#### 3.5.2 Symbol table format

From mmixal.w (or really, the generated mmixal.tex) in http://www-cs-faculty.stanford.edu/~knuth/programs/mmix.tar.gz): “Symbols are stored and retrieved by means of a ``ternary search trie`', following ideas of Bentley and Sedgewick. (See ACM–SIAM Symp. on Discrete Algorithms ``8`' (1997), 360–369; R.Sedgewick, ``Algorithms in C`' (Reading, Mass. Addison–Wesley, 1998), ``15.4`'.) 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.”

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.

First, there's a control byte `m`. If any of the listed bits in `m` is nonzero, we execute what stands at the right, in the listed order:

          (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 m:

                 (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 & 0xf).

                        (MMO3_REGQUAL_BITS)
                        j == 0xf: A register variable.  The following
                                  byte tells which register.
                        j <= 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 > 8:    As with j <= 8, but add (0x20 << 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.)

Let's look again at the `lop_stab` for the trivial file (see File layout).

          0x980b0000 - lop_stab for ":Main" = 0, serial 1.
          0x203a4040
          0x10404020
          0x4d206120
          0x69016e00
          0x81000000

This forms the trivial trie (note that the path between “:” and “M” is redundant):

          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.