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11.9 Binary Search on Ranges 257 Before moving on to the child, the algorithm must also check the internal bitmap to see if there are one or more stored prefixes corresponding to the path through the multibit node to position P. For example, suppose P is 101 and a 3-bit stride is used at the root node bitmap, as in Figure 11.16. The algorithm first checks to see whether there is a stored internal prefix 101*. Since 101* corresponds to the 13th bit position in the internal prefix bitmap, the algorithm can check if there is a 1 in that position (there is one in the example). If there was no 1 in this position, the algorithm would back up to check whether there is an internal prefix corresponding to 10*. Finally, if there is a 10* prefix, the algorithm checks for the prefix 1*. This search algorithm appears to require a number of iterations, proportional to the loga- rithm of the internal bitmap length. However, for bitmaps of up to 512 bits or so in hardware, this is just a matter of simple combinational logic. Intuitively, such logic performs all iterations in parallel and uses a priority encoder to return the longest matching stored prefix. Once it knows there is a matching stored prefix within a trie node, the algorithm does not immediately retrieve the corresponding next-hop information from the result node associated with the trie node. Instead, the algorithm moves to the child node while remembering the stored-prefix position and the corresponding parent trie node. The intent is to remember the last trie node T in the search path that contained a stored prefix, and the corresponding prefix position. Search terminates when it encounters a trie node with a 0 set in the corresponding position of the extending bitmap. At this point, the algorithm makes a final access to the result array corresponding to T to read off the next-hop information. Further tricks to reduce memory access width are described in Eatherton's MS thesis [Eat], which includes a number of other useful ideas. Intuitively, insertions in a tree bitmap are very similar to insertions in a simple multibit trie wihout leaf pushing. A prefix insertion may cause a trie node to be changed completely; a new copy of the node is created and linked in atomically to the existing trie. Compression results