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atrac3p:main_trees_list [2009/12/05 23:33] – tables for all ungrouped and pair-grouped trees megadiscmanatrac3p:main_trees_list [2010/07/23 17:41] (current) – quantizer -> quantization precision megadiscman
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-===== Main Spectral Data Encoding Trees ===== 
-==== General Intro ==== 
- 
-The quantized values are encoded using a prefix free binary code. To make matters more complicated there are up to 16 encoding scheme per quantizer (because the symbol set depends on the quantizer). In many cases, the symbols are built from a group of two or four quantized values instead of just one quantized value. For groups of size two, the trees are shown as table, the first symbol choosing the row, the second value the column. 
- 
-Another catch is that some of the encoding schemes encoded the signed quantized values, while others encode only the absolute values of the quantized values. If only the absolute values are encoded in a symbol, each symbol is followed by one bit per absolute value that is not zero. If that bit is set, the value is negative. 
- 
-The trees can be calculated as [[canonical huffman trees]]. Note that unsigned sorting  (on two's complement numbers) is used, so negative numbers sort behind positive ones. The sort order for the grouped symbols is lexicographically by the single quantized numbers. 
- 
 <html> <html>
     <!-- I know that CSS in the body violates the specs! -->     <!-- I know that CSS in the body violates the specs! -->
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     --></style>     --></style>
 </html> </html>
-==== Trees for Quantizer 1 ====+ 
 +===== Main Spectral Data Encoding Trees ===== 
 +==== General Intro ==== 
 + 
 +The quantized values are encoded using a prefix free binary code. To make matters more complicated there are up to 16 encoding scheme per quantization precision (symbol set depends on precision, so different encoding schemes must be used for different precisions.). In many cases, the symbols are built from a group of two or four quantized values instead of just one quantized value. For groups of size two, the trees are shown as table, the first symbol choosing the row, the second value the column. For groups of size four, the tables are organized so that the first symbol chooses the row block, the second symbol the exact row, the third symbol the column block and the fourth symbol the column. //I think about swapping second and third symbol, so be careful when coming back later!// 
 + 
 +Another catch is that some of the encoding schemes encoded the signed quantized values, while others encode only the absolute values of the quantized values. If only the absolute values are encoded in a symbol, each symbol is followed by one bit per absolute value that is not zero. If that bit is set, the value is negative. 
 + 
 +The trees can be calculated as [[canonical huffman trees]]. Note that unsigned sorting  (on two's complement numbers) is used, so negative numbers sort behind positive ones. The sort order for the grouped symbols is lexicographically by the single quantized numbers. 
 + 
 +==== Examples ==== 
 + 
 +=== Interpreting a group-by-four block === 
 + 
 +Let's take a look at Tree 1A. The shortest symbol is (0,0,0,0), encoded with one bit, and gets assigned the code ''0''. The next shortest symbol has 4 bits, there is only one of them, and it is (-1,0,0,0). So this symbol gets the code ''1000''. Now, there are seven symbols with 5 bits. From top to bottom in the table, the symbols are 
 + 
 +  * (0,-1,0,0) 
 +  * (0,0,-1,0) 
 +  * (0,0,0,-1) 
 +  * (0,0,0,1) 
 +  * (0,0,1,0) 
 +  * (0,1,0,0) 
 +  * (1,0,0,0) 
 + 
 +Now for sorting these symbols lexicographically, rember that negative values go past positive ones (if we had -2,-1,0,1,2 the sorted order would be 0,1,2,-2,-1 instead). In this case, the sorted order ist 
 +  * (0,0,0,1) -> ''10010'' 
 +  * (0,0,0,-1) -> ''10011'' 
 +  * (0,0,1,0) -> ''10100'' 
 +  * (0,0,-1,0) -> ''10101'' 
 +  * (0,1,0,0) -> ''10110'' 
 +  * (0,-1,0,0) -> ''10111'' 
 +  * (1,0,0,0) -> ''11000'' 
 + 
 +=== Interpreting absolute value encoding === 
 + 
 +Now take a look at Tree 1H. In this coding scheme, the prefix free code is built from positive values only. Applying the algorithm to build the canonical code from the given lengths, one gets the following code assignment: 
 + 
 +  * (0,0) -> ''0'' 
 +  * (1,0) -> ''10'' 
 +  * (0,1) -> ''110'' 
 +  * (1,1) -> ''111'' 
 + 
 +as the these codes are absolute value, they have to be interpreted as (0,0), (±1,0), (0,±1), (±1,±1) in fact, and the signs have to be specified afterwards. For each non-zero value from left to right, one bit being zero for positive and one for negative is appended to to the code, so you finally obtain 
 + 
 +  * (0,0) -> ''0'' 
 +  * (+1,0) -> ''10**0**''; (-1,0) -> ''10**1**'' 
 +  * (0,+1) -> ''110**0**''; (0,-1) -> ''110**1**'' 
 +  * (+1,+1) -> ''111**00**'', (-1,+1) -> ''111**10**'', (+1,-1) -> ''111**01**'', (-1,-1) -> ''111**11**'' 
 + 
 +==== Trees for Precision 1 ====
 (i.e. symbol set -1..+1) (i.e. symbol set -1..+1)
 === Tree 1A === === Tree 1A ===
 (used for A/0) (used for A/0)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>11</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 8</td><td>10</td><td> 7</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> 
 +      <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td>10</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1B === === Tree 1B ===
 (used for A/1) (used for A/1)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 6</td><td> 5</td><td> 7</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 7</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> 
 +      <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 9</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td>10</td><td>11</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1C === === Tree 1C ===
 (used for A/2, B/1) (used for A/2, B/1)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td>10</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 5</td><td> 8</td><td> 8</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>0</th><td> 8</td><td> 5</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 5</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 8</td><td> 5</td><td> 8</td><td>10</td><td> 8</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td>10</td><td>11</td><td>10</td><td> 8</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1D === === Tree 1D ===
 (used for A/3) (used for A/3)
Line 33: Line 139:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-1</th><th>0</th><th>1</th>  </tr></thead><tbody>     <th>-1</th><th>0</th><th>1</th>  </tr></thead><tbody>
-    <tr><th>-1</th><td>6</td><td>4</td><td>6</td></tr> +    <tr><th>-1</th><td> 6</td><td> 4</td><td> 6</td></tr> 
-    <tr><th>0</th><td>3</td><td>1</td><td>3</td></tr> +    <tr><th>0</th><td> 3</td><td> 1</td><td> 3</td></tr> 
-    <tr><th>1</th><td>6</td><td>3</td><td>6</td></tr>+    <tr><th>1</th><td> 6</td><td> 3</td><td> 6</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
 === Tree 1E === === Tree 1E ===
 (used for A/4, B/2, B/6) (used for A/4, B/2, B/6)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>12</td><td>11</td><td>12</td><td>12</td><td> 9</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 
 +      <tr><th>0</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 5</td><td> 9</td><td>11</td><td> 9</td><td>12</td></tr> 
 +      <tr><th>1</th><td>12</td><td>10</td><td>11</td><td>11</td><td> 9</td><td>11</td><td>12</td><td>11</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td>11</td><td>10</td><td>11</td><td> 9</td><td> 4</td><td> 9</td><td>10</td><td> 9</td><td>11</td></tr> 
 +      <tr><th>0</th><td> 9</td><td> 4</td><td> 9</td><td> 4</td><td> 1</td><td> 4</td><td> 9</td><td> 4</td><td> 9</td></tr> 
 +      <tr><th>1</th><td>11</td><td> 9</td><td>10</td><td> 9</td><td> 4</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>12</td><td>11</td><td>12</td><td>11</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr> 
 +      <tr><th>0</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 5</td><td> 9</td><td>11</td><td>10</td><td>12</td></tr> 
 +      <tr><th>1</th><td>12</td><td>11</td><td>12</td><td>11</td><td> 9</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1F === === Tree 1F ===
 (used for A/5, B/3) (used for A/5, B/3)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 6</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 6</td><td> 9</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 4</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 5</td><td> 7</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 6</td><td> 8</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 6</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> 
 +      <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1G === === Tree 1G ===
 (used for A/6, B/5) (used for A/6, B/5)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> 
 +      <tr><th>0</th><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>1</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 8</td><td> 7</td><td> 9</td><td> 8</td><td> 4</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 4</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 7</td><td> 4</td><td> 7</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>1</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1H === === Tree 1H ===
 (used for A/7) (used for A/7)
Line 54: Line 226:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th>  </tr></thead><tbody>     <th>0</th><th>1</th>  </tr></thead><tbody>
-    <tr><th>0</th><td>1</td><td>3</td></tr> +    <tr><th>0</th><td> 1</td><td> 3</td></tr> 
-    <tr><th>1</th><td>2</td><td>3</td></tr>+    <tr><th>1</th><td> 2</td><td> 3</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
 === Tree 1I === === Tree 1I ===
 (used for B/0) (used for B/0)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 8</td><td>10</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> 
 +      <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td>10</td><td> 8</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>12</td><td>10</td><td>11</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td>10</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>1</th><td>11</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1J === === Tree 1J ===
 (used for B/4) (used for B/4)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>11</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 7</td><td>10</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> 
 +      <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 1K === === Tree 1K ===
 (used for B/7) (used for B/7)
- +<html><table class="x" rules="groups" frame="void"> 
-==== Trees for Quantizer 2 ====+  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr> 
 +       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">-1</th> 
 +<th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td> 9</td><td>12</td><td>10</td><td>12</td></tr> 
 +      <tr><th>0</th><td>10</td><td> 7</td><td>10</td><td> 8</td><td> 4</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> 
 +      <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>-1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td>12</td></tr> 
 +      <tr><th>0</th><td> 9</td><td> 7</td><td>10</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr> 
 +      <tr><th>1</th><td>12</td><td>10</td><td>12</td><td> 9</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html> 
 +==== Trees for Precision 2 ====
 (i.e. symbol set -2..+2) (i.e. symbol set -2..+2)
 === Tree 2A === === Tree 2A ===
 (used for A/0) (used for A/0)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 2</td><td> 4</td><td> 8</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>12</td></tr> 
 +      <tr><th>1</th><td> 8</td><td> 8</td><td>11</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>12</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2B === === Tree 2B ===
 (used for A/1) (used for A/1)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 8</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 7</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 6</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2C === === Tree 2C ===
 (used for A/2) (used for A/2)
Line 83: Line 365:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
-    <tr><th>-2</th><td>9</td><td>8</td><td>6</td><td>7</td><td>8</td></tr> +    <tr><th>-2</th><td> 9</td><td> 8</td><td> 6</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>7</td><td>5</td><td>3</td><td>5</td><td>7</td></tr> +    <tr><th>-1</th><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td></tr> 
-    <tr><th>0</th><td>7</td><td>3</td><td>2</td><td>3</td><td>6</td></tr> +    <tr><th>0</th><td> 7</td><td> 3</td><td> 2</td><td> 3</td><td> 6</td></tr> 
-    <tr><th>1</th><td>7</td><td>5</td><td>3</td><td>5</td><td>7</td></tr> +    <tr><th>1</th><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td></tr> 
-    <tr><th>2</th><td>8</td><td>7</td><td>6</td><td>7</td><td>9</td></tr>+    <tr><th>2</th><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 93: Line 375:
 (used for A/3, B/2) (used for A/3, B/2)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 1</td><td> 4</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 7</td><td> 8</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 6</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>11</td><td> 9</td><td>10</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2E === === Tree 2E ===
 (used for A/4) (used for A/4)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2F === === Tree 2F ===
 (used for A/5) (used for A/5)
Line 104: Line 430:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
-    <tr><th>-2</th><td>10</td><td>9</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>-2</th><td>10</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>8</td><td>6</td><td>4</td><td>6</td><td>8</td></tr> +    <tr><th>-1</th><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td></tr> 
-    <tr><th>0</th><td>8</td><td>3</td><td>1</td><td>3</td><td>7</td></tr> +    <tr><th>0</th><td> 8</td><td> 3</td><td> 1</td><td> 3</td><td> 7</td></tr> 
-    <tr><th>1</th><td>8</td><td>6</td><td>4</td><td>6</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td></tr> 
-    <tr><th>2</th><td>9</td><td>8</td><td>7</td><td>8</td><td>10</td></tr>+    <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 117: Line 443:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
-    <tr><th>-2</th><td>8</td><td>7</td><td>6</td><td>6</td><td>7</td></tr> +    <tr><th>-2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>-1</th><td>6</td><td>5</td><td>3</td><td>4</td><td>6</td></tr> +    <tr><th>-1</th><td> 6</td><td> 5</td><td> 3</td><td> 4</td><td> 6</td></tr> 
-    <tr><th>0</th><td>6</td><td>3</td><td>3</td><td>3</td><td>6</td></tr> +    <tr><th>0</th><td> 6</td><td> 3</td><td> 3</td><td> 3</td><td> 6</td></tr> 
-    <tr><th>1</th><td>6</td><td>4</td><td>3</td><td>5</td><td>7</td></tr> +    <tr><th>1</th><td> 6</td><td> 4</td><td> 3</td><td> 5</td><td> 7</td></tr> 
-    <tr><th>2</th><td>7</td><td>6</td><td>6</td><td>7</td><td>8</td></tr>+    <tr><th>2</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 127: Line 453:
 (used for A/7) (used for A/7)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 2</td><td> 4</td><td> 7</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2I === === Tree 2I ===
 (used for B/0) (used for B/0)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 1</td><td> 4</td><td> 7</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 4</td><td> 6</td><td> 9</td><td> 6</td><td> 6</td><td> 9</td><td> 8</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 6</td><td> 9</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 7</td><td>10</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 8</td><td> 9</td><td>12</td><td> 9</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td></tr> 
 +      <tr><th>1</th><td> 8</td><td> 9</td><td>12</td><td> 9</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>12</td></tr> 
 +      <tr><th>2</th><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2J === === Tree 2J ===
 (used for B/1) (used for B/1)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 7</td><td> 7</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2K === === Tree 2K ===
 (used for B/3, B/7) (used for B/3, B/7)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 2</td><td> 4</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 6</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 6</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td>10</td><td>11</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 2L === === Tree 2L ===
 (used for B/4) (used for B/4)
Line 146: Line 560:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
-    <tr><th>-2</th><td>9</td><td>8</td><td>7</td><td>7</td><td>9</td></tr> +    <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>8</td><td>6</td><td>3</td><td>5</td><td>7</td></tr> +    <tr><th>-1</th><td> 8</td><td> 6</td><td> 3</td><td> 5</td><td> 7</td></tr> 
-    <tr><th>0</th><td>7</td><td>4</td><td>1</td><td>4</td><td>6</td></tr> +    <tr><th>0</th><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 6</td></tr> 
-    <tr><th>1</th><td>7</td><td>5</td><td>4</td><td>6</td><td>8</td></tr> +    <tr><th>1</th><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 8</td></tr> 
-    <tr><th>2</th><td>9</td><td>7</td><td>7</td><td>8</td><td>9</td></tr>+    <tr><th>2</th><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 159: Line 573:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>     <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
-    <tr><th>-2</th><td>9</td><td>8</td><td>7</td><td>7</td><td>9</td></tr> +    <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>8</td><td>6</td><td>4</td><td>5</td><td>7</td></tr> +    <tr><th>-1</th><td> 8</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td></tr> 
-    <tr><th>0</th><td>6</td><td>4</td><td>1</td><td>4</td><td>7</td></tr> +    <tr><th>0</th><td> 6</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td></tr> 
-    <tr><th>1</th><td>7</td><td>5</td><td>3</td><td>6</td><td>8</td></tr> +    <tr><th>1</th><td> 7</td><td> 5</td><td> 3</td><td> 6</td><td> 8</td></tr> 
-    <tr><th>2</th><td>9</td><td>7</td><td>7</td><td>8</td><td>9</td></tr>+    <tr><th>2</th><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 169: Line 583:
 (used for B/6) (used for B/6)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
- +<html><table class="x" rules="groups" frame="void"> 
-==== Trees for Quantizer 3 ====+  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <colgroup span=3 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="3">0</th> 
 +<th>0</th><td> 1</td><td> 4</td><td> 6</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 9</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">1</th> 
 +<th>0</th><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 7</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="3">2</th> 
 +<th>0</th><td> 5</td><td> 9</td><td>11</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html> 
 +==== Trees for Precision 3 ====
 (i.e. symbol set -3..+3) (i.e. symbol set -3..+3)
 === Tree 3A === === Tree 3A ===
Line 178: Line 614:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
-    <tr><th>-3</th><td>9</td><td>8</td><td>7</td><td>6</td><td>7</td><td>7</td><td>8</td></tr> +    <tr><th>-3</th><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>-2</th><td>8</td><td>7</td><td>6</td><td>6</td><td>6</td><td>7</td><td>7</td></tr> +    <tr><th>-2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td></tr> 
-    <tr><th>-1</th><td>7</td><td>6</td><td>4</td><td>4</td><td>4</td><td>6</td><td>7</td></tr> +    <tr><th>-1</th><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>0</th><td>7</td><td>6</td><td>4</td><td>3</td><td>4</td><td>6</td><td>7</td></tr> +    <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>1</th><td>7</td><td>6</td><td>4</td><td>4</td><td>4</td><td>6</td><td>7</td></tr> +    <tr><th>1</th><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>2</th><td>7</td><td>7</td><td>6</td><td>6</td><td>6</td><td>8</td><td>8</td></tr> +    <tr><th>2</th><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>3</th><td>8</td><td>7</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td></tr>+    <tr><th>3</th><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 193: Line 629:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
-    <tr><th>-3</th><td>10</td><td>9</td><td>8</td><td>8</td><td>8</td><td>9</td><td>10</td></tr> +    <tr><th>-3</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> 
-    <tr><th>-2</th><td>9</td><td>9</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>-2</th><td> 9</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>9</td><td>8</td><td>6</td><td>4</td><td>5</td><td>7</td><td>8</td></tr> +    <tr><th>-1</th><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>0</th><td>8</td><td>7</td><td>4</td><td>1</td><td>4</td><td>7</td><td>8</td></tr> +    <tr><th>0</th><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>1</th><td>8</td><td>7</td><td>5</td><td>4</td><td>6</td><td>8</td><td>9</td></tr> +    <tr><th>1</th><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>2</th><td>9</td><td>8</td><td>7</td><td>7</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>10</td><td>9</td><td>8</td><td>8</td><td>8</td><td>9</td><td>10</td></tr>+    <tr><th>3</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 208: Line 644:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
-    <tr><th>-3</th><td>9</td><td>9</td><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td></tr> +    <tr><th>-3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>-2</th><td>9</td><td>8</td><td>7</td><td>6</td><td>6</td><td>8</td><td>8</td></tr> +    <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>8</td><td>7</td><td>5</td><td>3</td><td>5</td><td>7</td><td>8</td></tr> +    <tr><th>-1</th><td> 8</td><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>0</th><td>7</td><td>6</td><td>3</td><td>3</td><td>3</td><td>6</td><td>7</td></tr> +    <tr><th>0</th><td> 7</td><td> 6</td><td> 3</td><td> 3</td><td> 3</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>1</th><td>8</td><td>7</td><td>5</td><td>3</td><td>5</td><td>7</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>2</th><td>8</td><td>8</td><td>6</td><td>6</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>2</th><td> 8</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>3</th><td>9</td><td>8</td><td>8</td><td>7</td><td>8</td><td>9</td><td>9</td></tr>+    <tr><th>3</th><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 220: Line 656:
 (used for A/3) (used for A/3)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="4">0</th> 
 +<th>0</th><td> 3</td><td> 5</td><td> 8</td><td>10</td><td> 4</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 5</td><td> 7</td><td> 8</td><td> 8</td><td> 7</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>10</td><td>12</td><td>12</td><td>11</td><td>10</td><td>12</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="4">1</th> 
 +<th>0</th><td> 5</td><td> 5</td><td> 8</td><td>10</td><td> 5</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>12</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td>11</td><td> 7</td><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 7</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td></tr> 
 +      <tr><th>3</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 9</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="4">2</th> 
 +<th>0</th><td> 7</td><td> 8</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 7</td><td> 7</td><td>10</td><td>12</td><td> 7</td><td> 8</td><td> 8</td><td>10</td><td>11</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>12</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 9</td><td>10</td><td>12</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td>11</td><td>10</td><td>12</td><td>12</td><td>11</td><td>10</td></tr> 
 +      <tr><th>3</th><td>11</td><td>10</td><td> 9</td><td>12</td><td>10</td><td> 9</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>12</td><td>12</td><td>12</td><td>12</td></tr> 
 +    <tbody><tr><th rowspan="4">3</th> 
 +<th>0</th><td>10</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td><td>12</td><td> 9</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 9</td><td>12</td><td>12</td><td> 8</td><td> 9</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td><td>12</td></tr> 
 +      <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>12</td><td> 8</td><td>10</td><td>10</td><td>12</td><td>12</td><td> 9</td><td>12</td><td>10</td><td>12</td><td>10</td><td>12</td><td>12</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td><td>12</td><td>10</td><td>12</td><td>12</td><td>12</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 3E === === Tree 3E ===
 (used for A/4) (used for A/4)
Line 240: Line 707:
 (used for A/6) (used for A/6)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="4">0</th> 
 +<th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 9</td><td> 5</td><td> 5</td><td> 7</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 9</td><td> 7</td><td>11</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> 
 +      <tr><th>3</th><td> 9</td><td> 9</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="4">1</th> 
 +<th>0</th><td> 5</td><td> 5</td><td> 8</td><td>11</td><td> 6</td><td> 6</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td>10</td><td> 9</td><td>11</td><td> 9</td><td>10</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 6</td><td> 5</td><td> 7</td><td>10</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>11</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 8</td><td>10</td><td>10</td></tr> 
 +      <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 8</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>11</td></tr> 
 +    <tbody><tr><th rowspan="4">2</th> 
 +<th>0</th><td> 7</td><td> 7</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 8</td><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>11</td></tr> 
 +      <tr><th>2</th><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>10</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="4">3</th> 
 +<th>0</th><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>11</td><td>11</td></tr> 
 +      <tr><th>2</th><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> 
 +      <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 3H === === Tree 3H ===
 (used for A/7) (used for A/7)
Line 247: Line 745:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
-    <tr><th>-3</th><td>10</td><td>9</td><td>9</td><td>8</td><td>7</td><td>8</td><td>10</td></tr> +    <tr><th>-3</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td></tr> 
-    <tr><th>-2</th><td>9</td><td>9</td><td>7</td><td>6</td><td>6</td><td>7</td><td>8</td></tr> +    <tr><th>-2</th><td> 9</td><td> 9</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>8</td><td>7</td><td>5</td><td>4</td><td>4</td><td>6</td><td>8</td></tr> +    <tr><th>-1</th><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 4</td><td> 6</td><td> 8</td></tr> 
-    <tr><th>0</th><td>8</td><td>6</td><td>4</td><td>2</td><td>3</td><td>6</td><td>8</td></tr> +    <tr><th>0</th><td> 8</td><td> 6</td><td> 4</td><td> 2</td><td> 3</td><td> 6</td><td> 8</td></tr> 
-    <tr><th>1</th><td>8</td><td>6</td><td>4</td><td>4</td><td>5</td><td>7</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 6</td><td> 4</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>2</th><td>8</td><td>7</td><td>6</td><td>6</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>3</th><td>9</td><td>9</td><td>8</td><td>8</td><td>9</td><td>10</td><td>10</td></tr>+    <tr><th>3</th><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 262: Line 760:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
-    <tr><th>-3</th><td>9</td><td>9</td><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td></tr> +    <tr><th>-3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>-2</th><td>9</td><td>9</td><td>8</td><td>7</td><td>7</td><td>9</td><td>9</td></tr> +    <tr><th>-2</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>8</td><td>7</td><td>6</td><td>4</td><td>6</td><td>7</td><td>8</td></tr> +    <tr><th>-1</th><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>0</th><td>7</td><td>6</td><td>4</td><td>1</td><td>4</td><td>7</td><td>7</td></tr> +    <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 7</td></tr> 
-    <tr><th>1</th><td>8</td><td>7</td><td>6</td><td>4</td><td>6</td><td>8</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>2</th><td>9</td><td>8</td><td>7</td><td>7</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>9</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>9</td></tr>+    <tr><th>3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 274: Line 772:
 (used for B/3) (used for B/3)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
 +<html><table class="x" rules="groups" frame="void"> 
 +  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="4">0</th> 
 +<th>0</th><td> 2</td><td> 5</td><td> 8</td><td>10</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
 +      <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td>10</td><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="4">1</th> 
 +<th>0</th><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="4">2</th> 
 +<th>0</th><td> 8</td><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="4">3</th> 
 +<th>0</th><td> 9</td><td>10</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td>12</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>3</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +  </tbody></table> 
 +</html>
 === Tree 3K === === Tree 3K ===
 (used for B/4) (used for B/4)
Line 281: Line 810:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>     <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
-    <tr><th>-3</th><td>9</td><td>8</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>-3</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>-2</th><td>8</td><td>8</td><td>7</td><td>6</td><td>6</td><td>8</td><td>8</td></tr> +    <tr><th>-2</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>7</td><td>6</td><td>5</td><td>3</td><td>5</td><td>6</td><td>7</td></tr> +    <tr><th>-1</th><td> 7</td><td> 6</td><td> 5</td><td> 3</td><td> 5</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>0</th><td>7</td><td>6</td><td>4</td><td>2</td><td>4</td><td>6</td><td>7</td></tr> +    <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 7</td></tr> 
-    <tr><th>1</th><td>7</td><td>6</td><td>5</td><td>4</td><td>5</td><td>7</td><td>7</td></tr> +    <tr><th>1</th><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td></tr> 
-    <tr><th>2</th><td>8</td><td>8</td><td>6</td><td>6</td><td>7</td><td>8</td><td>8</td></tr> +    <tr><th>2</th><td> 8</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>3</th><td>9</td><td>8</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td></tr>+    <tr><th>3</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 309: Line 838:
 (used for B/7) (used for B/7)
 (absolute values in followed by sign bits if nonzero) (absolute values in followed by sign bits if nonzero)
- +<html><table class="x" rules="groups" frame="void"> 
-==== Trees for Quantizer 4 ====+  <colgroup span=2 style="width:1.3em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <colgroup span=4 style="width:2em"> 
 +  <thead> 
 +    <tr class="c"><td colspan="2" rowspan="2"></td> 
 +           <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr> 
 +       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead> 
 +    <tbody><tr><th rowspan="4">0</th> 
 +<th>0</th><td> 1</td><td> 5</td><td> 9</td><td> 9</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 8</td><td>10</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>2</th><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 
 +    <tbody><tr><th rowspan="4">1</th> 
 +<th>0</th><td> 6</td><td> 7</td><td>10</td><td>11</td><td> 7</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 6</td><td> 7</td><td> 9</td><td>10</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>3</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="4">2</th> 
 +<th>0</th><td> 9</td><td> 9</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tbody><tr><th rowspan="4">3</th> 
 +<th>0</th><td> 8</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
 +      <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +      <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +  </tbody></table> 
 +</html> 
 +==== Trees for Precision 4 ====
 (i.e. symbol set -5..+5) (i.e. symbol set -5..+5)
 === Tree 4A === === Tree 4A ===
Line 325: Line 885:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>11</td><td>10</td><td>9</td><td>8</td><td>8</td><td>7</td><td>8</td><td>9</td><td>9</td><td>10</td><td>11</td></tr> +    <tr><th>-5</th><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>11</td></tr> 
-    <tr><th>-4</th><td>9</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>-4</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>-3</th><td>9</td><td>10</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>-3</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>-2</th><td>9</td><td>10</td><td>9</td><td>8</td><td>7</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>8</td></tr> +    <tr><th>-2</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>8</td><td>9</td><td>8</td><td>7</td><td>5</td><td>4</td><td>5</td><td>7</td><td>8</td><td>9</td><td>8</td></tr> +    <tr><th>-1</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>0</th><td>7</td><td>8</td><td>7</td><td>6</td><td>4</td><td>2</td><td>4</td><td>6</td><td>7</td><td>8</td><td>7</td></tr> +    <tr><th>0</th><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td></tr> 
-    <tr><th>1</th><td>8</td><td>8</td><td>8</td><td>7</td><td>5</td><td>4</td><td>6</td><td>7</td><td>8</td><td>9</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>2</th><td>9</td><td>10</td><td>9</td><td>8</td><td>7</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>8</td></tr> +    <tr><th>2</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>3</th><td>9</td><td>10</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>9</td></tr> +    <tr><th>3</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr> 
-    <tr><th>4</th><td>10</td><td>11</td><td>10</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>4</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>5</th><td>11</td><td>10</td><td>9</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td></tr>+    <tr><th>5</th><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
   </tbody></table>   </tbody></table>
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Line 360: Line 920:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>10</td></tr> +    <tr><th>-5</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> 
-    <tr><th>-4</th><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>-4</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>-3</th><td>9</td><td>9</td><td>9</td><td>8</td><td>7</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td><td>8</td></tr> +    <tr><th>-3</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>-2</th><td>8</td><td>9</td><td>8</td><td>7</td><td>6</td><td>6</td><td>6</td><td>7</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>-2</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>8</td><td>8</td><td>7</td><td>6</td><td>5</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>8</td></tr> +    <tr><th>-1</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>0</th><td>8</td><td>8</td><td>7</td><td>6</td><td>4</td><td>4</td><td>4</td><td>6</td><td>7</td><td>8</td><td>7</td></tr> +    <tr><th>0</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td></tr> 
-    <tr><th>1</th><td>8</td><td>8</td><td>7</td><td>6</td><td>5</td><td>4</td><td>5</td><td>6</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>2</th><td>8</td><td>8</td><td>8</td><td>7</td><td>6</td><td>6</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>8</td><td>9</td><td>8</td><td>8</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>3</th><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>4</th><td>9</td><td>10</td><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>4</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>5</th><td>10</td><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td></tr>+    <tr><th>5</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
   </tbody></table>   </tbody></table>
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Line 379: Line 939:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>9</td><td>9</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td><td>8</td><td>8</td></tr> +    <tr><th>-5</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-4</th><td>9</td><td>7</td><td>9</td><td>9</td><td>9</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>-4</th><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>-3</th><td>8</td><td>9</td><td>8</td><td>9</td><td>7</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>-3</th><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>-2</th><td>9</td><td>9</td><td>9</td><td>8</td><td>6</td><td>6</td><td>7</td><td>6</td><td>7</td><td>9</td><td>7</td></tr> +    <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td><td> 7</td></tr> 
-    <tr><th>-1</th><td>8</td><td>8</td><td>8</td><td>7</td><td>5</td><td>4</td><td>4</td><td>5</td><td>6</td><td>9</td><td>9</td></tr> +    <tr><th>-1</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>0</th><td>9</td><td>8</td><td>7</td><td>5</td><td>5</td><td>4</td><td>5</td><td>6</td><td>7</td><td>7</td><td>9</td></tr> +    <tr><th>0</th><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 9</td></tr> 
-    <tr><th>1</th><td>9</td><td>7</td><td>7</td><td>6</td><td>5</td><td>4</td><td>5</td><td>6</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>1</th><td> 9</td><td> 7</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>2</th><td>8</td><td>7</td><td>8</td><td>9</td><td>6</td><td>6</td><td>6</td><td>7</td><td>9</td><td>9</td><td>8</td></tr> +    <tr><th>2</th><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>3</th><td>9</td><td>8</td><td>8</td><td>7</td><td>6</td><td>6</td><td>9</td><td>9</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>3</th><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>4</th><td>9</td><td>9</td><td>9</td><td>9</td><td>9</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>4</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>5</th><td>9</td><td>9</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td><td>8</td><td>9</td></tr>+    <tr><th>5</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td></tr>
   </tbody></table>   </tbody></table>
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Line 398: Line 958:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>7</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>-5</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-4</th><td>8</td><td>8</td><td>8</td><td>8</td><td>7</td><td>7</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>-4</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-3</th><td>7</td><td>8</td><td>7</td><td>8</td><td>7</td><td>8</td><td>7</td><td>7</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>-3</th><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>-2</th><td>8</td><td>8</td><td>7</td><td>6</td><td>7</td><td>5</td><td>6</td><td>7</td><td>8</td><td>7</td><td>8</td></tr> +    <tr><th>-2</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>-1</th><td>9</td><td>8</td><td>6</td><td>5</td><td>6</td><td>7</td><td>7</td><td>7</td><td>7</td><td>8</td><td>9</td></tr> +    <tr><th>-1</th><td> 9</td><td> 8</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>0</th><td>8</td><td>7</td><td>7</td><td>5</td><td>5</td><td>4</td><td>5</td><td>5</td><td>6</td><td>7</td><td>8</td></tr> +    <tr><th>0</th><td> 8</td><td> 7</td><td> 7</td><td> 5</td><td> 5</td><td> 4</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>1</th><td>8</td><td>8</td><td>7</td><td>7</td><td>6</td><td>6</td><td>6</td><td>6</td><td>6</td><td>8</td><td>8</td></tr> +    <tr><th>1</th><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>2</th><td>8</td><td>8</td><td>7</td><td>7</td><td>6</td><td>5</td><td>6</td><td>7</td><td>7</td><td>7</td><td>8</td></tr> +    <tr><th>2</th><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 
-    <tr><th>3</th><td>7</td><td>7</td><td>8</td><td>7</td><td>7</td><td>7</td><td>7</td><td>7</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>3</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>4</th><td>8</td><td>8</td><td>8</td><td>7</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td></tr> +    <tr><th>4</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr> 
-    <tr><th>5</th><td>8</td><td>8</td><td>8</td><td>8</td><td>7</td><td>7</td><td>8</td><td>8</td><td>8</td><td>8</td><td>8</td></tr>+    <tr><th>5</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 417: Line 977:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>-5</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td></tr> +    <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td></tr> 
-    <tr><th>-3</th><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>11</td><td>10</td></tr> +    <tr><th>-3</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td></tr> 
-    <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>-1</th><td>10</td><td>10</td><td>9</td><td>8</td><td>6</td><td>4</td><td>6</td><td>8</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>-1</th><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>0</th><td>9</td><td>9</td><td>9</td><td>7</td><td>4</td><td>1</td><td>4</td><td>7</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>1</th><td>9</td><td>10</td><td>9</td><td>8</td><td>6</td><td>4</td><td>6</td><td>8</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>1</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>2</th><td>10</td><td>10</td><td>9</td><td>8</td><td>7</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>2</th><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>4</th><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td></tr> +    <tr><th>4</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td></tr> 
-    <tr><th>5</th><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>+    <tr><th>5</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 436: Line 996:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>-5</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>-4</th><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>-4</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>-3</th><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>-3</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>-2</th><td>9</td><td>9</td><td>9</td><td>8</td><td>7</td><td>6</td><td>7</td><td>7</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>9</td><td>9</td><td>8</td><td>7</td><td>5</td><td>4</td><td>5</td><td>7</td><td>8</td><td>9</td><td>8</td></tr> +    <tr><th>-1</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>0</th><td>8</td><td>8</td><td>8</td><td>6</td><td>4</td><td>2</td><td>4</td><td>6</td><td>8</td><td>9</td><td>8</td></tr> +    <tr><th>0</th><td> 8</td><td> 8</td><td> 8</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>1</th><td>8</td><td>9</td><td>8</td><td>7</td><td>5</td><td>4</td><td>5</td><td>7</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>1</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>2</th><td>9</td><td>9</td><td>8</td><td>7</td><td>6</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>9</td><td>9</td><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>3</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>4</th><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>11</td><td>10</td></tr> +    <tr><th>4</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td></tr> 
-    <tr><th>5</th><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td></tr>+    <tr><th>5</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 455: Line 1015:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>     <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
-    <tr><th>-5</th><td>12</td><td>11</td><td>10</td><td>9</td><td>9</td><td>8</td><td>9</td><td>10</td><td>10</td><td>11</td><td>12</td></tr> +    <tr><th>-5</th><td>12</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td></tr> 
-    <tr><th>-4</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>-4</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>-3</th><td>10</td><td>11</td><td>11</td><td>10</td><td>9</td><td>8</td><td>9</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>-3</th><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>-2</th><td>10</td><td>11</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>9</td></tr> +    <tr><th>-2</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>9</td><td>10</td><td>9</td><td>8</td><td>6</td><td>4</td><td>6</td><td>8</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>-1</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>0</th><td>8</td><td>9</td><td>8</td><td>7</td><td>4</td><td>1</td><td>4</td><td>7</td><td>8</td><td>9</td><td>8</td></tr> +    <tr><th>0</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> 
-    <tr><th>1</th><td>9</td><td>9</td><td>9</td><td>8</td><td>6</td><td>4</td><td>7</td><td>8</td><td>9</td><td>10</td><td>9</td></tr> +    <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> 
-    <tr><th>2</th><td>10</td><td>11</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>9</td></tr> +    <tr><th>2</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr> 
-    <tr><th>3</th><td>10</td><td>11</td><td>11</td><td>10</td><td>9</td><td>8</td><td>9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> +    <tr><th>3</th><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> 
-    <tr><th>4</th><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>4</th><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>5</th><td>12</td><td>11</td><td>10</td><td>10</td><td>9</td><td>8</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>+    <tr><th>5</th><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 489: Line 1049:
   * 5: 5 bits   * 5: 5 bits
  
-==== Trees for Quantizer 5 ====+==== Trees for Precision 5 ====
 (i.e. symbol set -7..+7) (i.e. symbol set -7..+7)
 === Tree 5A === === Tree 5A ===
Line 497: Line 1057:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
-    <tr><th>-7</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>-7</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>-6</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>-6</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>-5</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> +    <tr><th>-5</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> 
-    <tr><th>-4</th><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>9</td><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>-4</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>-3</th><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>-3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>-2</th><td>10</td><td>9</td><td>10</td><td>9</td><td>8</td><td>7</td><td>7</td><td>6</td><td>6</td><td>7</td><td>8</td><td>9</td><td>10</td><td>9</td><td>9</td></tr> +    <tr><th>-2</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>9</td><td>9</td><td>9</td><td>9</td><td>8</td><td>7</td><td>5</td><td>5</td><td>5</td><td>6</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>0</th><td>9</td><td>9</td><td>9</td><td>8</td><td>7</td><td>6</td><td>4</td><td>3</td><td>4</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>1</th><td>9</td><td>9</td><td>9</td><td>8</td><td>8</td><td>6</td><td>5</td><td>4</td><td>5</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>2</th><td>9</td><td>9</td><td>10</td><td>9</td><td>8</td><td>7</td><td>6</td><td>6</td><td>7</td><td>7</td><td>8</td><td>9</td><td>10</td><td>9</td><td>10</td></tr> +    <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
-    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>4</th><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> +    <tr><th>4</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> 
-    <tr><th>5</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>5</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>6</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>6</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td></tr>+    <tr><th>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td></tr>
   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
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-    <tr><th>-6</th><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>-6</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> 
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-    <tr><th>-1</th><td>9</td><td>9</td><td>9</td><td>8</td><td>7</td><td>6</td><td>5</td><td>5</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
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-    <tr><th>1</th><td>9</td><td>9</td><td>9</td><td>8</td><td>7</td><td>6</td><td>5</td><td>5</td><td>5</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
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-    <tr><th>-6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> +    <tr><th>-6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
-    <tr><th>-7</th><td>12</td><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>10</td><td>9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr> +    <tr><th>-7</th><td>12</td><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr> 
-    <tr><th>-6</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>9</td><td>8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>+    <tr><th>-6</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
     <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td><td>10</td><td>11</td></tr>     <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td><td>10</td><td>11</td></tr>
-    <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>10</td><td>9</td><td>9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> +    <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> 
-    <tr><th>-3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>9</td><td>9</td><td>9</td><td>8</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> +    <tr><th>-3</th><td>10</td><td>10</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> 
-    <tr><th>-2</th><td>9</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td></tr> +    <tr><th>-2</th><td> 9</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td></tr> 
-    <tr><th>-1</th><td>9</td><td>12</td><td>11</td><td>11</td><td>10</td><td>8</td><td>7</td><td>5</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>10</td><td>12</td></tr> +    <tr><th>-1</th><td> 9</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>12</td></tr> 
-    <tr><th>0</th><td>9</td><td>9</td><td>10</td><td>9</td><td>8</td><td>7</td><td>4</td><td>1</td><td>5</td><td>7</td><td>9</td><td>10</td><td>10</td><td>10</td><td>9</td></tr> +    <tr><th>0</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 5</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> 
-    <tr><th>1</th><td>9</td><td>10</td><td>10</td><td>9</td><td>9</td><td>8</td><td>6</td><td>4</td><td>6</td><td>8</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td></tr> +    <tr><th>1</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td></tr> 
-    <tr><th>2</th><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>10</td><td>9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> +    <tr><th>2</th><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> 
-    <tr><th>3</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>9</td><td>10</td></tr> +    <tr><th>3</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td> 9</td><td>10</td></tr> 
-    <tr><th>4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>11</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td></tr>+    <tr><th>4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td></tr>
     <tr><th>5</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>12</td><td>10</td><td>11</td></tr>     <tr><th>5</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>12</td><td>10</td><td>11</td></tr>
-    <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> +    <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> 
-    <tr><th>7</th><td>12</td><td>10</td><td>12</td><td>12</td><td>10</td><td>9</td><td>9</td><td>8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td></tr>+    <tr><th>7</th><td>12</td><td>10</td><td>12</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 692: Line 1252:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>     <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
-    <tr><th>-7</th><td>12</td><td>12</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td></tr>+    <tr><th>-7</th><td>12</td><td>12</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td></tr>
     <tr><th>-6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>     <tr><th>-6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
     <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td></tr>     <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td></tr>
-    <tr><th>-4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>9</td><td>10</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> +    <tr><th>-4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> 
-    <tr><th>-3</th><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>9</td><td>8</td><td>9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>11</td></tr> +    <tr><th>-3</th><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>11</td></tr> 
-    <tr><th>-2</th><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> +    <tr><th>-2</th><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> 
-    <tr><th>-1</th><td>10</td><td>10</td><td>12</td><td>10</td><td>9</td><td>8</td><td>7</td><td>3</td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> +    <tr><th>-1</th><td>10</td><td>10</td><td>12</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> 
-    <tr><th>0</th><td>9</td><td>9</td><td>10</td><td>9</td><td>8</td><td>7</td><td>3</td><td>2</td><td>3</td><td>7</td><td>9</td><td>9</td><td>10</td><td>9</td><td>9</td></tr> +    <tr><th>0</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 2</td><td> 3</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>1</th><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>8</td><td>7</td><td>3</td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> +    <tr><th>1</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> 
-    <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>9</td><td>8</td><td>7</td><td>8</td><td>9</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> +    <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> 
-    <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>8</td><td>9</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> +    <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> 
-    <tr><th>4</th><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td></tr>+    <tr><th>4</th><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td></tr>
     <tr><th>5</th><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>     <tr><th>5</th><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
-    <tr><th>6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td></tr> +    <tr><th>6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td></tr> 
-    <tr><th>7</th><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td></tr>+    <tr><th>7</th><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
-==== Trees for Quantizer 6 ====+==== Trees for Precision 6 ====
 (i.e. symbol set -15..+15) (i.e. symbol set -15..+15)
 === Tree 6A === === Tree 6A ===
Line 730: Line 1290:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
-    <tr><th>0</th><td>2</td><td>4</td><td>6</td><td>7</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>0</th><td> 2</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>1</th><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>8</td><td>8</td><td>9</td></tr> +    <tr><th>1</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>2</th><td>6</td><td>5</td><td>6</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>7</td><td>6</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>3</th><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> 
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-    <tr><th>5</th><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>5</th><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td> 9</td></tr> 
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     <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>     <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
     <tr><th>10</th><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>     <tr><th>10</th><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
     <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>     <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
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-    <tr><th>4</th><td>7</td><td>7</td><td>7</td><td>7</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>4</th><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>5</th><td>8</td><td>7</td><td>7</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>10</td></tr> +    <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
-    <tr><th>6</th><td>9</td><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>9</td><td>10</td></tr> +    <tr><th>6</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
-    <tr><th>7</th><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>9</td><td>10</td></tr> +    <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
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-    <tr><th>9</th><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>10</th><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>+    <tr><th>10</th><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
     <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>     <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
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-    <tr><th>4</th><td>7</td><td>6</td><td>7</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>4</th><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>5</th><td>8</td><td>7</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>5</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>6</th><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>6</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>7</th><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>8</th><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>8</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>9</th><td>10</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>10</th><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> +    <tr><th>10</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
-    <tr><th>11</th><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>11</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>12</th><td>10</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td><td>11</td></tr> 
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-    <tr><th>15</th><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr>+    <tr><th>15</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr>
   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
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-    <tr><th>7</th><td>8</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>7</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>8</th><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>8</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
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   </tbody></table>   </tbody></table>
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   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
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-    <tr><th>2</th><td>5</td><td>5</td><td>6</td><td>7</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>9</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>6</td><td>6</td><td>7</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>8</td><td>9</td><td>9</td></tr> +    <tr><th>3</th><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>4</th><td>7</td><td>7</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>4</th><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>5</th><td>8</td><td>7</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>5</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>6</th><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>9</td><td>9</td><td>10</td></tr> +    <tr><th>6</th><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
-    <tr><th>7</th><td>9</td><td>8</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>9</td><td>10</td><td>10</td></tr> +    <tr><th>7</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr> 
-    <tr><th>8</th><td>9</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>8</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>9</th><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>10</th><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> +    <tr><th>10</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
-    <tr><th>11</th><td>10</td><td>9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> +    <tr><th>11</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
-    <tr><th>12</th><td>10</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>13</th><td>9</td><td>8</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>14</th><td>9</td><td>8</td><td>8</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> +    <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 
-    <tr><th>15</th><td>9</td><td>9</td><td>9</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td></tr>+    <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
Line 962: Line 1522:
   <thead><tr><td></td>   <thead><tr><td></td>
     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>     <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
-    <tr><th>0</th><td>1</td><td>4</td><td>7</td><td>8</td><td>9</td><td>9</td><td>9</td><td>11</td><td>9</td><td>12</td><td>12</td><td>12</td><td>10</td><td>9</td><td>9</td><td>10</td></tr> +    <tr><th>0</th><td> 1</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td>12</td><td>12</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> 
-    <tr><th>1</th><td>4</td><td>4</td><td>6</td><td>8</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>8</td><td>8</td><td>9</td></tr> +    <tr><th>1</th><td> 4</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td> 8</td><td> 8</td><td> 9</td></tr> 
-    <tr><th>2</th><td>6</td><td>6</td><td>7</td><td>8</td><td>9</td><td>8</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>9</td><td>9</td><td>9</td></tr> +    <tr><th>2</th><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> 
-    <tr><th>3</th><td>8</td><td>7</td><td>8</td><td>9</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>9</td><td>9</td><td>9</td><td>10</td></tr> +    <tr><th>3</th><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
-    <tr><th>4</th><td>9</td><td>9</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td><td>9</td><td>11</td><td>9</td></tr> +    <tr><th>4</th><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td><td> 9</td><td>11</td><td> 9</td></tr> 
-    <tr><th>5</th><td>10</td><td>10</td><td>9</td><td>9</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> +    <tr><th>5</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> 
-    <tr><th>6</th><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> +    <tr><th>6</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 
-    <tr><th>7</th><td>10</td><td>9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>9</td></tr> +    <tr><th>7</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td> 9</td></tr> 
-    <tr><th>8</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>9</td><td>10</td><td>10</td></tr>+    <tr><th>8</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td> 9</td><td>10</td><td>10</td></tr>
     <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td></tr>     <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td></tr>
     <tr><th>10</th><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>     <tr><th>10</th><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
     <tr><th>11</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td></tr>     <tr><th>11</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td></tr>
-    <tr><th>12</th><td>11</td><td>9</td><td>10</td><td>9</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td></tr> +    <tr><th>12</th><td>11</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td></tr> 
-    <tr><th>13</th><td>9</td><td>9</td><td>8</td><td>9</td><td>10</td><td>9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td></tr> +    <tr><th>13</th><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td></tr> 
-    <tr><th>14</th><td>9</td><td>9</td><td>9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> +    <tr><th>14</th><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> 
-    <tr><th>15</th><td>10</td><td>10</td><td>9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>+    <tr><th>15</th><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
   </tbody></table>   </tbody></table>
 </html> </html>
-==== Trees for Quantizer 7 ====+==== Trees for Precision 7 ====
 (i.e. symbol set -31..+31) (i.e. symbol set -31..+31)
 === Tree 7A === === Tree 7A ===
Line 1266: Line 1826:
   * 28..30: 10 bits   * 28..30: 10 bits
   * 31: 11 bits   * 31: 11 bits
 +
 +===== Tree Sets =====
 +
 +This table shows the mapping of tree set IDs, tree IDs and quantization precisions to the code tables defined above. If the table says //n x Tree XX// it means that n symbols of that tree (which might groups of 1, 2 or 4 quantized coefficients) are clustered together. Each cluster is preceeded by an "data present" bit. If that bit is zero, all coefficients of the whole cluster are zero, and no codes for the cluster are stored. If that bit is one that at least one non-zero entry is present and the codes for this cluster follow as in non-clustered mode.
 +
 +The tree choice can be limited to a restricted tree set. The IDs inside the restricted tree set are in the range 0..3 instead of 0..7, and printed as R0..R3 in the table.
 +
 +==== Tree Set A====
 +|Quant\ID^ 0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ ^ R0^ R1^ R2^ R3^
 +^ 1| Tree 1A|  4 x Tree 1B| Tree 1C| Tree 1D| Tree 1E| Tree 1F|  2 x Tree 1G| Tree 1H| | Tree 1A| Tree 1F| Tree 1E| 4x Tree 1B|
 +^ 2| Tree 2A| Tree 2B| Tree 2C| Tree 2D| Tree 2E| Tree 2F| Tree 2G|  2 x Tree 2H| | Tree 2A| Tree 2B| Tree 2C| Tree 2D|
 +^ 3| Tree 3A| Tree 3B| Tree 3C| Tree 3D| Tree 3E| Tree 3F| Tree 3G| Tree 3H| | Tree 3D| Tree 3A| Tree 3E| Tree 3C|
 +^ 4| Tree 4A| Tree 4B| Tree 4C| Tree 4D| Tree 4E| Tree 4F| Tree 4G| Tree 4H| | Tree 4E| Tree 4A| Tree 4B| Tree 4C|
 +^ 5| Tree 5A| Tree 5B| Tree 5C| Tree 5D| Tree 5E| Tree 5F| Tree 5G| Tree 5H| | Tree 5B| Tree 5A| Tree 5E| Tree 5D|
 +^ 6| Tree 6A| Tree 6B| Tree 6C| Tree 6D| Tree 6E| Tree 6F| Tree 6G|  2 x Tree 6H| | Tree 6D| Tree 6A| Tree 6C| Tree 6B|
 +^ 7| Tree 7A| Tree 7B| Tree 7C| Tree 7D| Tree 7E| Tree 7F| Tree 7G|  4 x Tree 7A| | Tree 7A| Tree 7D| Tree 7B| Tree 7C|
 +
 +==== Tree Set B====
 +|Quant\ID^ 0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ ^ R0^ R1^ R2^ R3^
 +^ 1|  4 x Tree 1I| Tree 1C| 4 x Tree 1E|     Tree 1F|     Tree 1J| 2 x Tree 1G|     Tree 1E|     Tree 1K| |     Tree 1J| 4 x Tree 1I|     Tree 1C| 4 x Tree 1E|
 +^ 2|      Tree 2I| Tree 2J| 4 x Tree 2D|     Tree 2K| 4 x Tree 2L|     Tree 2M|     Tree 2N| 4 x Tree 2K| |     Tree 2I|     Tree 2K| 4 x Tree 2D|     Tree 2J|
 +^ 3|  4 x Tree 3I| Tree 3B|     Tree 3A|     Tree 3J|     Tree 3K| 4 x Tree 3L|     Tree 3M| 4 x Tree 3N| | 4 x Tree 3I|     Tree 3B|     Tree 3A|     Tree 3J|
 +^ 4|      Tree 4I| Tree 4J|     Tree 4E| 2 x Tree 4I| 4 x Tree 4J|     Tree 4C|     Tree 4K|     Tree 4L| |     Tree 4I|     Tree 4J|     Tree 4E| 4 x Tree 4J|
 +^ 5|      Tree 5I| Tree 5B| 2 x Tree 5I|     Tree 5J|     Tree 5E|     Tree 5F| 4 x Tree 5K|     Tree 5L| |     Tree 5I|     Tree 5B| 2 x Tree 5I|     Tree 5J|
 +^ 6|      Tree 6A| Tree 6I| 2 x Tree 6J|     Tree 6J|     Tree 6B|     Tree 6K|     Tree 6L|     Tree 6G| |     Tree 6I|     Tree 6B| 2 x Tree 6J|     Tree 6A|
 +^ 7|      Tree 7H| Tree 7A| 4 x Tree 7A|     Tree 7I|     Tree 7J| 2 x Tree 7H|     Tree 7K|     Tree 7L| |     Tree 7H|     Tree 7A| 4 x Tree 7A|     Tree 7I|
 +
 +
  
atrac3p/main_trees_list.1260056000.txt.gz · Last modified: 2009/12/05 23:33 by megadiscman

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