Implement alternative exponent for changing bands with pow().

However, testing shows that this version is not as good as the original
version.
Signed-off-by: Stefan Westerfeld <stefan@space.twc.de>

src/audiowmark.cc

@@ -331,34 +331,39 @@ compute_frame_ffts (const WavData& wav_data, size_t start_index, size_t frame_co
   return fft_out;
 }
 
+complex<float>
+mark_delta (complex<float> spect_value, double exponent)
+{
+  const float mag_factor = pow (abs (spect_value), exponent) / abs (spect_value);
+
+  return spect_value * (mag_factor - 1);
+}
+
 void
 mark_bit_linear (int f, const vector<complex<float>>& fft_out, vector<complex<float>>& fft_delta_spect, int data_bit, Random::Stream random_stream)
 {
   vector<int> up;
   vector<int> down;
   get_up_down (f, up, down, random_stream);
-  const double  data_bit_sign = data_bit > 0 ? 1 : -1;
+
+  const double exponent = data_bit ? 1 / (1 + Params::water_delta) : (1 + Params::water_delta);
   for (auto u : up)
     {
       /*
-       * for up bands, we want do use [for a 1 bit]  (pow (mag, 1 - water_delta))
+       * for up bands, we want do use [for a 1 bit]  (pow (mag, ...)))
        *
        * this actually increases the amount of energy because mag is less than 1.0
        */
-      const float mag_factor = pow (abs (fft_out[u]), -Params::water_delta * data_bit_sign);
-
-      fft_delta_spect[u] = fft_out[u] * (mag_factor - 1);
+      fft_delta_spect[u] = mark_delta (fft_out[u], exponent);
     }
   for (auto d : down)
     {
       /*
-       * for down bands, we want do use [for a 1 bit]   (pow (mag, 1 + water_delta))
+       * for down bands, we want do use [for a 1 bit]   (pow (mag, ...))
        *
        * this actually decreases the amount of energy because mag is less than 1.0
        */
-      const float mag_factor = pow (abs (fft_out[d]), Params::water_delta * data_bit_sign);
-
-      fft_delta_spect[d] = fft_out[d] * (mag_factor - 1);
+      fft_delta_spect[d] = mark_delta (fft_out[d], 1 / exponent);
     }
 }
 
@@ -418,21 +423,14 @@ mark_data (const WavData& wav_data, int start_frame, const vector<vector<complex
                   int b = f * Params::bands_per_frame + frame_b;
 
                   const int data_bit = bitvec[f / Params::frames_per_bit];
-                  const double  data_bit_sign = data_bit > 0 ? 1 : -1;
+                  const double exponent = data_bit ? 1 / (1 + Params::water_delta) : (1 + Params::water_delta);
 
                   const int u = mix_entries[b].up;
                   const int index = (start_frame + mix_entries[b].frame) * wav_data.n_channels() + ch;
-                  {
-                    const float mag_factor = pow (abs (fft_out[index][u]), -Params::water_delta * data_bit_sign);
+                  fft_delta_spect[index][u] = mark_delta (fft_out[index][u], exponent);
 
-                    fft_delta_spect[index][u] = fft_out[index][u] * (mag_factor - 1);
-                  }
                   const int d = mix_entries[b].down;
-                  {
-                    const float mag_factor = pow (abs (fft_out[index][d]), Params::water_delta * data_bit_sign);
-
-                    fft_delta_spect[index][d] = fft_out[index][d] * (mag_factor - 1);
-                  }
+                  fft_delta_spect[index][d] = mark_delta (fft_out[index][d], 1 / exponent);
                 }
             }
         }
@@ -457,6 +455,16 @@ mark_sync_frame_count()
   return Params::sync_bits * Params::sync_frames_per_bit;
 }
 
+double
+mags_to_raw_bit (double umag, double dmag)
+{
+  /* convert umag and dmag to soft bit, avoiding bias in either direction */
+  if (umag > dmag)
+    return 1 - umag / dmag;
+  else
+    return dmag / umag - 1;
+}
+
 void
 mark_sync (const WavData& wav_data, int start_frame, const vector<vector<complex<float>>>& fft_out, vector<vector<complex<float>>>& fft_delta_spect)
 {
@@ -705,7 +713,7 @@ mix_decode (vector<vector<complex<float>>>& fft_out, vector<vector<complex<float
         }
       if ((f % Params::frames_per_bit) == (Params::frames_per_bit - 1))
         {
-          raw_bit_vec.push_back (umag - dmag);
+          raw_bit_vec.push_back (mags_to_raw_bit (umag, dmag));
           umag = 0;
           dmag = 0;
         }
@@ -747,7 +755,7 @@ linear_decode (vector<vector<complex<float>>>& fft_out, vector<vector<complex<fl
         }
       if ((f % Params::frames_per_bit) == (Params::frames_per_bit - 1))
         {
-          raw_bit_vec.push_back (umag - dmag);
+          raw_bit_vec.push_back (mags_to_raw_bit (umag, dmag));
           umag = 0;
           dmag = 0;
         }
@@ -820,9 +828,9 @@ class SyncFinder
                 dmag += fft_out_db[index + down[bit][i]];
               }
           }
-        const int expect_data_bit = bit & 1; /* expect 010101 */
+        const int sign = (bit & 1) ? 1 : -1; /* expect 010101 */
 
-        const double q = expect_data_bit ? (1 - umag / dmag) : (umag / dmag - 1);
+        const double q = mags_to_raw_bit (umag, dmag) * sign;
         sync_quality += q;
       }
     sync_quality /= Params::sync_bits;