# Why is CUDA.FFT slow only when performed over the second dimension of a 3D array?

**URL:** <https://discourse.julialang.org/t/why-is-cuda-fft-slow-only-when-performed-over-the-second-dimension-of-a-3d-array/125358>\
**Category:** GPU\
**Tags:** cuda, fft\
**Created:** [January 29, 2025, 6:49pm UTC](https://discourse.julialang.org/t/why-is-cuda-fft-slow-only-when-performed-over-the-second-dimension-of-a-3d-array/125358 "2025-01-29T18:49:19Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![marcsgil](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marcsgil/32/33908_2.png) [@marcsgil](https://discourse.julialang.org/u/marcsgil)\
**Post date:** [January 29, 2025, 6:49pm UTC](https://discourse.julialang.org/t/why-is-cuda-fft-slow-only-when-performed-over-the-second-dimension-of-a-3d-array/125358/1 "2025-01-29T18:49:19Z")

</div>

Consider the following test on the CPU:

```julia
using CUDA, FFTW, BenchmarkTools

x = randn(ComplexF32, 2^7, 2^7, 2^7)

for dim ∈ 1:ndims(x)
    @info "FFT along dimension $dim"
    display(@benchmark CUDA.@sync fft($x, $dim))
end

```

I would expect the fastest case to be the one with `dim=1`, because then the points involved in the `fft` are contiguous in memory. The results are consistent with this intuition:

```julia
[ Info: FFT along dimension 1
BenchmarkTools.Trial: 929 samples with 1 evaluation per sample.
 Range (min … max): 2.109 ms … 9.301 ms ┊ GC (min … max): 0.00% … 9.20%
 Time (median): 5.512 ms ┊ GC (median): 0.00%
 Time (mean ± σ): 5.386 ms ± 2.190 ms ┊ GC (mean ± σ): 13.02% ± 20.68%

   █                                                         
  ▄█▅▂▂▂▁▂▁▁▁▁▁▁▁▁▁▁▁▂▃▅▆▆▄▃▂▃▂▂▂▂▂▁▁▁▁▁▁▁▂▁▁▃▆▇▅▅▃▅▅▇▆▃▄▂▃ ▃
  2.11 ms Histogram: frequency by time 8.22 ms <

 Memory estimate: 16.00 MiB, allocs estimate: 8.
[ Info: FFT along dimension 2
BenchmarkTools.Trial: 739 samples with 1 evaluation per sample.
 Range (min … max): 3.519 ms … 12.589 ms ┊ GC (min … max): 0.00% … 63.60%
 Time (median): 7.176 ms ┊ GC (median): 0.00%
 Time (mean ± σ): 6.769 ms ± 2.003 ms ┊ GC (mean ± σ): 12.64% ± 17.06%

   ▅█ ▁ ▄ ▄         
  ▂███▅▃▂▂▂▂▁▁▁▁▁▁▁▂▁▂▁▁▁▂▃▅██▇▅▄▃▃▃▂▃▁▁▁▁▃██▇▅▄▄▃▄▆██▄▅▅▄▄▃ ▃
  3.52 ms Histogram: frequency by time 9.52 ms <

 Memory estimate: 16.00 MiB, allocs estimate: 8.
[ Info: FFT along dimension 3
BenchmarkTools.Trial: 563 samples with 1 evaluation per sample.
 Range (min … max): 5.128 ms … 16.052 ms ┊ GC (min … max): 0.00% … 52.46%
 Time (median): 9.486 ms ┊ GC (median): 0.00%
 Time (mean ± σ): 8.879 ms ± 2.213 ms ┊ GC (mean ± σ): 10.83% ± 14.65%

     ▇█▆ ▄▂ ▂ ▆▆▂ ▁ ▁▁▃▁ ▁    
  ▅▇▇███▇▅▂▂▁▂▁▁▁▁▁▁▁▁▁▁▂▁▄▄▄▇████▆▄▄▄▃▃▂▂▄▅▄▆█████▇██████▇▆ ▄
  5.13 ms Histogram: frequency by time 11.7 ms <

 Memory estimate: 16.00 MiB, allocs estimate: 8.

```

When running the same thing with but with `x` on the GPU (`x = CUDA.randn(ComplexF32, 2^7, 2^7, 2^7)`, I get

```julia
[ Info: FFT along dimension 1
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min … max): 20.250 μs … 2.765 ms ┊ GC (min … max): 0.00% … 95.44%
 Time (median): 24.590 μs ┊ GC (median): 0.00%
 Time (mean ± σ): 35.452 μs ± 67.646 μs ┊ GC (mean ± σ): 25.01% ± 13.52%

  █▆▃ ▁
  ████▅▃▁▁▄▁▃▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▅▆▇▇▇▇▇▇▇ █
  20.2 μs Histogram: log(frequency) by time 356 μs <

 Memory estimate: 1.12 KiB, allocs estimate: 30.
[ Info: FFT along dimension 2
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min … max): 399.892 μs … 3.124 ms ┊ GC (min … max): 0.00% … 69.76%
 Time (median): 406.122 μs ┊ GC (median): 0.00%
 Time (mean ± σ): 436.497 μs ± 159.030 μs ┊ GC (mean ± σ): 4.26% ± 7.97%

  █▅▃▁ ▁
  █████▆▅▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▅▆▇▆▅▅▆▅▆▇▇▇▇▇ █
  400 μs Histogram: log(frequency) by time 1.33 ms <

 Memory estimate: 64.89 KiB, allocs estimate: 3221.
[ Info: FFT along dimension 3
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min … max): 21.680 μs … 504.712 μs ┊ GC (min … max): 0.00% … 82.88%
 Time (median): 25.130 μs ┊ GC (median): 0.00%
 Time (mean ± σ): 36.442 μs ± 61.370 μs ┊ GC (mean ± σ): 25.38% ± 13.70%

  █▄▂ ▁
  ███▇▄▁▁▁▁▁▁▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▅▇▇▇▇▇▇▇ █
  21.7 μs Histogram: log(frequency) by time 388 μs <

 Memory estimate: 1.12 KiB, allocs estimate: 30.

```

For me, there are two odd behaviors here:

- The slowdown is HUGE when `dim=2`.
- The slowdown is negligible when `dim=3`.

Could anyone help me understand this difference?