[FFmpeg-devel] [PATCH] libavutil: add an FFT & MDCT implementation

[Lynne]

This commit adds a new API to libavutil to allow for arbitrary transformations
on various types of data.
This is a partly new implementation, with the power of two transforms taken
from libavcodec/fft_template, the 5 and 15-point FFT taken from mdct15, while
the 3-point FFT was written from scratch.
The (i)mdct folding code is taken from mdct15 as well, as the mdct_template
code was somewhat old, messy and not easy to separate.

A notable feature of this implementation is that it allows for 3xM and 5xM
based transforms, where M is a power of two, e.g. 384, 640, 768, 1280, etc.
AC-4 uses 3xM transforms while Siren uses 5xM transforms, so the code will
allow for decoding of such streams.
A non-exaustive list of supported sizes:
4, 8, 12, 16, 20, 24, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240,
256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560...

The API was designed such that it allows for not only 1D transforms but also
2D transforms of certain block sizes. This was partly on accident as the stride
argument is required for Opus MDCTs, but can be used in the context of a 2D
transform as well.
Also, various data types would be implemented eventually as well, such as
"double" and "int32_t".

The avfft_transform() function is awkward but avoids some other more
awkward ideas to isolate the private parts of the structure and not
make them part of the API, as well as reducing call overhead from
an additional function call.

Some performance comparisons with libfftw3f (SIMD disabled for both):
120:
  22410 decicycles in     fftwf_execute,     1024 runs,      0 skips
  28878 decicycles in compound_fft_15x8,     1024 runs,      0 skips

28:
  22003 decicycles in       fftwf_execute,   1024 runs,      0 skips
  23132 decicycles in monolithic_fft_ptwo,   1024 runs,      0 skips

384:
  75939 decicycles in      fftwf_execute,    1024 runs,      0 skips
  73973 decicycles in compound_fft_3x128,    1024 runs,      0 skips

640:
104354 decicycles in       fftwf_execute,   1024 runs,      0 skips
149518 decicycles in compound_fft_5x128,    1024 runs,      0 skips

768:
109323 decicycles in      fftwf_execute,    1024 runs,      0 skips
164096 decicycles in compound_fft_3x256,    1024 runs,      0 skips

960:
182275 decicycles in      fftwf_execute,    1024 runs,      0 skips
260288 decicycles in compound_fft_15x64,    1024 runs,      0 skips

1024:
163464 decicycles in       fftwf_execute,   1024 runs,      0 skips
199686 decicycles in monolithic_fft_ptwo,   1024 runs,      0 skips

With SIMD we should be faster than fftw for 15xM transforms as our fft15 SIMD
is around 2x faster than theirs, even if our ptwo SIMD is slightly slower.

The goal is to remove the libavcodec/mdct15 code and deprecate the
libavcodec/avfft interface once aarch64 and x86 SIMD code has been ported.
It is unlikely that libavcodec/fft will be removed soon as there's much SIMD
written for exotic or old platforms there, but nevertheless new code
should use this new API throughout the project.

The implementation passes fate when used in Opus and AAC, and the output
is identical in ATRAC9 as well.

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