Remove the starting zero from ANS CDFs.

This brings it in line with the Daala CDFs and will make it easier to
share code.

Change-Id: Idfd2d2b33c3b9b2c4e72ce72fb3d8039013448b9
(cherry picked from aom/master commit af98507c)

aom_dsp/ans.h

@@ -36,8 +36,7 @@ typedef uint16_t AnsP10;
 #define IO_BASE 256
 // Range I = { L_BASE, L_BASE + 1, ..., L_BASE * IO_BASE - 1 }
 
-// This is now just a boring cdf. It starts with an explicit zero.
-// TODO(aconverse): Remove starting zero.
+// This is now just a boring cdf.
 typedef uint16_t rans_lut[16];
 
 void aom_rans_build_cdf_from_pdf(const AnsP10 token_probs[], rans_lut cdf_tab);

aom_dsp/ansreader.h

@@ -68,15 +68,16 @@ struct rans_dec_sym {
 
 static INLINE void fetch_sym(struct rans_dec_sym *out, const rans_lut cdf,
                              AnsP10 rem) {
-  int i = 0;
+  int i;
+  AnsP10 cum_prob = 0, top_prob;
   // TODO(skal): if critical, could be a binary search.
   // Or, better, an O(1) alias-table.
-  while (rem >= cdf[i]) {
-    ++i;
+  for (i = 0; rem >= (top_prob = cdf[i]); ++i) {
+    cum_prob = top_prob;
   }
-  out->val = i - 1;
-  out->prob = (AnsP10)(cdf[i] - cdf[i - 1]);
-  out->cum_prob = (AnsP10)cdf[i - 1];
+  out->val = i;
+  out->prob = top_prob - cum_prob;
+  out->cum_prob = cum_prob;
 }
 
 static INLINE int rans_read(struct AnsDecoder *ans, const rans_lut tab) {

aom_dsp/bitwriter.h

@@ -92,8 +92,8 @@ static INLINE void aom_write_symbol(aom_writer *w, int symb,
   struct rans_sym s;
   (void)nsymbs;
   assert(cdf);
-  s.cum_prob = cdf[symb];
-  s.prob = cdf[symb + 1] - s.cum_prob;
+  s.cum_prob = symb > 0 ? cdf[symb - 1] : 0;
+  s.prob = cdf[symb] - s.cum_prob;
   buf_rans_write(w, &s);
 #else
   (void)w;

av1/common/entropy.c

@@ -2801,6 +2801,14 @@ void av1_model_to_full_probs(const aom_prob *model, aom_prob *full) {
 }
 
 #if CONFIG_ANS
+static void build_token_cdfs(const aom_prob *pdf_model, rans_lut cdf) {
+  int i, sum = 0;
+  assert(pdf_model[2] != 0);
+  for (i = 0; i < ENTROPY_TOKENS - 2; ++i) {
+    cdf[i] = sum += av1_pareto8_token_probs[pdf_model[2] - 1][i];
+  }
+}
+
 void av1_coef_pareto_cdfs(FRAME_CONTEXT *fc) {
   TX_SIZE t;
   int i, j, k, l;
@@ -2809,11 +2817,8 @@ void av1_coef_pareto_cdfs(FRAME_CONTEXT *fc) {
       for (j = 0; j < REF_TYPES; ++j)
         for (k = 0; k < COEF_BANDS; ++k)
           for (l = 0; l < BAND_COEFF_CONTEXTS(k); ++l) {
-            const aom_prob *const tree_probs = fc->coef_probs[t][i][j][k][l];
-            aom_prob pivot = tree_probs[PIVOT_NODE];
-            assert(pivot != 0);
-            aom_rans_build_cdf_from_pdf(av1_pareto8_token_probs[pivot - 1],
-                                        fc->coef_cdfs[t][i][j][k][l]);
+            build_token_cdfs(fc->coef_probs[t][i][j][k][l],
+                             fc->coef_cdfs[t][i][j][k][l]);
           }
 }
 #endif  // CONFIG_ANS

test/ans_test.cc

@@ -98,9 +98,9 @@ std::vector<int> ans_encode_build_vals(const rans_sym *tab, int iters) {
 }
 
 void rans_build_dec_tab(const struct rans_sym sym_tab[], rans_lut dec_tab) {
-  dec_tab[0] = 0;
-  for (int i = 1; dec_tab[i - 1] < RANS_PRECISION; ++i) {
-    dec_tab[i] = dec_tab[i - 1] + sym_tab[i - 1].prob;
+  unsigned int sum = 0;
+  for (int i = 0; sum < RANS_PRECISION; ++i) {
+    dec_tab[i] = sum += sym_tab[i].prob;
   }
 }