Import aom library

This is the reference implementation for the Alliance for Open Media's av1 video code.

The commit used was 4d668d7feb1f8abd809d1bca0418570a7f142a36.

1 files changed, 988 insertions, 0 deletions

diff --git a/third_party/aom/av1/encoder/pvq_encoder.c b/third_party/aom/av1/encoder/pvq_encoder.c
new file mode 100644
index 000000000..ab63f1b7d
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@@ -0,0 +1,988 @@
+/*
+ * Copyright (c) 2001-2016, Alliance for Open Media. All rights reserved
+ *
+ * This source code is subject to the terms of the BSD 2 Clause License and
+ * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
+ * was not distributed with this source code in the LICENSE file, you can
+ * obtain it at www.aomedia.org/license/software. If the Alliance for Open
+ * Media Patent License 1.0 was not distributed with this source code in the
+ * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
+ */
+
+/* clang-format off */
+
+#ifdef HAVE_CONFIG_H
+# include "config.h"
+#endif
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include "aom_dsp/entcode.h"
+#include "aom_dsp/entenc.h"
+#include "av1/common/blockd.h"
+#include "av1/common/odintrin.h"
+#include "av1/common/partition.h"
+#include "av1/common/pvq_state.h"
+#include "av1/encoder/encodemb.h"
+#include "av1/encoder/pvq_encoder.h"
+#include "aom_ports/system_state.h"
+
+/*Shift to ensure that the upper bound (i.e. for the max blocksize) of the
+   dot-product of the 1st band of chroma with the luma ref doesn't overflow.*/
+#define OD_CFL_FLIP_SHIFT (OD_LIMIT_BSIZE_MAX + 0)
+
+void aom_write_symbol_pvq(aom_writer *w, int symb, aom_cdf_prob *cdf,
+    int nsymbs) {
+  if (cdf[0] == 0)
+    aom_cdf_init_q15_1D(cdf, nsymbs, CDF_SIZE(nsymbs));
+  aom_write_symbol(w, symb, cdf, nsymbs);
+}
+
+static void aom_encode_pvq_codeword(aom_writer *w, od_pvq_codeword_ctx *adapt,
+ const od_coeff *in, int n, int k) {
+  int i;
+  aom_encode_band_pvq_splits(w, adapt, in, n, k, 0);
+  for (i = 0; i < n; i++) if (in[i]) aom_write_bit(w, in[i] < 0);
+}
+
+/* Computes 1/sqrt(i) using a table for small values. */
+static double od_rsqrt_table(int i) {
+  static double table[16] = {
+    1.000000, 0.707107, 0.577350, 0.500000,
+    0.447214, 0.408248, 0.377964, 0.353553,
+    0.333333, 0.316228, 0.301511, 0.288675,
+    0.277350, 0.267261, 0.258199, 0.250000};
+  if (i <= 16) return table[i-1];
+  else return 1./sqrt(i);
+}
+
+/*Computes 1/sqrt(start+2*i+1) using a lookup table containing the results
+   where 0 <= i < table_size.*/
+static double od_custom_rsqrt_dynamic_table(const double* table,
+ const int table_size, const double start, const int i) {
+  if (i < table_size) return table[i];
+  else return od_rsqrt_table((int)(start + 2*i + 1));
+}
+
+/*Fills tables used in od_custom_rsqrt_dynamic_table for a given start.*/
+static void od_fill_dynamic_rsqrt_table(double *table, const int table_size,
+ const double start) {
+  int i;
+  for (i = 0; i < table_size; i++)
+    table[i] = od_rsqrt_table((int)(start + 2*i + 1));
+}
+
+/** Find the codepoint on the given PSphere closest to the desired
+ * vector. Double-precision PVQ search just to make sure our tests
+ * aren't limited by numerical accuracy.
+ *
+ * @param [in]      xcoeff  input vector to quantize (x in the math doc)
+ * @param [in]      n       number of dimensions
+ * @param [in]      k       number of pulses
+ * @param [out]     ypulse  optimal codevector found (y in the math doc)
+ * @param [out]     g2      multiplier for the distortion (typically squared
+ *                          gain units)
+ * @param [in] pvq_norm_lambda enc->pvq_norm_lambda for quantized RDO
+ * @param [in]      prev_k  number of pulses already in ypulse that we should
+ *                          reuse for the search (or 0 for a new search)
+ * @return                  cosine distance between x and y (between 0 and 1)
+ */
+double pvq_search_rdo_double_c(const od_val16 *xcoeff, int n, int k,
+ od_coeff *ypulse, double g2, double pvq_norm_lambda, int prev_k) {
+  int i, j;
+  double xy;
+  double yy;
+  /* TODO - This blows our 8kB stack space budget and should be fixed when
+   converting PVQ to fixed point. */
+  double x[MAXN];
+  double xx;
+  double lambda;
+  double norm_1;
+  int rdo_pulses;
+  double delta_rate;
+  xx = xy = yy = 0;
+  for (j = 0; j < n; j++) {
+    x[j] = fabs((float)xcoeff[j]);
+    xx += x[j]*x[j];
+  }
+  norm_1 = 1./sqrt(1e-30 + xx);
+  lambda = pvq_norm_lambda/(1e-30 + g2);
+  i = 0;
+  if (prev_k > 0 && prev_k <= k) {
+    /* We reuse pulses from a previous search so we don't have to search them
+       again. */
+    for (j = 0; j < n; j++) {
+      ypulse[j] = abs(ypulse[j]);
+      xy += x[j]*ypulse[j];
+      yy += ypulse[j]*ypulse[j];
+      i += ypulse[j];
+    }
+  }
+  else if (k > 2) {
+    double l1_norm;
+    double l1_inv;
+    l1_norm = 0;
+    for (j = 0; j < n; j++) l1_norm += x[j];
+    l1_inv = 1./OD_MAXF(l1_norm, 1e-100);
+    for (j = 0; j < n; j++) {
+      double tmp;
+      tmp = k*x[j]*l1_inv;
+      ypulse[j] = OD_MAXI(0, (int)floor(tmp));
+      xy += x[j]*ypulse[j];
+      yy += ypulse[j]*ypulse[j];
+      i += ypulse[j];
+    }
+  }
+  else OD_CLEAR(ypulse, n);
+
+  /* Only use RDO on the last few pulses. This not only saves CPU, but using
+     RDO on all pulses actually makes the results worse for reasons I don't
+     fully understand. */
+  rdo_pulses = 1 + k/4;
+  /* Rough assumption for now, the last position costs about 3 bits more than
+     the first. */
+  delta_rate = 3./n;
+  /* Search one pulse at a time */
+  for (; i < k - rdo_pulses; i++) {
+    int pos;
+    double best_xy;
+    double best_yy;
+    pos = 0;
+    best_xy = -10;
+    best_yy = 1;
+    for (j = 0; j < n; j++) {
+      double tmp_xy;
+      double tmp_yy;
+      tmp_xy = xy + x[j];
+      tmp_yy = yy + 2*ypulse[j] + 1;
+      tmp_xy *= tmp_xy;
+      if (j == 0 || tmp_xy*best_yy > best_xy*tmp_yy) {
+        best_xy = tmp_xy;
+        best_yy = tmp_yy;
+        pos = j;
+      }
+    }
+    xy = xy + x[pos];
+    yy = yy + 2*ypulse[pos] + 1;
+    ypulse[pos]++;
+  }
+  /* Search last pulses with RDO. Distortion is D = (x-y)^2 = x^2 - 2*x*y + y^2
+     and since x^2 and y^2 are constant, we just maximize x*y, plus a
+     lambda*rate term. Note that since x and y aren't normalized here,
+     we need to divide by sqrt(x^2)*sqrt(y^2). */
+  for (; i < k; i++) {
+    double rsqrt_table[4];
+    int rsqrt_table_size = 4;
+    int pos;
+    double best_cost;
+    pos = 0;
+    best_cost = -1e5;
+    /*Fill the small rsqrt lookup table with inputs relative to yy.
+      Specifically, the table of n values is filled with
+       rsqrt(yy + 1), rsqrt(yy + 2 + 1) .. rsqrt(yy + 2*(n-1) + 1).*/
+    od_fill_dynamic_rsqrt_table(rsqrt_table, rsqrt_table_size, yy);
+    for (j = 0; j < n; j++) {
+      double tmp_xy;
+      double tmp_yy;
+      tmp_xy = xy + x[j];
+      /*Calculate rsqrt(yy + 2*ypulse[j] + 1) using an optimized method.*/
+      tmp_yy = od_custom_rsqrt_dynamic_table(rsqrt_table, rsqrt_table_size,
+       yy, ypulse[j]);
+      tmp_xy = 2*tmp_xy*norm_1*tmp_yy - lambda*j*delta_rate;
+      if (j == 0 || tmp_xy > best_cost) {
+        best_cost = tmp_xy;
+        pos = j;
+      }
+    }
+    xy = xy + x[pos];
+    yy = yy + 2*ypulse[pos] + 1;
+    ypulse[pos]++;
+  }
+  for (i = 0; i < n; i++) {
+    if (xcoeff[i] < 0) ypulse[i] = -ypulse[i];
+  }
+  return xy/(1e-100 + sqrt(xx*yy));
+}
+
+/** Encodes the gain so that the return value increases with the
+ * distance |x-ref|, so that we can encode a zero when x=ref. The
+ * value x=0 is not covered because it is only allowed in the noref
+ * case.
+ *
+ * @param [in]      x      quantized gain to encode
+ * @param [in]      ref    quantized gain of the reference
+ * @return                 interleave-encoded quantized gain value
+ */
+static int neg_interleave(int x, int ref) {
+  if (x < ref) return -2*(x - ref) - 1;
+  else if (x < 2*ref) return 2*(x - ref);
+  else return x-1;
+}
+
+int od_vector_is_null(const od_coeff *x, int len) {
+  int i;
+  for (i = 0; i < len; i++) if (x[i]) return 0;
+  return 1;
+}
+
+static double od_pvq_rate(int qg, int icgr, int theta, int ts,
+  const od_adapt_ctx *adapt, const od_coeff *y0, int k, int n, int speed) {
+  double rate;
+  if (k == 0) rate = 0;
+  else if (speed > 0) {
+    int i;
+    int sum;
+    double f;
+    /* Compute "center of mass" of the pulse vector. */
+    sum = 0;
+    for (i = 0; i < n - (theta != -1); i++) sum += i*abs(y0[i]);
+    f = sum/(double)(k*n);
+    /* Estimates the number of bits it will cost to encode K pulses in
+       N dimensions based on hand-tuned fit for bitrate vs K, N and
+       "center of mass". */
+    rate = (1 + .4*f)*n*OD_LOG2(1 + OD_MAXF(0, log(n*2*(1*f + .025))*k/n)) + 3;
+  }
+  else {
+    aom_writer w;
+    od_pvq_codeword_ctx cd;
+    int tell;
+#if CONFIG_DAALA_EC
+    od_ec_enc_init(&w.ec, 1000);
+#else
+# error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+    OD_COPY(&cd, &adapt->pvq.pvq_codeword_ctx, 1);
+#if CONFIG_DAALA_EC
+    tell = od_ec_enc_tell_frac(&w.ec);
+#else
+# error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+    aom_encode_pvq_codeword(&w, &cd, y0, n - (theta != -1), k);
+#if CONFIG_DAALA_EC
+    rate = (od_ec_enc_tell_frac(&w.ec)-tell)/8.;
+    od_ec_enc_clear(&w.ec);
+#else
+# error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+  }
+  if (qg > 0 && theta >= 0) {
+    /* Approximate cost of entropy-coding theta */
+    rate += .9*OD_LOG2(ts);
+    if (qg == icgr) rate -= .5;
+  }
+  return rate;
+}
+
+#define MAX_PVQ_ITEMS (20)
+/* This stores the information about a PVQ search candidate, so we can sort
+   based on K. */
+typedef struct {
+  int gain;
+  int k;
+  od_val32 qtheta;
+  int theta;
+  int ts;
+  od_val32 qcg;
+} pvq_search_item;
+
+int items_compare(pvq_search_item *a, pvq_search_item *b) {
+  /* Break ties in K with gain to ensure a stable sort.
+     Otherwise, the order depends on qsort implementation. */
+  return a->k == b->k ? a->gain - b->gain : a->k - b->k;
+}
+
+/** Perform PVQ quantization with prediction, trying several
+ * possible gains and angles. See draft-valin-videocodec-pvq and
+ * http://jmvalin.ca/slides/pvq.pdf for more details.
+ *
+ * @param [out]    out         coefficients after quantization
+ * @param [in]     x0          coefficients before quantization
+ * @param [in]     r0          reference, aka predicted coefficients
+ * @param [in]     n           number of dimensions
+ * @param [in]     q0          quantization step size
+ * @param [out]    y           pulse vector (i.e. selected PVQ codevector)
+ * @param [out]    itheta      angle between input and reference (-1 if noref)
+ * @param [out]    vk          total number of pulses
+ * @param [in]     beta        per-band activity masking beta param
+ * @param [out]    skip_diff   distortion cost of skipping this block
+ *                             (accumulated)
+ * @param [in]     is_keyframe whether we're encoding a keyframe
+ * @param [in]     pli         plane index
+ * @param [in]     adapt       probability adaptation context
+ * @param [in]     qm          QM with magnitude compensation
+ * @param [in]     qm_inv      Inverse of QM with magnitude compensation
+ * @param [in] pvq_norm_lambda enc->pvq_norm_lambda for quantized RDO
+ * @param [in]     speed       Make search faster by making approximations
+ * @return         gain        index of the quatized gain
+*/
+static int pvq_theta(od_coeff *out, const od_coeff *x0, const od_coeff *r0,
+    int n, int q0, od_coeff *y, int *itheta, int *vk,
+    od_val16 beta, double *skip_diff, int is_keyframe, int pli,
+    const od_adapt_ctx *adapt, const int16_t *qm, const int16_t *qm_inv,
+    double pvq_norm_lambda, int speed) {
+  od_val32 g;
+  od_val32 gr;
+  od_coeff y_tmp[MAXN + 3];
+  int i;
+  /* Number of pulses. */
+  int k;
+  /* Companded gain of x and reference, normalized to q. */
+  od_val32 cg;
+  od_val32 cgr;
+  int icgr;
+  int qg;
+  /* Best RDO cost (D + lamdba*R) so far. */
+  double best_cost;
+  double dist0;
+  /* Distortion (D) that corresponds to the best RDO cost. */
+  double best_dist;
+  double dist;
+  /* Sign of Householder reflection. */
+  int s;
+  /* Dimension on which Householder reflects. */
+  int m;
+  od_val32 theta;
+  double corr;
+  int best_k;
+  od_val32 best_qtheta;
+  od_val32 gain_offset;
+  int noref;
+  double skip_dist;
+  int cfl_enabled;
+  int skip;
+  double gain_weight;
+  od_val16 x16[MAXN];
+  od_val16 r16[MAXN];
+  int xshift;
+  int rshift;
+  /* Give more weight to gain error when calculating the total distortion. */
+  gain_weight = 1.0;
+  OD_ASSERT(n > 1);
+  corr = 0;
+#if !defined(OD_FLOAT_PVQ)
+  /* Shift needed to make x fit in 16 bits even after rotation.
+     This shift value is not normative (it can be changed without breaking
+     the bitstream) */
+  xshift = OD_MAXI(0, od_vector_log_mag(x0, n) - 15);
+  /* Shift needed to make the reference fit in 15 bits, so that the Householder
+     vector can fit in 16 bits.
+     This shift value *is* normative, and has to match the decoder. */
+  rshift = OD_MAXI(0, od_vector_log_mag(r0, n) - 14);
+#else
+  xshift = 0;
+  rshift = 0;
+#endif
+  for (i = 0; i < n; i++) {
+#if defined(OD_FLOAT_PVQ)
+    /*This is slightly different from the original float PVQ code,
+       where the qm was applied in the accumulation in od_pvq_compute_gain and
+       the vectors were od_coeffs, not od_val16 (i.e. double).*/
+    x16[i] = x0[i]*(double)qm[i]*OD_QM_SCALE_1;
+    r16[i] = r0[i]*(double)qm[i]*OD_QM_SCALE_1;
+#else
+    x16[i] = OD_SHR_ROUND(x0[i]*qm[i], OD_QM_SHIFT + xshift);
+    r16[i] = OD_SHR_ROUND(r0[i]*qm[i], OD_QM_SHIFT + rshift);
+#endif
+    corr += OD_MULT16_16(x16[i], r16[i]);
+  }
+  cfl_enabled = is_keyframe && pli != 0 && !OD_DISABLE_CFL;
+  cg  = od_pvq_compute_gain(x16, n, q0, &g, beta, xshift);
+  cgr = od_pvq_compute_gain(r16, n, q0, &gr, beta, rshift);
+  if (cfl_enabled) cgr = OD_CGAIN_SCALE;
+  /* gain_offset is meant to make sure one of the quantized gains has
+     exactly the same gain as the reference. */
+#if defined(OD_FLOAT_PVQ)
+  icgr = (int)floor(.5 + cgr);
+#else
+  icgr = OD_SHR_ROUND(cgr, OD_CGAIN_SHIFT);
+#endif
+  gain_offset = cgr - OD_SHL(icgr, OD_CGAIN_SHIFT);
+  /* Start search with null case: gain=0, no pulse. */
+  qg = 0;
+  dist = gain_weight*cg*cg*OD_CGAIN_SCALE_2;
+  best_dist = dist;
+  best_cost = dist + pvq_norm_lambda*od_pvq_rate(0, 0, -1, 0, adapt, NULL, 0,
+    n, speed);
+  noref = 1;
+  best_k = 0;
+  *itheta = -1;
+  OD_CLEAR(y, n);
+  best_qtheta = 0;
+  m = 0;
+  s = 1;
+  corr = corr/(1e-100 + g*(double)gr/OD_SHL(1, xshift + rshift));
+  corr = OD_MAXF(OD_MINF(corr, 1.), -1.);
+  if (is_keyframe) skip_dist = gain_weight*cg*cg*OD_CGAIN_SCALE_2;
+  else {
+    skip_dist = gain_weight*(cg - cgr)*(cg - cgr)
+     + cgr*(double)cg*(2 - 2*corr);
+    skip_dist *= OD_CGAIN_SCALE_2;
+  }
+  if (!is_keyframe) {
+    /* noref, gain=0 isn't allowed, but skip is allowed. */
+    od_val32 scgr;
+    scgr = OD_MAXF(0,gain_offset);
+    if (icgr == 0) {
+      best_dist = gain_weight*(cg - scgr)*(cg - scgr)
+       + scgr*(double)cg*(2 - 2*corr);
+      best_dist *= OD_CGAIN_SCALE_2;
+    }
+    best_cost = best_dist + pvq_norm_lambda*od_pvq_rate(0, icgr, 0, 0, adapt,
+     NULL, 0, n, speed);
+    best_qtheta = 0;
+    *itheta = 0;
+    noref = 0;
+  }
+  dist0 = best_dist;
+  if (n <= OD_MAX_PVQ_SIZE && !od_vector_is_null(r0, n) && corr > 0) {
+    od_val16 xr[MAXN];
+    int gain_bound;
+    int prev_k;
+    pvq_search_item items[MAX_PVQ_ITEMS];
+    int idx;
+    int nitems;
+    double cos_dist;
+    idx = 0;
+    gain_bound = OD_SHR(cg - gain_offset, OD_CGAIN_SHIFT);
+    /* Perform theta search only if prediction is useful. */
+    theta = OD_ROUND32(OD_THETA_SCALE*acos(corr));
+    m = od_compute_householder(r16, n, gr, &s, rshift);
+    od_apply_householder(xr, x16, r16, n);
+    prev_k = 0;
+    for (i = m; i < n - 1; i++) xr[i] = xr[i + 1];
+    /* Compute all candidate PVQ searches within a reasonable range of gain
+       and theta. */
+    for (i = OD_MAXI(1, gain_bound - 1); i <= gain_bound + 1; i++) {
+      int j;
+      od_val32 qcg;
+      int ts;
+      int theta_lower;
+      int theta_upper;
+      /* Quantized companded gain */
+      qcg = OD_SHL(i, OD_CGAIN_SHIFT) + gain_offset;
+      /* Set angular resolution (in ra) to match the encoded gain */
+      ts = od_pvq_compute_max_theta(qcg, beta);
+      theta_lower = OD_MAXI(0, (int)floor(.5 +
+       theta*OD_THETA_SCALE_1*2/M_PI*ts) - 2);
+      theta_upper = OD_MINI(ts - 1, (int)ceil(theta*OD_THETA_SCALE_1*2/M_PI*ts));
+      /* Include the angles within a reasonable range. */
+      for (j = theta_lower; j <= theta_upper; j++) {
+        od_val32 qtheta;
+        qtheta = od_pvq_compute_theta(j, ts);
+        k = od_pvq_compute_k(qcg, j, 0, n, beta);
+        items[idx].gain = i;
+        items[idx].theta = j;
+        items[idx].k = k;
+        items[idx].qcg = qcg;
+        items[idx].qtheta = qtheta;
+        items[idx].ts = ts;
+        idx++;
+        OD_ASSERT(idx < MAX_PVQ_ITEMS);
+      }
+    }
+    nitems = idx;
+    cos_dist = 0;
+    /* Sort PVQ search candidates in ascending order of pulses K so that
+       we can reuse all the previously searched pulses across searches. */
+    qsort(items, nitems, sizeof(items[0]),
+     (int (*)(const void *, const void *))items_compare);
+    /* Search for the best gain/theta in order. */
+    for (idx = 0; idx < nitems; idx++) {
+      int j;
+      od_val32 qcg;
+      int ts;
+      double cost;
+      double dist_theta;
+      double sin_prod;
+      od_val32 qtheta;
+      /* Quantized companded gain */
+      qcg = items[idx].qcg;
+      i = items[idx].gain;
+      j = items[idx].theta;
+      /* Set angular resolution (in ra) to match the encoded gain */
+      ts = items[idx].ts;
+      /* Search for the best angle within a reasonable range. */
+      qtheta = items[idx].qtheta;
+      k = items[idx].k;
+      /* Compute the minimal possible distortion by not taking the PVQ
+         cos_dist into account. */
+      dist_theta = 2 - 2.*od_pvq_cos(theta - qtheta)*OD_TRIG_SCALE_1;
+      dist = gain_weight*(qcg - cg)*(qcg - cg) + qcg*(double)cg*dist_theta;
+      dist *= OD_CGAIN_SCALE_2;
+      /* If we have no hope of beating skip (including a 1-bit worst-case
+         penalty), stop now. */
+      if (dist > dist0 + 1.0*pvq_norm_lambda && k != 0) continue;
+      sin_prod = od_pvq_sin(theta)*OD_TRIG_SCALE_1*od_pvq_sin(qtheta)*
+       OD_TRIG_SCALE_1;
+      /* PVQ search, using a gain of qcg*cg*sin(theta)*sin(qtheta) since
+         that's the factor by which cos_dist is multiplied to get the
+         distortion metric. */
+      if (k == 0) {
+        cos_dist = 0;
+        OD_CLEAR(y_tmp, n-1);
+      }
+      else if (k != prev_k) {
+        cos_dist = pvq_search_rdo_double(xr, n - 1, k, y_tmp,
+         qcg*(double)cg*sin_prod*OD_CGAIN_SCALE_2, pvq_norm_lambda, prev_k);
+      }
+      prev_k = k;
+      /* See Jmspeex' Journal of Dubious Theoretical Results. */
+      dist_theta = 2 - 2.*od_pvq_cos(theta - qtheta)*OD_TRIG_SCALE_1
+       + sin_prod*(2 - 2*cos_dist);
+      dist = gain_weight*(qcg - cg)*(qcg - cg) + qcg*(double)cg*dist_theta;
+      dist *= OD_CGAIN_SCALE_2;
+      /* Do approximate RDO. */
+      cost = dist + pvq_norm_lambda*od_pvq_rate(i, icgr, j, ts, adapt, y_tmp,
+       k, n, speed);
+      if (cost < best_cost) {
+        best_cost = cost;
+        best_dist = dist;
+        qg = i;
+        best_k = k;
+        best_qtheta = qtheta;
+        *itheta = j;
+        noref = 0;
+        OD_COPY(y, y_tmp, n - 1);
+      }
+    }
+  }
+  /* Don't bother with no-reference version if there's a reasonable
+     correlation. */
+  if (n <= OD_MAX_PVQ_SIZE && (corr < .5
+        || cg < (od_val32)(OD_SHL(2, OD_CGAIN_SHIFT)))) {
+    int gain_bound;
+    int prev_k;
+    gain_bound = OD_SHR(cg, OD_CGAIN_SHIFT);
+    prev_k = 0;
+    /* Search for the best gain (haven't determined reasonable range yet). */
+    for (i = OD_MAXI(1, gain_bound); i <= gain_bound + 1; i++) {
+      double cos_dist;
+      double cost;
+      od_val32 qcg;
+      qcg = OD_SHL(i, OD_CGAIN_SHIFT);
+      k = od_pvq_compute_k(qcg, -1, 1, n, beta);
+      /* Compute the minimal possible distortion by not taking the PVQ
+         cos_dist into account. */
+      dist = gain_weight*(qcg - cg)*(qcg - cg);
+      dist *= OD_CGAIN_SCALE_2;
+      if (dist > dist0 && k != 0) continue;
+      cos_dist = pvq_search_rdo_double(x16, n, k, y_tmp,
+       qcg*(double)cg*OD_CGAIN_SCALE_2, pvq_norm_lambda, prev_k);
+      prev_k = k;
+      /* See Jmspeex' Journal of Dubious Theoretical Results. */
+      dist = gain_weight*(qcg - cg)*(qcg - cg)
+       + qcg*(double)cg*(2 - 2*cos_dist);
+      dist *= OD_CGAIN_SCALE_2;
+      /* Do approximate RDO. */
+      cost = dist + pvq_norm_lambda*od_pvq_rate(i, 0, -1, 0, adapt, y_tmp, k,
+       n, speed);
+      if (cost <= best_cost) {
+        best_cost = cost;
+        best_dist = dist;
+        qg = i;
+        noref = 1;
+        best_k = k;
+        *itheta = -1;
+        OD_COPY(y, y_tmp, n);
+      }
+    }
+  }
+  k = best_k;
+  theta = best_qtheta;
+  skip = 0;
+  if (noref) {
+    if (qg == 0) skip = OD_PVQ_SKIP_ZERO;
+  }
+  else {
+    if (!is_keyframe && qg == 0) {
+      skip = (icgr ? OD_PVQ_SKIP_ZERO : OD_PVQ_SKIP_COPY);
+    }
+    if (qg == icgr && *itheta == 0 && !cfl_enabled) skip = OD_PVQ_SKIP_COPY;
+  }
+  /* Synthesize like the decoder would. */
+  if (skip) {
+    if (skip == OD_PVQ_SKIP_COPY) OD_COPY(out, r0, n);
+    else OD_CLEAR(out, n);
+  }
+  else {
+    if (noref) gain_offset = 0;
+    g = od_gain_expand(OD_SHL(qg, OD_CGAIN_SHIFT) + gain_offset, q0, beta);
+    od_pvq_synthesis_partial(out, y, r16, n, noref, g, theta, m, s,
+     qm_inv);
+  }
+  *vk = k;
+  *skip_diff += skip_dist - best_dist;
+  /* Encode gain differently depending on whether we use prediction or not.
+     Special encoding on inter frames where qg=0 is allowed for noref=0
+     but not noref=1.*/
+  if (is_keyframe) return noref ? qg : neg_interleave(qg, icgr);
+  else return noref ? qg - 1 : neg_interleave(qg + 1, icgr + 1);
+}
+
+/** Encodes a single vector of integers (eg, a partition within a
+ *  coefficient block) using PVQ
+ *
+ * @param [in,out] w          multi-symbol entropy encoder
+ * @param [in]     qg         quantized gain
+ * @param [in]     theta      quantized post-prediction theta
+ * @param [in]     in         coefficient vector to code
+ * @param [in]     n          number of coefficients in partition
+ * @param [in]     k          number of pulses in partition
+ * @param [in,out] model      entropy encoder state
+ * @param [in,out] adapt      adaptation context
+ * @param [in,out] exg        ExQ16 expectation of gain value
+ * @param [in,out] ext        ExQ16 expectation of theta value
+ * @param [in]     cdf_ctx    selects which cdf context to use
+ * @param [in]     is_keyframe whether we're encoding a keyframe
+ * @param [in]     code_skip  whether the "skip rest" flag is allowed
+ * @param [in]     skip_rest  when set, we skip all higher bands
+ * @param [in]     encode_flip whether we need to encode the CfL flip flag now
+ * @param [in]     flip       value of the CfL flip flag
+ */
+void pvq_encode_partition(aom_writer *w,
+                                 int qg,
+                                 int theta,
+                                 const od_coeff *in,
+                                 int n,
+                                 int k,
+                                 generic_encoder model[3],
+                                 od_adapt_ctx *adapt,
+                                 int *exg,
+                                 int *ext,
+                                 int cdf_ctx,
+                                 int is_keyframe,
+                                 int code_skip,
+                                 int skip_rest,
+                                 int encode_flip,
+                                 int flip) {
+  int noref;
+  int id;
+  noref = (theta == -1);
+  id = (qg > 0) + 2*OD_MINI(theta + 1,3) + 8*code_skip*skip_rest;
+  if (is_keyframe) {
+    OD_ASSERT(id != 8);
+    if (id >= 8) id--;
+  }
+  else {
+    OD_ASSERT(id != 10);
+    if (id >= 10) id--;
+  }
+  /* Jointly code gain, theta and noref for small values. Then we handle
+     larger gain and theta values. For noref, theta = -1. */
+  aom_write_symbol_pvq(w, id, &adapt->pvq.pvq_gaintheta_cdf[cdf_ctx][0],
+   8 + 7*code_skip);
+  if (encode_flip) {
+    /* We could eventually do some smarter entropy coding here, but it would
+       have to be good enough to overcome the overhead of the entropy coder.
+       An early attempt using a "toogle" flag with simple adaptation wasn't
+       worth the trouble. */
+    aom_write_bit(w, flip);
+  }
+  if (qg > 0) {
+    int tmp;
+    tmp = *exg;
+    generic_encode(w, &model[!noref], qg - 1, &tmp, 2);
+    OD_IIR_DIADIC(*exg, qg << 16, 2);
+  }
+  if (theta > 1) {
+    int tmp;
+    tmp = *ext;
+    generic_encode(w, &model[2], theta - 2, &tmp, 2);
+    OD_IIR_DIADIC(*ext, theta << 16, 2);
+  }
+  aom_encode_pvq_codeword(w, &adapt->pvq.pvq_codeword_ctx, in,
+   n - (theta != -1), k);
+}
+
+/** Quantizes a scalar with rate-distortion optimization (RDO)
+ * @param [in] x      unquantized value
+ * @param [in] q      quantization step size
+ * @param [in] delta0 rate increase for encoding a 1 instead of a 0
+ * @param [in] pvq_norm_lambda enc->pvq_norm_lambda for quantized RDO
+ * @retval quantized value
+ */
+int od_rdo_quant(od_coeff x, int q, double delta0, double pvq_norm_lambda) {
+  int n;
+  /* Optimal quantization threshold is 1/2 + lambda*delta_rate/2. See
+     Jmspeex' Journal of Dubious Theoretical Results for details. */
+  n = OD_DIV_R0(abs(x), q);
+  if ((double)abs(x)/q < (double)n/2 + pvq_norm_lambda*delta0/(2*n)) {
+    return 0;
+  }
+  else {
+    return OD_DIV_R0(x, q);
+  }
+}
+
+/** Encode a coefficient block (excepting DC) using PVQ
+ *
+ * @param [in,out] enc     daala encoder context
+ * @param [in]     ref     'reference' (prediction) vector
+ * @param [in]     in      coefficient block to quantize and encode
+ * @param [out]    out     quantized coefficient block
+ * @param [in]     q0      scale/quantizer
+ * @param [in]     pli     plane index
+ * @param [in]     bs      log of the block size minus two
+ * @param [in]     beta    per-band activity masking beta param
+ * @param [in]     is_keyframe whether we're encoding a keyframe
+ * @param [in]     qm      QM with magnitude compensation
+ * @param [in]     qm_inv  Inverse of QM with magnitude compensation
+ * @param [in]     speed   Make search faster by making approximations
+ * @param [in]     pvq_info If null, conisdered as RDO search mode
+ * @return         Returns block skip info indicating whether DC/AC are coded.
+ *                 bit0: DC is coded, bit1: AC is coded (1 means coded)
+ *
+ */
+PVQ_SKIP_TYPE od_pvq_encode(daala_enc_ctx *enc,
+                   od_coeff *ref,
+                   const od_coeff *in,
+                   od_coeff *out,
+                   int q_dc,
+                   int q_ac,
+                   int pli,
+                   int bs,
+                   const od_val16 *beta,
+                   int is_keyframe,
+                   const int16_t *qm,
+                   const int16_t *qm_inv,
+                   int speed,
+                   PVQ_INFO *pvq_info){
+  int theta[PVQ_MAX_PARTITIONS];
+  int qg[PVQ_MAX_PARTITIONS];
+  int k[PVQ_MAX_PARTITIONS];
+  od_coeff y[OD_TXSIZE_MAX*OD_TXSIZE_MAX];
+  int *exg;
+  int *ext;
+  int nb_bands;
+  int i;
+  const int *off;
+  int size[PVQ_MAX_PARTITIONS];
+  generic_encoder *model;
+  double skip_diff;
+  int tell;
+  uint16_t *skip_cdf;
+  od_rollback_buffer buf;
+  int dc_quant;
+  int flip;
+  int cfl_encoded;
+  int skip_rest;
+  int skip_dir;
+  int skip_theta_value;
+  const unsigned char *pvq_qm;
+  double dc_rate;
+  int use_masking;
+  PVQ_SKIP_TYPE ac_dc_coded;
+
+  aom_clear_system_state();
+
+  use_masking = enc->use_activity_masking;
+
+  if (use_masking)
+    pvq_qm = &enc->state.pvq_qm_q4[pli][0];
+  else
+    pvq_qm = 0;
+
+  exg = &enc->state.adapt->pvq.pvq_exg[pli][bs][0];
+  ext = enc->state.adapt->pvq.pvq_ext + bs*PVQ_MAX_PARTITIONS;
+  skip_cdf = enc->state.adapt->skip_cdf[2*bs + (pli != 0)];
+  model = enc->state.adapt->pvq.pvq_param_model;
+  nb_bands = OD_BAND_OFFSETS[bs][0];
+  off = &OD_BAND_OFFSETS[bs][1];
+
+  if (use_masking)
+    dc_quant = OD_MAXI(1, q_dc * pvq_qm[od_qm_get_index(bs, 0)] >> 4);
+  else
+    dc_quant = OD_MAXI(1, q_dc);
+
+  tell = 0;
+  for (i = 0; i < nb_bands; i++) size[i] = off[i+1] - off[i];
+  skip_diff = 0;
+  flip = 0;
+  /*If we are coding a chroma block of a keyframe, we are doing CfL.*/
+  if (pli != 0 && is_keyframe) {
+    od_val32 xy;
+    xy = 0;
+    /*Compute the dot-product of the first band of chroma with the luma ref.*/
+    for (i = off[0]; i < off[1]; i++) {
+#if defined(OD_FLOAT_PVQ)
+      xy += ref[i]*(double)qm[i]*OD_QM_SCALE_1*
+       (double)in[i]*(double)qm[i]*OD_QM_SCALE_1;
+#else
+      od_val32 rq;
+      od_val32 inq;
+      rq = ref[i]*qm[i];
+      inq = in[i]*qm[i];
+      xy += OD_SHR(rq*(int64_t)inq, OD_SHL(OD_QM_SHIFT + OD_CFL_FLIP_SHIFT,
+       1));
+#endif
+    }
+    /*If cos(theta) < 0, then |theta| > pi/2 and we should negate the ref.*/
+    if (xy < 0) {
+      flip = 1;
+      for(i = off[0]; i < off[nb_bands]; i++) ref[i] = -ref[i];
+    }
+  }
+  for (i = 0; i < nb_bands; i++) {
+    int q;
+
+    if (use_masking)
+      q = OD_MAXI(1, q_ac * pvq_qm[od_qm_get_index(bs, i + 1)] >> 4);
+    else
+      q = OD_MAXI(1, q_ac);
+
+    qg[i] = pvq_theta(out + off[i], in + off[i], ref + off[i], size[i],
+     q, y + off[i], &theta[i], &k[i], beta[i], &skip_diff, is_keyframe,
+     pli, enc->state.adapt, qm + off[i], qm_inv + off[i],
+     enc->pvq_norm_lambda, speed);
+  }
+  od_encode_checkpoint(enc, &buf);
+  if (is_keyframe) out[0] = 0;
+  else {
+    int n;
+    n = OD_DIV_R0(abs(in[0] - ref[0]), dc_quant);
+    if (n == 0) {
+      out[0] = 0;
+    } else {
+      int tell2;
+      od_rollback_buffer dc_buf;
+
+      dc_rate = -OD_LOG2((double)(skip_cdf[3] - skip_cdf[2])/
+       (double)(skip_cdf[2] - skip_cdf[1]));
+      dc_rate += 1;
+
+#if CONFIG_DAALA_EC
+      tell2 = od_ec_enc_tell_frac(&enc->w.ec);
+#else
+#error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+      od_encode_checkpoint(enc, &dc_buf);
+      generic_encode(&enc->w, &enc->state.adapt->model_dc[pli],
+       n - 1, &enc->state.adapt->ex_dc[pli][bs][0], 2);
+#if CONFIG_DAALA_EC
+      tell2 = od_ec_enc_tell_frac(&enc->w.ec) - tell2;
+#else
+#error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+      dc_rate += tell2/8.0;
+      od_encode_rollback(enc, &dc_buf);
+
+      out[0] = od_rdo_quant(in[0] - ref[0], dc_quant, dc_rate,
+       enc->pvq_norm_lambda);
+    }
+  }
+#if CONFIG_DAALA_EC
+  tell = od_ec_enc_tell_frac(&enc->w.ec);
+#else
+#error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+  /* Code as if we're not skipping. */
+  aom_write_symbol(&enc->w, 2 + (out[0] != 0), skip_cdf, 4);
+  ac_dc_coded = AC_CODED + (out[0] != 0);
+  cfl_encoded = 0;
+  skip_rest = 1;
+  skip_theta_value = is_keyframe ? -1 : 0;
+  for (i = 1; i < nb_bands; i++) {
+    if (theta[i] != skip_theta_value || qg[i]) skip_rest = 0;
+  }
+  skip_dir = 0;
+  if (nb_bands > 1) {
+    for (i = 0; i < 3; i++) {
+      int j;
+      int tmp;
+      tmp = 1;
+      // ToDo(yaowu): figure out better stop condition without gcc warning.
+      for (j = i + 1; j < nb_bands && j < PVQ_MAX_PARTITIONS; j += 3) {
+        if (theta[j] != skip_theta_value || qg[j]) tmp = 0;
+      }
+      skip_dir |= tmp << i;
+    }
+  }
+  if (theta[0] == skip_theta_value && qg[0] == 0 && skip_rest) nb_bands = 0;
+
+  /* NOTE: There was no other better place to put this function. */
+  if (pvq_info)
+    av1_store_pvq_enc_info(pvq_info, qg, theta, k, y, nb_bands, off, size,
+      skip_rest, skip_dir, bs);
+
+  for (i = 0; i < nb_bands; i++) {
+    int encode_flip;
+    /* Encode CFL flip bit just after the first time it's used. */
+    encode_flip = pli != 0 && is_keyframe && theta[i] != -1 && !cfl_encoded;
+    if (i == 0 || (!skip_rest && !(skip_dir & (1 << ((i - 1)%3))))) {
+      pvq_encode_partition(&enc->w, qg[i], theta[i], y + off[i],
+       size[i], k[i], model, enc->state.adapt, exg + i, ext + i,
+       (pli != 0)*OD_TXSIZES*PVQ_MAX_PARTITIONS + bs*PVQ_MAX_PARTITIONS + i,
+       is_keyframe, i == 0 && (i < nb_bands - 1), skip_rest, encode_flip, flip);
+    }
+    if (i == 0 && !skip_rest && bs > 0) {
+      aom_write_symbol(&enc->w, skip_dir,
+       &enc->state.adapt->pvq.pvq_skip_dir_cdf[(pli != 0) + 2*(bs - 1)][0], 7);
+    }
+    if (encode_flip) cfl_encoded = 1;
+  }
+#if CONFIG_DAALA_EC
+  tell = od_ec_enc_tell_frac(&enc->w.ec) - tell;
+#else
+#error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+  /* Account for the rate of skipping the AC, based on the same DC decision
+     we made when trying to not skip AC. */
+  {
+    double skip_rate;
+    if (out[0] != 0) {
+      skip_rate = -OD_LOG2((skip_cdf[1] - skip_cdf[0])/
+     (double)skip_cdf[3]);
+    }
+    else {
+      skip_rate = -OD_LOG2(skip_cdf[0]/
+     (double)skip_cdf[3]);
+    }
+    tell -= (int)floor(.5+8*skip_rate);
+  }
+  if (nb_bands == 0 || skip_diff <= enc->pvq_norm_lambda/8*tell) {
+    if (is_keyframe) out[0] = 0;
+    else {
+      int n;
+      n = OD_DIV_R0(abs(in[0] - ref[0]), dc_quant);
+      if (n == 0) {
+        out[0] = 0;
+      } else {
+        int tell2;
+        od_rollback_buffer dc_buf;
+
+        dc_rate = -OD_LOG2((double)(skip_cdf[1] - skip_cdf[0])/
+         (double)skip_cdf[0]);
+        dc_rate += 1;
+
+#if CONFIG_DAALA_EC
+        tell2 = od_ec_enc_tell_frac(&enc->w.ec);
+#else
+#error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+        od_encode_checkpoint(enc, &dc_buf);
+        generic_encode(&enc->w, &enc->state.adapt->model_dc[pli],
+         n - 1, &enc->state.adapt->ex_dc[pli][bs][0], 2);
+#if CONFIG_DAALA_EC
+        tell2 = od_ec_enc_tell_frac(&enc->w.ec) - tell2;
+#else
+#error "CONFIG_PVQ currently requires CONFIG_DAALA_EC."
+#endif
+        dc_rate += tell2/8.0;
+        od_encode_rollback(enc, &dc_buf);
+
+        out[0] = od_rdo_quant(in[0] - ref[0], dc_quant, dc_rate,
+         enc->pvq_norm_lambda);
+      }
+    }
+    /* We decide to skip, roll back everything as it was before. */
+    od_encode_rollback(enc, &buf);
+    aom_write_symbol(&enc->w, out[0] != 0, skip_cdf, 4);
+    ac_dc_coded = (out[0] != 0);
+    if (is_keyframe) for (i = 1; i < 1 << (2*bs + 4); i++) out[i] = 0;
+    else for (i = 1; i < 1 << (2*bs + 4); i++) out[i] = ref[i];
+  }
+  if (pvq_info)
+    pvq_info->ac_dc_coded = ac_dc_coded;
+  return ac_dc_coded;
+}