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<a name="Symbol_002dtable"></a>
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<hr>
<a name="Symbol-table-format"></a>
<h4 class="subsection">3.5.2 Symbol table format</h4>
<p>From mmixal.w (or really, the generated mmixal.tex) in
<a href="http://www-cs-faculty.stanford.edu/~knuth/programs/mmix.tar.gz">http://www-cs-faculty.stanford.edu/~knuth/programs/mmix.tar.gz</a>):
&ldquo;Symbols are stored and retrieved by means of a &lsquo;<samp>ternary
search trie</samp>&rsquo;, following ideas of Bentley and Sedgewick. (See
ACM&ndash;SIAM Symp. on Discrete Algorithms &lsquo;<samp>8</samp>&rsquo; (1997), 360&ndash;369;
R.Sedgewick, &lsquo;<samp>Algorithms in C</samp>&rsquo; (Reading, Mass.
Addison&ndash;Wesley, 1998), &lsquo;<samp>15.4</samp>&rsquo;.)  Each trie node stores a
character, and there are branches to subtries for the cases where
a given character is less than, equal to, or greater than the
character in the trie.  There also is a pointer to a symbol table
entry if a symbol ends at the current node.&rdquo;
</p>
<p>So it&rsquo;s a tree encoded as a stream of bytes.  The stream of bytes
acts on a single virtual global symbol, adding and removing
characters and signalling complete symbol points.  Here, we read
the stream and create symbols at the completion points.
</p>
<p>First, there&rsquo;s a control byte <code>m</code>.  If any of the listed bits
in <code>m</code> is nonzero, we execute what stands at the right, in
the listed order:
</p>
<div class="example">
<pre class="example"> (MMO3_LEFT)
 0x40 - Traverse left trie.
        (Read a new command byte and recurse.)

 (MMO3_SYMBITS)
 0x2f - Read the next byte as a character and store it in the
        current character position; increment character position.
        Test the bits of <code>m</code>:

        (MMO3_WCHAR)
        0x80 - The character is 16-bit (so read another byte,
               merge into current character.

        (MMO3_TYPEBITS)
        0xf  - We have a complete symbol; parse the type, value
               and serial number and do what should be done
               with a symbol.  The type and length information
               is in j = (m &amp; 0xf).

               (MMO3_REGQUAL_BITS)
               j == 0xf: A register variable.  The following
                         byte tells which register.
               j &lt;= 8:   An absolute symbol.  Read j bytes as the
                         big-endian number the symbol equals.
                         A j = 2 with two zero bytes denotes an
                         unknown symbol.
               j &gt; 8:    As with j &lt;= 8, but add (0x20 &lt;&lt; 56)
                         to the value in the following j - 8
                         bytes.

               Then comes the serial number, as a variant of
               uleb128, but better named ubeb128:
               Read bytes and shift the previous value left 7
               (multiply by 128).  Add in the new byte, repeat
               until a byte has bit 7 set.  The serial number
               is the computed value minus 128.

        (MMO3_MIDDLE)
        0x20 - Traverse middle trie.  (Read a new command byte
               and recurse.)  Decrement character position.

 (MMO3_RIGHT)
 0x10 - Traverse right trie.  (Read a new command byte and
        recurse.)
</pre></div>

<p>Let&rsquo;s look again at the <code>lop_stab</code> for the trivial file
(see <a href="File-layout.html#File-layout">File layout</a>).
</p>
<div class="example">
<pre class="example"> 0x980b0000 - lop_stab for &quot;:Main&quot; = 0, serial 1.
 0x203a4040
 0x10404020
 0x4d206120
 0x69016e00
 0x81000000
</pre></div>

<p>This forms the trivial trie (note that the path between &ldquo;:&rdquo; and
&ldquo;M&rdquo; is redundant):
</p>
<div class="example">
<pre class="example"> 203a     &quot;:&quot;
 40       /
 40      /
 10      \
 40      /
 40     /
 204d  &quot;M&quot;
 2061  &quot;a&quot;
 2069  &quot;i&quot;
 016e  &quot;n&quot; is the last character in a full symbol, and
       with a value represented in one byte.
 00    The value is 0.
 81    The serial number is 1.
</pre></div>

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