DokuWiki

User Tools

Site Tools

Trace:
atrac3p:main_trees_list

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
atrac3p:main_trees_list [2009/11/28 00:10] – megadiscmanatrac3p:main_trees_list [2010/07/23 17:41] (current) – quantizer -> quantization precision megadiscman
Line 1: Line 1:
 +<html>
 +    <!-- I know that CSS in the body violates the specs! -->
 +    <style type="text/css"><!-- 
 +.x td {text-align:right;padding:0.2em;}
 +.x tr th {text-align:right;padding:0.2em;background-color:#aaf;}
 +tr.c th {text-align:center;}
 +    --></style>
 +</html>
 +
 ===== Main Spectral Data Encoding Trees ===== ===== Main Spectral Data Encoding Trees =====
 ==== General Intro ==== ==== 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.+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. 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 codes]]. 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.+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.
  
-==== Trees for Quantizer 1 ==== +==== Examples ==== 
-(i.e. symbol set -1,0,1)+ 
 +=== 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)
 === 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 and 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)
- +<html><table class="x" rules="groups" frame="void"> 
-|     ^  -1  ^   0  ^  +1  ^ +  <col style="width:1.3em"><colgroup span=3 style="width:2em"> 
-^ -1  |  6   |   4  |   6  | +  <thead><tr><td></td> 
-^  0  |  3   |   1  |   3  | +    <th>-1</th><th>0</th><th>1</th>  </tr></thead><tbody> 
-^ +1  |  6   |   3  |   6  | +    <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>1</th><td> 6</td><td> 3</td><td> 6</td></tr> 
 +  </tbody></table> 
 +</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)
- +(absolute values in followed by sign bits if nonzero) 
-(absolute values followed by sign bits for nonzero) +<html><table class="x" rules="groups" frame="void"> 
-|     ^   0  ^   1  ^ +  <col style="width:1.3em"><colgroup span=2 style="width:2em"> 
-^  0  |   1  |   3  | +  <thead><tr><td></td> 
-^  1  |   2  |   3  | +    <th>0</th><th>1</th>  </tr></thead><tbody> 
- +    <tr><th>0</th><td> 1</td><td> 3</td></tr> 
 +    <tr><th>1</th><td> 2</td><td> 3</td></tr> 
 +  </tbody></table> 
 +</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 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">-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) 
 +=== Tree 2A === 
 +(used for A/0) 
 +(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 === 
 +(used for A/1) 
 +(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 === 
 +(used for A/2) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=5 style="width:2em"> 
 +  <thead><tr><td></td> 
 +    <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>-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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 2D === 
 +(used for A/3, B/2) 
 +(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 === 
 +(used for A/4) 
 +(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 === 
 +(used for A/5) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=5 style="width:2em"> 
 +  <thead><tr><td></td> 
 +    <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>-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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 2G === 
 +(used for A/6) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=5 style="width:2em"> 
 +  <thead><tr><td></td> 
 +    <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>-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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 2H === 
 +(used for A/7) 
 +(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 === 
 +(used for B/0) 
 +(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 === 
 +(used for B/1) 
 +(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 === 
 +(used for B/3, B/7) 
 +(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 === 
 +(used for B/4) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=5 style="width:2em"> 
 +  <thead><tr><td></td> 
 +    <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>-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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 2M === 
 +(used for B/5) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=5 style="width:2em"> 
 +  <thead><tr><td></td> 
 +    <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>-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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 2N === 
 +(used for B/6) 
 +(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> 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 ===
 (used for A/0, B/2) (used for A/0, B/2)
-|    ^ -3 ^ -2 ^ -1 ^  0 ^ +1 ^ +2 ^ +3 ^ +<html><table class="x" rules="groups" frame="void"> 
-^ -3 |  9 |  8 |  7 |  6 |  7 |  7 |  8 | +  <col style="width:1.3em"><colgroup span=7 style="width:2em"> 
-^ -2 |  8 |  7 |  6 |  6 |  6 |  7 |  7 | +  <thead><tr><td></td> 
-^ -1 |  7 |  6 |  4 |  4 |  4 |  6 |  7 | +    <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody> 
-^  0 |  7 |  6 |  4 |  3 |  4 |  6 |  7 | +    <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> 
-^ +1 |  7 |  6 |  4 |  4 |  4 |  6 |  7 | +    <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> 
-^ +2 |  7 |  7 |  6 |  6 |  7 |  8 |  8 | +    <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> 
-^ +3 |  8 |  7 |  7 |  7 |  7 |  8 |  9 |+    <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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 3B === 
 +(used for A/1, B/1) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=7 style="width:2em"> 
 +  <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> 
 +    <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>-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>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>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> 
 +</html> 
 +=== Tree 3C === 
 +(used for A/2) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=7 style="width:2em"> 
 +  <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> 
 +    <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>-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>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>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> 
 +</html> 
 +=== Tree 3D === 
 +(used for A/3) 
 +(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 === 
 +(used for A/4) 
 +  * -3: 4 bits 
 +  * -2: 3 bits 
 +  * -1,0: 2 bits 
 +  * 1,2: 3 bits 
 +  * 3: 4 bits 
 + 
 +=== Tree 3F === 
 +(used for A/5) 
 +  * -3: 4 bits 
 +  * -2,-1: 3 bits 
 +  * 0,1: 2 bits 
 +  * 2: 3 bits 
 +  * 3: 4 bits 
 + 
 +=== Tree 3G === 
 +(used for A/6) 
 +(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 === 
 +(used for A/7) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=7 style="width:2em"> 
 +  <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> 
 +    <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>-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>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>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> 
 +</html> 
 +=== Tree 3I === 
 +(used for B/0) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=7 style="width:2em"> 
 +  <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> 
 +    <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>-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>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>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> 
 +</html> 
 +=== Tree 3J === 
 +(used for B/3) 
 +(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 === 
 +(used for B/4) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=7 style="width:2em"> 
 +  <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> 
 +    <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>-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>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>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> 
 +</html> 
 +=== Tree 3L === 
 +(used for B/5) 
 +  * -3,-2: 5 bits 
 +  * -1: 2 bits 
 +  * 0: 1 bits 
 +  * 1: 3 bits 
 +  * 2,3: 5 bits 
 + 
 +=== Tree 3M === 
 +(used for B/6) 
 +  * -3,-2: 5 bits 
 +  * -1: 3 bits 
 +  * 0: 1 bits 
 +  * 1: 2 bits 
 +  * 2,3: 5 bits 
 + 
 +=== Tree 3N === 
 +(used for B/7) 
 +(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> 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) 
 +=== Tree 4A === 
 +(used for A/0) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 3 bits 
 +  * 1,2: 2 bits 
 +  * 3..5: 3 bits 
 + 
 +=== Tree 4B === 
 +(used for A/1) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4C === 
 +(used for A/2, B/5) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0..2: 2 bits 
 +  * 3: 3 bits 
 +  * 4,5: 4 bits 
 + 
 +=== Tree 4D === 
 +(used for A/3) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 2 bits 
 +  * 1: 1 bits 
 +  * 2: 3 bits 
 +  * 3: 4 bits 
 +  * 4,5: 5 bits 
 + 
 +=== Tree 4E === 
 +(used for A/4, B/2) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4F === 
 +(used for A/5) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4G === 
 +(used for A/6) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4H === 
 +(used for A/7) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4I === 
 +(used for B/0, B/3) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4J === 
 +(used for B/1, B/4) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=11 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>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>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>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> 
 +</html> 
 +=== Tree 4K === 
 +(used for B/6) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 2 bits 
 +  * 1: 1 bits 
 +  * 2: 3 bits 
 +  * 3,4: 5 bits 
 +  * 5: 4 bits 
 + 
 +=== Tree 4L === 
 +(used for B/7) 
 +  * -5,-4: 6 bits 
 +  * -3: 5 bits 
 +  * -2: 4 bits 
 +  * -1: 3 bits 
 +  * 0: 1 bits 
 +  * 1: 3 bits 
 +  * 2: 4 bits 
 +  * 3,4: 6 bits 
 +  * 5: 5 bits 
 + 
 +==== Trees for Precision 5 ==== 
 +(i.e. symbol set -7..+7) 
 +=== Tree 5A === 
 +(used for A/0) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>-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>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>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>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>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> 
 +</html> 
 +=== Tree 5B === 
 +(used for A/1, B/1) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <tr><th>-7</th><td>11</td><td>10</td><td>10</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><td>10</td><td>10</td><td>10</td><td>11</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> 
 +    <tr><th>-5</th><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> 9</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> 9</td><td> 9</td><td> 9</td><td> 9</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> 9</td><td> 9</td></tr> 
 +    <tr><th>-3</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><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> 9</td></tr> 
 +    <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</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> 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> 
 +    <tr><th>0</th><td> 8</td><td> 8</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> 8</td><td> 8</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> 
 +    <tr><th>2</th><td> 9</td><td> 9</td><td> 9</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> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>3</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><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> 9</td></tr> 
 +    <tr><th>4</th><td>10</td><td> 9</td><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> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
 +    <tr><th>5</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> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</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>10</td><td>10</td><td>10</td></tr> 
 +    <tr><th>7</th><td>11</td><td>10</td><td>10</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><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 5C === 
 +(used for A/2) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 3 bits 
 +  * 1: 2 bits 
 +  * 2..5: 3 bits 
 +  * 6,7: 4 bits 
 + 
 +=== Tree 5D === 
 +(used for A/3) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <tr><th>-7</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 
 +    <tr><th>-6</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>10</td><td>10</td></tr> 
 +    <tr><th>-5</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>10</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> 9</td><td> 9</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>10</td><td>10</td></tr> 
 +    <tr><th>-3</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
 +    <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 7</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 
 +    <tr><th>-1</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> 
 +    <tr><th>0</th><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 7</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> 7</td><td> 7</td><td> 7</td><td>10</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>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td></tr> 
 +    <tr><th>4</th><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 
 +    <tr><th>5</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</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> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> 
 +    <tr><th>7</th><td>10</td><td>10</td><td>10</td><td> 9</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> 9</td><td>10</td><td>10</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 5E === 
 +(used for A/4, B/4) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 3 bits 
 +  * 1,2: 2 bits 
 +  * 3: 3 bits 
 +  * 4..7: 4 bits 
 + 
 +=== Tree 5F === 
 +(used for A/5, B/5) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 1 bits 
 +  * 1: 2 bits 
 +  * 2: 3 bits 
 +  * 3: 5 bits 
 +  * 4,5: 6 bits 
 +  * 6,7: 5 bits 
 + 
 +=== Tree 5G === 
 +(used for A/6) 
 +  * -7: 7 bits 
 +  * -6: 6 bits 
 +  * -5: 7 bits 
 +  * -4: 6 bits 
 +  * -3: 5 bits 
 +  * -2: 4 bits 
 +  * -1..1: 2 bits 
 +  * 2,3: 5 bits 
 +  * 4: 6 bits 
 +  * 5: 7 bits 
 +  * 6: 6 bits 
 +  * 7: 7 bits 
 + 
 +=== Tree 5H === 
 +(used for A/7) 
 +  * -7: 6 bits 
 +  * -6: 5 bits 
 +  * -5: 6 bits 
 +  * -4: 5 bits 
 +  * -3: 4 bits 
 +  * -2,-1: 3 bits 
 +  * 0: 2 bits 
 +  * 1: 3 bits 
 +  * 2,3: 4 bits 
 +  * 4: 5 bits 
 +  * 5: 6 bits 
 +  * 6: 5 bits 
 +  * 7: 6 bits 
 + 
 +=== Tree 5I === 
 +(used for B/0, B/2) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <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> 8</td><td> 9</td><td> 9</td><td> 9</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> 
 +    <tr><th>-5</th><td>10</td><td>10</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>11</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>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> 
 +    <tr><th>-3</th><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</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><td>10</td><td> 9</td></tr> 
 +    <tr><th>-2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</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> 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>0</th><td> 8</td><td> 8</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> 8</td><td> 8</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> 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> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>3</th><td> 9</td><td> 9</td><td>10</td><td>10</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>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> 
 +    <tr><th>5</th><td>10</td><td>10</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>11</td><td>11</td><td>10</td><td>10</td></tr> 
 +    <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</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>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</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>11</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 5J === 
 +(used for B/3) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <tr><th>-7</th><td>12</td><td>11</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>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>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>11</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>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 
 +    <tr><th>-4</th><td>11</td><td>11</td><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>11</td><td>12</td><td>12</td><td>11</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> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</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>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</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> 9</td><td>11</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 1</td><td> 5</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>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> 
 +    <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td>11</td><td>11</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> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</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>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</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>12</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>11</td><td>11</td></tr> 
 +    <tr><th>6</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</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>11</td><td>11</td></tr> 
 +    <tr><th>7</th><td>12</td><td>11</td><td>11</td><td>11</td><td>11</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>12</td><td>12</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 5K === 
 +(used for B/6) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>-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>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>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>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>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> 
 +</html> 
 +=== Tree 5L === 
 +(used for B/7) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=15 style="width:2em"> 
 +  <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> 
 +    <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>-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>-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>-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>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>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>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>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> 
 +</html> 
 +==== Trees for Precision 6 ==== 
 +(i.e. symbol set -15..+15) 
 +=== Tree 6A === 
 +(used for A/0, B/0) 
 +(absolute values in followed by sign bits if nonzero) 
 +  * 0: 3 bits 
 +  * 1: 2 bits 
 +  * 2,3: 3 bits 
 +  * 4,5: 4 bits 
 +  * 6..9: 5 bits 
 +  * 10..12: 6 bits 
 +  * 13,14: 5 bits 
 +  * 15: 6 bits 
 + 
 +=== Tree 6B === 
 +(used for A/1, B/4) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <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>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>4</th><td> 8</td><td> 7</td><td> 7</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>11</td><td>10</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> 
 +    <tr><th>6</th><td> 9</td><td> 8</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>10</td><td> 9</td><td>10</td><td>10</td></tr> 
 +    <tr><th>7</th><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><td>11</td><td>12</td><td>12</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr> 
 +    <tr><th>8</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>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>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>12</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>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +    <tr><th>13</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> 9</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>10</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>10</td><td> 9</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>11</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 6C === 
 +(used for A/2) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <tr><th>0</th><td> 4</td><td> 5</td><td> 6</td><td> 6</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> 9</td><td> 9</td><td>10</td></tr> 
 +    <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><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> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>2</th><td> 6</td><td> 5</td><td> 5</td><td> 6</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> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>3</th><td> 6</td><td> 6</td><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> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>4</th><td> 7</td><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> 9</td><td> 9</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> 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> 9</td><td> 9</td><td>10</td></tr> 
 +    <tr><th>6</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>7</th><td> 9</td><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>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> 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>9</th><td> 9</td><td> 8</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><td>10</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> 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>11</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>11</td><td>11</td></tr> 
 +    <tr><th>12</th><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>10</td><td>10</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> 9</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> 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>11</td><td>11</td><td>11</td><td>11</td></tr> 
 +    <tr><th>15</th><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>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 6D === 
 +(used for A/3) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 7</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> 9</td><td>10</td><td>10</td></tr> 
 +    <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</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> 5</td><td> 6</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> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>3</th><td> 7</td><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> 8</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>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>8</th><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>10</td><td>11</td><td>11</td><td>10</td><td> 9</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>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>12</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>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</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> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 
 +    <tr><th>14</th><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>10</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>15</th><td>10</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>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 6E === 
 +(used for A/4) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <tr><th>0</th><td> 6</td><td> 7</td><td> 8</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>1</th><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 6</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>2</th><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td></tr> 
 +    <tr><th>3</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>4</th><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><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> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>5</th><td> 7</td><td> 7</td><td> 7</td><td> 7</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> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>6</th><td> 7</td><td> 9</td><td> 6</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>7</th><td> 8</td><td> 9</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 9</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></tr> 
 +    <tr><th>8</th><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>9</th><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</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></tr> 
 +    <tr><th>10</th><td> 8</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> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>11</th><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> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>12</th><td> 9</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> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>13</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> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>14</th><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> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>15</th><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> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 6F === 
 +(used for A/5) 
 +  * -15,-14: 7 bits 
 +  * -13: 6 bits 
 +  * -12: 7 bits 
 +  * -11..-9: 6 bits 
 +  * -8,-7: 5 bits 
 +  * -6: 6 bits 
 +  * -5: 5 bits 
 +  * -4..3: 4 bits 
 +  * 4: 3 bits 
 +  * 5..7: 5 bits 
 +  * 8,9: 6 bits 
 +  * 10..13: 7 bits 
 +  * 14: 6 bits 
 +  * 15: 7 bits 
 + 
 +=== Tree 6G === 
 +(used for A/6, B/7) 
 +  * -15: 5 bits 
 +  * -14: 10 bits 
 +  * -13,-12: 8 bits 
 +  * -11..-9: 7 bits 
 +  * -8..-5: 6 bits 
 +  * -4,-3: 5 bits 
 +  * -2: 4 bits 
 +  * -1: 3 bits 
 +  * 0: 2 bits 
 +  * 1: 3 bits 
 +  * 2: 4 bits 
 +  * 3,4: 5 bits 
 +  * 5..8: 6 bits 
 +  * 9..11: 7 bits 
 +  * 12: 8 bits 
 +  * 13: 9 bits 
 +  * 14: 10 bits 
 +  * 15: 5 bits 
 + 
 +=== Tree 6H === 
 +(used for A/7) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <tr><th>0</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> 9</td><td> 9</td></tr> 
 +    <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><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> 9</td><td> 8</td><td> 8</td><td> 8</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> 8</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> 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> 8</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>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>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>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>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>13</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>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>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></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> 
 +</html> 
 +=== Tree 6I === 
 +(used for B/1) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <tr><th>0</th><td> 4</td><td> 4</td><td> 5</td><td> 6</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></tr> 
 +    <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><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> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr> 
 +    <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 6</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> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>3</th><td> 6</td><td> 6</td><td> 6</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> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 
 +    <tr><th>4</th><td> 7</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> 9</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> 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> 8</td><td> 7</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> 9</td><td> 9</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>9</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>10</th><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>11</td><td>11</td><td>11</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> 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>11</td><td>10</td><td>10</td><td>11</td></tr> 
 +    <tr><th>12</th><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><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>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>11</td><td>11</td><td>11</td><td>11</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>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 6J === 
 +(used for B/2, B/3) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</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>1</th><td> 3</td><td> 4</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> 9</td><td> 8</td><td> 8</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>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>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>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>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>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>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> 
 +  </tbody></table> 
 +</html> 
 +=== Tree 6K === 
 +(used for B/5) 
 +  * -15..-13: 7 bits 
 +  * -12..-7: 8 bits 
 +  * -6..-4: 7 bits 
 +  * -3: 6 bits 
 +  * -2: 5 bits 
 +  * -1: 3 bits 
 +  * 0: 1 bits 
 +  * 1: 3 bits 
 +  * 2: 5 bits 
 +  * 3,4: 6 bits 
 +  * 5..7: 7 bits 
 +  * 8,9: 8 bits 
 +  * 10,11: 9 bits 
 +  * 12: 8 bits 
 +  * 13: 6 bits 
 +  * 14,15: 7 bits 
 + 
 +=== Tree 6L === 
 +(used for B/6) 
 +(absolute values in followed by sign bits if nonzero) 
 +<html><table class="x" rules="groups" frame="void"> 
 +  <col style="width:1.3em"><colgroup span=16 style="width:2em"> 
 +  <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> 
 +    <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>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>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>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>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>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>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>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> 
 +  </tbody></table> 
 +</html> 
 +==== Trees for Precision 7 ==== 
 +(i.e. symbol set -31..+31) 
 +=== Tree 7A === 
 +(used for A/0, A/7, B/1, B/2) 
 +  * -31..-29: 8 bits 
 +  * -28..-26: 7 bits 
 +  * -25: 8 bits 
 +  * -24: 10 bits 
 +  * -23..-18: 9 bits 
 +  * -17..-11: 8 bits 
 +  * -10..-7: 7 bits 
 +  * -6..-4: 6 bits 
 +  * -3: 5 bits 
 +  * -2: 4 bits 
 +  * -1: 3 bits 
 +  * 0: 2 bits 
 +  * 1: 3 bits 
 +  * 2: 4 bits 
 +  * 3: 5 bits 
 +  * 4..6: 6 bits 
 +  * 7..10: 7 bits 
 +  * 11..16: 8 bits 
 +  * 17..23: 9 bits 
 +  * 24: 10 bits 
 +  * 25: 8 bits 
 +  * 26..28: 7 bits 
 +  * 29..31: 8 bits 
 + 
 +=== Tree 7B === 
 +(used for A/1) 
 +  * -31..-29: 8 bits 
 +  * -28..-26: 7 bits 
 +  * -25: 8 bits 
 +  * -24..-22: 9 bits 
 +  * -21..-15: 8 bits 
 +  * -14..-9: 7 bits 
 +  * -8..-6: 6 bits 
 +  * -5..-3: 5 bits 
 +  * -2: 4 bits 
 +  * -1..1: 3 bits 
 +  * 2: 4 bits 
 +  * 3,4: 5 bits 
 +  * 5..8: 6 bits 
 +  * 9..14: 7 bits 
 +  * 15..21: 8 bits 
 +  * 22..24: 9 bits 
 +  * 25: 8 bits 
 +  * 26,27: 7 bits 
 +  * 28..31: 8 bits 
 + 
 +=== Tree 7C === 
 +(used for A/2) 
 +  * -31..-26: 8 bits 
 +  * -25: 7 bits 
 +  * -24..-22: 8 bits 
 +  * -21..-16: 7 bits 
 +  * -15: 6 bits 
 +  * -14,-13: 7 bits 
 +  * -12,-11: 6 bits 
 +  * -10..-8: 5 bits 
 +  * -7: 6 bits 
 +  * -6..-1: 5 bits 
 +  * 0: 4 bits 
 +  * 1: 5 bits 
 +  * 2,3: 4 bits 
 +  * 4: 6 bits 
 +  * 5..7: 5 bits 
 +  * 8: 6 bits 
 +  * 9: 5 bits 
 +  * 10..12: 6 bits 
 +  * 13: 7 bits 
 +  * 14: 6 bits 
 +  * 15..19: 7 bits 
 +  * 20,21: 8 bits 
 +  * 22,23: 7 bits 
 +  * 24: 8 bits 
 +  * 25,26: 7 bits 
 +  * 27..29: 8 bits 
 +  * 30: 7 bits 
 +  * 31: 8 bits 
 + 
 +=== Tree 7D === 
 +(used for A/3) 
 +  * -31,-30: 8 bits 
 +  * -29..-26: 7 bits 
 +  * -25..-17: 8 bits 
 +  * -16..-11: 7 bits 
 +  * -10..-7: 6 bits 
 +  * -6..-4: 5 bits 
 +  * -3..3: 4 bits 
 +  * 4..6: 5 bits 
 +  * 7..10: 6 bits 
 +  * 11..16: 7 bits 
 +  * 17..24: 8 bits 
 +  * 25..30: 7 bits 
 +  * 31: 8 bits 
 + 
 +=== Tree 7E === 
 +(used for A/4) 
 +  * -31,-30: 9 bits 
 +  * -29: 8 bits 
 +  * -28,-27: 7 bits 
 +  * -26: 8 bits 
 +  * -25: 7 bits 
 +  * -24,-23: 8 bits 
 +  * -22: 7 bits 
 +  * -21: 8 bits 
 +  * -20: 9 bits 
 +  * -19..-13: 8 bits 
 +  * -12: 7 bits 
 +  * -11: 6 bits 
 +  * -10: 5 bits 
 +  * -9: 6 bits 
 +  * -8..-3: 5 bits 
 +  * -2..2: 4 bits 
 +  * 3..6: 5 bits 
 +  * 7: 6 bits 
 +  * 8: 5 bits 
 +  * 9..14: 6 bits 
 +  * 15..21: 7 bits 
 +  * 22: 8 bits 
 +  * 23,24: 9 bits 
 +  * 25: 8 bits 
 +  * 26,27: 9 bits 
 +  * 28: 8 bits 
 +  * 29..31: 9 bits 
 + 
 +=== Tree 7F === 
 +(used for A/5) 
 +  * -31..-29: 8 bits 
 +  * -28..-26: 7 bits 
 +  * -25: 8 bits 
 +  * -24..-22: 9 bits 
 +  * -21..-16: 8 bits 
 +  * -15..-11: 7 bits 
 +  * -10..-7: 6 bits 
 +  * -6..-4: 5 bits 
 +  * -3..-1: 4 bits 
 +  * 0: 3 bits 
 +  * 1,2: 4 bits 
 +  * 3..6: 5 bits 
 +  * 7..10: 6 bits 
 +  * 11..15: 7 bits 
 +  * 16..21: 8 bits 
 +  * 22: 9 bits 
 +  * 23..25: 8 bits 
 +  * 26..28: 7 bits 
 +  * 29..31: 8 bits 
 + 
 +=== Tree 7G === 
 +(used for A/6) 
 +  * -31..-27: 8 bits 
 +  * -26: 7 bits 
 +  * -25: 8 bits 
 +  * -24..-20: 9 bits 
 +  * -19..-13: 8 bits 
 +  * -12..-8: 7 bits 
 +  * -7..-5: 6 bits 
 +  * -4,-3: 5 bits 
 +  * -2,-1: 4 bits 
 +  * 0: 2 bits 
 +  * 1: 3 bits 
 +  * 2: 4 bits 
 +  * 3,4: 5 bits 
 +  * 5..7: 6 bits 
 +  * 8..13: 7 bits 
 +  * 14..19: 8 bits 
 +  * 20..24: 9 bits 
 +  * 25: 8 bits 
 +  * 26: 7 bits 
 +  * 27..31: 8 bits 
 + 
 +=== Tree 7H === 
 +(used for B/0, B/5) 
 +  * -31..-25: 7 bits 
 +  * -24..-20: 9 bits 
 +  * -19..-14: 8 bits 
 +  * -13..-9: 7 bits 
 +  * -8..-5: 6 bits 
 +  * -4,-3: 5 bits 
 +  * -2: 4 bits 
 +  * -1..1: 3 bits 
 +  * 2: 4 bits 
 +  * 3,4: 5 bits 
 +  * 5..8: 6 bits 
 +  * 9..12: 7 bits 
 +  * 13..19: 8 bits 
 +  * 20..24: 9 bits 
 +  * 25..31: 7 bits 
 + 
 +=== Tree 7I === 
 +(used for B/3) 
 +  * -31: 9 bits 
 +  * -30,-29: 8 bits 
 +  * -28: 9 bits 
 +  * -27..-25: 8 bits 
 +  * -24: 11 bits 
 +  * -23: 10 bits 
 +  * -22: 11 bits 
 +  * -21..-16: 10 bits 
 +  * -15..-10: 9 bits 
 +  * -9..-7: 8 bits 
 +  * -6..-4: 7 bits 
 +  * -3: 6 bits 
 +  * -2: 5 bits 
 +  * -1: 3 bits 
 +  * 0: 1 bits 
 +  * 1: 3 bits 
 +  * 2: 5 bits 
 +  * 3: 6 bits 
 +  * 4..6: 7 bits 
 +  * 7..10: 8 bits 
 +  * 11: 9 bits 
 +  * 12: 10 bits 
 +  * 13..15: 9 bits 
 +  * 16..19: 10 bits 
 +  * 20: 11 bits 
 +  * 21: 10 bits 
 +  * 22..24: 11 bits 
 +  * 25..29: 8 bits 
 +  * 30,31: 9 bits 
 + 
 +=== Tree 7J === 
 +(used for B/4) 
 +  * -31..-28: 8 bits 
 +  * -27,-26: 7 bits 
 +  * -25: 8 bits 
 +  * -24..-19: 9 bits 
 +  * -18..-13: 8 bits 
 +  * -12..-8: 7 bits 
 +  * -7..-5: 6 bits 
 +  * -4,-3: 5 bits 
 +  * -2,-1: 4 bits 
 +  * 0: 2 bits 
 +  * 1: 3 bits 
 +  * 2: 4 bits 
 +  * 3,4: 5 bits 
 +  * 5..7: 6 bits 
 +  * 8..12: 7 bits 
 +  * 13..18: 8 bits 
 +  * 19..24: 9 bits 
 +  * 25: 8 bits 
 +  * 26,27: 7 bits 
 +  * 28..31: 8 bits 
 + 
 +=== Tree 7K === 
 +(used for B/6) 
 +  * -31..-25: 8 bits 
 +  * -24..-19: 9 bits 
 +  * -18..-13: 8 bits 
 +  * -12..-8: 7 bits 
 +  * -7..-5: 6 bits 
 +  * -4,-3: 5 bits 
 +  * -2: 4 bits 
 +  * -1: 3 bits 
 +  * 0: 2 bits 
 +  * 1: 3 bits 
 +  * 2,3: 5 bits 
 +  * 4..7: 6 bits 
 +  * 8..12: 7 bits 
 +  * 13..18: 8 bits 
 +  * 19..24: 9 bits 
 +  * 25..31: 8 bits 
 + 
 +=== Tree 7L === 
 +(used for B/7) 
 +  * -31,-30: 11 bits 
 +  * -29: 10 bits 
 +  * -28: 11 bits 
 +  * -27..-20: 9 bits 
 +  * -19,-18: 8 bits 
 +  * -17: 7 bits 
 +  * -16: 8 bits 
 +  * -15..-11: 7 bits 
 +  * -10..-6: 6 bits 
 +  * -5..-3: 5 bits 
 +  * -2,-1: 4 bits 
 +  * 0: 2 bits 
 +  * 1,2: 4 bits 
 +  * 3..5: 5 bits 
 +  * 6..10: 6 bits 
 +  * 11..16: 7 bits 
 +  * 17..20: 8 bits 
 +  * 21..27: 9 bits 
 +  * 28..30: 10 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.1259367038.txt.gz · Last modified: 2009/11/28 00:10 by megadiscman
Donate Powered by PHP Valid HTML5 Valid CSS Driven by DokuWiki