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2020-03-24lavu/tx: add 2-point FFT transformLynne
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).
2020-02-14lavu/tx: improve 3-point fixed precisionLynne
There's just no reason not to when its so easy (albeit messy) and its also reducing the precision of all non-power-of-two transforms that use it.
2020-02-13lavu/tx: slightly optimize fft15Lynne
Saves 2 additions.
2020-02-13lavu/tx: undef the correct macroLynne
It was renamed and no warning was given for undeffing a nonexisting one.
2020-02-13lavu/tx: implement 32 bit fixed point FFT and MDCTLynne
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.
2019-08-02lavu/tx: add support for double precision FFT and MDCTLynne
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.