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[WIP] starting to integrate AbstractFFTs
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‎.github/workflows/Documentation.yml

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name: Documentation
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on:
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push:
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branches:
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- master
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tags: '*'
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pull_request:
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jobs:
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build:
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runs-on: ubuntu-latest
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steps:
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- uses: actions/checkout@v2
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- uses: julia-actions/setup-julia@latest
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with:
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version: '1.6'
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- name: Install dependencies
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run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
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- name: Build and deploy
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env:
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GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} # If authenticating with GitHub Actions token
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DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # If authenticating with SSH deploy key
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run: julia --project=docs/ docs/make.jl

‎.gitignore

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/Manifest.toml
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docs/build

‎Project.toml

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name = "FFTA"
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uuid = "b86e33f2-c0db-4aa1-a6e0-ab43e668529e"
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authors = ["Danny Sharp <[email protected]> and contributors"]
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version = "0.2.1"
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version = "0.2.2"
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[deps]
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AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
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DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
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LoopVectorization = "bdcacae8-1622-11e9-2a5c-532679323890"
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Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
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MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
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Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
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Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
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[compat]
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DocStringExtensions = "0.8"
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LoopVectorization = "0.12"
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Documenter = "0.27"
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MuladdMacro = "0.2"
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Primes = "0.5"
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julia = "1"

‎README.md

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## A library by Danny Sharp
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[![Github Action CI](https://github.com/dannys4/FFTA.jl/workflows/CI/badge.svg)](https://github.com/dannys4/FFTA.jl/actions)
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[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://dannys4.github.io/FFTA.jl/stable/)
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[![codecov](https://codecov.io/gh/dannys4/FFTA.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/dannys4/FFTA.jl)
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This is a *pure Julia* implementation of FFTs, with the goal that this could supplant other FFTs for applications that require odd Julia objects. Currently this supports `AbstractArray{T,N}` where `N` in `{1,2}` (i.e. `AbstractVector` and `AbstractMatrix`). If you're looking for more performance, checkout `FFTW.jl`. Regardless of `T`, `one(::Type{T})` must be defined. Additionally, if `T<:Complex`, then `convert(::Type{T},ComplexF64)` has to be defined and if `T<:Real`, then `convert(::Type{T}, Float64)` has to be defined.
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This is a *pure Julia* implementation of FFTs, with the goal that this could supplant other FFTs for applications that require odd Julia objects. Currently this supports `AbstractArray{T,N}` where `N` in `{1,2}` (i.e. `AbstractVector` and `AbstractMatrix`). If you're looking for more performance, checkout `FFTW.jl`. Regardless of `T`, `one(::Type{T})` must be defined. Additionally, if `T<:Real`, then `convert(::Type{T}, Float64)` has to be defined. Otherwise, `convert(::Type{T},ComplexF64)` must be defined.
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Path Forward:
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- Make the code more readable.
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- Use `@inbounds`
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- Use `AbstractFFTs` interface
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Some ideas outside the feature requests in Issues:
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- Make the code more readable
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- Use `StaticArrays` for the workspace in small cases
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- Strictly generate code for certain cases
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- Create a SIMD type for Complex numbers
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- E-Graphs for the call-graph
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- Accelerate dynamic dispatching?
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- Other performance left on the table....
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Interface:
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- `fft(x::AbstractVector{<:Union{Real,Complex})`-- Forward FFT
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- `fft(x::AbstractMatrix{<:Union{Real,Complex}})`-- Forward FFT
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- `bfft(x::AbstractVector{<:Union{Real,Complex}})`-- Backward FFT (unscaled inverse FFT)
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- `bfft(x::AbstractMatrix{<:Union{Real,Complex}})`-- Backward FFT (unscaled inverse FFT)
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- `fft(x::AbstractVector)`-- Forward FFT
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- `fft(x::AbstractMatrix})`-- Forward FFT
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- `bfft(x::AbstractVector})`-- Backward FFT (unscaled inverse FFT)
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- `bfft(x::AbstractMatrix})`-- Backward FFT (unscaled inverse FFT)
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NOTE: Currently, my C++ code is actually faster than this, so "Fastest Fourier Transform in my Apartment" is a bit of a misnomer.
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‎docs/.gitignore

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build/
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site/

‎docs/Project.toml

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[deps]
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Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"

‎docs/make.jl

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using Documenter
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using FFTA
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makedocs(
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sitename = "FFTA",
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format = Documenter.HTML(),
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pages = ["Development Tools" => "dev.md"],
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modules = [FFTA]
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)
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# Documenter can also automatically deploy documentation to gh-pages.
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# See "Hosting Documentation" and deploydocs() in the Documenter manual
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# for more information.
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deploydocs(
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repo = "github.com/dannys4/FFTA.jl.git"
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)

‎docs/src/dev.md

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# Development Documentation
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Here is the documentation for key parts of the development side of the package.
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```@docs
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CallGraphNode
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CallGraph
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CallGraphNode!
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fft!
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fft_dft!
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fft_pow2!
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fft_pow3!
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fft_pow4!
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```

‎docs/src/index.md

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# FFTA.jl
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Documentation for FFTA.jl
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```@docs
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fft
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bfft
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```

‎src/FFTA.jl

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module FFTA
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using Primes, DocStringExtensions, LoopVectorization, MuladdMacro, AbstractFFTs, ComputedFieldTypes
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using Primes, DocStringExtensions, MuladdMacro, AbstractFFTs, ComputedFieldTypes
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export fft, bfft
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include("callgraph.jl")
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include("algos.jl")
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#= function fft(x::AbstractVector{T}) where {T}
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#=
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"""
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$(TYPEDSIGNATURES)
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Perform a fast Fourier transform of a vector. Preserves types given by the
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user.
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# Arguments
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x::AbstractVector: The vector to transform.
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# Examples
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```julia
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julia> x = rand(ComplexF64, 10)
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julia> y = fft(x)
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```
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"""
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function fft(x::AbstractVector{T}) where {T}
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y = similar(x)
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g = CallGraph{T}(length(x))
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fft!(y, x, 1, 1, FFT_FORWARD, g[1].type, g, 1)
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y
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end
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"""
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$(TYPEDSIGNATURES)
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Perform a fast Fourier transform of a matrix. Preserves types given by the
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user.
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# Arguments
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x::AbstractMatrix: The matrix to transform (columnwise then rowwise).
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# Examples
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```julia
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julia> x = rand(ComplexF64, 10, 10)
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julia> y = fft(x)
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```
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"""
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function fft(x::AbstractMatrix{T}) where {T}
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M,N = size(x)
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y1 = similar(x)
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y2
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end
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"""
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$(TYPEDSIGNATURES)
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Perform a backward fast Fourier transform of a vector, where "backward"
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indicates the same output signal down to a constant factor. Preserves types
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given by the user.
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# Arguments
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x::AbstractVector: The vector to transform
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# Examples
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```julia
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julia> x = rand(ComplexF64, 10)
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julia> y = bfft(x)
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julia> z = fft(y)
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julia> x ≈ z/10
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true
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```
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"""
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function bfft(x::AbstractVector{T}) where {T}
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y = similar(x)
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g = CallGraph{T}(length(x))
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y
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end
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"""
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$(TYPEDSIGNATURES)
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Perform a backward fast Fourier transform of a matrix, where "backward"
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indicates the same output signal down to a constant factor. Preserves types
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given by the user.
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# Arguments
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x::AbstractMatrix: The matrix to transform
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# Examples
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```julia
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julia> x = rand(ComplexF64, 10, 10)
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julia> y = bfft(x)
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julia> z = fft(y)
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julia> x ≈ z/100
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true
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```
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"""
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function bfft(x::AbstractMatrix{T}) where {T}
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M,N = size(x)
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y1 = similar(x)

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