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atrac3p:main_trees_list [2009/11/28 08:15] – linkfix megadiscman | atrac3p:main_trees_list [2010/07/23 17:41] (current) – quantizer -> quantization precision megadiscman |
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===== Main Spectral Data Encoding Trees ===== | ===== Main Spectral Data Encoding Trees ===== |
==== General Intro ==== | ==== General Intro ==== |
| |
The quantized values are encoded using a prefix free binary code. To make matters more complicated there are up to 16 encoding scheme per quantizer (because the symbol set depends on the quantizer). In many cases, the symbols are built from a group of two or four quantized values instead of just one quantized value. For groups of size two, the trees are shown as table, the first symbol choosing the row, the second value the column. | The quantized values are encoded using a prefix free binary code. To make matters more complicated there are up to 16 encoding scheme per quantization precision (symbol set depends on precision, so different encoding schemes must be used for different precisions.). In many cases, the symbols are built from a group of two or four quantized values instead of just one quantized value. For groups of size two, the trees are shown as table, the first symbol choosing the row, the second value the column. For groups of size four, the tables are organized so that the first symbol chooses the row block, the second symbol the exact row, the third symbol the column block and the fourth symbol the column. //I think about swapping second and third symbol, so be careful when coming back later!// |
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Another catch is that some of the encoding schemes encoded the signed quantized values, while others encode only the absolute values of the quantized values. If only the absolute values are encoded in a symbol, each symbol is followed by one bit per absolute value that is not zero. If that bit is set, the value is negative. | Another catch is that some of the encoding schemes encoded the signed quantized values, while others encode only the absolute values of the quantized values. If only the absolute values are encoded in a symbol, each symbol is followed by one bit per absolute value that is not zero. If that bit is set, the value is negative. |
The trees can be calculated as [[canonical huffman 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. | The trees can be calculated as [[canonical huffman trees]]. Note that unsigned sorting (on two's complement numbers) is used, so negative numbers sort behind positive ones. The sort order for the grouped symbols is lexicographically by the single quantized numbers. |
| |
==== Trees for Quantizer 1 ==== | ==== Examples ==== |
(i.e. symbol set -1,0,1) | |
| === Interpreting a group-by-four block === |
| |
| Let's take a look at Tree 1A. The shortest symbol is (0,0,0,0), encoded with one bit, and gets assigned the code ''0''. The next shortest symbol has 4 bits, there is only one of them, and it is (-1,0,0,0). So this symbol gets the code ''1000''. Now, there are seven symbols with 5 bits. From top to bottom in the table, the symbols are |
| |
| * (0,-1,0,0) |
| * (0,0,-1,0) |
| * (0,0,0,-1) |
| * (0,0,0,1) |
| * (0,0,1,0) |
| * (0,1,0,0) |
| * (1,0,0,0) |
| |
| Now for sorting these symbols lexicographically, rember that negative values go past positive ones (if we had -2,-1,0,1,2 the sorted order would be 0,1,2,-2,-1 instead). In this case, the sorted order ist |
| * (0,0,0,1) -> ''10010'' |
| * (0,0,0,-1) -> ''10011'' |
| * (0,0,1,0) -> ''10100'' |
| * (0,0,-1,0) -> ''10101'' |
| * (0,1,0,0) -> ''10110'' |
| * (0,-1,0,0) -> ''10111'' |
| * (1,0,0,0) -> ''11000'' |
| |
| === Interpreting absolute value encoding === |
| |
| Now take a look at Tree 1H. In this coding scheme, the prefix free code is built from positive values only. Applying the algorithm to build the canonical code from the given lengths, one gets the following code assignment: |
| |
| * (0,0) -> ''0'' |
| * (1,0) -> ''10'' |
| * (0,1) -> ''110'' |
| * (1,1) -> ''111'' |
| |
| as the these codes are absolute value, they have to be interpreted as (0,0), (±1,0), (0,±1), (±1,±1) in fact, and the signs have to be specified afterwards. For each non-zero value from left to right, one bit being zero for positive and one for negative is appended to to the code, so you finally obtain |
| |
| * (0,0) -> ''0'' |
| * (+1,0) -> ''10**0**''; (-1,0) -> ''10**1**'' |
| * (0,+1) -> ''110**0**''; (0,-1) -> ''110**1**'' |
| * (+1,+1) -> ''111**00**'', (-1,+1) -> ''111**10**'', (+1,-1) -> ''111**01**'', (-1,-1) -> ''111**11**'' |
| |
| ==== Trees for Precision 1 ==== |
| (i.e. symbol set -1..+1) |
=== Tree 1A === | === Tree 1A === |
(used for A/0) | (used for A/0) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>11</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> |
| <tr><th>0</th><td>10</td><td> 8</td><td>10</td><td> 7</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> |
| <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> |
| <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td>10</td><td> 8</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1B === | === Tree 1B === |
(used for A/1) | (used for A/1) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> |
| <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> |
| <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 6</td><td> 5</td><td> 7</td></tr> |
| <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 7</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> |
| <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 9</td><td> 8</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td>10</td><td>11</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1C === | === Tree 1C === |
(used for A/2 and B/1) | (used for A/2, B/1) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> |
| <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td>10</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 5</td><td> 8</td><td> 8</td><td> 7</td><td>10</td></tr> |
| <tr><th>0</th><td> 8</td><td> 5</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 5</td><td> 8</td></tr> |
| <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 8</td><td> 5</td><td> 8</td><td>10</td><td> 8</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> |
| <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td>10</td><td>11</td><td>10</td><td> 8</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1D === | === Tree 1D === |
(used for A/3) | (used for A/3) |
| <html><table class="x" rules="groups" frame="void"> |
| ^ -1 ^ 0 ^ +1 ^ | <col style="width:1.3em"><colgroup span=3 style="width:2em"> |
^ -1 | 6 | 4 | 6 | | <thead><tr><td></td> |
^ 0 | 3 | 1 | 3 | | <th>-1</th><th>0</th><th>1</th> </tr></thead><tbody> |
^ +1 | 6 | 3 | 6 | | <tr><th>-1</th><td> 6</td><td> 4</td><td> 6</td></tr> |
| <tr><th>0</th><td> 3</td><td> 1</td><td> 3</td></tr> |
| <tr><th>1</th><td> 6</td><td> 3</td><td> 6</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1E === | === Tree 1E === |
(used for A/4, B/2, B/6) | (used for A/4, B/2, B/6) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>12</td><td>11</td><td>12</td><td>12</td><td> 9</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>0</th><td>12</td><td>10</td><td>11</td><td> 9</td><td> 5</td><td> 9</td><td>11</td><td> 9</td><td>12</td></tr> |
| <tr><th>1</th><td>12</td><td>10</td><td>11</td><td>11</td><td> 9</td><td>11</td><td>12</td><td>11</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td>11</td><td>10</td><td>11</td><td> 9</td><td> 4</td><td> 9</td><td>10</td><td> 9</td><td>11</td></tr> |
| <tr><th>0</th><td> 9</td><td> 4</td><td> 9</td><td> 4</td><td> 1</td><td> 4</td><td> 9</td><td> 4</td><td> 9</td></tr> |
| <tr><th>1</th><td>11</td><td> 9</td><td>10</td><td> 9</td><td> 4</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>12</td><td>11</td><td>12</td><td>11</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr> |
| <tr><th>0</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 5</td><td> 9</td><td>11</td><td>10</td><td>12</td></tr> |
| <tr><th>1</th><td>12</td><td>11</td><td>12</td><td>11</td><td> 9</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1F === | === Tree 1F === |
(used for A/5, B/3) | (used for A/5, B/3) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>11</td><td>10</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> |
| <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr> |
| <tr><th>1</th><td>11</td><td> 8</td><td> 9</td><td> 9</td><td> 6</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 6</td><td> 9</td></tr> |
| <tr><th>0</th><td> 7</td><td> 4</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 5</td><td> 7</td></tr> |
| <tr><th>1</th><td> 9</td><td> 6</td><td> 8</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 6</td><td> 9</td><td> 9</td><td> 8</td><td>11</td></tr> |
| <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1G === | === Tree 1G === |
(used for A/6, B/5) | (used for A/6, B/5) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>11</td><td> 9</td><td>11</td></tr> |
| <tr><th>0</th><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td> 9</td></tr> |
| <tr><th>1</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 8</td><td> 7</td><td> 9</td><td> 8</td><td> 4</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> |
| <tr><th>0</th><td> 7</td><td> 4</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 7</td><td> 4</td><td> 7</td></tr> |
| <tr><th>1</th><td> 9</td><td> 7</td><td> 8</td><td> 7</td><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>11</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tr><th>0</th><td> 9</td><td> 7</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr> |
| <tr><th>1</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1H === | === Tree 1H === |
(used for A/7) | (used for A/7) |
| (absolute values in followed by sign bits if nonzero) |
(absolute values followed by sign bits for nonzero) | <html><table class="x" rules="groups" frame="void"> |
| ^ 0 ^ 1 ^ | <col style="width:1.3em"><colgroup span=2 style="width:2em"> |
^ 0 | 1 | 3 | | <thead><tr><td></td> |
^ 1 | 2 | 3 | | <th>0</th><th>1</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 1</td><td> 3</td></tr> |
| <tr><th>1</th><td> 2</td><td> 3</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1I === | === Tree 1I === |
(used for B/0) | (used for B/0) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> |
| <tr><th>0</th><td>10</td><td> 8</td><td>10</td><td> 8</td><td> 4</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>11</td><td>10</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 5</td><td> 8</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> |
| <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 8</td><td> 5</td><td> 8</td><td>10</td><td> 8</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>12</td><td>10</td><td>11</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> |
| <tr><th>0</th><td>10</td><td> 8</td><td> 9</td><td> 8</td><td> 4</td><td> 8</td><td>10</td><td> 8</td><td>10</td></tr> |
| <tr><th>1</th><td>11</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1J === | === Tree 1J === |
(used for B/4) | (used for B/4) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>11</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> |
| <tr><th>0</th><td>10</td><td> 7</td><td>10</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td>10</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> |
| <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>12</td></tr> |
| <tr><th>0</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 4</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
=== Tree 1K === | === Tree 1K === |
(used for B/7) | (used for B/7) |
| <html><table class="x" rules="groups" frame="void"> |
==== Trees for Quantizer 3 ==== | <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">-1</th> <th colspan="3">0</th> <th colspan="3">1</th> </tr><tr> |
| <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> <th>-1</th> <th>0</th> <th>1</th> </tr></thead> |
| <tbody><tr><th rowspan="3">-1</th> |
| <th>-1</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 7</td><td> 9</td><td>12</td><td>10</td><td>12</td></tr> |
| <tr><th>0</th><td>10</td><td> 7</td><td>10</td><td> 8</td><td> 4</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> |
| <tr><th>1</th><td>12</td><td> 9</td><td>10</td><td> 9</td><td> 7</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>-1</th><td> 9</td><td> 7</td><td>10</td><td> 8</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td>10</td></tr> |
| <tr><th>0</th><td> 7</td><td> 5</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 5</td><td> 7</td></tr> |
| <tr><th>1</th><td>10</td><td> 7</td><td> 9</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>-1</th><td>12</td><td>10</td><td>12</td><td>10</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td>12</td></tr> |
| <tr><th>0</th><td> 9</td><td> 7</td><td>10</td><td> 7</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td>10</td></tr> |
| <tr><th>1</th><td>12</td><td>10</td><td>12</td><td> 9</td><td> 7</td><td>10</td><td>12</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| ==== Trees for Precision 2 ==== |
| (i.e. symbol set -2..+2) |
| === Tree 2A === |
| (used for A/0) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 2</td><td> 4</td><td> 8</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 8</td><td>10</td></tr> |
| <tr><th>1</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 8</td><td>10</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 8</td><td>10</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>12</td></tr> |
| <tr><th>1</th><td> 8</td><td> 8</td><td>11</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2B === |
| (used for A/1) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 8</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>1</th><td> 6</td><td> 6</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2C === |
| (used for A/2) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=5 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th> </tr></thead><tbody> |
| <tr><th>-2</th><td> 9</td><td> 8</td><td> 6</td><td> 7</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td></tr> |
| <tr><th>0</th><td> 7</td><td> 3</td><td> 2</td><td> 3</td><td> 6</td></tr> |
| <tr><th>1</th><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td></tr> |
| <tr><th>2</th><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2D === |
| (used for A/3, B/2) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 1</td><td> 4</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 5</td><td> 7</td><td> 8</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td></tr> |
| <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 6</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>1</th><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>11</td><td> 9</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2E === |
| (used for A/4) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>1</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2F === |
| (used for A/5) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=5 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th> </tr></thead><tbody> |
| <tr><th>-2</th><td>10</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td></tr> |
| <tr><th>0</th><td> 8</td><td> 3</td><td> 1</td><td> 3</td><td> 7</td></tr> |
| <tr><th>1</th><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td></tr> |
| <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2G === |
| (used for A/6) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=5 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th> </tr></thead><tbody> |
| <tr><th>-2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td></tr> |
| <tr><th>-1</th><td> 6</td><td> 5</td><td> 3</td><td> 4</td><td> 6</td></tr> |
| <tr><th>0</th><td> 6</td><td> 3</td><td> 3</td><td> 3</td><td> 6</td></tr> |
| <tr><th>1</th><td> 6</td><td> 4</td><td> 3</td><td> 5</td><td> 7</td></tr> |
| <tr><th>2</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2H === |
| (used for A/7) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 2</td><td> 4</td><td> 7</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>1</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 5</td><td> 8</td><td> 8</td><td> 7</td><td> 9</td></tr> |
| <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>1</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2I === |
| (used for B/0) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 1</td><td> 4</td><td> 7</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td>10</td></tr> |
| <tr><th>1</th><td> 4</td><td> 6</td><td> 9</td><td> 6</td><td> 6</td><td> 9</td><td> 8</td><td> 9</td><td>10</td></tr> |
| <tr><th>2</th><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>12</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 6</td><td> 9</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>11</td></tr> |
| <tr><th>1</th><td> 6</td><td> 7</td><td>10</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 8</td><td> 9</td><td>12</td><td> 9</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td></tr> |
| <tr><th>1</th><td> 8</td><td> 9</td><td>12</td><td> 9</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>12</td></tr> |
| <tr><th>2</th><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2J === |
| (used for B/1) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 9</td></tr> |
| <tr><th>1</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 7</td><td> 5</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 7</td><td> 7</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>1</th><td> 7</td><td> 7</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2K === |
| (used for B/3, B/7) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 2</td><td> 4</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 4</td><td> 5</td><td> 7</td><td> 5</td><td> 6</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 5</td><td> 8</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 6</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>1</th><td> 7</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td> 9</td><td>10</td><td>11</td></tr> |
| <tr><th>2</th><td> 8</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2L === |
| (used for B/4) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=5 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th> </tr></thead><tbody> |
| <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 6</td><td> 3</td><td> 5</td><td> 7</td></tr> |
| <tr><th>0</th><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 6</td></tr> |
| <tr><th>1</th><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 8</td></tr> |
| <tr><th>2</th><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2M === |
| (used for B/5) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=5 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th> </tr></thead><tbody> |
| <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td></tr> |
| <tr><th>0</th><td> 6</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td></tr> |
| <tr><th>1</th><td> 7</td><td> 5</td><td> 3</td><td> 6</td><td> 8</td></tr> |
| <tr><th>2</th><td> 9</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 2N === |
| (used for B/6) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <colgroup span=3 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="3">0</th> <th colspan="3">1</th> <th colspan="3">2</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> <th>0</th> <th>1</th> <th>2</th> </tr></thead> |
| <tbody><tr><th rowspan="3">0</th> |
| <th>0</th><td> 1</td><td> 4</td><td> 6</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 5</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td></tr> |
| <tr><th>2</th><td> 7</td><td> 9</td><td>10</td><td> 7</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">1</th> |
| <th>0</th><td> 4</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>1</th><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>2</th><td> 7</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tbody><tr><th rowspan="3">2</th> |
| <th>0</th><td> 5</td><td> 9</td><td>11</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td></tr> |
| <tr><th>1</th><td> 6</td><td> 9</td><td>11</td><td> 8</td><td> 9</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>2</th><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| ==== Trees for Precision 3 ==== |
(i.e. symbol set -3..+3) | (i.e. symbol set -3..+3) |
| |
=== Tree 3A === | === Tree 3A === |
(used for A/0, B/2) | (used for A/0, B/2) |
| ^ -3 ^ -2 ^ -1 ^ 0 ^ +1 ^ +2 ^ +3 ^ | <html><table class="x" rules="groups" frame="void"> |
^ -3 | 9 | 8 | 7 | 6 | 7 | 7 | 8 | | <col style="width:1.3em"><colgroup span=7 style="width:2em"> |
^ -2 | 8 | 7 | 6 | 6 | 6 | 7 | 7 | | <thead><tr><td></td> |
^ -1 | 7 | 6 | 4 | 4 | 4 | 6 | 7 | | <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th> </tr></thead><tbody> |
^ 0 | 7 | 6 | 4 | 3 | 4 | 6 | 7 | | <tr><th>-3</th><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td></tr> |
^ +1 | 7 | 6 | 4 | 4 | 4 | 6 | 7 | | <tr><th>-2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td></tr> |
^ +2 | 7 | 7 | 6 | 6 | 7 | 8 | 8 | | <tr><th>-1</th><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td></tr> |
^ +3 | 8 | 7 | 7 | 7 | 7 | 8 | 9 | | <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td></tr> |
| <tr><th>1</th><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td></tr> |
| <tr><th>2</th><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> |
| <tr><th>3</th><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3B === |
| (used for A/1, B/1) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=7 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th> </tr></thead><tbody> |
| <tr><th>-3</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td></tr> |
| <tr><th>0</th><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3C === |
| (used for A/2) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=7 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th> </tr></thead><tbody> |
| <tr><th>-3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td><td> 8</td></tr> |
| <tr><th>0</th><td> 7</td><td> 6</td><td> 3</td><td> 3</td><td> 3</td><td> 6</td><td> 7</td></tr> |
| <tr><th>1</th><td> 8</td><td> 7</td><td> 5</td><td> 3</td><td> 5</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>3</th><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3D === |
| (used for A/3) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="4">0</th> <th colspan="4">1</th> <th colspan="4">2</th> <th colspan="4">3</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> </tr></thead> |
| <tbody><tr><th rowspan="4">0</th> |
| <th>0</th><td> 3</td><td> 5</td><td> 8</td><td>10</td><td> 4</td><td> 5</td><td> 7</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 5</td><td> 7</td><td> 8</td><td> 8</td><td> 7</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>10</td><td>12</td><td>12</td><td>11</td><td>10</td><td>12</td><td>11</td></tr> |
| <tbody><tr><th rowspan="4">1</th> |
| <th>0</th><td> 5</td><td> 5</td><td> 8</td><td>10</td><td> 5</td><td> 5</td><td> 8</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>12</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td>11</td><td> 7</td><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 7</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td> 9</td><td>12</td><td>10</td><td> 9</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>12</td></tr> |
| <tbody><tr><th rowspan="4">2</th> |
| <th>0</th><td> 7</td><td> 8</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td></tr> |
| <tr><th>1</th><td> 7</td><td> 7</td><td>10</td><td>12</td><td> 7</td><td> 8</td><td> 8</td><td>10</td><td>11</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>12</td></tr> |
| <tr><th>2</th><td> 8</td><td> 9</td><td>10</td><td>12</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td>11</td><td>10</td><td>12</td><td>12</td><td>11</td><td>10</td></tr> |
| <tr><th>3</th><td>11</td><td>10</td><td> 9</td><td>12</td><td>10</td><td> 9</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>12</td><td>12</td><td>12</td><td>12</td></tr> |
| <tbody><tr><th rowspan="4">3</th> |
| <th>0</th><td>10</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td><td>12</td><td> 9</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td>12</td><td>12</td><td> 8</td><td> 9</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td><td>12</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>12</td><td> 8</td><td>10</td><td>10</td><td>12</td><td>12</td><td> 9</td><td>12</td><td>10</td><td>12</td><td>10</td><td>12</td><td>12</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td><td>12</td><td>10</td><td>12</td><td>12</td><td>12</td><td>10</td><td>12</td><td>10</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3E === |
| (used for A/4) |
| * -3: 4 bits |
| * -2: 3 bits |
| * -1,0: 2 bits |
| * 1,2: 3 bits |
| * 3: 4 bits |
| |
| === Tree 3F === |
| (used for A/5) |
| * -3: 4 bits |
| * -2,-1: 3 bits |
| * 0,1: 2 bits |
| * 2: 3 bits |
| * 3: 4 bits |
| |
| === Tree 3G === |
| (used for A/6) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="4">0</th> <th colspan="4">1</th> <th colspan="4">2</th> <th colspan="4">3</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> </tr></thead> |
| <tbody><tr><th rowspan="4">0</th> |
| <th>0</th><td> 3</td><td> 4</td><td> 7</td><td> 9</td><td> 5</td><td> 5</td><td> 7</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>10</td></tr> |
| <tr><th>2</th><td> 9</td><td> 7</td><td>11</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td> 9</td><td> 9</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tbody><tr><th rowspan="4">1</th> |
| <th>0</th><td> 5</td><td> 5</td><td> 8</td><td>11</td><td> 6</td><td> 6</td><td> 8</td><td> 9</td><td> 9</td><td> 7</td><td>10</td><td> 9</td><td>11</td><td> 9</td><td>10</td><td>11</td></tr> |
| <tr><th>1</th><td> 5</td><td> 5</td><td> 8</td><td> 9</td><td> 6</td><td> 5</td><td> 7</td><td>10</td><td> 7</td><td> 8</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>11</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 8</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 8</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>11</td></tr> |
| <tbody><tr><th rowspan="4">2</th> |
| <th>0</th><td> 7</td><td> 7</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 8</td><td> 8</td><td> 8</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>11</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tbody><tr><th rowspan="4">3</th> |
| <th>0</th><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td></tr> |
| <tr><th>1</th><td> 9</td><td> 8</td><td>10</td><td>11</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>11</td><td>11</td></tr> |
| <tr><th>2</th><td>10</td><td> 9</td><td>10</td><td>11</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td> 9</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3H === |
| (used for A/7) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=7 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th> </tr></thead><tbody> |
| <tr><th>-3</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 4</td><td> 6</td><td> 8</td></tr> |
| <tr><th>0</th><td> 8</td><td> 6</td><td> 4</td><td> 2</td><td> 3</td><td> 6</td><td> 8</td></tr> |
| <tr><th>1</th><td> 8</td><td> 6</td><td> 4</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td></tr> |
| <tr><th>2</th><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>3</th><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3I === |
| (used for B/0) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=7 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th> </tr></thead><tbody> |
| <tr><th>-3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td></tr> |
| <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 7</td></tr> |
| <tr><th>1</th><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td></tr> |
| <tr><th>2</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3J === |
| (used for B/3) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="4">0</th> <th colspan="4">1</th> <th colspan="4">2</th> <th colspan="4">3</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> </tr></thead> |
| <tbody><tr><th rowspan="4">0</th> |
| <th>0</th><td> 2</td><td> 5</td><td> 8</td><td>10</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>1</th><td> 5</td><td> 6</td><td> 8</td><td>10</td><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td>10</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tbody><tr><th rowspan="4">1</th> |
| <th>0</th><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 8</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 6</td><td> 6</td><td> 8</td><td>10</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="4">2</th> |
| <th>0</th><td> 8</td><td> 8</td><td> 9</td><td>11</td><td> 8</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 8</td><td> 7</td><td>10</td><td>10</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="4">3</th> |
| <th>0</th><td> 9</td><td>10</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td>12</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3K === |
| (used for B/4) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=7 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th> </tr></thead><tbody> |
| <tr><th>-3</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 7</td><td> 6</td><td> 5</td><td> 3</td><td> 5</td><td> 6</td><td> 7</td></tr> |
| <tr><th>0</th><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 7</td></tr> |
| <tr><th>1</th><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td></tr> |
| <tr><th>3</th><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 3L === |
| (used for B/5) |
| * -3,-2: 5 bits |
| * -1: 2 bits |
| * 0: 1 bits |
| * 1: 3 bits |
| * 2,3: 5 bits |
| |
| === Tree 3M === |
| (used for B/6) |
| * -3,-2: 5 bits |
| * -1: 3 bits |
| * 0: 1 bits |
| * 1: 2 bits |
| * 2,3: 5 bits |
| |
| === Tree 3N === |
| (used for B/7) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <colgroup span=2 style="width:1.3em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <colgroup span=4 style="width:2em"> |
| <thead> |
| <tr class="c"><td colspan="2" rowspan="2"></td> |
| <th colspan="4">0</th> <th colspan="4">1</th> <th colspan="4">2</th> <th colspan="4">3</th> </tr><tr> |
| <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> </tr></thead> |
| <tbody><tr><th rowspan="4">0</th> |
| <th>0</th><td> 1</td><td> 5</td><td> 9</td><td> 9</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 6</td><td> 8</td><td>10</td><td>10</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>2</th><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tbody><tr><th rowspan="4">1</th> |
| <th>0</th><td> 6</td><td> 7</td><td>10</td><td>11</td><td> 7</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 6</td><td> 7</td><td> 9</td><td>10</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="4">2</th> |
| <th>0</th><td> 9</td><td> 9</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tbody><tr><th rowspan="4">3</th> |
| <th>0</th><td> 8</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| ==== Trees for Precision 4 ==== |
| (i.e. symbol set -5..+5) |
| === Tree 4A === |
| (used for A/0) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 3 bits |
| * 1,2: 2 bits |
| * 3..5: 3 bits |
| |
| === Tree 4B === |
| (used for A/1) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>11</td></tr> |
| <tr><th>-4</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-3</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-2</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> |
| <tr><th>0</th><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td></tr> |
| <tr><th>1</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> |
| <tr><th>2</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td></tr> |
| <tr><th>3</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>4</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>5</th><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4C === |
| (used for A/2, B/5) |
| (absolute values in followed by sign bits if nonzero) |
| * 0..2: 2 bits |
| * 3: 3 bits |
| * 4,5: 4 bits |
| |
| === Tree 4D === |
| (used for A/3) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 2 bits |
| * 1: 1 bits |
| * 2: 3 bits |
| * 3: 4 bits |
| * 4,5: 5 bits |
| |
| === Tree 4E === |
| (used for A/4, B/2) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td></tr> |
| <tr><th>-4</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-3</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> |
| <tr><th>-2</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td></tr> |
| <tr><th>0</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 4</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td></tr> |
| <tr><th>1</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>4</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>5</th><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4F === |
| (used for A/5) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-4</th><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-3</th><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td><td> 7</td></tr> |
| <tr><th>-1</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 9</td><td> 9</td></tr> |
| <tr><th>0</th><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 9</td></tr> |
| <tr><th>1</th><td> 9</td><td> 7</td><td> 7</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 6</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td></tr> |
| <tr><th>3</th><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 9</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>4</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4G === |
| (used for A/6) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-4</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-3</th><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>-2</th><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 8</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 8</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td></tr> |
| <tr><th>0</th><td> 8</td><td> 7</td><td> 7</td><td> 5</td><td> 5</td><td> 4</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td></tr> |
| <tr><th>1</th><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 8</td></tr> |
| <tr><th>2</th><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td></tr> |
| <tr><th>3</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>4</th><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>5</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4H === |
| (used for A/7) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td></tr> |
| <tr><th>-3</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td></tr> |
| <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>-1</th><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>1</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>4</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td></tr> |
| <tr><th>5</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4I === |
| (used for B/0, B/3) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>-4</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>-3</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> |
| <tr><th>0</th><td> 8</td><td> 8</td><td> 8</td><td> 6</td><td> 4</td><td> 2</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td> 8</td></tr> |
| <tr><th>1</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>4</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td></tr> |
| <tr><th>5</th><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4J === |
| (used for B/1, B/4) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=11 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th> </tr></thead><tbody> |
| <tr><th>-5</th><td>12</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td></tr> |
| <tr><th>-4</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>-3</th><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>-2</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>0</th><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td></tr> |
| <tr><th>2</th><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>3</th><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> |
| <tr><th>4</th><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>5</th><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 4K === |
| (used for B/6) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 2 bits |
| * 1: 1 bits |
| * 2: 3 bits |
| * 3,4: 5 bits |
| * 5: 4 bits |
| |
| === Tree 4L === |
| (used for B/7) |
| * -5,-4: 6 bits |
| * -3: 5 bits |
| * -2: 4 bits |
| * -1: 3 bits |
| * 0: 1 bits |
| * 1: 3 bits |
| * 2: 4 bits |
| * 3,4: 6 bits |
| * 5: 5 bits |
| |
| ==== Trees for Precision 5 ==== |
| (i.e. symbol set -7..+7) |
| === Tree 5A === |
| (used for A/0) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>-6</th><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>-5</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>-4</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-2</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 6</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>4</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>5</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>6</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 5B === |
| (used for A/1, B/1) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>-6</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>-5</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-4</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-3</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>0</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tr><th>5</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>6</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>7</th><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 5C === |
| (used for A/2) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 3 bits |
| * 1: 2 bits |
| * 2..5: 3 bits |
| * 6,7: 4 bits |
| |
| === Tree 5D === |
| (used for A/3) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>-6</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-5</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>-4</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>-3</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tr><th>-2</th><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 7</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 7</td><td> 9</td><td>10</td><td> 9</td><td>10</td></tr> |
| <tr><th>-1</th><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>0</th><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 7</td><td> 6</td><td> 4</td><td> 2</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>2</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>4</th><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>5</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>6</th><td>10</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>7</th><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 5E === |
| (used for A/4, B/4) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 3 bits |
| * 1,2: 2 bits |
| * 3: 3 bits |
| * 4..7: 4 bits |
| |
| === Tree 5F === |
| (used for A/5, B/5) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 1 bits |
| * 1: 2 bits |
| * 2: 3 bits |
| * 3: 5 bits |
| * 4,5: 6 bits |
| * 6,7: 5 bits |
| |
| === Tree 5G === |
| (used for A/6) |
| * -7: 7 bits |
| * -6: 6 bits |
| * -5: 7 bits |
| * -4: 6 bits |
| * -3: 5 bits |
| * -2: 4 bits |
| * -1..1: 2 bits |
| * 2,3: 5 bits |
| * 4: 6 bits |
| * 5: 7 bits |
| * 6: 6 bits |
| * 7: 7 bits |
| |
| === Tree 5H === |
| (used for A/7) |
| * -7: 6 bits |
| * -6: 5 bits |
| * -5: 6 bits |
| * -4: 5 bits |
| * -3: 4 bits |
| * -2,-1: 3 bits |
| * 0: 2 bits |
| * 1: 3 bits |
| * 2,3: 4 bits |
| * 4: 5 bits |
| * 5: 6 bits |
| * 6: 5 bits |
| * 7: 6 bits |
| |
| === Tree 5I === |
| (used for B/0, B/2) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>-6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>-5</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>-4</th><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>-3</th><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>-2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>0</th><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 4</td><td> 3</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 8</td></tr> |
| <tr><th>1</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 4</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>4</th><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>5</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>7</th><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 5J === |
| (used for B/3) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>12</td><td>12</td></tr> |
| <tr><th>-6</th><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>-4</th><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td></tr> |
| <tr><th>-3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>-2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td> 9</td><td>11</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 5</td><td> 6</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>0</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 7</td><td> 5</td><td> 1</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td>10</td></tr> |
| <tr><th>4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>11</td></tr> |
| <tr><th>5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> |
| <tr><th>6</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td></tr> |
| <tr><th>7</th><td>12</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 5K === |
| (used for B/6) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>12</td><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>11</td><td>11</td><td>10</td><td>12</td></tr> |
| <tr><th>-6</th><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> |
| <tr><th>-4</th><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> |
| <tr><th>-3</th><td>10</td><td>10</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> |
| <tr><th>-2</th><td> 9</td><td>10</td><td>11</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td></tr> |
| <tr><th>-1</th><td> 9</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 8</td><td> 7</td><td> 5</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>12</td></tr> |
| <tr><th>0</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 4</td><td> 1</td><td> 5</td><td> 7</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>1</th><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td> 6</td><td> 4</td><td> 6</td><td> 8</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td></tr> |
| <tr><th>2</th><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> |
| <tr><th>3</th><td>11</td><td>10</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td> 9</td><td>10</td></tr> |
| <tr><th>4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td>11</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td></tr> |
| <tr><th>5</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>12</td><td>10</td><td>11</td></tr> |
| <tr><th>6</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> |
| <tr><th>7</th><td>12</td><td>10</td><td>12</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td> 8</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 5L === |
| (used for B/7) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=15 style="width:2em"> |
| <thead><tr><td></td> |
| <th>-7</th><th>-6</th><th>-5</th><th>-4</th><th>-3</th><th>-2</th><th>-1</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th> </tr></thead><tbody> |
| <tr><th>-7</th><td>12</td><td>12</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td></tr> |
| <tr><th>-6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>-5</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td></tr> |
| <tr><th>-4</th><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> |
| <tr><th>-3</th><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>11</td><td>11</td></tr> |
| <tr><th>-2</th><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td></tr> |
| <tr><th>-1</th><td>10</td><td>10</td><td>12</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>0</th><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 2</td><td> 3</td><td> 7</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 3</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>2</th><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td></tr> |
| <tr><th>3</th><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td></tr> |
| <tr><th>4</th><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td></tr> |
| <tr><th>5</th><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>6</th><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td></tr> |
| <tr><th>7</th><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| ==== Trees for Precision 6 ==== |
| (i.e. symbol set -15..+15) |
| === Tree 6A === |
| (used for A/0, B/0) |
| (absolute values in followed by sign bits if nonzero) |
| * 0: 3 bits |
| * 1: 2 bits |
| * 2,3: 3 bits |
| * 4,5: 4 bits |
| * 6..9: 5 bits |
| * 10..12: 6 bits |
| * 13,14: 5 bits |
| * 15: 6 bits |
| |
| === Tree 6B === |
| (used for A/1, B/4) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 2</td><td> 4</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 6</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>6</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>7</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>8</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>12</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6C === |
| (used for A/2) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 6</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 6</td><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>6</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>8</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>11</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>14</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>15</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6D === |
| (used for A/3) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 5</td><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>6</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>8</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>11</th><td>11</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>14</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>15</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6E === |
| (used for A/4) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 6</td><td> 7</td><td> 8</td><td> 6</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 7</td><td> 7</td><td> 6</td><td> 6</td><td> 6</td><td> 8</td><td> 6</td><td> 9</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>2</th><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 6</td><td> 7</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td></tr> |
| <tr><th>3</th><td> 7</td><td> 7</td><td> 8</td><td> 7</td><td> 6</td><td> 6</td><td> 7</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 8</td><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 7</td><td> 7</td><td> 7</td><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>6</th><td> 7</td><td> 9</td><td> 6</td><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>7</th><td> 8</td><td> 9</td><td> 6</td><td> 8</td><td> 9</td><td> 7</td><td> 7</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>8</th><td> 8</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 7</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>9</th><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>10</th><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>11</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>12</th><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>13</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>14</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6F === |
| (used for A/5) |
| * -15,-14: 7 bits |
| * -13: 6 bits |
| * -12: 7 bits |
| * -11..-9: 6 bits |
| * -8,-7: 5 bits |
| * -6: 6 bits |
| * -5: 5 bits |
| * -4..3: 4 bits |
| * 4: 3 bits |
| * 5..7: 5 bits |
| * 8,9: 6 bits |
| * 10..13: 7 bits |
| * 14: 6 bits |
| * 15: 7 bits |
| |
| === Tree 6G === |
| (used for A/6, B/7) |
| * -15: 5 bits |
| * -14: 10 bits |
| * -13,-12: 8 bits |
| * -11..-9: 7 bits |
| * -8..-5: 6 bits |
| * -4,-3: 5 bits |
| * -2: 4 bits |
| * -1: 3 bits |
| * 0: 2 bits |
| * 1: 3 bits |
| * 2: 4 bits |
| * 3,4: 5 bits |
| * 5..8: 6 bits |
| * 9..11: 7 bits |
| * 12: 8 bits |
| * 13: 9 bits |
| * 14: 10 bits |
| * 15: 5 bits |
| |
| === Tree 6H === |
| (used for A/7) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 8</td></tr> |
| <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 7</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>6</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>7</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>8</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>11</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>13</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>15</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6I === |
| (used for B/1) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 4</td><td> 4</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 6</td><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 7</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 8</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>6</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>7</th><td> 8</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>8</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>11</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>12</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>15</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6J === |
| (used for B/2, B/3) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>1</th><td> 3</td><td> 4</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td> 9</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 5</td><td> 5</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td> 9</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 6</td><td> 6</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td> 8</td><td> 9</td><td> 9</td></tr> |
| <tr><th>4</th><td> 7</td><td> 7</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>5</th><td> 8</td><td> 7</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>6</th><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>7</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>8</th><td> 9</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>11</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>12</th><td>10</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>13</th><td> 9</td><td> 8</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>14</th><td> 9</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| <tr><th>15</th><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>12</td></tr> |
| </tbody></table> |
| </html> |
| === Tree 6K === |
| (used for B/5) |
| * -15..-13: 7 bits |
| * -12..-7: 8 bits |
| * -6..-4: 7 bits |
| * -3: 6 bits |
| * -2: 5 bits |
| * -1: 3 bits |
| * 0: 1 bits |
| * 1: 3 bits |
| * 2: 5 bits |
| * 3,4: 6 bits |
| * 5..7: 7 bits |
| * 8,9: 8 bits |
| * 10,11: 9 bits |
| * 12: 8 bits |
| * 13: 6 bits |
| * 14,15: 7 bits |
| |
| === Tree 6L === |
| (used for B/6) |
| (absolute values in followed by sign bits if nonzero) |
| <html><table class="x" rules="groups" frame="void"> |
| <col style="width:1.3em"><colgroup span=16 style="width:2em"> |
| <thead><tr><td></td> |
| <th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th><th>13</th><th>14</th><th>15</th> </tr></thead><tbody> |
| <tr><th>0</th><td> 1</td><td> 4</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td> 9</td><td>11</td><td> 9</td><td>12</td><td>12</td><td>12</td><td>10</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>1</th><td> 4</td><td> 4</td><td> 6</td><td> 8</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>10</td><td> 8</td><td> 8</td><td> 9</td></tr> |
| <tr><th>2</th><td> 6</td><td> 6</td><td> 7</td><td> 8</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td> 9</td><td> 9</td></tr> |
| <tr><th>3</th><td> 8</td><td> 7</td><td> 8</td><td> 9</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td> 9</td><td> 9</td><td> 9</td><td>10</td></tr> |
| <tr><th>4</th><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>11</td><td>10</td><td>12</td><td>10</td><td>10</td><td>11</td><td> 9</td><td>11</td><td> 9</td></tr> |
| <tr><th>5</th><td>10</td><td>10</td><td> 9</td><td> 9</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>11</td><td>11</td></tr> |
| <tr><th>6</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>7</th><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>10</td><td>10</td><td> 9</td></tr> |
| <tr><th>8</th><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td> 9</td><td>10</td><td>10</td></tr> |
| <tr><th>9</th><td>10</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td></tr> |
| <tr><th>10</th><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>11</td><td>10</td><td>10</td><td>10</td><td>11</td></tr> |
| <tr><th>11</th><td>10</td><td>10</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>11</td><td>12</td><td>12</td><td>12</td><td>12</td><td>12</td><td>10</td><td>10</td><td>10</td></tr> |
| <tr><th>12</th><td>11</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td></tr> |
| <tr><th>13</th><td> 9</td><td> 9</td><td> 8</td><td> 9</td><td>10</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td>11</td><td>11</td><td>12</td><td>11</td><td>12</td><td>10</td></tr> |
| <tr><th>14</th><td> 9</td><td> 9</td><td> 9</td><td>10</td><td>11</td><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>12</td><td>11</td><td>11</td><td>12</td><td>10</td><td>11</td></tr> |
| <tr><th>15</th><td>10</td><td>10</td><td> 9</td><td>10</td><td>10</td><td>10</td><td>10</td><td>10</td><td>11</td><td>11</td><td>11</td><td>11</td><td>10</td><td>11</td><td>11</td><td>11</td></tr> |
| </tbody></table> |
| </html> |
| ==== Trees for Precision 7 ==== |
| (i.e. symbol set -31..+31) |
| === Tree 7A === |
| (used for A/0, A/7, B/1, B/2) |
| * -31..-29: 8 bits |
| * -28..-26: 7 bits |
| * -25: 8 bits |
| * -24: 10 bits |
| * -23..-18: 9 bits |
| * -17..-11: 8 bits |
| * -10..-7: 7 bits |
| * -6..-4: 6 bits |
| * -3: 5 bits |
| * -2: 4 bits |
| * -1: 3 bits |
| * 0: 2 bits |
| * 1: 3 bits |
| * 2: 4 bits |
| * 3: 5 bits |
| * 4..6: 6 bits |
| * 7..10: 7 bits |
| * 11..16: 8 bits |
| * 17..23: 9 bits |
| * 24: 10 bits |
| * 25: 8 bits |
| * 26..28: 7 bits |
| * 29..31: 8 bits |
| |
| === Tree 7B === |
| (used for A/1) |
| * -31..-29: 8 bits |
| * -28..-26: 7 bits |
| * -25: 8 bits |
| * -24..-22: 9 bits |
| * -21..-15: 8 bits |
| * -14..-9: 7 bits |
| * -8..-6: 6 bits |
| * -5..-3: 5 bits |
| * -2: 4 bits |
| * -1..1: 3 bits |
| * 2: 4 bits |
| * 3,4: 5 bits |
| * 5..8: 6 bits |
| * 9..14: 7 bits |
| * 15..21: 8 bits |
| * 22..24: 9 bits |
| * 25: 8 bits |
| * 26,27: 7 bits |
| * 28..31: 8 bits |
| |
| === Tree 7C === |
| (used for A/2) |
| * -31..-26: 8 bits |
| * -25: 7 bits |
| * -24..-22: 8 bits |
| * -21..-16: 7 bits |
| * -15: 6 bits |
| * -14,-13: 7 bits |
| * -12,-11: 6 bits |
| * -10..-8: 5 bits |
| * -7: 6 bits |
| * -6..-1: 5 bits |
| * 0: 4 bits |
| * 1: 5 bits |
| * 2,3: 4 bits |
| * 4: 6 bits |
| * 5..7: 5 bits |
| * 8: 6 bits |
| * 9: 5 bits |
| * 10..12: 6 bits |
| * 13: 7 bits |
| * 14: 6 bits |
| * 15..19: 7 bits |
| * 20,21: 8 bits |
| * 22,23: 7 bits |
| * 24: 8 bits |
| * 25,26: 7 bits |
| * 27..29: 8 bits |
| * 30: 7 bits |
| * 31: 8 bits |
| |
| === Tree 7D === |
| (used for A/3) |
| * -31,-30: 8 bits |
| * -29..-26: 7 bits |
| * -25..-17: 8 bits |
| * -16..-11: 7 bits |
| * -10..-7: 6 bits |
| * -6..-4: 5 bits |
| * -3..3: 4 bits |
| * 4..6: 5 bits |
| * 7..10: 6 bits |
| * 11..16: 7 bits |
| * 17..24: 8 bits |
| * 25..30: 7 bits |
| * 31: 8 bits |
| |
| === Tree 7E === |
| (used for A/4) |
| * -31,-30: 9 bits |
| * -29: 8 bits |
| * -28,-27: 7 bits |
| * -26: 8 bits |
| * -25: 7 bits |
| * -24,-23: 8 bits |
| * -22: 7 bits |
| * -21: 8 bits |
| * -20: 9 bits |
| * -19..-13: 8 bits |
| * -12: 7 bits |
| * -11: 6 bits |
| * -10: 5 bits |
| * -9: 6 bits |
| * -8..-3: 5 bits |
| * -2..2: 4 bits |
| * 3..6: 5 bits |
| * 7: 6 bits |
| * 8: 5 bits |
| * 9..14: 6 bits |
| * 15..21: 7 bits |
| * 22: 8 bits |
| * 23,24: 9 bits |
| * 25: 8 bits |
| * 26,27: 9 bits |
| * 28: 8 bits |
| * 29..31: 9 bits |
| |
| === Tree 7F === |
| (used for A/5) |
| * -31..-29: 8 bits |
| * -28..-26: 7 bits |
| * -25: 8 bits |
| * -24..-22: 9 bits |
| * -21..-16: 8 bits |
| * -15..-11: 7 bits |
| * -10..-7: 6 bits |
| * -6..-4: 5 bits |
| * -3..-1: 4 bits |
| * 0: 3 bits |
| * 1,2: 4 bits |
| * 3..6: 5 bits |
| * 7..10: 6 bits |
| * 11..15: 7 bits |
| * 16..21: 8 bits |
| * 22: 9 bits |
| * 23..25: 8 bits |
| * 26..28: 7 bits |
| * 29..31: 8 bits |
| |
| === Tree 7G === |
| (used for A/6) |
| * -31..-27: 8 bits |
| * -26: 7 bits |
| * -25: 8 bits |
| * -24..-20: 9 bits |
| * -19..-13: 8 bits |
| * -12..-8: 7 bits |
| * -7..-5: 6 bits |
| * -4,-3: 5 bits |
| * -2,-1: 4 bits |
| * 0: 2 bits |
| * 1: 3 bits |
| * 2: 4 bits |
| * 3,4: 5 bits |
| * 5..7: 6 bits |
| * 8..13: 7 bits |
| * 14..19: 8 bits |
| * 20..24: 9 bits |
| * 25: 8 bits |
| * 26: 7 bits |
| * 27..31: 8 bits |
| |
| === Tree 7H === |
| (used for B/0, B/5) |
| * -31..-25: 7 bits |
| * -24..-20: 9 bits |
| * -19..-14: 8 bits |
| * -13..-9: 7 bits |
| * -8..-5: 6 bits |
| * -4,-3: 5 bits |
| * -2: 4 bits |
| * -1..1: 3 bits |
| * 2: 4 bits |
| * 3,4: 5 bits |
| * 5..8: 6 bits |
| * 9..12: 7 bits |
| * 13..19: 8 bits |
| * 20..24: 9 bits |
| * 25..31: 7 bits |
| |
| === Tree 7I === |
| (used for B/3) |
| * -31: 9 bits |
| * -30,-29: 8 bits |
| * -28: 9 bits |
| * -27..-25: 8 bits |
| * -24: 11 bits |
| * -23: 10 bits |
| * -22: 11 bits |
| * -21..-16: 10 bits |
| * -15..-10: 9 bits |
| * -9..-7: 8 bits |
| * -6..-4: 7 bits |
| * -3: 6 bits |
| * -2: 5 bits |
| * -1: 3 bits |
| * 0: 1 bits |
| * 1: 3 bits |
| * 2: 5 bits |
| * 3: 6 bits |
| * 4..6: 7 bits |
| * 7..10: 8 bits |
| * 11: 9 bits |
| * 12: 10 bits |
| * 13..15: 9 bits |
| * 16..19: 10 bits |
| * 20: 11 bits |
| * 21: 10 bits |
| * 22..24: 11 bits |
| * 25..29: 8 bits |
| * 30,31: 9 bits |
| |
| === Tree 7J === |
| (used for B/4) |
| * -31..-28: 8 bits |
| * -27,-26: 7 bits |
| * -25: 8 bits |
| * -24..-19: 9 bits |
| * -18..-13: 8 bits |
| * -12..-8: 7 bits |
| * -7..-5: 6 bits |
| * -4,-3: 5 bits |
| * -2,-1: 4 bits |
| * 0: 2 bits |
| * 1: 3 bits |
| * 2: 4 bits |
| * 3,4: 5 bits |
| * 5..7: 6 bits |
| * 8..12: 7 bits |
| * 13..18: 8 bits |
| * 19..24: 9 bits |
| * 25: 8 bits |
| * 26,27: 7 bits |
| * 28..31: 8 bits |
| |
| === Tree 7K === |
| (used for B/6) |
| * -31..-25: 8 bits |
| * -24..-19: 9 bits |
| * -18..-13: 8 bits |
| * -12..-8: 7 bits |
| * -7..-5: 6 bits |
| * -4,-3: 5 bits |
| * -2: 4 bits |
| * -1: 3 bits |
| * 0: 2 bits |
| * 1: 3 bits |
| * 2,3: 5 bits |
| * 4..7: 6 bits |
| * 8..12: 7 bits |
| * 13..18: 8 bits |
| * 19..24: 9 bits |
| * 25..31: 8 bits |
| |
| === Tree 7L === |
| (used for B/7) |
| * -31,-30: 11 bits |
| * -29: 10 bits |
| * -28: 11 bits |
| * -27..-20: 9 bits |
| * -19,-18: 8 bits |
| * -17: 7 bits |
| * -16: 8 bits |
| * -15..-11: 7 bits |
| * -10..-6: 6 bits |
| * -5..-3: 5 bits |
| * -2,-1: 4 bits |
| * 0: 2 bits |
| * 1,2: 4 bits |
| * 3..5: 5 bits |
| * 6..10: 6 bits |
| * 11..16: 7 bits |
| * 17..20: 8 bits |
| * 21..27: 9 bits |
| * 28..30: 10 bits |
| * 31: 11 bits |
| |
| ===== Tree Sets ===== |
| |
| This table shows the mapping of tree set IDs, tree IDs and quantization precisions to the code tables defined above. If the table says //n x Tree XX// it means that n symbols of that tree (which might groups of 1, 2 or 4 quantized coefficients) are clustered together. Each cluster is preceeded by an "data present" bit. If that bit is zero, all coefficients of the whole cluster are zero, and no codes for the cluster are stored. If that bit is one that at least one non-zero entry is present and the codes for this cluster follow as in non-clustered mode. |
| |
| The tree choice can be limited to a restricted tree set. The IDs inside the restricted tree set are in the range 0..3 instead of 0..7, and printed as R0..R3 in the table. |
| |
| ==== Tree Set A==== |
| |Quant\ID^ 0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ ^ R0^ R1^ R2^ R3^ |
| ^ 1| Tree 1A| 4 x Tree 1B| Tree 1C| Tree 1D| Tree 1E| Tree 1F| 2 x Tree 1G| Tree 1H| | Tree 1A| Tree 1F| Tree 1E| 4x Tree 1B| |
| ^ 2| Tree 2A| Tree 2B| Tree 2C| Tree 2D| Tree 2E| Tree 2F| Tree 2G| 2 x Tree 2H| | Tree 2A| Tree 2B| Tree 2C| Tree 2D| |
| ^ 3| Tree 3A| Tree 3B| Tree 3C| Tree 3D| Tree 3E| Tree 3F| Tree 3G| Tree 3H| | Tree 3D| Tree 3A| Tree 3E| Tree 3C| |
| ^ 4| Tree 4A| Tree 4B| Tree 4C| Tree 4D| Tree 4E| Tree 4F| Tree 4G| Tree 4H| | Tree 4E| Tree 4A| Tree 4B| Tree 4C| |
| ^ 5| Tree 5A| Tree 5B| Tree 5C| Tree 5D| Tree 5E| Tree 5F| Tree 5G| Tree 5H| | Tree 5B| Tree 5A| Tree 5E| Tree 5D| |
| ^ 6| Tree 6A| Tree 6B| Tree 6C| Tree 6D| Tree 6E| Tree 6F| Tree 6G| 2 x Tree 6H| | Tree 6D| Tree 6A| Tree 6C| Tree 6B| |
| ^ 7| Tree 7A| Tree 7B| Tree 7C| Tree 7D| Tree 7E| Tree 7F| Tree 7G| 4 x Tree 7A| | Tree 7A| Tree 7D| Tree 7B| Tree 7C| |
| |
| ==== Tree Set B==== |
| |Quant\ID^ 0^ 1^ 2^ 3^ 4^ 5^ 6^ 7^ ^ R0^ R1^ R2^ R3^ |
| ^ 1| 4 x Tree 1I| Tree 1C| 4 x Tree 1E| Tree 1F| Tree 1J| 2 x Tree 1G| Tree 1E| Tree 1K| | Tree 1J| 4 x Tree 1I| Tree 1C| 4 x Tree 1E| |
| ^ 2| Tree 2I| Tree 2J| 4 x Tree 2D| Tree 2K| 4 x Tree 2L| Tree 2M| Tree 2N| 4 x Tree 2K| | Tree 2I| Tree 2K| 4 x Tree 2D| Tree 2J| |
| ^ 3| 4 x Tree 3I| Tree 3B| Tree 3A| Tree 3J| Tree 3K| 4 x Tree 3L| Tree 3M| 4 x Tree 3N| | 4 x Tree 3I| Tree 3B| Tree 3A| Tree 3J| |
| ^ 4| Tree 4I| Tree 4J| Tree 4E| 2 x Tree 4I| 4 x Tree 4J| Tree 4C| Tree 4K| Tree 4L| | Tree 4I| Tree 4J| Tree 4E| 4 x Tree 4J| |
| ^ 5| Tree 5I| Tree 5B| 2 x Tree 5I| Tree 5J| Tree 5E| Tree 5F| 4 x Tree 5K| Tree 5L| | Tree 5I| Tree 5B| 2 x Tree 5I| Tree 5J| |
| ^ 6| Tree 6A| Tree 6I| 2 x Tree 6J| Tree 6J| Tree 6B| Tree 6K| Tree 6L| Tree 6G| | Tree 6I| Tree 6B| 2 x Tree 6J| Tree 6A| |
| ^ 7| Tree 7H| Tree 7A| 4 x Tree 7A| Tree 7I| Tree 7J| 2 x Tree 7H| Tree 7K| Tree 7L| | Tree 7H| Tree 7A| 4 x Tree 7A| Tree 7I| |
| |
| |