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This commit adds support for in-place FFT transforms. Since our
internal transforms were all in-place anyway, this only changes
the permutation on the input.
Unfortunately, research papers were of no help here. All focused
on dry hardware implementations, where permutes are free, or on
software implementations where binary bloat is of no concern so
storing dozen times the transforms for each permutation and version
is not considered bad practice.
Still, for a pure C implementation, it's only around 28% slower
than the multi-megabyte FFTW3 in unaligned mode.
Unlike a closed permutation like with PFA, split-radix FFT bit-reversals
contain multiple NOPs, multiple simple swaps, and a few chained swaps,
so regular single-loop single-state permute loops were not possible.
Instead, we filter out parts of the input indices which are redundant.
This allows for a single branch, and with some clever AVX512 asm,
could possibly be SIMD'd without refactoring.
The inplace_idx array is guaranteed to never be larger than the
revtab array, and in practice only requires around log2(len) entries.
The power-of-two MDCTs can be done in-place as well. And it's
possible to eliminate a copy in the compound MDCTs too, however
it'll be slower than doing them out of place, and we'd need to dirty
the input array.
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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".
Some performance comparisons with libfftw3f (SIMD disabled for both):
120:
22353 decicycles in fftwf_execute, 1024 runs, 0 skips
21836 decicycles in compound_fft_15x8, 1024 runs, 0 skips
128:
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:
186210 decicycles in fftwf_execute, 1024 runs, 0 skips
215256 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.
New code throughout the project should use this API.
The implementation passes fate when used in Opus, AAC and Vorbis, and the output
is identical with ATRAC9 as well.
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