The design of the tree goes from the row-cache needs, which are
1. Insert/Remove do not invalidate iterators
2. Elements are LSA-manageable
3. Low key overhead
4. External tri-comparator
5. As little actions on insert/remove as possible
With the above the design is
Two types of nodes -- inner and leaf. Both types keep pointer on parent nodes
and N pointers on keys (not keys themselves). Two differences: inner nodes have
array of pointers on kids, leaf nodes keep pointer on the tree (to update left-
and rightmost tree pointers on node move).
Nodes do not keep pointers/references on trees, thus we have O(1) move of any
object, but O(logN) to get the tree size. Fortunately, with big keys-per-node
value this won't result in too many steps.
In turn, the tree has 3 pointers -- root, left- and rightmost leaves. The latter
is for constant-time begin() and end().
Keys are managed by user with the help of embeddable member_hook instance,
which is 1 pointer in size.
The code was copied from the B+ tree one, then heavily reworked, the internal
algorythms turned out to differ quite significantly.
For the sake of mutation_partition::apply_monotonically(), which needs to move
an element from one tree into another, there's a key_grabber helping wrapper
that allows doing this move respecting the exception-safety requirement.
As measured by the perf_collections test the B-tree with 8 keys is faster, than
the std::set, but slower than the B+tree:
vs set vs b+tree
fill: +13% -6%
find: +23% -35%
Another neat thing is that 1-key insertion-removal is ~40% faster than
for BST (the same number of allocations, but the key object is smaller,
less pointers to set-up and less instructions to execute when linking
node with root).
v4:
- equip insertion methods with on_alloc_point() calls to catch
potential exception guarantees violations eariler
- add unlink_leftmost_without_rebalance. The method is borrowed from
boost intrusive set, and is added to kill two birds -- provide it,
as it turns out to be popular, and use a bit faster step-by-step
tree destruction than plain begin+erase loop
v3:
- introduce "inline" root node that is embedded into tree object and in
which the 1st key is inserted. This greatly improves the 1-key-tree
performance, which is pretty common case for rows cache
v2:
- introduce "linear" root leaf that grows on demand
This improves the memory consumption for small trees. This linear node may
and should over-grow the NodeSize parameter. This comes from the fact that
there are two big per-key memory spikes on small trees -- 1-key root leaf
and the first split, when the tree becomes 1-key root with two half-filled
leaves. If the linear extention goes above NodeSize it can flatten even the
2nd peak
- mitigate the keys indirection a bit
Prefetching the keys while doing the intra-node linear scan and the nodes
while descending the tree gives ~+5% of fill and find
- generalize stress tests for B and B+ trees
- cosmetic changes
TODO:
- fix few inefficincies in the core code (walks the sub-tree twice sometimes)
- try to optimize the leaf nodes, that are not lef-/righmost not to carry
unused tree pointer on board
Signed-off-by: Pavel Emelyanov <xemul@scylladb.com>
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