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atrac3p:main_trees_list

Table of Contents

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.x td {text-align:right;padding:0.2em;} .x tr th {text-align:right;padding:0.2em;background-color:#aaf;} tr.c th {text-align:center;}

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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>

<th>-1</th><td>11</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> 

    <tr><th>0</th><td>10</td><td> 8</td><td>10</td><td> 7</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 

    <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr>
    <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> 

    <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td>10</td><td> 8</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>11</td></tr>
</tbody></table>

</html> === Tree 1B === (used for A/1) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr>
     <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead>
  <tbody><tr><th rowspan="3">-1</th>

<th>-1</th><td>10</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> 

    <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> 

    <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 6</td><td> 5</td><td> 7</td></tr>
    <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 7</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> 

    <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 9</td><td> 8</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td>10</td><td>11</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 1C === (used for A/2, B/1) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr>
     <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead>
  <tbody><tr><th rowspan="3">-1</th>

<th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> 

    <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td>10</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 5</td><td> 8</td><td> 8</td><td> 7</td><td>10</td></tr> 

    <tr><th>0</th><td> 8</td><td> 5</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 5</td><td> 8</td></tr>
    <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 8</td><td> 5</td><td> 8</td><td>10</td><td> 8</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> 

    <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td>10</td><td>11</td><td>10</td><td> 8</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 1D === (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>

<th>-1</th><td>12</td><td>11</td><td>12</td><td>12</td><td> 9</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 

    <tr><th>0</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 5</td><td> 9</td><td>11</td><td> 9</td><td>12</td></tr>
    <tr><th>1</th><td>12</td><td>10</td><td>11</td><td>11</td><td> 9</td><td>11</td><td>12</td><td>11</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td>11</td><td>10</td><td>11</td><td> 9</td><td> 4</td><td> 9</td><td>10</td><td> 9</td><td>11</td></tr> 

    <tr><th>0</th><td> 9</td><td> 4</td><td> 9</td><td> 4</td><td> 1</td><td> 4</td><td> 9</td><td> 4</td><td> 9</td></tr>
    <tr><th>1</th><td>11</td><td> 9</td><td>10</td><td> 9</td><td> 4</td><td>10</td><td>11</td><td>10</td><td>11</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>12</td><td>11</td><td>12</td><td>11</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr> 

    <tr><th>0</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 5</td><td> 9</td><td>11</td><td>10</td><td>12</td></tr>
    <tr><th>1</th><td>12</td><td>11</td><td>12</td><td>11</td><td> 9</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
</tbody></table>

</html> === Tree 1F === (used for A/5, B/3) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr>
     <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead>
  <tbody><tr><th rowspan="3">-1</th>

<th>-1</th><td>10</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> 

    <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr>
    <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 6</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 6</td><td> 9</td></tr> 

    <tr><th>0</th><td> 7</td><td> 4</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 5</td><td> 7</td></tr>
    <tr><th>1</th><td> 9</td><td> 6</td><td> 8</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 6</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> 

    <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 1G === (used for A/6, B/5) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr>
     <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead>
  <tbody><tr><th rowspan="3">-1</th>

<th>-1</th><td>10</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> 

    <tr><th>0</th><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td> 9</td></tr>
    <tr><th>1</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 8</td><td> 7</td><td> 9</td><td> 8</td><td> 4</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> 

    <tr><th>0</th><td> 7</td><td> 4</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 7</td><td> 4</td><td> 7</td></tr>
    <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>10</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> 

    <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr>
    <tr><th>1</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 1H === (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>

<th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> 

    <tr><th>0</th><td>10</td><td> 8</td><td>10</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> 

    <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr>
    <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td>10</td><td> 8</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>12</td><td>10</td><td>11</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> 

    <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td>10</td><td> 8</td><td>10</td></tr>
    <tr><th>1</th><td>11</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 1J === (used for B/4) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">-1</th>       <th colspan="3">0</th>       <th colspan="3">1</th>    </tr><tr>
     <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>       <th>-1</th>       <th>0</th>       <th>1</th>    </tr></thead>
  <tbody><tr><th rowspan="3">-1</th>

<th>-1</th><td>11</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> 

    <tr><th>0</th><td>10</td><td> 7</td><td>10</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 

    <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr>
    <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> 

    <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>11</td></tr>
</tbody></table>

</html> === Tree 1K === (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>

<th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td> 9</td><td>12</td><td>10</td><td>12</td></tr> 

    <tr><th>0</th><td>10</td><td> 7</td><td>10</td><td> 8</td><td> 4</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr>
    <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">0</th>

<th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> 

    <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr>
    <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>-1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td>12</td></tr> 

    <tr><th>0</th><td> 9</td><td> 7</td><td>10</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr>
    <tr><th>1</th><td>12</td><td>10</td><td>12</td><td> 9</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> ==== Trees for Precision 2 ==== (i.e. symbol set -2..+2) === Tree 2A === (used for A/0) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 2</td><td> 4</td><td> 8</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 8</td><td>10</td></tr> 

    <tr><th>1</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 8</td><td>10</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td>10</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>12</td></tr> 

    <tr><th>1</th><td> 8</td><td> 8</td><td>11</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
    <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>12</td></tr>
</tbody></table>

</html> === Tree 2B === (used for A/1) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 8</td><td> 7</td><td> 8</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr>
    <tr><th>2</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr>
    <tr><th>2</th><td> 7</td><td> 7</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 

    <tr><th>1</th><td> 6</td><td> 6</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td></tr>
</tbody></table>

</html> === Tree 2C === (used for A/2) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=5 style="width:2em">
<thead><tr><td></td>
  <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
  <tr><th>-2</th><td> 9</td><td> 8</td><td> 6</td><td> 7</td><td> 8</td></tr>
  <tr><th>-1</th><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td></tr>
  <tr><th>0</th><td> 7</td><td> 3</td><td> 2</td><td> 3</td><td> 6</td></tr>
  <tr><th>1</th><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td></tr>
  <tr><th>2</th><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 2D === (used for A/3, B/2) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 1</td><td> 4</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td></tr> 

    <tr><th>1</th><td> 5</td><td> 7</td><td> 8</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td></tr>
    <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> 

    <tr><th>1</th><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 6</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 

    <tr><th>1</th><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
    <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>11</td><td> 9</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> === Tree 2E === (used for A/4) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr>
    <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr>
    <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 

    <tr><th>1</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr>
    <tr><th>2</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 2F === (used for A/5) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=5 style="width:2em">
<thead><tr><td></td>
  <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
  <tr><th>-2</th><td>10</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td></tr>
  <tr><th>-1</th><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td></tr>
  <tr><th>0</th><td> 8</td><td> 3</td><td> 1</td><td> 3</td><td> 7</td></tr>
  <tr><th>1</th><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td></tr>
  <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td></tr>
</tbody></table>

</html> === Tree 2G === (used for A/6) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=5 style="width:2em">
<thead><tr><td></td>
  <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
  <tr><th>-2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td></tr>
  <tr><th>-1</th><td> 6</td><td> 5</td><td> 3</td><td> 4</td><td> 6</td></tr>
  <tr><th>0</th><td> 6</td><td> 3</td><td> 3</td><td> 3</td><td> 6</td></tr>
  <tr><th>1</th><td> 6</td><td> 4</td><td> 3</td><td> 5</td><td> 7</td></tr>
  <tr><th>2</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td></tr>
</tbody></table>

</html> === Tree 2H === (used for A/7) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 2</td><td> 4</td><td> 7</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> 

    <tr><th>1</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 7</td><td> 9</td></tr>
    <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 

    <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 

    <tr><th>1</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
    <tr><th>2</th><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> === Tree 2I === (used for B/0) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 1</td><td> 4</td><td> 7</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td>10</td></tr> 

    <tr><th>1</th><td> 4</td><td> 6</td><td> 9</td><td> 6</td><td> 6</td><td> 9</td><td> 8</td><td> 9</td><td>10</td></tr>
    <tr><th>2</th><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>12</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 6</td><td> 9</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>11</td></tr> 

    <tr><th>1</th><td> 6</td><td> 7</td><td>10</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
    <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 8</td><td> 9</td><td>12</td><td> 9</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td></tr> 

    <tr><th>1</th><td> 8</td><td> 9</td><td>12</td><td> 9</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>12</td></tr>
    <tr><th>2</th><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
</tbody></table>

</html> === Tree 2J === (used for B/1) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 9</td></tr> 

    <tr><th>1</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr>
    <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr>
    <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 7</td><td> 7</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 

    <tr><th>1</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
    <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td></tr>
</tbody></table>

</html> === Tree 2K === (used for B/3, B/7) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 2</td><td> 4</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> 

    <tr><th>1</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 6</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td></tr>
    <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> 

    <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr>
    <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 6</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> 

    <tr><th>1</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td>10</td><td>11</td></tr>
    <tr><th>2</th><td> 8</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> === Tree 2L === (used for B/4) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=5 style="width:2em">
<thead><tr><td></td>
  <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
  <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td></tr>
  <tr><th>-1</th><td> 8</td><td> 6</td><td> 3</td><td> 5</td><td> 7</td></tr>
  <tr><th>0</th><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 6</td></tr>
  <tr><th>1</th><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 8</td></tr>
  <tr><th>2</th><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 2M === (used for B/5) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=5 style="width:2em">
<thead><tr><td></td>
  <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th>  </tr></thead><tbody>
  <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td></tr>
  <tr><th>-1</th><td> 8</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td></tr>
  <tr><th>0</th><td> 6</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td></tr>
  <tr><th>1</th><td> 7</td><td> 5</td><td> 3</td><td> 6</td><td> 8</td></tr>
  <tr><th>2</th><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 2N === (used for B/6) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<colgroup span=3 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="3">0</th>       <th colspan="3">1</th>       <th colspan="3">2</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>0</th>       <th>1</th>       <th>2</th>    </tr></thead>
  <tbody><tr><th rowspan="3">0</th>

<th>0</th><td> 1</td><td> 4</td><td> 6</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td></tr> 

    <tr><th>1</th><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td></tr>
    <tr><th>2</th><td> 7</td><td> 9</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">1</th>

<th>0</th><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> 

    <tr><th>1</th><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
    <tr><th>2</th><td> 7</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tbody><tr><th rowspan="3">2</th>

<th>0</th><td> 5</td><td> 9</td><td>11</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td></tr> 

    <tr><th>1</th><td> 6</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
    <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> ==== Trees for Precision 3 ==== (i.e. symbol set -3..+3) === 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>

<th>0</th><td> 3</td><td> 5</td><td> 8</td><td>10</td><td> 4</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 5</td><td> 7</td><td> 8</td><td> 8</td><td> 7</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>10</td><td>12</td><td>12</td><td>11</td><td>10</td><td>12</td><td>11</td></tr>
  <tbody><tr><th rowspan="4">1</th>

<th>0</th><td> 5</td><td> 5</td><td> 8</td><td>10</td><td> 5</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>12</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td>11</td><td> 7</td><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 7</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td></tr>
    <tr><th>3</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 9</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>12</td></tr>
  <tbody><tr><th rowspan="4">2</th>

<th>0</th><td> 7</td><td> 8</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td></tr> 

    <tr><th>1</th><td> 7</td><td> 7</td><td>10</td><td>12</td><td> 7</td><td> 8</td><td> 8</td><td>10</td><td>11</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>12</td></tr>
    <tr><th>2</th><td> 8</td><td> 9</td><td>10</td><td>12</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td>11</td><td>10</td><td>12</td><td>12</td><td>11</td><td>10</td></tr>
    <tr><th>3</th><td>11</td><td>10</td><td> 9</td><td>12</td><td>10</td><td> 9</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>12</td><td>12</td><td>12</td><td>12</td></tr>
  <tbody><tr><th rowspan="4">3</th>

<th>0</th><td>10</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td><td>12</td><td> 9</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> 

    <tr><th>1</th><td> 9</td><td> 9</td><td>12</td><td>12</td><td> 8</td><td> 9</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td><td>12</td></tr>
    <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>12</td><td> 8</td><td>10</td><td>10</td><td>12</td><td>12</td><td> 9</td><td>12</td><td>10</td><td>12</td><td>10</td><td>12</td><td>12</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td><td>12</td><td>10</td><td>12</td><td>12</td><td>12</td><td>10</td><td>12</td><td>10</td><td>12</td></tr>
</tbody></table>

</html> === Tree 3E === (used for A/4)

  • -3: 4 bits
  • -2: 3 bits
  • -1,0: 2 bits
  • 1,2: 3 bits
  • 3: 4 bits

=== Tree 3F === (used for A/5)

  • -3: 4 bits
  • -2,-1: 3 bits
  • 0,1: 2 bits
  • 2: 3 bits
  • 3: 4 bits

=== Tree 3G === (used for A/6) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead>
  <tbody><tr><th rowspan="4">0</th>

<th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 9</td><td> 5</td><td> 5</td><td> 7</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>10</td></tr>
    <tr><th>2</th><td> 9</td><td> 7</td><td>11</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
    <tr><th>3</th><td> 9</td><td> 9</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tbody><tr><th rowspan="4">1</th>

<th>0</th><td> 5</td><td> 5</td><td> 8</td><td>11</td><td> 6</td><td> 6</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td>10</td><td> 9</td><td>11</td><td> 9</td><td>10</td><td>11</td></tr> 

    <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 6</td><td> 5</td><td> 7</td><td>10</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>11</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 8</td><td>10</td><td>10</td></tr>
    <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 8</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>11</td></tr>
  <tbody><tr><th rowspan="4">2</th>

<th>0</th><td> 7</td><td> 7</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 8</td><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>11</td></tr>
    <tr><th>2</th><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>10</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tbody><tr><th rowspan="4">3</th>

<th>0</th><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td></tr> 

    <tr><th>1</th><td> 9</td><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>11</td><td>11</td></tr>
    <tr><th>2</th><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
    <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> === Tree 3H === (used for A/7) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=7 style="width:2em">
<thead><tr><td></td>
  <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
  <tr><th>-3</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td></tr>
  <tr><th>-2</th><td> 9</td><td> 9</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td></tr>
  <tr><th>-1</th><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 4</td><td> 6</td><td> 8</td></tr>
  <tr><th>0</th><td> 8</td><td> 6</td><td> 4</td><td> 2</td><td> 3</td><td> 6</td><td> 8</td></tr>
  <tr><th>1</th><td> 8</td><td> 6</td><td> 4</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td></tr>
  <tr><th>2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td></tr>
  <tr><th>3</th><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr>
</tbody></table>

</html> === Tree 3I === (used for B/0) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=7 style="width:2em">
<thead><tr><td></td>
  <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
  <tr><th>-3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tr><th>-2</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td></tr>
  <tr><th>-1</th><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td></tr>
  <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 7</td></tr>
  <tr><th>1</th><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td></tr>
  <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 3J === (used for B/3) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead>
  <tbody><tr><th rowspan="4">0</th>

<th>0</th><td> 2</td><td> 5</td><td> 8</td><td>10</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> 

    <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td>10</td><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
    <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tbody><tr><th rowspan="4">1</th>

<th>0</th><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tbody><tr><th rowspan="4">2</th>

<th>0</th><td> 8</td><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tbody><tr><th rowspan="4">3</th>

<th>0</th><td> 9</td><td>10</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td>12</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>3</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 3K === (used for B/4) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=7 style="width:2em">
<thead><tr><td></td>
  <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th>  </tr></thead><tbody>
  <tr><th>-3</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
  <tr><th>-2</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr>
  <tr><th>-1</th><td> 7</td><td> 6</td><td> 5</td><td> 3</td><td> 5</td><td> 6</td><td> 7</td></tr>
  <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 7</td></tr>
  <tr><th>1</th><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td></tr>
  <tr><th>2</th><td> 8</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td></tr>
  <tr><th>3</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 3L === (used for B/5)

  • -3,-2: 5 bits
  • -1: 2 bits
  • 0: 1 bits
  • 1: 3 bits
  • 2,3: 5 bits

=== Tree 3M === (used for B/6)

  • -3,-2: 5 bits
  • -1: 3 bits
  • 0: 1 bits
  • 1: 2 bits
  • 2,3: 5 bits

=== Tree 3N === (used for B/7) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<colgroup span=2 style="width:1.3em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<colgroup span=4 style="width:2em">
<thead>
  <tr class="c"><td colspan="2" rowspan="2"></td>
         <th colspan="4">0</th>       <th colspan="4">1</th>       <th colspan="4">2</th>       <th colspan="4">3</th>    </tr><tr>
     <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>       <th>0</th>       <th>1</th>       <th>2</th>       <th>3</th>    </tr></thead>
  <tbody><tr><th rowspan="4">0</th>

<th>0</th><td> 1</td><td> 5</td><td> 9</td><td> 9</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 6</td><td> 8</td><td>10</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
    <tr><th>2</th><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
    <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tbody><tr><th rowspan="4">1</th>

<th>0</th><td> 6</td><td> 7</td><td>10</td><td>11</td><td> 7</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 6</td><td> 7</td><td> 9</td><td>10</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>3</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tbody><tr><th rowspan="4">2</th>

<th>0</th><td> 9</td><td> 9</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tbody><tr><th rowspan="4">3</th>

<th>0</th><td> 8</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> 

    <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
    <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
</tbody></table>

</html> ==== Trees for Precision 4 ==== (i.e. symbol set -5..+5) === Tree 4A === (used for A/0) (absolute values in followed by sign bits if nonzero)

  • 0: 3 bits
  • 1,2: 2 bits
  • 3..5: 3 bits

=== Tree 4B === (used for A/1) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>11</td></tr>
  <tr><th>-4</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-3</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-2</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td></tr>
  <tr><th>-1</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr>
  <tr><th>0</th><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td></tr>
  <tr><th>1</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr>
  <tr><th>2</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td></tr>
  <tr><th>3</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>4</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>5</th><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
</tbody></table>

</html> === Tree 4C === (used for A/2, B/5) (absolute values in followed by sign bits if nonzero)

  • 0..2: 2 bits
  • 3: 3 bits
  • 4,5: 4 bits

=== Tree 4D === (used for A/3) (absolute values in followed by sign bits if nonzero)

  • 0: 2 bits
  • 1: 1 bits
  • 2: 3 bits
  • 3: 4 bits
  • 4,5: 5 bits

=== Tree 4E === (used for A/4, B/2) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr>
  <tr><th>-4</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>-3</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr>
  <tr><th>-2</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>-1</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td></tr>
  <tr><th>0</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td></tr>
  <tr><th>1</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>2</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>4</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>5</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
</tbody></table>

</html> === Tree 4F === (used for A/5) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td></tr>
  <tr><th>-4</th><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>-3</th><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td><td> 7</td></tr>
  <tr><th>-1</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 9</td><td> 9</td></tr>
  <tr><th>0</th><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 9</td></tr>
  <tr><th>1</th><td> 9</td><td> 7</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td></tr>
  <tr><th>3</th><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td></tr>
  <tr><th>4</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 4G === (used for A/6) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>-4</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>-3</th><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>-2</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td></tr>
  <tr><th>-1</th><td> 9</td><td> 8</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr>
  <tr><th>0</th><td> 8</td><td> 7</td><td> 7</td><td> 5</td><td> 5</td><td> 4</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td></tr>
  <tr><th>1</th><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr>
  <tr><th>2</th><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr>
  <tr><th>3</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>4</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>5</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr>
</tbody></table>

</html> === Tree 4H === (used for A/7) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td></tr>
  <tr><th>-3</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td></tr>
  <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>-1</th><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>1</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>2</th><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>4</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td></tr>
  <tr><th>5</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> === Tree 4I === (used for B/0, B/3) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>-4</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>-3</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr>
  <tr><th>0</th><td> 8</td><td> 8</td><td> 8</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td> 8</td></tr>
  <tr><th>1</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>4</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td></tr>
  <tr><th>5</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
</tbody></table>

</html> === Tree 4J === (used for B/1, B/4) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=11 style="width:2em">
<thead><tr><td></td>
  <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th>  </tr></thead><tbody>
  <tr><th>-5</th><td>12</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td></tr>
  <tr><th>-4</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>-3</th><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>-2</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>0</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr>
  <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr>
  <tr><th>2</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>3</th><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr>
  <tr><th>4</th><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>5</th><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> === Tree 4K === (used for B/6) (absolute values in followed by sign bits if nonzero)

  • 0: 2 bits
  • 1: 1 bits
  • 2: 3 bits
  • 3,4: 5 bits
  • 5: 4 bits

=== Tree 4L === (used for B/7)

  • -5,-4: 6 bits
  • -3: 5 bits
  • -2: 4 bits
  • -1: 3 bits
  • 0: 1 bits
  • 1: 3 bits
  • 2: 4 bits
  • 3,4: 6 bits
  • 5: 5 bits

==== Trees for Precision 5 ==== (i.e. symbol set -7..+7) === Tree 5A === (used for A/0) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>-6</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>-5</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>-4</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-2</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr>
  <tr><th>3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>4</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>5</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>6</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td></tr>
</tbody></table>

</html> === Tree 5B === (used for A/1, B/1) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>-6</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>-5</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-4</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>-3</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>0</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td></tr>
  <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr>
  <tr><th>5</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>6</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>7</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> === Tree 5C === (used for A/2) (absolute values in followed by sign bits if nonzero)

  • 0: 3 bits
  • 1: 2 bits
  • 2..5: 3 bits
  • 6,7: 4 bits

=== Tree 5D === (used for A/3) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>-6</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-5</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>-4</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>-3</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr>
  <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 7</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr>
  <tr><th>-1</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>0</th><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>2</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>4</th><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>5</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>6</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>7</th><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
</tbody></table>

</html> === Tree 5E === (used for A/4, B/4) (absolute values in followed by sign bits if nonzero)

  • 0: 3 bits
  • 1,2: 2 bits
  • 3: 3 bits
  • 4..7: 4 bits

=== Tree 5F === (used for A/5, B/5) (absolute values in followed by sign bits if nonzero)

  • 0: 1 bits
  • 1: 2 bits
  • 2: 3 bits
  • 3: 5 bits
  • 4,5: 6 bits
  • 6,7: 5 bits

=== Tree 5G === (used for A/6)

  • -7: 7 bits
  • -6: 6 bits
  • -5: 7 bits
  • -4: 6 bits
  • -3: 5 bits
  • -2: 4 bits
  • -1..1: 2 bits
  • 2,3: 5 bits
  • 4: 6 bits
  • 5: 7 bits
  • 6: 6 bits
  • 7: 7 bits

=== Tree 5H === (used for A/7)

  • -7: 6 bits
  • -6: 5 bits
  • -5: 6 bits
  • -4: 5 bits
  • -3: 4 bits
  • -2,-1: 3 bits
  • 0: 2 bits
  • 1: 3 bits
  • 2,3: 4 bits
  • 4: 5 bits
  • 5: 6 bits
  • 6: 5 bits
  • 7: 6 bits

=== Tree 5I === (used for B/0, B/2) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>-6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>-5</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>-4</th><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>-3</th><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>-2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>0</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td></tr>
  <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>4</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>5</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> === Tree 5J === (used for B/3) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>12</td><td>12</td></tr>
  <tr><th>-6</th><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td></tr>
  <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
  <tr><th>-4</th><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td></tr>
  <tr><th>-3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>-2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td></tr>
  <tr><th>4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>11</td></tr>
  <tr><th>5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td></tr>
  <tr><th>6</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td></tr>
  <tr><th>7</th><td>12</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td></tr>
</tbody></table>

</html> === Tree 5K === (used for B/6) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>12</td><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr>
  <tr><th>-6</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td><td>10</td><td>11</td></tr>
  <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr>
  <tr><th>-3</th><td>10</td><td>10</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td></tr>
  <tr><th>-2</th><td> 9</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td></tr>
  <tr><th>-1</th><td> 9</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>12</td></tr>
  <tr><th>0</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 5</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>1</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td></tr>
  <tr><th>2</th><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr>
  <tr><th>3</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td> 9</td><td>10</td></tr>
  <tr><th>4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td></tr>
  <tr><th>5</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>12</td><td>10</td><td>11</td></tr>
  <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td></tr>
  <tr><th>7</th><td>12</td><td>10</td><td>12</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td></tr>
</tbody></table>

</html> === Tree 5L === (used for B/7) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=15 style="width:2em">
<thead><tr><td></td>
  <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th>  </tr></thead><tbody>
  <tr><th>-7</th><td>12</td><td>12</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td></tr>
  <tr><th>-6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
  <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td></tr>
  <tr><th>-4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td></tr>
  <tr><th>-3</th><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>11</td></tr>
  <tr><th>-2</th><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td></tr>
  <tr><th>-1</th><td>10</td><td>10</td><td>12</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>0</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 2</td><td> 3</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr>
  <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td></tr>
  <tr><th>4</th><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td></tr>
  <tr><th>5</th><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr>
  <tr><th>6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td></tr>
  <tr><th>7</th><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td></tr>
</tbody></table>

</html> ==== Trees for Precision 6 ==== (i.e. symbol set -15..+15) === Tree 6A === (used for A/0, B/0) (absolute values in followed by sign bits if nonzero)

  • 0: 3 bits
  • 1: 2 bits
  • 2,3: 3 bits
  • 4,5: 4 bits
  • 6..9: 5 bits
  • 10..12: 6 bits
  • 13,14: 5 bits
  • 15: 6 bits

=== Tree 6B === (used for A/1, B/4) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 2</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tr><th>2</th><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>6</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>7</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>8</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>12</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> === Tree 6C === (used for A/2) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 6</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>6</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>8</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>11</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>14</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>15</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> === Tree 6D === (used for A/3) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>6</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>8</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>14</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>15</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> === Tree 6E === (used for A/4) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 6</td><td> 7</td><td> 8</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 6</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>2</th><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td></tr>
  <tr><th>3</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>6</th><td> 7</td><td> 9</td><td> 6</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>7</th><td> 8</td><td> 9</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>8</th><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>9</th><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>10</th><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>11</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>12</th><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>13</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>14</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr>
</tbody></table>

</html> === Tree 6F === (used for A/5)

  • -15,-14: 7 bits
  • -13: 6 bits
  • -12: 7 bits
  • -11..-9: 6 bits
  • -8,-7: 5 bits
  • -6: 6 bits
  • -5: 5 bits
  • -4..3: 4 bits
  • 4: 3 bits
  • 5..7: 5 bits
  • 8,9: 6 bits
  • 10..13: 7 bits
  • 14: 6 bits
  • 15: 7 bits

=== Tree 6G === (used for A/6, B/7)

  • -15: 5 bits
  • -14: 10 bits
  • -13,-12: 8 bits
  • -11..-9: 7 bits
  • -8..-5: 6 bits
  • -4,-3: 5 bits
  • -2: 4 bits
  • -1: 3 bits
  • 0: 2 bits
  • 1: 3 bits
  • 2: 4 bits
  • 3,4: 5 bits
  • 5..8: 6 bits
  • 9..11: 7 bits
  • 12: 8 bits
  • 13: 9 bits
  • 14: 10 bits
  • 15: 5 bits

=== Tree 6H === (used for A/7) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td></tr>
  <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>6</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>8</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>11</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>13</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>15</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr>
</tbody></table>

</html> === Tree 6I === (used for B/1) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>6</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>7</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>8</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>11</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>12</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>15</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr>
</tbody></table>

</html> === Tree 6J === (used for B/2, B/3) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>1</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr>
  <tr><th>4</th><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>5</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>6</th><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>7</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>8</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>11</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
  <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td></tr>
</tbody></table>

</html> === Tree 6K === (used for B/5)

  • -15..-13: 7 bits
  • -12..-7: 8 bits
  • -6..-4: 7 bits
  • -3: 6 bits
  • -2: 5 bits
  • -1: 3 bits
  • 0: 1 bits
  • 1: 3 bits
  • 2: 5 bits
  • 3,4: 6 bits
  • 5..7: 7 bits
  • 8,9: 8 bits
  • 10,11: 9 bits
  • 12: 8 bits
  • 13: 6 bits
  • 14,15: 7 bits

=== Tree 6L === (used for B/6) (absolute values in followed by sign bits if nonzero) <html><table class="x" rules="groups" frame="void"> 

<col style="width:1.3em"><colgroup span=16 style="width:2em">
<thead><tr><td></td>
  <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th>  </tr></thead><tbody>
  <tr><th>0</th><td> 1</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td>12</td><td>12</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>1</th><td> 4</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td> 8</td><td> 8</td><td> 9</td></tr>
  <tr><th>2</th><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr>
  <tr><th>3</th><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr>
  <tr><th>4</th><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td><td> 9</td><td>11</td><td> 9</td></tr>
  <tr><th>5</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr>
  <tr><th>6</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>7</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td> 9</td></tr>
  <tr><th>8</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td> 9</td><td>10</td><td>10</td></tr>
  <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td></tr>
  <tr><th>10</th><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td></tr>
  <tr><th>11</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td></tr>
  <tr><th>12</th><td>11</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td></tr>
  <tr><th>13</th><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td></tr>
  <tr><th>14</th><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr>
  <tr><th>15</th><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td></tr>
</tbody></table>

</html> ==== Trees for Precision 7 ==== (i.e. symbol set -31..+31) === Tree 7A === (used for A/0, A/7, B/1, B/2)

  • -31..-29: 8 bits
  • -28..-26: 7 bits
  • -25: 8 bits
  • -24: 10 bits
  • -23..-18: 9 bits
  • -17..-11: 8 bits
  • -10..-7: 7 bits
  • -6..-4: 6 bits
  • -3: 5 bits
  • -2: 4 bits
  • -1: 3 bits
  • 0: 2 bits
  • 1: 3 bits
  • 2: 4 bits
  • 3: 5 bits
  • 4..6: 6 bits
  • 7..10: 7 bits
  • 11..16: 8 bits
  • 17..23: 9 bits
  • 24: 10 bits
  • 25: 8 bits
  • 26..28: 7 bits
  • 29..31: 8 bits

=== Tree 7B === (used for A/1)

  • -31..-29: 8 bits
  • -28..-26: 7 bits
  • -25: 8 bits
  • -24..-22: 9 bits
  • -21..-15: 8 bits
  • -14..-9: 7 bits
  • -8..-6: 6 bits
  • -5..-3: 5 bits
  • -2: 4 bits
  • -1..1: 3 bits
  • 2: 4 bits
  • 3,4: 5 bits
  • 5..8: 6 bits
  • 9..14: 7 bits
  • 15..21: 8 bits
  • 22..24: 9 bits
  • 25: 8 bits
  • 26,27: 7 bits
  • 28..31: 8 bits

=== Tree 7C === (used for A/2)

  • -31..-26: 8 bits
  • -25: 7 bits
  • -24..-22: 8 bits
  • -21..-16: 7 bits
  • -15: 6 bits
  • -14,-13: 7 bits
  • -12,-11: 6 bits
  • -10..-8: 5 bits
  • -7: 6 bits
  • -6..-1: 5 bits
  • 0: 4 bits
  • 1: 5 bits
  • 2,3: 4 bits
  • 4: 6 bits
  • 5..7: 5 bits
  • 8: 6 bits
  • 9: 5 bits
  • 10..12: 6 bits
  • 13: 7 bits
  • 14: 6 bits
  • 15..19: 7 bits
  • 20,21: 8 bits
  • 22,23: 7 bits
  • 24: 8 bits
  • 25,26: 7 bits
  • 27..29: 8 bits
  • 30: 7 bits
  • 31: 8 bits

=== Tree 7D === (used for A/3)

  • -31,-30: 8 bits
  • -29..-26: 7 bits
  • -25..-17: 8 bits
  • -16..-11: 7 bits
  • -10..-7: 6 bits
  • -6..-4: 5 bits
  • -3..3: 4 bits
  • 4..6: 5 bits
  • 7..10: 6 bits
  • 11..16: 7 bits
  • 17..24: 8 bits
  • 25..30: 7 bits
  • 31: 8 bits

=== Tree 7E === (used for A/4)

  • -31,-30: 9 bits
  • -29: 8 bits
  • -28,-27: 7 bits
  • -26: 8 bits
  • -25: 7 bits
  • -24,-23: 8 bits
  • -22: 7 bits
  • -21: 8 bits
  • -20: 9 bits
  • -19..-13: 8 bits
  • -12: 7 bits
  • -11: 6 bits
  • -10: 5 bits
  • -9: 6 bits
  • -8..-3: 5 bits
  • -2..2: 4 bits
  • 3..6: 5 bits
  • 7: 6 bits
  • 8: 5 bits
  • 9..14: 6 bits
  • 15..21: 7 bits
  • 22: 8 bits
  • 23,24: 9 bits
  • 25: 8 bits
  • 26,27: 9 bits
  • 28: 8 bits
  • 29..31: 9 bits

=== Tree 7F === (used for A/5)

  • -31..-29: 8 bits
  • -28..-26: 7 bits
  • -25: 8 bits
  • -24..-22: 9 bits
  • -21..-16: 8 bits
  • -15..-11: 7 bits
  • -10..-7: 6 bits
  • -6..-4: 5 bits
  • -3..-1: 4 bits
  • 0: 3 bits
  • 1,2: 4 bits
  • 3..6: 5 bits
  • 7..10: 6 bits
  • 11..15: 7 bits
  • 16..21: 8 bits
  • 22: 9 bits
  • 23..25: 8 bits
  • 26..28: 7 bits
  • 29..31: 8 bits

=== Tree 7G === (used for A/6)

  • -31..-27: 8 bits
  • -26: 7 bits
  • -25: 8 bits
  • -24..-20: 9 bits
  • -19..-13: 8 bits
  • -12..-8: 7 bits
  • -7..-5: 6 bits
  • -4,-3: 5 bits
  • -2,-1: 4 bits
  • 0: 2 bits
  • 1: 3 bits
  • 2: 4 bits
  • 3,4: 5 bits
  • 5..7: 6 bits
  • 8..13: 7 bits
  • 14..19: 8 bits
  • 20..24: 9 bits
  • 25: 8 bits
  • 26: 7 bits
  • 27..31: 8 bits

=== Tree 7H === (used for B/0, B/5)

  • -31..-25: 7 bits
  • -24..-20: 9 bits
  • -19..-14: 8 bits
  • -13..-9: 7 bits
  • -8..-5: 6 bits
  • -4,-3: 5 bits
  • -2: 4 bits
  • -1..1: 3 bits
  • 2: 4 bits
  • 3,4: 5 bits
  • 5..8: 6 bits
  • 9..12: 7 bits
  • 13..19: 8 bits
  • 20..24: 9 bits
  • 25..31: 7 bits

=== Tree 7I === (used for B/3)

  • -31: 9 bits
  • -30,-29: 8 bits
  • -28: 9 bits
  • -27..-25: 8 bits
  • -24: 11 bits
  • -23: 10 bits
  • -22: 11 bits
  • -21..-16: 10 bits
  • -15..-10: 9 bits
  • -9..-7: 8 bits
  • -6..-4: 7 bits
  • -3: 6 bits
  • -2: 5 bits
  • -1: 3 bits
  • 0: 1 bits
  • 1: 3 bits
  • 2: 5 bits
  • 3: 6 bits
  • 4..6: 7 bits
  • 7..10: 8 bits
  • 11: 9 bits
  • 12: 10 bits
  • 13..15: 9 bits
  • 16..19: 10 bits
  • 20: 11 bits
  • 21: 10 bits
  • 22..24: 11 bits
  • 25..29: 8 bits
  • 30,31: 9 bits

=== Tree 7J === (used for B/4)

  • -31..-28: 8 bits
  • -27,-26: 7 bits
  • -25: 8 bits
  • -24..-19: 9 bits
  • -18..-13: 8 bits
  • -12..-8: 7 bits
  • -7..-5: 6 bits
  • -4,-3: 5 bits
  • -2,-1: 4 bits
  • 0: 2 bits
  • 1: 3 bits
  • 2: 4 bits
  • 3,4: 5 bits
  • 5..7: 6 bits
  • 8..12: 7 bits
  • 13..18: 8 bits
  • 19..24: 9 bits
  • 25: 8 bits
  • 26,27: 7 bits
  • 28..31: 8 bits

=== Tree 7K === (used for B/6)

  • -31..-25: 8 bits
  • -24..-19: 9 bits
  • -18..-13: 8 bits
  • -12..-8: 7 bits
  • -7..-5: 6 bits
  • -4,-3: 5 bits
  • -2: 4 bits
  • -1: 3 bits
  • 0: 2 bits
  • 1: 3 bits
  • 2,3: 5 bits
  • 4..7: 6 bits
  • 8..12: 7 bits
  • 13..18: 8 bits
  • 19..24: 9 bits
  • 25..31: 8 bits

=== Tree 7L === (used for B/7)

  • -31,-30: 11 bits
  • -29: 10 bits
  • -28: 11 bits
  • -27..-20: 9 bits
  • -19,-18: 8 bits
  • -17: 7 bits
  • -16: 8 bits
  • -15..-11: 7 bits
  • -10..-6: 6 bits
  • -5..-3: 5 bits
  • -2,-1: 4 bits
  • 0: 2 bits
  • 1,2: 4 bits
  • 3..5: 5 bits
  • 6..10: 6 bits
  • 11..16: 7 bits
  • 17..20: 8 bits
  • 21..27: 9 bits
  • 28..30: 10 bits
  • 31: 11 bits

===== Tree Sets ===== This table shows the mapping of tree set IDs, tree IDs and quantization precisions to the code tables defined above. If the table says n x Tree XX it means that n symbols of that tree (which might groups of 1, 2 or 4 quantized coefficients) are clustered together. Each cluster is preceeded by an "data present" bit. If that bit is zero, all coefficients of the whole cluster are zero, and no codes for the cluster are stored. If that bit is one that at least one non-zero entry is present and the codes for this cluster follow as in non-clustered mode. The tree choice can be limited to a restricted tree set. The IDs inside the restricted tree set are in the range 0..3 instead of 0..7, and printed as R0..R3 in the table. ==== Tree Set A====

Quant\ID 0 1 2 3 4 5 6 7 R0 R1 R2 R3
1 Tree 1A 4 x Tree 1B Tree 1C Tree 1D Tree 1E Tree 1F 2 x Tree 1G Tree 1H Tree 1A Tree 1F Tree 1E 4x Tree 1B
2 Tree 2A Tree 2B Tree 2C Tree 2D Tree 2E Tree 2F Tree 2G 2 x Tree 2H Tree 2A Tree 2B Tree 2C Tree 2D
3 Tree 3A Tree 3B Tree 3C Tree 3D Tree 3E Tree 3F Tree 3G Tree 3H Tree 3D Tree 3A Tree 3E Tree 3C
4 Tree 4A Tree 4B Tree 4C Tree 4D Tree 4E Tree 4F Tree 4G Tree 4H Tree 4E Tree 4A Tree 4B Tree 4C
5 Tree 5A Tree 5B Tree 5C Tree 5D Tree 5E Tree 5F Tree 5G Tree 5H Tree 5B Tree 5A Tree 5E Tree 5D
6 Tree 6A Tree 6B Tree 6C Tree 6D Tree 6E Tree 6F Tree 6G 2 x Tree 6H Tree 6D Tree 6A Tree 6C Tree 6B
7 Tree 7A Tree 7B Tree 7C Tree 7D Tree 7E Tree 7F Tree 7G 4 x Tree 7A Tree 7A Tree 7D Tree 7B Tree 7C

==== Tree Set B====

Quant\ID 0 1 2 3 4 5 6 7 R0 R1 R2 R3
1 4 x Tree 1I Tree 1C 4 x Tree 1E Tree 1F Tree 1J 2 x Tree 1G Tree 1E Tree 1K Tree 1J 4 x Tree 1I Tree 1C 4 x Tree 1E
2 Tree 2I Tree 2J 4 x Tree 2D Tree 2K 4 x Tree 2L Tree 2M Tree 2N 4 x Tree 2K Tree 2I Tree 2K 4 x Tree 2D Tree 2J
3 4 x Tree 3I Tree 3B Tree 3A Tree 3J Tree 3K 4 x Tree 3L Tree 3M 4 x Tree 3N 4 x Tree 3I Tree 3B Tree 3A Tree 3J
4 Tree 4I Tree 4J Tree 4E 2 x Tree 4I 4 x Tree 4J Tree 4C Tree 4K Tree 4L Tree 4I Tree 4J Tree 4E 4 x Tree 4J
5 Tree 5I Tree 5B 2 x Tree 5I Tree 5J Tree 5E Tree 5F 4 x Tree 5K Tree 5L Tree 5I Tree 5B 2 x Tree 5I Tree 5J
6 Tree 6A Tree 6I 2 x Tree 6J Tree 6J Tree 6B Tree 6K Tree 6L Tree 6G Tree 6I Tree 6B 2 x Tree 6J Tree 6A
7 Tree 7H Tree 7A 4 x Tree 7A Tree 7I Tree 7J 2 x Tree 7H Tree 7K Tree 7L Tree 7H Tree 7A 4 x Tree 7A Tree 7I
atrac3p/main_trees_list.txt · Last modified: 2010/07/23 17:41 by megadiscman
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