).
- `dct_slow.jl`: performs sequential 1D FFTs along each dimension.
**Benchmarks**
Here are some performance results for **3D DCTs** on varying grid sizes (N^3). Results collected using in-place `mul!` to exclude allocation overhead. Lower is better.
**GPU Performance (Nvidia RTX 2080 Ti)**
| Grid Size (N^3) | `cuFFT` (Baseline) | **`Opt 3D DCT`** | `Batched DCT` (Old) |
| --- | --- | --- | --- |
| **16^3** | 0.068 ms | **0.104 ms** | 0.883 ms |
| **32^3** | 0.064 ms | **0.117 ms** | 0.908 ms |
| **64^3** | 0.112 ms | **0.237 ms** | 1.138 ms |
| **128^3** | 0.818 ms | **1.414 ms** | 3.228 ms |
| **256^3** | 5.980 ms | **10.455 ms** | 23.120 ms |
> **Note** : `Opt 3D DCT` maintains excellent performance across all sizes. For N=256, it is **\>2.2x faster** than the batched implementation.
**CPU Performance (8 Threads, Intel Xeon Gold 6132)**
| Grid Size (N^3) | `FFTW rfft` | **`Opt 3D DCT`** | `FFTW dct` | `Batched DCT` |
| --- | --- | --- | --- | --- |
| **16^3** | 0.015 ms | **0.150 ms** | 0.058 ms | 0.424 ms |
| **32^3** | 0.100 ms | **0.508 ms** | 0.426 ms | 0.693 ms |
| **64^3** | 1.241 ms | **3.856 ms** | 4.336 ms | 8.703 ms |
| **128^3** | 14.905 ms | **38.795 ms** | 47.904 ms | 96.860 ms |
| **256^3** | 243.146 ms | **332.595 ms** | 420.537 ms | 1066.093 ms |
> **Note** : On multi-threaded CPU, `Opt 3D DCT` (332ms) **outperforms** `FFTW.dct` (420ms) at large sizes (N=256) by being ~1.26x faster!
**Feedback**
I am looking for feedback from the community. If anyone can help verify the correctness of the results (they are verified preliminary in the `test`) or confirm the performance benefits, that would be very helpful. Pull requests are also welcome.
Repository: [GitHub - liuyxpp/AcceleratedDCTs.jl: Device agnostic implementation of 1D/2D/3D DCTs.](https://github.com/liuyxpp/AcceleratedDCTs.jl)
---
### Author:  [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)
#### Post date: [February 23, 2026, 6:17am UTC](https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274/2 "2026-02-23T06:17:13Z")
New version: v0.4.1
This release integrates the newly registered [`VkDCT_jll`](https://github.com/JuliaBinaryWrappers/VkDCT_jll.jl) (v1.3.4) package, eliminating the need for manual CUDA shim compilation. GPU-accelerated 3D DCT-I transforms based on [VkFFT](https://github.com/DTolm/VkFFT) now work out of the box.
Unlike cuFFT, VkFFT provides DCTs natively and they are much faster than our own implementation in AcceleratedDCTs.jl.
---
### Author:  [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)
#### Post date: [April 30, 2026, 1:43am UTC](https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274/3 "2026-04-30T01:43:06Z")
@goerz Can you help me merge this PR for AcceleratedDCTs.jl v0.5.0 ( #151622)? I cannot make the auto merge work, but I do think I provide the changelog correctly. Sorry, I don’t have a Slack account.
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### Author:  [@goerz](https://discourse.julialang.org/u/goerz)
#### Post date: [April 30, 2026, 2:48am UTC](https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274/4 "2026-04-30T02:48:08Z")
You have a typo in [“Realease notes”](https://github.com/liuyxpp/AcceleratedDCTs.jl/commit/308f859f5749febdb34d7e8674c6b4a5ad9c6d2c#commitcomment-180903909). Just remove the extra “a”
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### Author:  [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)
#### Post date: [May 2, 2026, 3:08am UTC](https://discourse.julialang.org/t/ann-accelerateddcts-jl-device-agnostic-1d-2d-3d-dcts/135274/5 "2026-05-02T03:08:35Z")
Ah, this is embarrassing. Now, AcceleratedDCTs.jl v0.5.0 is available in the General Registry. Thank you!