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Ganesh Ajjanagadde dd68cde28a lavu/libm: add erf hack and make dynaudnorm available everywhere 
Source code is from Boost:
http://www.boost.org/doc/libs/1_46_1/boost/math/special_functions/erf.hpp
with appropriate modifications for FFmpeg.

Tested on interval -6 to 6 (beyond which it saturates), +/-NAN, +/-INFINITY
under -fsanitize=undefined on clang to test for possible undefined behavior.

This function turns out to actually be essentially as accurate and faster than the
libm (GNU/BSD's/Mac OS X), and I can think of 3 reasons why upstream
does not use this:
1. They are not aware of it.
2. They are concerned about licensing - this applies especially to GNU
libm.
3. They do not know and/or appreciate the benefits of rational
approximations over polynomial approximations. Boost uses them to great
effect, see e.g swr/resample for bessel derived from them, which is also
similarly superior to libm variants.

First, performance.
sample benchmark (clang -O3, Haswell, GNU/Linux):

3e8 values evenly spaced from 0 to 6
time (libm):
./test  13.39s user 0.00s system 100% cpu 13.376 total
time (boost based):
./test  9.20s user 0.00s system 100% cpu 9.190 total

Second, accuracy.
1e8 eval pts from 0 to 6
maxdiff (absolute): 2.2204460492503131e-16
occuring at point where libm erf is correctly rounded, this is not.

Illustration of superior rounding of this function:
arg   : 0.83999999999999997
erf   : 0.76514271145499457
boost : 0.76514271145499446
real  : 0.76514271145499446

i.e libm is actually incorrectly rounded. Note that this is clear from:
https://github.com/JuliaLang/openlibm/blob/master/src/s_erf.c (the Sun
implementation used by both BSD and GNU libm's), where only 1 ulp is
guaranteed.

Reasons it is not easy/worthwhile to create a "correctly rounded"
variant of this function (i.e 0.5ulp):
1. Upstream libm's don't do it anyway, so we can't guarantee this unless
we force this implementation on all platforms. This is not easy, as the
linker would complain unless measures are taken.
2. Nothing in FFmpeg cares or can care about such things, due to the
above and FFmpeg's nature.
3. Creating a correctly rounded function will in practice need some use of long
double/fma. long double, although C89/C90, unfortunately has problems on
ppc. This needs fixing of toolchain flags/configure. In any case this
will be slower for miniscule gain.

Reviewed-by: James Almer <jamrial@gmail.com>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>
2015-12-21 09:03:11 -08:00
..
aarch64 Merge commit '780cd20b00a69e26bbfffbb8eec16fbe999ea793' 2014-12-09 12:08:29 +01:00
arm avutil/attributes: add AV_GCC_VERSION_AT_MOST 2015-09-18 12:41:29 -03:00
avr32
bfin Merge commit '880e2aa23645ed9871c66ee1cbd00f93c72d2d73' 2014-06-02 19:38:01 +02:00
mips mips: intreadwrite: Only execute that code for mips r1 or r2 2015-09-29 11:10:37 +02:00
ppc avutil/ppc/cpu: add include avassert.h 2015-06-05 19:12:58 +02:00
sh4
tomi
x86 avutil/x86/bswap: Remove warning about bswap intrinsics with msvc. 2015-11-23 23:03:32 +11:00
adler32.c avutil/adler32: Fix data type in test code 2015-06-19 02:25:48 +02:00
adler32.h adler32: Fix doxy group definition 2014-04-07 01:31:02 +02:00
aes_ctr.c libavutil: add aes-ctr support 2015-12-15 14:16:28 +01:00
aes_ctr.h libavutil: add aes-ctr support 2015-12-15 14:16:28 +01:00
aes_internal.h lavu/aes: align AVAES struct members 2015-10-28 04:23:14 -05:00
aes.c lavu/aes: test CBC functionality 2015-10-28 09:38:21 -05:00
aes.h lavu: Drop deprecated context size variables 2015-08-28 16:04:27 +02:00
atomic_gcc.h lavu/atomic: add support for the new memory model aware gcc built-ins 2014-10-29 14:09:58 -03:00
atomic_suncc.h
atomic_win32.h msvc: Fix compilation errors due to header include order. 2014-11-27 12:40:18 +01:00
atomic.c avutil/atomic: reuse ret to avoid dereferencing twice the same value. 2014-12-27 22:14:23 +01:00
atomic.h Merge remote-tracking branch 'qatar/master' 2013-12-20 13:16:56 +01:00
attributes.h avutil/attributes: add av_warn_unused_result 2015-10-05 19:30:20 +02:00
audio_fifo.c avfilter: add showfreqs filter 2015-08-19 16:15:13 +00:00
audio_fifo.h avutil/audio_fifo: add av_warn_unused_result 2015-10-28 23:05:31 -04:00
avassert.h
avstring.c avutil/avstring: Inline some tiny functions 2015-10-03 13:45:37 +02:00
avstring.h avutil/avstring: add av_warn_unused_result 2015-10-27 23:16:09 -04:00
avutil.h doxygen: Remove lavu_internal group 2015-08-22 10:07:05 -07:00
avutilres.rc Add Windows resource file support for shared libraries 2013-12-05 23:42:07 +01:00
base64.c Merge commit 'fb0c9d41d685abb58575c5482ca33b8cd457c5ec' 2014-01-26 01:54:55 +01:00
base64.h
blowfish.c avutil: undo FF_API_CRYPTO_CONTEXT deprecation 2015-10-16 19:13:38 -03:00
blowfish.h avutil: undo FF_API_CRYPTO_CONTEXT deprecation 2015-10-16 19:13:38 -03:00
bprint.c avutil & avdevice: remove av_bprint_fd_contents() 2014-07-15 21:49:56 +02:00
bprint.h avutil/bprint: C++ compatible AVBPrint definition. 2014-11-29 03:51:35 +01:00
bswap.h Fix compile error on bfin. 2014-08-05 01:54:47 +02:00
buffer_internal.h Merge commit 'fbd6c97f9ca858140df16dd07200ea0d4bdc1a83' 2014-11-27 23:42:16 +01:00
buffer.c avutil/buffer: Avoid moving the AVBufferRef to a new place in memory in av_buffer_make_writable() 2015-03-12 02:15:28 +01:00
buffer.h Revert "lavu/buffer: add release function" 2014-03-06 03:23:40 +01:00
camellia.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
camellia.h avutil/camellia: fix documentation for av_camellia_crypt() 2015-01-02 21:23:45 +01:00
cast5.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
cast5.h avutil/cast5: update Doxygen for av_cast5_init with return information 2015-10-15 22:32:58 -04:00
channel_layout.c libavutil/channel_layout: Check strtol*() for failure 2015-11-05 19:28:19 +01:00
channel_layout.h Merge commit 'e23f84d9652474353d8bbc42787a56ec1991908f' 2015-08-24 10:40:24 +02:00
color_utils.c avutil/color_utils: Add basic transfer functions for each AVColorTransferCharacteristic 2015-09-10 23:53:05 +02:00
color_utils.h avutil/color_utils: Add basic transfer functions for each AVColorTransferCharacteristic 2015-09-10 23:53:05 +02:00
colorspace.h avutil/colorspace: Remove RGB_TO_Y/U/V 2015-06-06 18:21:01 +02:00
common.h avutil: Move av_rint64_clip_* to internal.h 2015-11-15 03:47:09 +01:00
cpu_internal.h Merge commit 'cae39851201b7781f1262e1c23627b45e6e80bb4' 2015-05-31 23:59:48 +02:00
cpu.c lavu: add AESNI CPU flag 2015-10-28 04:23:14 -05:00
cpu.h lavu: add AESNI CPU flag 2015-10-28 04:23:14 -05:00
crc.c avutil/crc: use EINVAL instead of -1 for the return code of av_crc_init() 2015-10-16 03:24:36 +02:00
crc.h avutil/crc: avoid needless space wastage of hardcoded crc table 2015-12-02 18:31:56 -05:00
des.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
des.h avutil: undo FF_API_CRYPTO_CONTEXT deprecation 2015-10-16 19:13:38 -03:00
dict.c Merge commit '11c5f438ff83da5040e85bfa6299f56b321d32ef' 2015-10-14 14:01:11 +02:00
dict.h Merge commit '11c5f438ff83da5040e85bfa6299f56b321d32ef' 2015-10-14 14:01:11 +02:00
display.c Merge commit 'e4fe535d12f4f30df2dd672e30304af112a5a827' 2015-03-24 01:14:31 +01:00
display.h Merge commit 'e4fe535d12f4f30df2dd672e30304af112a5a827' 2015-03-24 01:14:31 +01:00
downmix_info.c Merge commit 'c98f3169bfb578c1a4e407b44524f0bfa3b4dc0c' 2014-02-16 02:05:29 +01:00
downmix_info.h fix spelling errors 2014-07-12 22:33:27 +02:00
dynarray.h fix spelling errors 2014-07-12 22:33:27 +02:00
error.c lavu/error: add missing error messages for errors supported on all platforms 2015-12-18 04:04:14 +01:00
error.h avutil/error: Introduce new error codes for 4XX and 5XX replies from remote servers 2014-10-19 22:32:14 +02:00
eval.c lavu/eval: remove pow and exp2 for postfixes 2015-12-16 07:56:54 -05:00
eval.h avutil/eval: minor typo 2015-11-01 19:35:01 -05:00
fifo.c avutil/fifo: add function av_fifo_generic_peek_at() 2015-10-14 20:23:58 +02:00
fifo.h avutil/fifo: add function av_fifo_generic_peek_at() 2015-10-14 20:23:58 +02:00
file_open.c avutil/file_open: avoid file handle inheritance on Windows 2015-11-02 17:40:49 +01:00
file.c Merge commit 'bf704132a51f5d838365158331d4e535e1df4c8e' 2015-02-14 21:27:44 +01:00
file.h avutil/file: add av_warn_unused_result to av_file_map 2015-10-16 17:18:39 -04:00
fixed_dsp.c avutil/fixed_dsp: remove ff_ prefix from static function 2015-06-20 03:39:09 -03:00
fixed_dsp.h libavutil: Add new fixed dsp functions. 2015-06-03 22:50:53 +02:00
float_dsp.c avutil: merge avpriv_float_dsp_init into avpriv_float_dsp_alloc 2015-10-21 00:24:58 +02:00
float_dsp.h avutil: merge avpriv_float_dsp_init into avpriv_float_dsp_alloc 2015-10-21 00:24:58 +02:00
frame.c lavu/frame: use AVPALETTE_SIZE instead of 1024 2015-12-08 17:50:40 +01:00
frame.h Merge commit '1aa24df74c052a73175c43e57d35b4835e537ec8' 2015-10-03 09:52:39 +02:00
hash.c lavu/hash.c: Add missing "static const". 2014-08-31 10:33:02 +02:00
hash.h lavu/hash: add hash_final helpers. 2014-04-29 13:24:11 +02:00
hmac.c lavu/hmac: remove deprecated type ids 2015-09-05 18:07:20 +02:00
hmac.h lavu/hmac: remove deprecated type ids 2015-09-05 18:07:20 +02:00
imgutils.c imgutils: Use designated initializers for AVClass 2015-11-23 18:30:25 -08:00
imgutils.h Replace a few leftover instances of enum PixelFormat with enum AVPixelFormat 2015-03-17 23:53:33 +02:00
integer.c avutil/integer: Fix av_mod_i() with negative dividend 2015-12-01 13:26:12 +01:00
integer.h
internal.h cosmetics: Fix weird indentations 2015-12-07 10:43:43 -08:00
intfloat.h Reinstate proper FFmpeg license for all files. 2013-08-30 15:47:38 +00:00
intmath.c intmath: remove av_ctz. 2015-10-11 18:03:10 -04:00
intmath.h lavu/intmath: add faster clz support 2015-12-19 09:35:34 -08:00
intreadwrite.h libavutil: document side effects of macros 2014-07-19 14:55:46 +02:00
lfg.c
lfg.h
libavutil.v lavu: stop exporting internal functions 2014-08-12 04:35:52 +02:00
libm.h lavu/libm: add erf hack and make dynaudnorm available everywhere 2015-12-21 09:03:11 -08:00
lls.c avutil/lls: speed up performance of solve_lls 2015-11-26 09:20:46 -05:00
lls.h lavu: Drop deprecated private lls functions 2015-08-28 16:04:27 +02:00
log2_tab.c
log.c avutil/log: fix zero length gnu_printf format string warning 2015-09-17 18:58:01 +02:00
log.h avutil/log: modify AV_LOG_MAX_OFFSET for AV_LOG_TRACE 2015-06-26 14:02:35 +02:00
lzo.c avutil/lzo: fix resource leak 2014-10-11 12:15:26 +02:00
lzo.h
macros.h Merge remote-tracking branch 'qatar/master' 2013-12-30 11:23:32 +01:00
Makefile libavutil: add aes-ctr support 2015-12-15 14:16:28 +01:00
mathematics.c avutil/mathematics: Fix division by 0 2015-12-09 17:39:38 +01:00
mathematics.h avutil/mathematics: correct documentation for av_gcd 2015-10-30 13:42:04 -04:00
md5.c lavu: Drop deprecated context size variables 2015-08-28 16:04:27 +02:00
md5.h lavu: Drop deprecated context size variables 2015-08-28 16:04:27 +02:00
mem_internal.h avutil/mem_internal: add missing header includes 2015-07-13 21:54:15 -03:00
mem.c avutil/mem: Add av_fast_mallocz() 2015-11-18 22:05:16 +01:00
mem.h avutil/mem: Add av_fast_mallocz() 2015-11-18 22:05:16 +01:00
motion_vector.h avutil/motion_vector: export subpel motion information 2015-11-23 10:55:15 +01:00
murmur3.c avutil/murmur3: Add () to protect the ROT() arguments 2015-02-17 00:18:15 +01:00
murmur3.h
opencl_internal.c lavu: rename ff_opencl_set_parameter() to avpriv_opencl_set_parameter() 2014-08-12 03:49:45 +02:00
opencl_internal.h avutil/opencl_internal: add av_warn_unused_result 2015-10-31 10:40:54 -04:00
opencl.c lavu/opencl: restore #if HAVE_THREADS 2015-12-07 20:28:30 +01:00
opencl.h opencl: Force the use of 1.2 APIs 2015-10-17 01:16:50 -07:00
opt.c lavu/opt: enhance printing durations. 2015-11-07 16:04:09 +01:00
opt.h lavu/opt: add flag to return NULL when applicable in av_opt_get 2015-10-09 04:12:57 -05:00
parseutils.c Merge commit '219b39a71a5694b1c14a07b86477f665a5b6849b' 2015-07-21 16:55:39 +02:00
parseutils.h Merge commit '27f274628234c1f934b9a6a6380ed567c1b4ceae' 2015-04-07 20:46:25 +02:00
pca.c avutil/pca: Check for av_malloc* failures 2015-03-30 04:37:42 +02:00
pca.h avutil/pca: Make argument of ff_pca_add() const 2014-09-28 16:17:18 +02:00
pixdesc.c pixfmt: Add new SMPTE color primaries and transfer characteristic values 2015-09-17 10:31:43 +02:00
pixdesc.h Merge commit '7b02cb29d9d60cdd5ef321043d11d02023e7dc8f' 2015-09-12 13:03:04 +02:00
pixelutils.c avutil: check pixdescs in a different place 2015-02-10 15:45:02 +01:00
pixelutils.h avutil: add pixelutils API 2014-08-05 21:05:52 +02:00
pixfmt.h pixfmt: Add new SMPTE color primaries and transfer characteristic values 2015-09-17 10:31:43 +02:00
qsort.h avutil/qsort: use the do while form for AV_QSORT, AV_MSORT 2015-10-23 08:41:16 -04:00
random_seed.c lavu/random_seed: use arc4random() when available 2015-12-17 08:12:41 -08:00
random_seed.h
rational.c avutil/rational: Test av_rescale_rnd() with combinations of "special" values 2015-12-02 21:38:11 +01:00
rational.h avutil: Add av_q2intfloat() 2015-05-26 18:31:53 +02:00
rc4.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
rc4.h avutil: undo FF_API_CRYPTO_CONTEXT deprecation 2015-10-16 19:13:38 -03:00
replaygain.h Merge commit '8542f9c4f17125d483c40c0c5723842f1c982f81' 2014-04-04 22:52:12 +02:00
reverse.c avutil: add ff_reverse as av_reverse replacement 2015-08-12 00:14:14 +02:00
ripemd.c avutil/ripemd: make rol macro more robust by adding parentheses 2015-10-28 21:42:15 -04:00
ripemd.h
samplefmt.c avutil: remove obsolete FF_API_SAMPLES_UTILS_RETURN_ZERO cruft 2014-10-05 17:09:56 -03:00
samplefmt.h avutil: remove obsolete FF_API_GET_BITS_PER_SAMPLE_FMT cruft 2014-10-05 17:09:49 -03:00
sha512.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
sha512.h
sha.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
sha.h lavu: Drop deprecated context size variables 2015-08-28 16:04:27 +02:00
softfloat_tables.h avutil/softfloat_tables: add missing stdint.h include 2015-04-30 17:38:41 -03:00
softfloat.c avutil/softfloat: Include negative numbers in cmp/gt tests 2015-11-08 15:04:05 +01:00
softfloat.h avutil/softfloat: Assert that the exponent did not overflow the legal range in av_normalize1_sf() 2015-12-11 13:39:21 +01:00
stereo3d.c Merge commit '159a06dfc83d189f753c4583583ddfb571552ff5' 2014-08-14 00:17:47 +02:00
stereo3d.h Merge commit '440842c4eb1d7709654ec97cd687663d11ef499c' 2014-06-19 23:47:10 +02:00
tablegen.h libavutil/tablegen: add missing math.h include 2015-12-04 14:49:35 +01:00
tea.c Add support for TEA (Tiny Encryption Algorithm) 2015-07-21 23:10:44 +02:00
tea.h Add support for TEA (Tiny Encryption Algorithm) 2015-07-21 23:10:44 +02:00
thread.h Merge commit 'c53e796f8b69799b7ad6d28fbab981d37edf1bc9' 2015-10-14 23:02:35 +02:00
threadmessage.c lavc, lavu: use avutil/thread.h instead of redundant conditional includes 2015-12-07 17:25:51 +01:00
threadmessage.h avutil/threadmessage: add av_thread_message_flush() 2015-12-07 11:39:28 +01:00
time_internal.h avutil/time_internal: do not attempt to override *time_r() macros 2014-11-05 18:44:15 +01:00
time.c Merge commit '1bd0bdcdc236099d5c0d179696951f35f5310fa5' 2014-10-24 11:06:56 +02:00
time.h Merge commit '1bd0bdcdc236099d5c0d179696951f35f5310fa5' 2014-10-24 11:06:56 +02:00
timecode.c avutil/timecode: Fix fps check 2015-12-03 04:09:48 +01:00
timecode.h
timer.h avutil/timer: give each printed value of STOP_TIMER a fixed length 2015-03-27 04:44:58 +01:00
timestamp.h avutil/timestamp: Warn about missing __STDC_FORMAT_MACROS for C++ use 2014-03-13 17:32:15 +01:00
tree.c avutil/tree: clean up pointer incompatibility warnings 2015-10-25 12:45:10 -04:00
tree.h avutil/tree: Document the guaranteed ordering of compare arguments for av_tree_find() 2015-10-25 17:28:47 +01:00
twofish.c avutil: use EINVAL instead of -1 for the return code of crypto related init functions 2015-10-18 15:17:58 -04:00
twofish.h libavutil: Added twofish symmetric block cipher 2015-01-29 01:56:11 +01:00
utf8.c avutil/utf8: put under #ifdef TEST 2013-11-22 17:16:11 +01:00
utils.c lavu: disable wrong value check in get_version() upon api bump. 2015-08-18 15:57:20 -04:00
version.h libavutil: add aes-ctr support 2015-12-15 14:16:28 +01:00
wchar_filename.h avutil/wchar_filename: add av_warn_unused_result 2015-10-30 13:47:28 -04:00
x86_cpu.h
xga_font_data.c
xga_font_data.h
xtea.c Merge commit '588b6215b4c74945994eb9636b0699028c069ed2' 2015-11-22 14:29:09 +00:00
xtea.h Merge commit '588b6215b4c74945994eb9636b0699028c069ed2' 2015-11-22 14:29:09 +00:00