lavu/tx: implement 32 bit fixed point FFT and MDCT

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.

1 files changed, 3 insertions, 0 deletions

diff --git a/doc/APIchanges b/doc/APIchanges
index 30f188d6aa..761f37f2d2 100644
--- a/doc/APIchanges
+++ b/doc/APIchanges
@@ -15,6 +15,9 @@ libavutil:     2017-10-21
 
 API changes, most recent first:
 
+2020-02-13 - xxxxxxxxxx - lavu 56.41.100 - tx.h
+  Add AV_TX_INT32_FFT and AV_TX_INT32_MDCT
+
 2020-02-12 - xxxxxxxxxx - lavu 56.40.100 - log.h
   Add av_log_once().