daala_ec: Convert the encoder to use iCDFs

This only changes the internal coding engine. We convert CDFs into
iCDFs at the "bool" writer <-> daala_ec boundary.

Encoder output should not change, and all streams should remain
decodable without decoder changes.

Change-Id: Id3ac7352926497bf6f7bc371ab9bc76e9a3569d5

aom_dsp/daalaboolwriter.h

@@ -50,7 +50,7 @@ static INLINE void aom_daala_write(daala_writer *w, int bit, int prob) {
   bitstream_queue_push(bit, cdf, 2);
 #endif
 
-  od_ec_encode_bool_q15(&w->ec, bit, p);
+  od_ec_encode_bool_q15(&w->ec, bit, OD_ICDF(p));
 }
 
 #if CONFIG_RAWBITS
@@ -73,7 +73,16 @@ static INLINE void daala_write_symbol(daala_writer *w, int symb,
   bitstream_queue_push(symb, cdf, nsymbs);
 #endif
 
+#if CONFIG_EC_SMALLMUL
+  {
+    aom_cdf_prob icdf[16];
+    int i;
+    for (i = 0; i < nsymbs; i++) icdf[i] = OD_ICDF(cdf[i]);
+    od_ec_encode_cdf_q15(&w->ec, symb, icdf, nsymbs);
+  }
+#else
   od_ec_encode_cdf_q15(&w->ec, symb, cdf, nsymbs);
+#endif
 }
 
 #ifdef __cplusplus

aom_dsp/entcode.h

@@ -28,6 +28,16 @@ typedef uint32_t od_ec_window;
    3 => 1/8th bits.*/
 #define OD_BITRES (3)
 
+/*With CONFIG_EC_SMALLMUL, the value stored in a CDF is 32768 minus the actual
+   Q15 cumulative probability (an "inverse" CDF).
+  This function converts from one representation to the other (and is its own
+   inverse).*/
+#if CONFIG_EC_SMALLMUL
+#define OD_ICDF(x) (32768U - (x))
+#else
+#define OD_ICDF(x) (x)
+#endif
+
 /*See entcode.c for further documentation.*/
 
 OD_WARN_UNUSED_RESULT uint32_t od_ec_tell_frac(uint32_t nbits_total,

aom_dsp/entenc.c

@@ -146,27 +146,30 @@ void od_ec_enc_clear(od_ec_enc *enc) {
   fl: The cumulative frequency of all symbols that come before the one to be
        encoded.
   fh: The cumulative frequency of all symbols up to and including the one to
-       be encoded.*/
+       be encoded.
+  {EC_SMALLMUL} Both values are 32768 minus that.*/
 static void od_ec_encode_q15(od_ec_enc *enc, unsigned fl, unsigned fh) {
   od_ec_window l;
   unsigned r;
   unsigned u;
   unsigned v;
-  OD_ASSERT(fl < fh);
-  OD_ASSERT(fh <= 32768U);
   l = enc->low;
   r = enc->rng;
   OD_ASSERT(32768U <= r);
 #if CONFIG_EC_SMALLMUL
-  if (fl > 0) {
-    u = (r >> 8) * (uint32_t)(32768U - fl) >> 7;
-    v = (r >> 8) * (uint32_t)(32768U - fh) >> 7;
+  OD_ASSERT(fh < fl);
+  OD_ASSERT(fl <= 32768U);
+  if (fl < 32768U) {
+    u = (r >> 8) * (uint32_t)fl >> 7;
+    v = (r >> 8) * (uint32_t)fh >> 7;
     l += r - u;
     r = u - v;
   } else {
-    r -= (r >> 8) * (uint32_t)(32768U - fh) >> 7;
+    r -= (r >> 8) * (uint32_t)fh >> 7;
   }
 #else
+  OD_ASSERT(fl < fh);
+  OD_ASSERT(fh <= 32768U);
   u = fl * (uint32_t)r >> 15;
   v = fh * (uint32_t)r >> 15;
   r = v - u;
@@ -174,33 +177,37 @@ static void od_ec_encode_q15(od_ec_enc *enc, unsigned fl, unsigned fh) {
 #endif
   od_ec_enc_normalize(enc, l, r);
 #if OD_MEASURE_EC_OVERHEAD
-  enc->entropy -= OD_LOG2((double)(fh - fl) / 32768.);
+  enc->entropy -= OD_LOG2((double)(OD_ICDF(fh) - OD_ICDF(fl)) / 32768.);
   enc->nb_symbols++;
 #endif
 }
 
-/*Encode a bit that has an fz probability of being a zero in Q15.
+/*Encode a single binary value.
   val: The value to encode (0 or 1).
-  fz: The probability that val is zero, scaled by 32768.*/
-void od_ec_encode_bool_q15(od_ec_enc *enc, int val, unsigned fz) {
+  {EC_SMALLMUL} f: The probability that the val is one, scaled by 32768.
+  {else} f: The probability that val is zero, scaled by 32768.*/
+void od_ec_encode_bool_q15(od_ec_enc *enc, int val, unsigned f) {
   od_ec_window l;
   unsigned r;
   unsigned v;
-  OD_ASSERT(0 < fz);
-  OD_ASSERT(fz < 32768U);
+  OD_ASSERT(0 < f);
+  OD_ASSERT(f < 32768U);
   l = enc->low;
   r = enc->rng;
   OD_ASSERT(32768U <= r);
 #if CONFIG_EC_SMALLMUL
-  v = r - ((r >> 8) * (uint32_t)(32768U - fz) >> 7);
+  v = (r >> 8) * (uint32_t)f >> 7;
+  if (val) l += r - v;
+  r = val ? v : r - v;
 #else
-  v = fz * (uint32_t)r >> 15;
-#endif
+  v = f * (uint32_t)r >> 15;
   if (val) l += v;
   r = val ? r - v : v;
+#endif
   od_ec_enc_normalize(enc, l, r);
 #if OD_MEASURE_EC_OVERHEAD
-  enc->entropy -= OD_LOG2((double)(val ? 32768 - fz : fz) / 32768.);
+  enc->entropy -=
+      OD_LOG2((double)(val ? 32768 - OD_ICDF(f) : OD_ICDF(f)) / 32768.);
   enc->nb_symbols++;
 #endif
 }
@@ -218,8 +225,8 @@ void od_ec_encode_cdf_q15(od_ec_enc *enc, int s, const uint16_t *cdf,
   (void)nsyms;
   OD_ASSERT(s >= 0);
   OD_ASSERT(s < nsyms);
-  OD_ASSERT(cdf[nsyms - 1] == 32768U);
-  od_ec_encode_q15(enc, s > 0 ? cdf[s - 1] : 0, cdf[s]);
+  OD_ASSERT(cdf[nsyms - 1] == OD_ICDF(32768U));
+  od_ec_encode_q15(enc, s > 0 ? cdf[s - 1] : OD_ICDF(0), cdf[s]);
 }
 
 #if CONFIG_RAWBITS

aom_dsp/entenc.h

@@ -62,7 +62,7 @@ void od_ec_enc_init(od_ec_enc *enc, uint32_t size) OD_ARG_NONNULL(1);
 void od_ec_enc_reset(od_ec_enc *enc) OD_ARG_NONNULL(1);
 void od_ec_enc_clear(od_ec_enc *enc) OD_ARG_NONNULL(1);
 
-void od_ec_encode_bool_q15(od_ec_enc *enc, int val, unsigned fz_q15)
+void od_ec_encode_bool_q15(od_ec_enc *enc, int val, unsigned f_q15)
     OD_ARG_NONNULL(1);
 void od_ec_encode_cdf_q15(od_ec_enc *enc, int s, const uint16_t *cdf, int nsyms)
     OD_ARG_NONNULL(1) OD_ARG_NONNULL(3);