• Ganesh Ajjanagadde's avatar
    lavu/libm: add erf hack and make dynaudnorm available everywhere · dd68cde2
    Ganesh Ajjanagadde authored
    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: 's avatarJames Almer <jamrial@gmail.com>
    Signed-off-by: 's avatarGanesh Ajjanagadde <gajjanagadde@gmail.com>
    dd68cde2
configure 204 KB