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Further adjustment of RD behaviour with Q and Zbin.

Following conversations with Tim T (Derf) I ran a large number of
tests comparing the existing polynomial expression with a simpler
^2 variant. Though the polynomial was sometimes a little better at
the extremes of Q it was possible to get close for most clips and
even a little better on some.

This code also changes the way the RD multiplier is calculated
when the ZBIN is extended to use a variant of the same ^2
expression.

I hope that this simpler expression will be easier to tune further
as we expand our test set and consider adjustments based on content.

Change-Id: I73b2564346e74d1332c33e2c1964ae093437456c

--- a/vp8/encoder/rdopt.c

+++ b/vp8/encoder/rdopt.c

@@ -231,19 +231,30 @@

     int i;

     int *thresh;

     int threshmult;

+    double capped_q = (Qvalue < 160) ? (double)Qvalue : 160.0;

+    double rdconst = 3.00;

-    int capped_q = (Qvalue < 160) ? Qvalue : 160;

-

     vp8_clear_system_state();  //__asm emms;

-    cpi->RDMULT = (int)( (0.0001 * (capped_q * capped_q * capped_q * capped_q))

-                        -(0.015 * (capped_q * capped_q * capped_q))

-                        +(3.25 * (capped_q * capped_q))

-                        -(17.5 * capped_q) + 125.0);

+    // Further tests required to see if optimum is different

+    // for key frames, golden frames and arf frames.

+    // if (cpi->common.refresh_golden_frame ||

+    //     cpi->common.refresh_alt_ref_frame)

+    cpi->RDMULT = (int)(rdconst * (capped_q * capped_q));

-    if (cpi->RDMULT < 125)

-        cpi->RDMULT = 125;

+    // Extend rate multiplier along side quantizer zbin increases

+    if (cpi->zbin_over_quant  > 0)

+    {

+        double oq_factor;

+        double modq;

+        // Experimental code using the same basic equation as used for Q above

+        // The units of cpi->zbin_over_quant are 1/128 of Q bin size

+        oq_factor = 1.0 + ((double)0.0015625 * cpi->zbin_over_quant);

+        modq = (int)((double)capped_q * oq_factor);

+        cpi->RDMULT = (int)(rdconst * (modq * modq));

+    }

+

     if (cpi->pass == 2 && (cpi->common.frame_type != KEY_FRAME))

     {

         if (cpi->next_iiratio > 31)

@@ -252,17 +263,8 @@

             cpi->RDMULT += (cpi->RDMULT * rd_iifactor[cpi->next_iiratio]) >> 4;

     }

-

-    // Extend rate multiplier along side quantizer zbin increases

-    if (cpi->zbin_over_quant  > 0)

-    {

-        double oq_factor = pow(1.006,  cpi->zbin_over_quant);

-

-        if (oq_factor > (1.0 + ((double)cpi->zbin_over_quant / 64.0)))

-            oq_factor = (1.0 + (double)cpi->zbin_over_quant / 64.0);

-

-        cpi->RDMULT = (int)(oq_factor * cpi->RDMULT);

-    }

+    if (cpi->RDMULT < 125)

+        cpi->RDMULT = 125;

     cpi->mb.errorperbit = (cpi->RDMULT / 100);