atrac3p:main_trees

Main Spectral Data Encoding Trees

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Main Spectral Data Encoding Trees

General Intro

The quantized values are encoded using a prefix free binary code. To make matters more complicated there are up to 16 encoding scheme per quantization precision (symbol set depends on precision, so different encoding schemes must be used for different precisions.). In many cases, the symbols are built from a group of two or four quantized values instead of just one quantized value. For groups of size two, the trees are shown as table, the first symbol choosing the row, the second value the column. For groups of size four, the tables are organized so that the first symbol chooses the row block, the second symbol the exact row, the third symbol the column block and the fourth symbol the column. I think about swapping second and third symbol, so be careful when coming back later!

Another catch is that some of the encoding schemes encoded the signed quantized values, while others encode only the absolute values of the quantized values. If only the absolute values are encoded in a symbol, each symbol is followed by one bit per absolute value that is not zero. If that bit is set, the value is negative.

The trees can be calculated as canonical huffman trees. Note that unsigned sorting (on two's complement numbers) is used, so negative numbers sort behind positive ones. The sort order for the grouped symbols is lexicographically by the single quantized numbers.

Examples

Interpreting a group-by-four block

Let's take a look at Tree 1A. The shortest symbol is (0,0,0,0), encoded with one bit, and gets assigned the code 0. The next shortest symbol has 4 bits, there is only one of them, and it is (-1,0,0,0). So this symbol gets the code 1000. Now, there are seven symbols with 5 bits. From top to bottom in the table, the symbols are

(0,-1,0,0)
(0,0,-1,0)
(0,0,0,-1)
(0,0,0,1)
(0,0,1,0)
(0,1,0,0)
(1,0,0,0)

Now for sorting these symbols lexicographically, rember that negative values go past positive ones (if we had -2,-1,0,1,2 the sorted order would be 0,1,2,-2,-1 instead). In this case, the sorted order ist

(0,0,0,1) → 10010
(0,0,0,-1) → 10011
(0,0,1,0) → 10100
(0,0,-1,0) → 10101
(0,1,0,0) → 10110
(0,-1,0,0) → 10111
(1,0,0,0) → 11000

Interpreting absolute value encoding

Now take a look at Tree 1H. In this coding scheme, the prefix free code is built from positive values only. Applying the algorithm to build the canonical code from the given lengths, one gets the following code assignment:

(0,0) → 0
(1,0) → 10
(0,1) → 110
(1,1) → 111

as the these codes are absolute value, they have to be interpreted as (0,0), (±1,0), (0,±1), (±1,±1) in fact, and the signs have to be specified afterwards. For each non-zero value from left to right, one bit being zero for positive and one for negative is appended to to the code, so you finally obtain

(0,0) → 0
(+1,0) → 100; (-1,0) → 101
(0,+1) → 1100; (0,-1) → 1101
(+1,+1) → 11100, (-1,+1) → 11110, (+1,-1) → 11101, (-1,-1) → 11111

Trees for Precision 1

(i.e. symbol set -1..+1)

Tree 1A

(used for A/0) <html>

<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>

    <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>

    <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>

    <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 === (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>

    <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>

    <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>

    <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 === (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>

    <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>

    <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>

    <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 === (used for A/3) <html><table class="x" rules="groups" frame="void">

<col style="width:1.3em"><colgroup span=3 style="width:2em">
<thead><tr><td></td>
  <th>-1</th><th>0</th><th>1</th>  </tr></thead><tbody>
  <tr><th>-1</th><td> 6</td><td> 4</td><td> 6</td></tr>
  <tr><th>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 === (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>

    <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>

    <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>

    <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 === (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>

    <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>

    <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>

    <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 === (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>

    <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>

    <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>

    <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 === (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=2 style="width:2em">
<thead><tr><td></td>
  <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 === (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>

    <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>

    <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>

    <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 === (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>

    <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>

    <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>

    <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 === (used for B/7) <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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) === Tree 3A === (used for A/0, B/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> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td></tr>
  <tr><th>-2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td></tr>
  <tr><th>-1</th><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td></tr>
  <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td></tr>
  <tr><th>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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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>

    <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

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