Change to damping in vbr_rate_correction()

Code changed in line with VP9.

Some gain in psnr and slightly larger in ssim (overall psnr, ssim):

Low Res: -0.144, -0.385
UGC 360: -0.300, -0.486
Mid Res: -0.014, -0.182
HD Res Pending.

STATS_CHANGED

Change-Id: I41b303a390491ae2dd0806aeb9404e6bf88c94ec

av1/encoder/ratectrl.c

diff --git a/av1/encoder/ratectrl.c b/av1/encoder/ratectrl.c
index cd56c1f..e0e82e4 100644
--- a/av1/encoder/ratectrl.c
+++ b/av1/encoder/ratectrl.c
@@ -1705,17 +1705,16 @@
   RATE_CONTROL *const rc = &cpi->rc;
   int64_t vbr_bits_off_target = rc->vbr_bits_off_target;
   int max_delta;
-  double position_factor = 1.0;
+  const int frame_window =
+      AOMMIN(16, (int)cpi->twopass.total_stats.count -
+                     cpi->common.current_frame.frame_number);
 
-  // How far through the clip are we.
-  // This number is used to damp the per frame rate correction.
-  // Range 0 - 1.0
-  if (cpi->twopass.total_stats.count != 0.) {
-    position_factor = sqrt((double)cpi->common.current_frame.frame_number /
-                           cpi->twopass.total_stats.count);
-  }
-  max_delta = (int)(position_factor *
-                    ((*this_frame_target * VBR_PCT_ADJUSTMENT_LIMIT) / 100));
+  max_delta = (vbr_bits_off_target > 0)
+                  ? (int)(vbr_bits_off_target / frame_window)
+                  : (int)(-vbr_bits_off_target / frame_window);
+
+  max_delta = AOMMIN(max_delta,
+                     ((*this_frame_target * VBR_PCT_ADJUSTMENT_LIMIT) / 100));
 
   // vbr_bits_off_target > 0 means we have extra bits to spend
   if (vbr_bits_off_target > 0) {