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<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 <span class="samp">ternary
search trie</span>, following ideas of Bentley and Sedgewick. (See
ACM&ndash;SIAM Symp. on Discrete Algorithms <span class="samp">8</span> (1997), 360&ndash;369;
R.Sedgewick, <span class="samp">Algorithms in C</span> (Reading, Mass. 
Addison&ndash;Wesley, 1998), <span class="samp">15.4</span>.)  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>So it'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>First, there'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:

<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>
   <p>Let's look again at the <code>lop_stab</code> for the trivial file
(see <a href="File-layout.html#File-layout">File layout</a>).

<pre class="example">      0x980b0000 - lop_stab for ":Main" = 0, serial 1.
      0x203a4040
      0x10404020
      0x4d206120
      0x69016e00
      0x81000000
</pre>
   <p>This forms the trivial trie (note that the path between &ldquo;:&rdquo; and
&ldquo;M&rdquo; is redundant):

<pre class="example">      203a     ":"
      40       /
      40      /
      10      \
      40      /
      40     /
      204d  "M"
      2061  "a"
      2069  "i"
      016e  "n" 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>
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