avcodec/jpeg2000: replace naive pow call with smarter exp2fi

pow is a very wasteful function for this purpose. A low hanging fruit
would be simply to replace with exp2f, and that does yield some speedup.
However, there are 2 drawbacks of this:
1. It does not exploit the integer nature of the argument.
2. (minor) Some platforms lack a proper exp2f routine, making benefits available
only to non broken libm.
3. exp2f does not solve the same issue that plagues pow, namely terrible
worst case performance. This is a fundamental issue known as the
"table-maker's dilemma" recognized by Prof. Kahan himself and
subsequently elaborated and researched by many others. All this is clear from benchmarks below.

This exploits the IEEE-754 format to get very good performance even in
the worst case for integer powers of 2. This solves all the issues noted
above. Function tested with clang usan over [-1000, 1000] (beyond range of
relevance for this, which is [-255, 255]), patch itself with FATE.

Benchmarks obtained on x86-64, Haswell, GNU-Linux via 10^5 iterations of
the pow call, START/STOP, and command ffplay ~/samples/jpeg2000/chiens_dcinema2K.mxf.
Low number of runs also given to prove the point about worst case:

pow:
 216270 decicycles in pow,       1 runs,      0 skips
 110175 decicycles in pow,       2 runs,      0 skips
  56085 decicycles in pow,       4 runs,      0 skips
  29013 decicycles in pow,       8 runs,      0 skips
  15472 decicycles in pow,      16 runs,      0 skips
   8689 decicycles in pow,      32 runs,      0 skips
   5295 decicycles in pow,      64 runs,      0 skips
   3599 decicycles in pow,     128 runs,      0 skips
   2748 decicycles in pow,     256 runs,      0 skips
   2304 decicycles in pow,     511 runs,      1 skips
   2072 decicycles in pow,    1022 runs,      2 skips
   1963 decicycles in pow,    2044 runs,      4 skips
   1894 decicycles in pow,    4091 runs,      5 skips
   1860 decicycles in pow,    8184 runs,      8 skips

exp2f:
 134140 decicycles in pow,       1 runs,      0 skips
  68110 decicycles in pow,       2 runs,      0 skips
  34530 decicycles in pow,       4 runs,      0 skips
  17677 decicycles in pow,       8 runs,      0 skips
   9175 decicycles in pow,      16 runs,      0 skips
   4931 decicycles in pow,      32 runs,      0 skips
   2808 decicycles in pow,      64 runs,      0 skips
   1747 decicycles in pow,     128 runs,      0 skips
   1208 decicycles in pow,     256 runs,      0 skips
    952 decicycles in pow,     512 runs,      0 skips
    822 decicycles in pow,    1024 runs,      0 skips
    765 decicycles in pow,    2047 runs,      1 skips
    722 decicycles in pow,    4094 runs,      2 skips
    693 decicycles in pow,    8190 runs,      2 skips

exp2fi:
   2740 decicycles in pow,       1 runs,      0 skips
   1530 decicycles in pow,       2 runs,      0 skips
    955 decicycles in pow,       4 runs,      0 skips
    622 decicycles in pow,       8 runs,      0 skips
    477 decicycles in pow,      16 runs,      0 skips
    368 decicycles in pow,      32 runs,      0 skips
    317 decicycles in pow,      64 runs,      0 skips
    291 decicycles in pow,     128 runs,      0 skips
    277 decicycles in pow,     256 runs,      0 skips
    268 decicycles in pow,     512 runs,      0 skips
    265 decicycles in pow,    1024 runs,      0 skips
    263 decicycles in pow,    2048 runs,      0 skips
    263 decicycles in pow,    4095 runs,      1 skips
    260 decicycles in pow,    8191 runs,      1 skips

Reviewed-by: Michael Niedermayer <michael@niedermayer.cc>
Signed-off-by: Ganesh Ajjanagadde <gajjanagadde@gmail.com>

1 files changed, 16 insertions, 1 deletions

diff --git a/libavcodec/jpeg2000.c b/libavcodec/jpeg2000.c
index c98840971f..afd0966103 100644
--- a/libavcodec/jpeg2000.c
+++ b/libavcodec/jpeg2000.c
@@ -192,6 +192,21 @@ void ff_jpeg2000_set_significance(Jpeg2000T1Context *t1, int x, int y,
 
 // static const uint8_t lut_gain[2][4] = { { 0, 0, 0, 0 }, { 0, 1, 1, 2 } }; (unused)
 
+static inline float exp2fi(int x) {
+    /* Normal range */
+    if (-126 <= x && x <= 128)
+        return av_int2float(x+127 << 23);
+    /* Too large */
+    else if (x > 128)
+        return INFINITY;
+    /* Subnormal numbers */
+    else if (x > -150)
+        return av_int2float(1 << (x+149));
+    /* Negligibly small */
+    else
+        return 0;
+}
+
 static void init_band_stepsize(AVCodecContext *avctx,
                                Jpeg2000Band *band,
                                Jpeg2000CodingStyle *codsty,
@@ -221,7 +236,7 @@ static void init_band_stepsize(AVCodecContext *avctx,
          * R_b = R_I + log2 (gain_b )
          * see ISO/IEC 15444-1:2002 E.1.1 eqn. E-3 and E-4 */
         gain            = cbps;
-        band->f_stepsize  = pow(2.0, gain - qntsty->expn[gbandno]);
+        band->f_stepsize  = exp2fi(gain - qntsty->expn[gbandno]);
         band->f_stepsize *= qntsty->mant[gbandno] / 2048.0 + 1.0;
         break;
     default: