lavu/libm: add exp10 support

exp10 is a function available in GNU libm. Looks like no other common
libm has it. This adds support for it to FFmpeg.

There are essentially 2 ways of handling the fallback:
1. Using pow(10, x)
2. Using exp2(M_LOG2_10 * x).

First one represents a Pareto improvement, with no speed or accuracy
regression anywhere, but speed improvement limited to GNU libm.

Second one represents a slight accuracy loss (relative error ~ 1e-13)
for non GNU libm. Speedup of > 2x is obtained on non GNU libm platforms,
~30% on GNU libm. These are "average case numbers", another benefit is
the lack of triggering of the well-known terrible worst case paths
through pow.

Based on reviews, second one chosen. Comment added accordingly.

Reviewed-by: Hendrik Leppkes <h.leppkes@gmail.com>
Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Reviewed-by: Ronald S. Bultje <rsbultje@gmail.com>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>

1 files changed, 19 insertions, 0 deletions

diff --git a/libavutil/libm.h b/libavutil/libm.h
index 146768aac6..6f9ac1b349 100644
--- a/libavutil/libm.h
+++ b/libavutil/libm.h
@@ -29,6 +29,7 @@
 #include "config.h"
 #include "attributes.h"
 #include "intfloat.h"
+#include "mathematics.h"
 
 #if HAVE_MIPSFPU && HAVE_INLINE_ASM
 #include "libavutil/mips/libm_mips.h"
@@ -292,6 +293,24 @@ static inline double erf(double z)
 #define exp2f(x) ((float)exp2(x))
 #endif /* HAVE_EXP2F */
 
+/* Somewhat inaccurate fallbacks, relative error ~ 1e-13 concentrated on very
+small and very large values. For perfection accuracy-wise, should use pow.
+Speed benefits (>2x average, with no super slow paths) deemed to be worth the
+accuracy tradeoff */
+#if !HAVE_EXP10
+static av_always_inline double exp10(double x)
+{
+    return exp2(M_LOG2_10 * x);
+}
+#endif /* HAVE_EXP10 */
+
+#if !HAVE_EXP10F
+static av_always_inline float exp10f(float x)
+{
+    return exp2f(M_LOG2_10 * x);
+}
+#endif /* HAVE_EXP10F */
+
 #if !HAVE_ISINF
 #undef isinf
 /* Note: these do not follow the BSD/Apple/GNU convention of returning -1 for