This may be a slightly surprising optimization, but is actually based on
an understanding of how math libraries compute trigonometric functions.
Explanation is given here so that future development uses libm more effectively
across the codebase.

All libm's essentially compute transcendental functions via some kind of
polynomial approximation, be it Taylor-Maclaurin or Chebyshev.
Correction terms are added via polynomial correction factors when needed
to squeeze out the last bits of accuracy. Lookup tables are also
inserted strategically.

In the case of trigonometric functions, periodicity is exploited via
first doing a range reduction to an interval around zero, and then using
some polynomial approximation.

This range reduction is the most natural way of doing things - else one
would need polynomials for ranges in different periods which makes no
sense whatsoever.

To avoid the need for the range reduction, it is helpful to feed in
arguments as close to the origin as possible for the trigonometric
functions. In fact, this also makes sense from an accuracy point of view:
IEEE floating point has far more resolution for small numbers than big ones.

This patch does this for the Blackman-Nuttall filter, and yields a
non-negligible speedup.

Sample benchmark (x86-64, Haswell, GNU/Linux)
test: fate-swr-resample-dblp-2626-44100
old:
18893514 decicycles in build_filter (loop 1000),     256 runs,      0 skips
18599863 decicycles in build_filter (loop 1000),     512 runs,      0 skips
18445574 decicycles in build_filter (loop 1000),    1000 runs,     24 skips

new:
16290697 decicycles in build_filter (loop 1000),     256 runs,      0 skips
16267172 decicycles in build_filter (loop 1000),     512 runs,      0 skips
16251105 decicycles in build_filter (loop 1000),    1000 runs,     24 skips
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>

When upsampling, factor is set to 1 and sines need to be evaluated only
once for each phase, and the complexity should not depend on the number
of filter taps. This does the desired precomputation, yielding
significant speedups. Hard guarantees on the gain are not possible, but gains
themselves are obvious and are illustrated below.

Sample benchmark (x86-64, Haswell, GNU/Linux)
test: fate-swr-resample-dblp-2626-44100
old:
29161085 decicycles in build_filter (loop 1000),     256 runs,      0 skips
28821467 decicycles in build_filter (loop 1000),     512 runs,      0 skips
28668201 decicycles in build_filter (loop 1000),    1000 runs,     24 skips

new:
14351936 decicycles in build_filter (loop 1000),     256 runs,      0 skips
14306652 decicycles in build_filter (loop 1000),     512 runs,      0 skips
14299923 decicycles in build_filter (loop 1000),    1000 runs,     24 skips

Note that this does not statically allocate the sin lookup table. This
may be done for the default 1024 phases, yielding a 512*8 = 4kB array
which should be small enough.
This should yield a small improvement. Nevertheless, this is separate from
this patch, is more ambiguous due to the binary increase, and requires a
lut to be generated offline.
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>

Signed-off-by: Simon Thelen <ffmpeg-dev@c-14.de>
Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Fixes a segfault when trying to write nonexistent rtp information.
Signed-off-by: Simon Thelen <ffmpeg-dev@c-14.de>
Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

cache protocol indexes its cache using AVTreeNodes which require a cmp
function for inserting and searching new cache-entries. This cmp
function expects a 32-bit int return value (negative, zero, or positive)
but the cache cmp function returns an int64_t which can overflow the
int, giving negative numbers for when it should be positive, vice versa.
This manifests itself only for very large files (e.g. 4GB+)
Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Timo Rothenpieler <timo@rothenpieler.org>

Signed-off-by: Matt Oliver <protogonoi@gmail.com>

Signed-off-by: Paul B Mahol <onemda@gmail.com>

This improves accuracy for the bessel function at large arguments, and this in turn
should improve the quality of the Kaiser window. It also improves the
performance of the bessel function and hence build_filter by ~ 20%.
Details are given below.

Algorithm: taken from the Boost project, who have done a detailed
investigation of the accuracy of their method, as compared with e.g the
GNU Scientific Library (GSL):
http://www.boost.org/doc/libs/1_52_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html.
Boost source code (also cited and licensed in the code):
https://searchcode.com/codesearch/view/14918379/.

Accuracy: sample values may be obtained as follows. i0 denotes the old bessel code,
i0_boost the approach here, and i0_real an arbitrary precision result (truncated) from Wolfram Alpha:
type "bessel i0(6.0)" to reproduce. These are evaluation points that occur for
the default kaiser_beta = 9.

Some illustrations:
bessel(8.0)
i0      (8.000000) = 427.564115721804739678191254
i0_boost(8.000000) = 427.564115721804796521610115
i0_real (8.000000) = 427.564115721804785177396791

bessel(6.0)
i0      (6.000000) = 67.234406976477956163762428
i0_boost(6.000000) = 67.234406976477970374617144
i0_real (6.000000) = 67.234406976477975326188025

Reason for accuracy: Main accuracy benefits come at larger bessel arguments, where the
Taylor-Maclaurin method is not that good: 23+ iterations
(at large arguments, since the series is about 0) can cause
significant floating point error accumulation.

Benchmarks: Obtained on x86-64, Haswell, GNU/Linux via a loop calling
build_filter 1000 times:
test: fate-swr-resample-dblp-44100-2626

new:
995894468 decicycles in build_filter(loop 1000),     256 runs,      0 skips
1029719302 decicycles in build_filter(loop 1000),     512 runs,      0 skips
984101131 decicycles in build_filter(loop 1000),    1024 runs,      0 skips

old:
1250020763 decicycles in build_filter(loop 1000),     256 runs,      0 skips
1246353282 decicycles in build_filter(loop 1000),     512 runs,      0 skips
1220017565 decicycles in build_filter(loop 1000),    1024 runs,      0 skips

A further ~ 5% may be squeezed by enabling -ftree-vectorize. However,
this is a separate issue from this patch.
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>

Kaiser windows inherently don't require beta to be an integer. This was
an arbitrary restriction. Moreover, soxr does not require it, and in
fact often estimates beta to a non-integral value.

Thus, this patch allows greater flexibility for swresample clients.
Micro version is updated.
Reviewed-by: Derek Buitenhuis <derek.buitenhuis@gmail.com>
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>

Otherwise v=INT_MIN doesn't get normalized and thus triggers av_assert2
in other functions.
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Andreas Cadhalpun <Andreas.Cadhalpun@googlemail.com>

The correct result can't be expressed in SoftFloat.
Currently it returns a random value from an out of bounds read.
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Andreas Cadhalpun <Andreas.Cadhalpun@googlemail.com>

Signed-off-by: Kyle Swanson <k@ylo.ph>
Signed-off-by: Paul B Mahol <onemda@gmail.com>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

This case should not be possible if the input has a exponent within
the valid range

This reverts commit 0269fb11.

Otherwise the exponent could eventually underflow
Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

Reviewed-by: Ronald S. Bultje <rsbultje@gmail.com>
Reviewed-by: James Almer <jamrial@gmail.com>

Fixes: e214333cbd94c91228e624ff39329ce6/asan_generic_4a5159_6412_96cda2530e80607210ab41ccae3d456d.tak

Found-by: Mateusz "j00ru" Jurczyk and Gynvael Coldwind
Signed-off-by: Michael Niedermayer <michael@niedermayer.cc>

The assert in ffmmal_stop_decoder() could trigger sometimes. The
packets_buffered counter was indeed not correctly maintained, and
packets were not subtracted from it if they were still in the waiting
queue.

For some reason, this happened especially with VC-1.

It was only useful for very specific testing purposes
and appears to be currently partially broken.