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This PR revises the docstring for plan_fft.

My main impetus was to add a warning about serializing/sharing plans. Due to the name, I naively had assumed that "plans" were simply descriptive ("use this algorithm") and could be shared across processes (e.g., via @Everywhere). This seems to be a relatively common mistake, so I thought it was worth a warning.

I also did some light copy-editing and reformatting while adding that, which I think makes the text clearer.

- Added warnings about serialization and overwriting inputs.
- Section breaks and more info on FFTW planning.
- Light copyediting.
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codecov bot commented Nov 14, 2025

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.77%. Comparing base (04a14f5) to head (1f98169).

Additional details and impacted files
@@            Coverage Diff             @@
##           master     #148      +/-   ##
==========================================
- Coverage   94.83%   94.77%   -0.06%     
==========================================
  Files           4        4              
  Lines         445      440       -5     
==========================================
- Hits          422      417       -5     
  Misses         23       23              

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@mrkrause
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The failed integration test is due this issue with FastTransfoms.jl: to JuliaApproximation/FastTransforms.jl#263

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