Filter: Update trie documentation

/*

 *	Filters: Trie for prefix sets

 *

 *	Copyright 2009 Ondrej Zajicek <santiago@crfreenet.org>

 *	(c) 2009--2020 Ondrej Zajicek <santiago@crfreenet.org>

 *	(c) 2009--2020 CZ.NIC z.s.p.o.

 *

 *	Can be freely distributed and used under the terms of the GNU GPL.

 */

/**

 * DOC: Trie for prefix sets

 *

 * We use a (compressed) trie to represent prefix sets. Every node

 * in the trie represents one prefix (&addr/&plen) and &plen also

 * indicates the index of the bit in the address that is used to

 * branch at the node. If we need to represent just a set of

 * prefixes, it would be simple, but we have to represent a

 * set of prefix patterns. Each prefix pattern consists of

 * &ppaddr/&pplen and two integers: &low and &high, and a prefix

 * &paddr/&plen matches that pattern if the first MIN(&plen, &pplen)

 * bits of &paddr and &ppaddr are the same and &low <= &plen <= &high.

 * We use a (compressed) trie to represent prefix sets. Every node in the trie

 * represents one prefix (&addr/&plen) and &plen also indicates the index of

 * bits in the address that are used to branch at the node. Note that such

 * prefix is not necessary a member of the prefix set, it is just a canonical

 * prefix associated with a node. Prefix lengths of nodes are aligned to

 * multiples of &TRIE_STEP (4) and there is 16-way branching in each

 * node. Therefore, we say that a node is associated with a range of prefix

 * lengths (&plen .. &plen + TRIE_STEP - 1).

 *

 * We use a bitmask (&accept) to represent accepted prefix lengths

 * at a node. As there are 33 prefix lengths (0..32 for IPv4), but

 * there is just one prefix of zero length in the whole trie so we

 * have &zero flag in &f_trie (indicating whether the trie accepts

 * prefix 0.0.0.0/0) as a special case, and &accept bitmask

 * The prefix set is not just a set of prefixes, it is defined by a set of

 * prefix patterns. Each prefix pattern consists of &ppaddr/&pplen and two

 * integers: &low and &high. The tested prefix &paddr/&plen matches that pattern

 * if the first MIN(&plen, &pplen) bits of &paddr and &ppaddr are the same and

 * &low <= &plen <= &high.

 *

 * There are two ways to represent accepted prefixes for a node. First, there is

 * a bitmask &local, which represents independently all 15 prefixes that extend

 * the canonical prefix of the node and are within a range of prefix lengths

 * associated with the node. E.g., for node 10.0.0.0/8 they are 10.0.0.0/8,

 * 10.0.0.0/9, 10.128.0.0/9, .. 10.224.0.0/11. This order (first by length, then

 * lexicographically) is used for indexing the bitmask &local, starting at

 * position 1. I.e., index is 2^(plen - base) + offset within the same length,

 * see function trie_local_mask6() for details.

 *

 * Second, we use a bitmask &accept to represent accepted prefix lengths at a

 * node. The bit is set means that all prefixes of given length that are either

 * subprefixes or superprefixes of the canonical prefix are accepted. As there

 * are 33 prefix lengths (0..32 for IPv4), but there is just one prefix of zero

 * length in the whole trie so we have &zero flag in &f_trie (indicating whether

 * the trie accepts prefix 0.0.0.0/0) as a special case, and &accept bitmask

 * represents accepted prefix lengths from 1 to 32.

 *

 * There are two cases in prefix matching - a match when the length

 * of the prefix is smaller that the length of the prefix pattern,

 * (&plen < &pplen) and otherwise. The second case is simple - we

 * just walk through the trie and look at every visited node

 * whether that prefix accepts our prefix length (&plen). The

 * first case is tricky - we don't want to examine every descendant

 * of a final node, so (when we create the trie) we have to propagate

 * that information from nodes to their ascendants.

 * One complication is handling of prefix patterns with unaligned prefix length.

 * When such pattern is to be added, we add a primary node above (with rounded

 * down prefix length &nlen) and a set of secondary nodes below (with rounded up

 * prefix lengths &slen). Accepted prefix lengths of the original prefix pattern

 * are then represented in different places based on their lengths. For prefixes

 * shorter than &nlen, it is &accept bitmask of the primary node, for prefixes

 * between &nlen and &slen - 1 it is &local bitmask of the primary node, and for

 * prefixes longer of equal &slen it is &accept bitmasks of secondary nodes.

 *

 * Suppose that we have two masks (M1 and M2) for a node. Mask M1

 * represents accepted prefix lengths by just the node and mask M2

 * represents accepted prefix lengths by the node or any of its

 * descendants. Therefore M2 is a bitwise or of M1 and children's

 * M2 and this is a maintained invariant during trie building.

 * Basically, when we want to match a prefix, we walk through the trie,

 * check mask M1 for our prefix length and when we came to

 * final node, we check mask M2.

 * There are two cases in prefix matching - a match when the length of the

 * prefix is smaller that the length of the prefix pattern, (&plen < &pplen) and

 * otherwise. The second case is simple - we just walk through the trie and look

 * at every visited node whether that prefix accepts our prefix length (&plen).

 * The first case is tricky - we do not want to examine every descendant of a

 * final node, so (when we create the trie) we have to propagate that

 * information from nodes to their ascendants.

 *

 * There are two differences in the real implementation. First,

 * we use a compressed trie so there is a case that we skip our

 * final node (if it is not in the trie) and we came to node that

 * is either extension of our prefix, or completely out of path

 * In the first case, we also have to check M2.

 * There are two kinds of propagations - propagation from child's &accept

 * bitmask to parent's &accept bitmask, and propagation from child's &accept

 * bitmask to parent's &local bitmask. The first kind is simple - as all

 * superprefixes of a parent are also all superprefixes of appropriate length of

 * a child, then we can just add (by bitwise or) a child &accept mask masked by

 * parent prefix length mask to the parent &accept mask. This handles prefixes

 * shorter than node &plen.

 *

 * Second, we really need not to maintain two separate bitmasks.

 * Checks for mask M1 are always larger than &applen and we need

 * just the first &pplen bits of mask M2 (if trie compression

 * hadn't been used it would suffice to know just $applen-th bit),

 * so we have to store them together in &accept mask - the first

 * &pplen bits of mask M2 and then mask M1.

 * The second kind of propagation is necessary to handle superprefixes of a

 * child that are represented by parent &local mask - that are in the range of

 * prefix lengths associated with the parent. For each accepted (by child

 * &accept mask) prefix length from that range, we need to set appropriate bit

 * in &local mask. See function trie_amask_to_local() for details.

 *

 * There are four cases when we walk through a trie:

 *

 * - we are beyond the end of path (node length > &plen)

 * - we are still on path and keep walking (node length < &plen)

 *

 * The walking code in trie_match_prefix() is structured according to

 * these cases.

 * The walking code in trie_match_net() is structured according to these cases.

 */

#include "nest/bird.h"

}

/*

 * Compute appropriate mask representing prefix px/plen in local bitmask of node

 * with prefix length nlen. Assuming that nlen <= plen < (nlen + TRIE_STEP).

 */

static inline uint

trie_local_mask4(ip4_addr px, uint plen, uint nlen)

{

  return 1u << pos;

}

/*

 * Compute an appropriate local mask (for a node with prefix length nlen)

 * representing prefixes of px that are accepted by amask and fall within the

 * range associated with that node. Used for propagation of child accept mask

 * to parent local mask.

 */

static inline uint

trie_amask_to_local(ip_addr px, ip_addr amask, uint nlen)

{