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Add zfft interfaces, FORD docs, a related test.
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‎.github/workflows/fpm.yml

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- name: Run tests
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run: |
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gfortran --version
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fpm test --flag "-O2" tstfft
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fpm test --flag "-O2"

‎.gitignore

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*.o
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*.a
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*.so
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*.x
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*.x
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# API-doc
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API-doc/

‎API-doc-FORD-file.md

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---
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project: fftpack
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summary: A opensource package fftpack v4.0.0 for (modern) Fortran
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src_dir: src/
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output_dir: API-doc
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page_dir: doc/
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media_dir: doc/media
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display: public
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protected
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source: true
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proc_internals: true
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md_extensions: markdown.extensions.toc
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graph: true
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graph_maxnodes: 250
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graph_maxdepth: 5
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coloured_edges: true
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sort: permission-alpha
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extra_mods: iso_fortran_env:https://gcc.gnu.org/onlinedocs/gfortran/ISO_005fFORTRAN_005fENV.html
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iso_c_binding:https://gcc.gnu.org/onlinedocs/gfortran/ISO_005fC_005fBINDING.html#ISO_005fC_005fBINDING
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print_creation_date: true
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creation_date: %Y-%m-%d %H:%M %z
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project_github: https://github.com/certik/fftpack
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license: by-sa
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author: Paul N. Swarztrauber & fftpack contributors
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github: https://github.com/certik/fftpack
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dbg: true
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parallel: 4
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---
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[TOC]
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@warning This API documentation for the certik/fftpack v4.0.0 is a work in progress.
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Fortran FFTPACK API Documentation
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=================================
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This is the main API documentation landing page generated by [FORD].
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The documentation for comment markup in source code, running [FORD] and the [FORD project file] are all maintained on the [FORD wiki].
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[FORD]: https://github.com/Fortran-FOSS-Programmers/ford#readme
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[FORD wiki]: https://github.com/Fortran-FOSS-Programmers/ford/wiki
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[FORD project file]: https://github.com/certik/fftpack/blob/master/API-doc-FORD-file.md
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A package of fortran subprograms for the fast fourier transform of periodic and other symmetric sequences.
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## Getting started
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### Get the code
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```bash
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git clone https://github.com/certik/fftpack.git
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cd fftpack
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```
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### Build with [fortran-lang/fpm](https://github.com/fortran-lang/fpm)
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Fortran Package Manager (fpm) is a great package manager and build system for Fortran.
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You can build using provided `fpm.toml`:
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```bash
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fpm build --flag "-O2"
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fpm test --flag "-O2" tstfft
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```
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To use `fftpack` within your `fpm` project, add the following to your `fpm.toml` file:
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```toml
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[dependencies]
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fftpack = { git="https://github.com/certik/fftpack.git" }
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```
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## Build with Make
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Alternatively, you can build using provided `Makefile`:
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```bash
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make
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```
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## Links
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[netlib/dfftpack1.0(fftpack4.0)](http://www.netlib.org/fftpack/)
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‎doc/index.md

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---
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title: Contributing and specs
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---
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@warning
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This page is currently under construction!

‎doc/specs/fftpack.md

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---
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title: FFTPACK
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---
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# The `fftpack` module
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[TOC]
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## `zffti`
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### Description
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Initializes the array `wsave` which is used in both `zfftf` and `zfftb`.
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The prime factorization of `n` together with a tabulation of the trigonometric functions are computed and
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stored in `wsave`.
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### Status
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Experimental.
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### Class
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Pure function.
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### Snytax
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`call [[fftpack(module):zffti(interface)]](n, wsave)`
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### Argument
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`n`: Shall be an `integer` scalar.
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This argument is `intent(in)`.
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The length of the sequence to be transformed.
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`wsave`: Shall be a `real` array.
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This argument is `intent(out)`.
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A work array which must be dimensioned at least `4*n+15`.
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The same work array can be used for both `zfftf` and `zfftb`
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as long as `n` remains unchanged. Different `wsave` arrays
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are required for different values of `n`.
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#### Warning
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The contents of `wsave` must not be changed between calls of `zfftf` or `zfftb`.
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### Example
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```fortran
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program demo_zffti
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use fftpack, only: zffti
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complex(kind=8) :: x(4)
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real(kind=8) :: w(31)
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x = [real(kind=8) :: 1.0, 2.0, 3.0, 4.0]
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call zffti(4,w)
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end program demo_zffti
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```
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## `zfftf`
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### Description
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Computes the forward complex discrete fourier
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transform (the fourier analysis).
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Equivalently, `zfftf` computes
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the fourier coefficients of a complex periodic sequence.
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the transform is defined below at output parameter `c`.
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The transform is not normalized. to obtain a normalized transform
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the output must be divided by `n`. otherwise a call of `zfftf`
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followed by a call of `zfftb` will multiply the sequence by `n`.
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The array `wsave` which is used by subroutine `zfftf` must be
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initialized by calling subroutine `zffti(n,wsave)`.
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### Status
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Experimental.
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### Class
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Pure function.
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### Snytax
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`call [[fftpack(module):zfftf(interface)]](n, c, wsave)`
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### Argument
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`n`: Shall be an `integer` scalar.
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This argument is `intent(in)`.
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The length of the `complex` sequence `c`. The method is more efficient when `n` is the product of small primes.
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`c`: Shall be a `complex` array.
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This argument is `intent(inout)`.
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A `complex` array of length `n` which contains the sequence.
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```
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for j=1,...,n
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c(j)=the sum from k=1,...,n of
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c(k)*exp(-i*(j-1)*(k-1)*2*pi/n)
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where i=sqrt(-1)
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```
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`wsave`: Shall be a `real` array.
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This argument is `intent(inout)`.
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A `real` work array which must be dimensioned at least `4n+15` in the program that calls `zfftf`. The wsave array must be initialized by calling subroutine `zffti(n,wsave)` and a different wsave array must be used for each different value of `n`. This initialization does not have to be repeated so long as `n` remains unchanged thus subsequent transforms can be obtained faster than the first. The same wsave array can be used by `zfftf` and `zfftb`.
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Contains initialization calculations which must not be destroyed between calls of subroutine `zfftf` or `zfftb`.
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#### Warning
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The contents of `wsave` must not be changed between calls of `zfftf` or `zfftb`.
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### Example
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```fortran
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program demo_zfftf
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use fftpack, only: zffti, zfftf
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complex(kind=8) :: x(4)
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real(kind=8) :: w(31)
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x = [real(kind=8) :: 1.0, 2.0, 3.0, 4.0]
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call zffti(4,w)
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call zfftf(4,x,w) !! `x` returns [(10.0,0.0), (-2.0,2.0), (-2.0,0.0), (-2.0,-2.0)].
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end program demo_zfftf
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```
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## `zfftb`
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### Description
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Unnormalized inverse of `zfftf`.
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Computes the backward `complex` discrete fourier
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transform (the fourier synthesis). Equivalently, `zfftb` computes
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a `complex` periodic sequence from its fourier coefficients.
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The transform is defined below at output parameter `c`.
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The transform is not normalized. to obtain a normalized transform
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the output must be divided by `n`. otherwise a call of `zfftf`
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followed by a call of `zfftb` will multiply the sequence by `n`.
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The array `wsave` which is used by subroutine `zfftf` must be
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initialized by calling subroutine `zffti(n,wsave)`.
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### Status
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Experimental.
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### Class
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Pure function.
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### Snytax
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`call [[fftpack(module):zfftb(interface)]](n, c, wsave)`
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### Argument
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`n`: Shall be an `integer` scalar.
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This argument is `intent(in)`.
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The length of the `complex` sequence `c`. The method is more efficient when `n` is the product of small primes.
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`c`: Shall be a `complex` array.
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This argument is `intent(inout)`.
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A `complex` array of length `n` which contains the sequence.
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```
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for j=1,...,n
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c(j)=the sum from k=1,...,n of
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c(k)*exp(-i*(j-1)*(k-1)*2*pi/n)
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where i=sqrt(-1)
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```
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`wsave`: Shall be a `real` array.
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This argument is `intent(inout)`.
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A `real` work array which must be dimensioned at least `4n+15` in the program that calls `zfftf`. The wsave array must be initialized by calling subroutine `zffti(n,wsave)` and a different wsave array must be used for each different value of `n`. This initialization does not have to be repeated so long as `n` remains unchanged thus subsequent transforms can be obtained faster than the first. The same wsave array can be used by `zfftf` and `zfftb`.
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Contains initialization calculations which must not be destroyed between calls of subroutine `zfftf` or `zfftb`.
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#### Warning
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The contents of `wsave` must not be changed between calls of `zfftf` or `zfftb`.
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### Example
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```fortran
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program demo_zfftb
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use fftpack, only: zffti, zfftf, zfftb
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complex(kind=8) :: x(4)
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real(kind=8) :: w(31)
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x = [real(kind=8) :: 1.0, 2.0, 3.0, 4.0]
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call zffti(4,w)
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call zfftf(4,x,w) !! `x` returns [(10.0,0.0), (-2.0,2.0), (-2.0,0.0), (-2.0,-2.0)].
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call zfftb(4,x,w) !! `x` returns [(4.0,0.0), (8.0,0.0), (12.0,0.0), (16.0,0.0)].
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end program demo_zfftb
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```

‎doc/specs/index.md

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---
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title: Specifications (specs)
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---
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# Fortran fftpack Specifications (specs)
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[TOC]
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## Experimental Features & Modules
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- [fftpack](./fftpack.html) - fftpack module.
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## Released/Stable Features & Modules
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- (None yet)

‎fpm.toml

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[[test]]
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name = "tstfft"
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source-dir = "test"
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main = "tstfft.f"
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main = "tstfft.f"
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[[test]]
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name = "fftpack_zfft"
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source-dir = "test"
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main = "test_fftpack_zfft.f90"

‎src/fftpack.f90

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module fftpack
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use iso_fortran_env, only: dp => real64
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implicit none
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private
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public :: zffti, zfftf, zfftb
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interface
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!> Version: experimental
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!>
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!> Initialize `zfftf` and `zfftb`.
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!> ([Specification](../page/specs/fftpack.html#zffti))
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pure subroutine zffti(n, wsave)
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import dp
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integer, intent(in) :: n
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real(kind=dp), intent(out) :: wsave(*)
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end subroutine zffti
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!> Version: experimental
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!>
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!> Forward transform of a double complex periodic sequence.
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!> ([Specification](../page/specs/fftpack.html#zfftf))
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pure subroutine zfftf(n, c, wsave)
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import dp
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integer, intent(in) :: n
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complex(kind=dp), intent(inout) :: c(*)
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real(kind=dp), intent(inout) :: wsave(*)
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end subroutine zfftf
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!> Version: experimental
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!>
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!> Unnormalized inverse of `zfftf`.
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!> ([Specification](../page/specs/fftpack.html#zfftb))
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pure subroutine zfftb(n, c, wsave)
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import dp
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integer, intent(in) :: n
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complex(kind=dp), intent(inout) :: c(*)
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real(kind=dp), intent(inout) :: wsave(*)
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end subroutine zfftb
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end interface
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end module fftpack

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