By itself, this allows 6-point, 10-point and 30-point transforms.
When the 9-point transform is added it allows for 18-point FFT,
and also for a 36-point MDCT (used by MP3).
Required minimal changes to the code so made sense to implement.
FFT and MDCT tested, the output of both was properly rounded.
Fun fact: the non-power-of-two fixed-point FFT and MDCT are the fastest ever
non-power-of-two fixed-point FFT and MDCT written.
This can replace the power of two integer MDCTs in aac and ac3 if the
MIPS optimizations are ported across.
Unfortunately the ac3 encoder uses a 16-bit fixed point forward transform,
unlike the encoder which uses a 32bit inverse transform, so some modifications
might be required there.
The 3-point FFT is somewhat less accurate than it otherwise could be,
having minor rounding errors with bigger transforms. However, this
could be improved later, and the way its currently written is the way one
would write assembly for it.
Similar rounding errors can also be found throughout the power of two FFTs
as well, though those are more difficult to correct.
Despite this, the integer transforms are more than accurate enough.
Simply moves and templates the actual transforms to support an
additional data type.
Unlike the float version, which is equal or better than libfftw3f,
double precision output is bit identical with libfftw3.
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.
Lynne
Ruiling Song