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/*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*/
package org.apache.cassandra.utils.btree;
import java.util.*;
import java.util.function.BiConsumer;
import java.util.function.BiFunction;
import java.util.function.Consumer;
import java.util.function.Function;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.base.Preconditions;
import com.google.common.collect.Iterators;
import com.google.common.collect.Ordering;
import org.apache.cassandra.utils.BiLongAccumulator;
import org.apache.cassandra.utils.BulkIterator;
import org.apache.cassandra.utils.LongAccumulator;
import org.apache.cassandra.utils.ObjectSizes;
import org.apache.cassandra.utils.caching.TinyThreadLocalPool;
import static java.lang.Math.max;
import static java.lang.Math.min;
public class BTree
{
/**
* The {@code BRANCH_FACTOR} is defined as the maximum number of children of each branch, with between
* BRANCH_FACTOR/2-1 and BRANCH_FACTOR-1 keys being stored in every node. This yields a minimum tree size of
* {@code (BRANCH_FACTOR/2)^height - 1} and a maximum tree size of {@code BRANCH_FACTOR^height - 1}.
*
* Branches differ from leaves only in that they contain a suffix region containing the child nodes that occur
* either side of the keys, and a sizeMap in the last position, permitting seeking by index within the tree.
* Nodes are disambiguated by the length of the array that represents them: an even number is a branch, odd a leaf.
*
* Leaf Nodes are represented by an odd-length array of keys, with the final element possibly null, i.e.
* Object[V1, V2, ...,null?]
*
* Branch nodes: Object[V1, V2, ..., child[<V1.key], child[<V2.key], ..., child[< Inf], sizeMap]
* Each child is either a branch or leaf, i.e., always an Object[].
* The key elements in a branch node occupy the first half of the array (minus one)
*
* BTrees are immutable; updating one returns a new tree that reuses unmodified nodes.
*
* There are no references back to a parent node from its children (this would make it impossible to re-use
* subtrees when modifying the tree, since the modified tree would need new parent references).
* Instead, we store these references in a Path as needed when navigating the tree.
*/
public static final int BRANCH_SHIFT = Integer.getInteger("cassandra.btree.branchshift", 5);
private static final int BRANCH_FACTOR = 1 << BRANCH_SHIFT;
public static final int MIN_KEYS = BRANCH_FACTOR / 2 - 1;
public static final int MAX_KEYS = BRANCH_FACTOR - 1;
// An empty BTree Leaf - which is the same as an empty BTree
private static final Object[] EMPTY_LEAF = new Object[1];
private static final int[][] DENSE_SIZE_MAPS = buildBalancedSizeMaps(BRANCH_SHIFT);
private static final long[] PERFECT_DENSE_SIZE_ON_HEAP = sizeOnHeapOfPerfectTrees(BRANCH_SHIFT);
/**
* Represents the direction of iteration.
*/
public enum Dir
{
ASC, DESC;
public Dir invert()
{
return this == ASC ? DESC : ASC;
}
public static Dir desc(boolean desc)
{
return desc ? DESC : ASC;
}
}
/**
* Returns an empty BTree
*
* @return an empty BTree
*/
public static Object[] empty()
{
return EMPTY_LEAF;
}
/**
* Create a BTree containing only the specified object
*
* @return an new BTree containing only the specified object
*/
public static Object[] singleton(Object value)
{
return new Object[]{ value };
}
@Deprecated
public static Object[] build(Collection source)
{
return build(source, UpdateFunction.noOp());
}
@Deprecated
public static Object[] build(Collection source, UpdateFunction updateF)
{
return build(BulkIterator.of(source.iterator()), source.size(), updateF);
}
public static Object[] build(BulkIterator source, int size, UpdateFunction updateF)
{
assert size >= 0;
if (size == 0)
return EMPTY_LEAF;
if (size <= MAX_KEYS)
return buildLeaf(source, size, updateF);
return buildRoot(source, size, updateF);
}
/**
* Build a leaf with {@code size} elements taken in bulk from {@code insert}, and apply {@code updateF} to these elements
*/
private static Object[] buildLeaf(BulkIterator insert,
int size,
UpdateFunction updateF)
{
Object[] values = new Object[size | 1]; // ensure that we have an odd-length array
insert.fetch(values, 0, size);
if (!isSimple(updateF))
{
updateF.onAllocatedOnHeap(ObjectSizes.sizeOfReferenceArray(values.length));
for (int i = 0; i < size; i++)
values[i] = updateF.insert((I) values[i]);
}
return values;
}
/**
* Build a leaf with {@code size} elements taken in bulk from {@code insert}, and apply {@code updateF} to these elements
* Do not invoke {@code updateF.onAllocated}. Used by {@link #buildPerfectDenseWithoutSizeTracking} which
* track the size for the entire tree they build in order to save on work.
*/
private static Object[] buildLeafWithoutSizeTracking(BulkIterator insert, int size, UpdateFunction updateF)
{
Object[] values = new Object[size | 1]; // ensure that we have an odd-length array
insert.fetch(values, 0, size);
if (!isSimple(updateF))
{
for (int i = 0; i < size; i++)
values[i] = updateF.insert((I) values[i]);
}
return values;
}
/**
* Build a root node from the first {@code size} elements from {@code source}, applying {@code updateF} to those elements.
* A root node is permitted to have as few as two children, if a branch (i.e. if {@code size > MAX_SIZE}.
*/
private static Object[] buildRoot(BulkIterator source, int size, UpdateFunction updateF)
{
// first calculate the minimum height needed for this size of tree
int height = minHeight(size);
assert height > 1;
assert height * BRANCH_SHIFT < 32;
int denseChildSize = denseSize(height - 1);
// Divide the size by the child size + 1, adjusting size by +1 to compensate for not having an upper key on the
// last child and rounding up, i.e. (size + 1 + div - 1) / div == size / div + 1 where div = childSize + 1
int childCount = size / (denseChildSize + 1) + 1;
return buildMaximallyDense(source, childCount, size, height, updateF);
}
/**
* Build a tree containing only dense nodes except at most two on any level. This matches the structure that
* a FastBuilder would create, with some optimizations in constructing the dense nodes.
*
* We do this by repeatedly constructing fully dense children until we reach a threshold, chosen so that we would
* not be able to create another child with fully dense children and at least MIN_KEYS keys. After the threshold,
* the remainder may fit a single node, or is otherwise split roughly halfway to create one child with at least
* MIN_KEYS+1 fully dense children, and one that has at least MIN_KEYS-1 fully dense and up to two non-dense.
*/
private static Object[] buildMaximallyDense(BulkIterator source,
int childCount,
int size,
int height,
UpdateFunction updateF)
{
assert childCount <= MAX_KEYS + 1;
int keyCount = childCount - 1;
int[] sizeMap = new int[childCount];
Object[] branch = new Object[childCount * 2];
if (height == 2)
{
// we use the _exact same logic_ as below, only we invoke buildLeaf
int remaining = size;
int threshold = MAX_KEYS + 1 + MIN_KEYS;
int i = 0;
while (remaining >= threshold)
{
branch[keyCount + i] = buildLeaf(source, MAX_KEYS, updateF);
branch[i] = isSimple(updateF) ? source.next() : updateF.insert(source.next());
remaining -= MAX_KEYS + 1;
sizeMap[i++] = size - remaining - 1;
}
if (remaining > MAX_KEYS)
{
int childSize = remaining / 2;
branch[keyCount + i] = buildLeaf(source, childSize, updateF);
branch[i] = isSimple(updateF) ? source.next() : updateF.insert(source.next());
remaining -= childSize + 1;
sizeMap[i++] = size - remaining - 1;
}
branch[keyCount + i] = buildLeaf(source, remaining, updateF);
sizeMap[i++] = size;
assert i == childCount;
}
else
{
--height;
int denseChildSize = denseSize(height);
int denseGrandChildSize = denseSize(height - 1);
// The threshold is the point after which we can't add a dense child and still add another child with
// at least MIN_KEYS fully dense children plus at least one more key.
int threshold = denseChildSize + 1 + MIN_KEYS * (denseGrandChildSize + 1);
int remaining = size;
int i = 0;
// Add dense children until we reach the threshold.
while (remaining >= threshold)
{
branch[keyCount + i] = buildPerfectDense(source, height, updateF);
branch[i] = isSimple(updateF) ? source.next() : updateF.insert(source.next());
remaining -= denseChildSize + 1;
sizeMap[i++] = size - remaining - 1;
}
// At this point the remainder either fits in one child, or too much for one but too little for one
// perfectly dense and a second child with enough grandchildren to be valid. In the latter case, the
// remainder should be split roughly in half, where the first child only has dense grandchildren.
if (remaining > denseChildSize)
{
int grandChildCount = remaining / ((denseGrandChildSize + 1) * 2);
assert grandChildCount >= MIN_KEYS + 1;
int childSize = grandChildCount * (denseGrandChildSize + 1) - 1;
branch[keyCount + i] = buildMaximallyDense(source, grandChildCount, childSize, height, updateF);
branch[i] = isSimple(updateF) ? source.next() : updateF.insert(source.next());
remaining -= childSize + 1;
sizeMap[i++] = size - remaining - 1;
}
// Put the remainder in the last child, it is now guaranteed to fit and have the required minimum of children.
int grandChildCount = remaining / (denseGrandChildSize + 1) + 1;
assert grandChildCount >= MIN_KEYS + 1;
int childSize = remaining;
branch[keyCount + i] = buildMaximallyDense(source, grandChildCount, childSize, height, updateF);
sizeMap[i++] = size;
assert i == childCount;
}
branch[2 * keyCount + 1] = sizeMap;
if (!isSimple(updateF))
updateF.onAllocatedOnHeap(ObjectSizes.sizeOfArray(branch) + ObjectSizes.sizeOfArray(sizeMap));
return branch;
}
private static Object[] buildPerfectDense(BulkIterator source, int height, UpdateFunction updateF)
{
Object[] result = buildPerfectDenseWithoutSizeTracking(source, height, updateF);
updateF.onAllocatedOnHeap(PERFECT_DENSE_SIZE_ON_HEAP[height]);
return result;
}
/**
* Build a tree of size precisely {@code branchFactor^height - 1}
*/
private static Object[] buildPerfectDenseWithoutSizeTracking(BulkIterator source, int height, UpdateFunction updateF)
{
int keyCount = (1 << BRANCH_SHIFT) - 1;
Object[] node = new Object[(1 << BRANCH_SHIFT) * 2];
if (height == 2)
{
int childSize = treeSize2n(1, BRANCH_SHIFT);
for (int i = 0; i < keyCount; i++)
{
node[keyCount + i] = buildLeafWithoutSizeTracking(source, childSize, updateF);
node[i] = isSimple(updateF) ? source.next() : updateF.insert(source.next());
}
node[2 * keyCount] = buildLeafWithoutSizeTracking(source, childSize, updateF);
}
else
{
for (int i = 0; i < keyCount; i++)
{
Object[] child = buildPerfectDenseWithoutSizeTracking(source, height - 1, updateF);
node[keyCount + i] = child;
node[i] = isSimple(updateF) ? source.next() : updateF.insert(source.next());
}
node[2 * keyCount] = buildPerfectDenseWithoutSizeTracking(source, height - 1, updateF);
}
node[keyCount * 2 + 1] = DENSE_SIZE_MAPS[height - 2];
return node;
}
public static Object[] update(Object[] toUpdate, Object[] insert, Comparator comparator)
{
return BTree.update(toUpdate, insert, comparator, UpdateFunction.noOp());
}
/**
* Inserts {@code insert} into {@code update}, applying {@code updateF} to each new item in {@code insert},
* as well as any matched items in {@code update}.
*
* Note that {@code UpdateFunction.noOp} is assumed to indicate a lack of interest in which value survives.
*/
public static Object[] update(Object[] toUpdate,
Object[] insert,
Comparator comparator,
UpdateFunction updateF)
{
// perform some initial obvious optimisations
if (isEmpty(insert))
return toUpdate; // do nothing if update is empty
if (isEmpty(toUpdate))
{
if (isSimple(updateF))
return insert; // if update is empty and updateF is trivial, return our new input
// if update is empty and updateF is non-trivial, perform a simple fast transformation of the input tree
insert = BTree.transform(insert, updateF::insert);
updateF.onAllocatedOnHeap(sizeOnHeapOf(insert));
return insert;
}
if (isLeaf(toUpdate) && isLeaf(insert))
{
// if both are leaves, perform a tight-loop leaf variant of update
// possibly flipping the input order if sizes suggest and updateF permits
if (updateF == (UpdateFunction) UpdateFunction.noOp && toUpdate.length < insert.length)
{
Object[] tmp = toUpdate;
toUpdate = insert;
insert = tmp;
}
Object[] merged = updateLeaves(toUpdate, insert, comparator, updateF);
updateF.onAllocatedOnHeap(sizeOnHeapOf(merged) - sizeOnHeapOf(toUpdate));
return merged;
}
if (!isLeaf(insert) && isSimple(updateF))
{
// consider flipping the order of application, if update is much larger than insert and applying unary no-op
int updateSize = size(toUpdate);
int insertSize = size(insert);
int scale = Integer.numberOfLeadingZeros(updateSize) - Integer.numberOfLeadingZeros(insertSize);
if (scale >= 4)
{
// i.e. at roughly 16x the size, or one tier deeper - very arbitrary, should pick more carefully
// experimentally, at least at 64x the size the difference in performance is ~10x
Object[] tmp = insert;
insert = toUpdate;
toUpdate = tmp;
if (updateF != (UpdateFunction) UpdateFunction.noOp)
updateF = ((UpdateFunction.Simple) updateF).flip();
}
}
try (Updater updater = Updater.get())
{
return updater.update(toUpdate, insert, comparator, updateF);
}
}
/**
* A fast tight-loop variant of updating one btree with another, when both are leaves.
*/
public static Object[] updateLeaves(Object[] unode,
Object[] inode,
Comparator comparator,
UpdateFunction updateF)
{
int upos = -1, usz = sizeOfLeaf(unode);
Existing uk = (Existing) unode[0];
int ipos = 0, isz = sizeOfLeaf(inode);
Insert ik = (Insert) inode[0];
Existing merged = null;
int c = -1;
while (c <= 0) // optimistic: find the first point in the original leaf that is modified (if any)
{
if (c < 0)
{
upos = exponentialSearch(comparator, unode, upos + 1, usz, ik);
c = upos < 0 ? 1 : 0; // positive or zero
if (upos < 0)
upos = -(1 + upos);
if (upos == usz)
break;
uk = (Existing) unode[upos];
}
else // c == 0
{
merged = updateF.merge(uk, ik);
if (merged != uk)
break;
if (++ipos == isz)
return unode;
if (++upos == usz)
break;
c = comparator.compare(uk = (Existing) unode[upos], ik = (Insert) inode[ipos]);
}
}
// exit conditions: c == 0 && merged != uk
// or: c > 0
// or: upos == usz
try (FastBuilder builder = fastBuilder())
{
if (upos > 0)
{
// copy any initial section that is unmodified
builder.leaf().copy(unode, 0, upos);
}
// handle prior loop's exit condition
// we always have either an ik, or an ik merged with uk, to handle
if (upos < usz)
{
if (c == 0)
{
builder.add(merged);
if (++upos < usz)
uk = (Existing) unode[upos];
}
else // c > 0
{
builder.add(updateF.insert(ik));
}
if (++ipos < isz)
ik = (Insert) inode[ipos];
if (upos < usz && ipos < isz)
{
// note: this code is _identical_ to equivalent section in FastUpdater
c = comparator.compare(uk, ik);
while (true)
{
if (c == 0)
{
builder.leaf().addKey(updateF.merge(uk, ik));
++upos;
++ipos;
if (upos == usz || ipos == isz)
break;
c = comparator.compare(uk = (Existing) unode[upos], ik = (Insert) inode[ipos]);
}
else if (c < 0)
{
int until = exponentialSearch(comparator, unode, upos + 1, usz, ik);
c = until < 0 ? 1 : 0; // must find greater or equal; set >= 0 (equal) to 0; set < 0 (greater) to c=+ve
if (until < 0)
until = -(1 + until);
builder.leaf().copy(unode, upos, until - upos);
if ((upos = until) == usz)
break;
uk = (Existing) unode[upos];
}
else
{
int until = exponentialSearch(comparator, inode, ipos + 1, isz, uk);
c = until & 0x80000000; // must find less or equal; set >= 0 (equal) to 0, otherwise leave intact
if (until < 0)
until = -(1 + until);
builder.leaf().copy(inode, ipos, until - ipos, updateF);
if ((ipos = until) == isz)
break;
ik = (Insert) inode[ipos];
}
}
}
if (upos < usz)
{
// ipos == isz
builder.leaf().copy(unode, upos, usz - upos);
}
}
if (ipos < isz)
{
// upos == usz
builder.leaf().copy(inode, ipos, isz - ipos, updateF);
}
return builder.build();
}
}
public static void reverseInSitu(Object[] tree)
{
reverseInSitu(tree, height(tree), true);
}
/**
* The internal implementation of {@link #reverseInSitu(Object[])}.
* Takes two arguments that help minimise garbage generation, by testing sizeMaps against
* known globallyl shared sizeMap for dense nodes that do not need to be modified, and
* for permitting certain users (namely FastBuilder) to declare that non-matching sizeMap
* can be mutated directly without allocating {@code new int[]}
*
* @param tree the tree to reverse in situ
* @param height the height of the tree
* @param copySizeMaps whether or not to copy any non-globally-shared sizeMap before reversing them
*/
private static void reverseInSitu(Object[] tree, int height, boolean copySizeMaps)
{
if (isLeaf(tree))
{
reverse(tree, 0, sizeOfLeaf(tree));
}
else
{
int keyCount = shallowSizeOfBranch(tree);
reverse(tree, 0, keyCount);
reverse(tree, keyCount, keyCount * 2 + 1);
for (int i = keyCount; i <= keyCount * 2; ++i)
reverseInSitu((Object[]) tree[i], height - 1, copySizeMaps);
int[] sizeMap = (int[]) tree[2 * keyCount + 1];
if (sizeMap != DENSE_SIZE_MAPS[height - 2]) // no need to reverse a dense map; same in both directions
{
if (copySizeMaps)
sizeMap = sizeMap.clone();
sizeMapToSizes(sizeMap);
reverse(sizeMap, 0, sizeMap.length);
sizesToSizeMap(sizeMap);
}
}
}
public static Iterator iterator(Object[] btree)
{
return iterator(btree, Dir.ASC);
}
public static Iterator iterator(Object[] btree, Dir dir)
{
return isLeaf(btree) ? new LeafBTreeSearchIterator<>(btree, null, dir)
: new FullBTreeSearchIterator<>(btree, null, dir);
}
public static Iterator iterator(Object[] btree, int lb, int ub, Dir dir)
{
return isLeaf(btree) ? new LeafBTreeSearchIterator<>(btree, null, dir, lb, ub)
: new FullBTreeSearchIterator<>(btree, null, dir, lb, ub);
}
public static Iterable iterable(Object[] btree)
{
return iterable(btree, Dir.ASC);
}
public static Iterable iterable(Object[] btree, Dir dir)
{
return () -> iterator(btree, dir);
}
public static Iterable iterable(Object[] btree, int lb, int ub, Dir dir)
{
return () -> iterator(btree, lb, ub, dir);
}
/**
* Returns an Iterator over the entire tree
*
* @param btree the tree to iterate over
* @param dir direction of iteration
* @param
* @return
*/
public static BTreeSearchIterator slice(Object[] btree, Comparator comparator, Dir dir)
{
return isLeaf(btree) ? new LeafBTreeSearchIterator<>(btree, comparator, dir)
: new FullBTreeSearchIterator<>(btree, comparator, dir);
}
/**
* @param btree the tree to iterate over
* @param comparator the comparator that defines the ordering over the items in the tree
* @param start the beginning of the range to return, inclusive (in ascending order)
* @param end the end of the range to return, exclusive (in ascending order)
* @param dir if false, the iterator will start at the last item and move backwards
* @return an Iterator over the defined sub-range of the tree
*/
public static BTreeSearchIterator slice(Object[] btree, Comparator comparator, K start, K end, Dir dir)
{
return slice(btree, comparator, start, true, end, false, dir);
}
/**
* @param btree the tree to iterate over
* @param comparator the comparator that defines the ordering over the items in the tree
* @param startIndex the start index of the range to return, inclusive
* @param endIndex the end index of the range to return, inclusive
* @param dir if false, the iterator will start at the last item and move backwards
* @return an Iterator over the defined sub-range of the tree
*/
public static BTreeSearchIterator slice(Object[] btree, Comparator comparator, int startIndex, int endIndex, Dir dir)
{
return isLeaf(btree) ? new LeafBTreeSearchIterator<>(btree, comparator, dir, startIndex, endIndex)
: new FullBTreeSearchIterator<>(btree, comparator, dir, startIndex, endIndex);
}
/**
* @param btree the tree to iterate over
* @param comparator the comparator that defines the ordering over the items in the tree
* @param start low bound of the range
* @param startInclusive inclusivity of lower bound
* @param end high bound of the range
* @param endInclusive inclusivity of higher bound
* @param dir direction of iteration
* @return an Iterator over the defined sub-range of the tree
*/
public static BTreeSearchIterator slice(Object[] btree, Comparator comparator, K start, boolean startInclusive, K end, boolean endInclusive, Dir dir)
{
int inclusiveLowerBound = max(0,
start == null ? Integer.MIN_VALUE
: startInclusive ? ceilIndex(btree, comparator, start)
: higherIndex(btree, comparator, start));
int inclusiveUpperBound = min(size(btree) - 1,
end == null ? Integer.MAX_VALUE
: endInclusive ? floorIndex(btree, comparator, end)
: lowerIndex(btree, comparator, end));
return isLeaf(btree) ? new LeafBTreeSearchIterator<>(btree, comparator, dir, inclusiveLowerBound, inclusiveUpperBound)
: new FullBTreeSearchIterator<>(btree, comparator, dir, inclusiveLowerBound, inclusiveUpperBound);
}
/**
* @return the item in the tree that sorts as equal to the search argument, or null if no such item
*/
public static V find(Object[] node, Comparator comparator, V find)
{
while (true)
{
int keyEnd = getKeyEnd(node);
int i = Arrays.binarySearch((V[]) node, 0, keyEnd, find, comparator);
if (i >= 0)
return (V) node[i];
if (isLeaf(node))
return null;
i = -1 - i;
node = (Object[]) node[keyEnd + i];
}
}
/**
* Modifies the provided btree directly. THIS SHOULD NOT BE USED WITHOUT EXTREME CARE as BTrees are meant to be immutable.
* Finds and replaces the item provided by index in the tree.
*/
public static void replaceInSitu(Object[] tree, int index, V replace)
{
// WARNING: if semantics change, see also InternalCursor.seekTo, which mirrors this implementation
if ((index < 0) | (index >= size(tree)))
throw new IndexOutOfBoundsException(index + " not in range [0.." + size(tree) + ")");
while (!isLeaf(tree))
{
final int[] sizeMap = getSizeMap(tree);
int boundary = Arrays.binarySearch(sizeMap, index);
if (boundary >= 0)
{
// exact match, in this branch node
assert boundary < sizeMap.length - 1;
tree[boundary] = replace;
return;
}
boundary = -1 - boundary;
if (boundary > 0)
{
assert boundary < sizeMap.length;
index -= (1 + sizeMap[boundary - 1]);
}
tree = (Object[]) tree[getChildStart(tree) + boundary];
}
assert index < getLeafKeyEnd(tree);
tree[index] = replace;
}
/**
* Modifies the provided btree directly. THIS SHOULD NOT BE USED WITHOUT EXTREME CARE as BTrees are meant to be immutable.
* Finds and replaces the provided item in the tree. Both should sort as equal to each other (although this is not enforced)
*/
public static void replaceInSitu(Object[] node, Comparator comparator, V find, V replace)
{
while (true)
{
int keyEnd = getKeyEnd(node);
int i = Arrays.binarySearch((V[]) node, 0, keyEnd, find, comparator);
if (i >= 0)
{
assert find == node[i];
node[i] = replace;
return;
}
if (isLeaf(node))
throw new NoSuchElementException();
i = -1 - i;
node = (Object[]) node[keyEnd + i];
}
}
/**
* Honours result semantics of {@link Arrays#binarySearch}, as though it were performed on the tree flattened into an array
*
* @return index of item in tree, or (-(insertion point) - 1) if not present
*/
public static int findIndex(Object[] node, Comparator comparator, V find)
{
int lb = 0;
while (true)
{
int keyEnd = getKeyEnd(node);
int i = Arrays.binarySearch((V[]) node, 0, keyEnd, find, comparator);
boolean exact = i >= 0;
if (isLeaf(node))
return exact ? lb + i : i - lb;
if (!exact)
i = -1 - i;
int[] sizeMap = getSizeMap(node);
if (exact)
return lb + sizeMap[i];
else if (i > 0)
lb += sizeMap[i - 1] + 1;
node = (Object[]) node[keyEnd + i];
}
}
/**
* @return the value at the index'th position in the tree, in tree order
*/
public static V findByIndex(Object[] tree, int index)
{
// WARNING: if semantics change, see also InternalCursor.seekTo, which mirrors this implementation
if ((index < 0) | (index >= size(tree)))
throw new IndexOutOfBoundsException(index + " not in range [0.." + size(tree) + ")");
Object[] node = tree;
while (true)
{
if (isLeaf(node))
{
int keyEnd = getLeafKeyEnd(node);
assert index < keyEnd;
return (V) node[index];
}
int[] sizeMap = getSizeMap(node);
int boundary = Arrays.binarySearch(sizeMap, index);
if (boundary >= 0)
{
// exact match, in this branch node
assert boundary < sizeMap.length - 1;
return (V) node[boundary];
}
boundary = -1 - boundary;
if (boundary > 0)
{
assert boundary < sizeMap.length;
index -= (1 + sizeMap[boundary - 1]);
}
node = (Object[]) node[getChildStart(node) + boundary];
}
}
/* since we have access to binarySearch semantics within indexOf(), we can use this to implement
* lower/upper/floor/higher very trivially
*
* this implementation is *not* optimal; it requires two logarithmic traversals, although the second is much cheaper
* (having less height, and operating over only primitive arrays), and the clarity is compelling
*/
public static int lowerIndex(Object[] btree, Comparator comparator, V find)
{
int i = findIndex(btree, comparator, find);
if (i < 0)
i = -1 - i;
return i - 1;
}
public static V lower(Object[] btree, Comparator comparator, V find)
{
int i = lowerIndex(btree, comparator, find);
return i >= 0 ? findByIndex(btree, i) : null;
}
public static int floorIndex(Object[] btree, Comparator comparator, V find)
{
int i = findIndex(btree, comparator, find);
if (i < 0)
i = -2 - i;
return i;
}
public static V floor(Object[] btree, Comparator comparator, V find)
{
int i = floorIndex(btree, comparator, find);
return i >= 0 ? findByIndex(btree, i) : null;
}
public static int higherIndex(Object[] btree, Comparator comparator, V find)
{
int i = findIndex(btree, comparator, find);
if (i < 0)
i = -1 - i;
else
i++;
return i;
}
public static V higher(Object[] btree, Comparator comparator, V find)
{
int i = higherIndex(btree, comparator, find);
return i < size(btree) ? findByIndex(btree, i) : null;
}
public static int ceilIndex(Object[] btree, Comparator comparator, V find)
{
int i = findIndex(btree, comparator, find);
if (i < 0)
i = -1 - i;
return i;
}
public static V ceil(Object[] btree, Comparator comparator, V find)
{
int i = ceilIndex(btree, comparator, find);
return i < size(btree) ? findByIndex(btree, i) : null;
}
// UTILITY METHODS
// get the upper bound we should search in for keys in the node
static int getKeyEnd(Object[] node)
{
if (isLeaf(node))
return getLeafKeyEnd(node);
else
return getBranchKeyEnd(node);
}
// get the last index that is non-null in the leaf node
static int getLeafKeyEnd(Object[] node)
{
int len = node.length;
return node[len - 1] == null ? len - 1 : len;
}
// return the boundary position between keys/children for the branch node
// == number of keys, as they are indexed from zero
static int getBranchKeyEnd(Object[] branchNode)
{
return (branchNode.length / 2) - 1;
}
/**
* @return first index in a branch node containing child nodes
*/
static int getChildStart(Object[] branchNode)
{
return getBranchKeyEnd(branchNode);
}
/**
* @return last index + 1 in a branch node containing child nodes
*/
static int getChildEnd(Object[] branchNode)
{
return branchNode.length - 1;
}
/**
* @return number of children in a branch node
*/
static int getChildCount(Object[] branchNode)
{
return branchNode.length / 2;
}
/**
* @return the size map for the branch node
*/
static int[] getSizeMap(Object[] branchNode)
{
return (int[]) branchNode[getChildEnd(branchNode)];
}
/**
* @return the size map for the branch node
*/
static int lookupSizeMap(Object[] branchNode, int index)
{
return getSizeMap(branchNode)[index];
}
// get the size from the btree's index (fails if not present)
public static int size(Object[] tree)
{
if (isLeaf(tree))
return getLeafKeyEnd(tree);
int length = tree.length;
// length - 1 == getChildEnd == getPositionOfSizeMap
// (length / 2) - 1 == getChildCount - 1 == position of full tree size
// hard code this, as will be used often;
return ((int[]) tree[length - 1])[(length / 2) - 1];
}
public static long sizeOfStructureOnHeap(Object[] tree)
{
long size = ObjectSizes.sizeOfArray(tree);
if (isLeaf(tree))
return size;
for (int i = getChildStart(tree); i < getChildEnd(tree); i++)
size += sizeOfStructureOnHeap((Object[]) tree[i]);
return size;
}
/**
* Checks is the node is a leaf.
*
* @return {@code true} if the provided node is a leaf, {@code false} if it is a branch.
*/
public static boolean isLeaf(Object[] node)
{
// Nodes are disambiguated by the length of the array that represents them: an even number is a branch, odd a leaf
return (node.length & 1) == 1;
}
public static boolean isEmpty(Object[] tree)
{
return tree == EMPTY_LEAF;
}
// get the upper bound we should search in for keys in the node
static int shallowSize(Object[] node)
{
if (isLeaf(node))
return sizeOfLeaf(node);
else
return shallowSizeOfBranch(node);
}
static int sizeOfLeaf(Object[] leaf)
{
int len = leaf.length;
return leaf[len - 1] == null ? len - 1 : len;
}
// return the boundary position between keys/children for the branch node
// == number of keys, as they are indexed from zero
static int shallowSizeOfBranch(Object[] branch)
{
return (branch.length / 2) - 1;
}
/**
* @return first index in a branch node containing child nodes
*/
static int childOffset(Object[] branch)
{
return shallowSizeOfBranch(branch);
}
/**
* @return last index + 1 in a branch node containing child nodes
*/
static int childEndOffset(Object[] branch)
{
return branch.length - 1;
}
public static int depth(Object[] tree)
{
int depth = 1;
while (!isLeaf(tree))
{
depth++;
tree = (Object[]) tree[getKeyEnd(tree)];
}
return depth;
}
/**
* Fill the target array with the contents of the provided subtree, in ascending order, starting at targetOffset
*
* @param tree source
* @param target array
* @param targetOffset offset in target array
* @return number of items copied (size of tree)
*/
public static int toArray(Object[] tree, Object[] target, int targetOffset)
{
return toArray(tree, 0, size(tree), target, targetOffset);
}
public static int toArray(Object[] tree, int treeStart, int treeEnd, Object[] target, int targetOffset)
{
if (isLeaf(tree))
{
int count = treeEnd - treeStart;
System.arraycopy(tree, treeStart, target, targetOffset, count);
return count;
}
int newTargetOffset = targetOffset;
int childCount = getChildCount(tree);
int childOffset = getChildStart(tree);
for (int i = 0; i < childCount; i++)
{
int childStart = treeIndexOffsetOfChild(tree, i);
int childEnd = treeIndexOfBranchKey(tree, i);
if (childStart <= treeEnd && childEnd >= treeStart)
{
newTargetOffset += toArray((Object[]) tree[childOffset + i], max(0, treeStart - childStart), min(childEnd, treeEnd) - childStart,
target, newTargetOffset);
if (treeStart <= childEnd && treeEnd > childEnd) // this check will always fail for the non-existent key
target[newTargetOffset++] = tree[i];
}
}
return newTargetOffset - targetOffset;
}
/**
* An efficient transformAndFilter implementation suitable for a tree consisting of a single leaf root
* NOTE: codewise *identical* to {@link #transformAndFilterLeaf(Object[], BiFunction, Object)}
*/
private static Object[] transformAndFilterLeaf(Object[] leaf, Function apply)
{
int i = 0, sz = sizeOfLeaf(leaf);
I in;
O out;
do // optimistic loop, looking for first point transformation modifies the input (if any)
{
in = (I) leaf[i];
out = apply.apply(in);
} while (in == out && ++i < sz);
// in == out -> i == sz
// otherwise in == leaf[i]
int identicalUntil = i;
if (out == null && ++i < sz)
{
// optimistic loop, looking for first key {@code apply} modifies without removing it (if any)
do
{
in = (I) leaf[i];
out = apply.apply(in);
} while (null == out && ++i < sz);
}
// out == null -> i == sz
// otherwise out == apply.apply(leaf[i])
if (i == sz)
{
// if we have reached the end of the input, we're either:
// 1) returning input unmodified; or
// 2) copying some (possibly empty) prefix of it
if (identicalUntil == sz)
return leaf;
if (identicalUntil == 0)
return empty();
Object[] copy = new Object[identicalUntil | 1];
System.arraycopy(leaf, 0, copy, 0, identicalUntil);
return copy;
}
try (FastBuilder builder = fastBuilder())
{
// otherwise copy the initial part that was unmodified, insert the non-null modified key, and continue
if (identicalUntil > 0)
builder.leaf().copyNoOverflow(leaf, 0, identicalUntil);
builder.leaf().addKeyNoOverflow(out);
while (++i < sz)
{
in = (I) leaf[i];
out = apply.apply(in);
if (out != null)
builder.leaf().addKeyNoOverflow(out);
}
return builder.build();
}
}
/**
* Takes a tree and transforms it using the provided function, filtering out any null results.
* The result of any transformation must sort identically as their originals, wrt other results.
*
* If no modifications are made, the original is returned.
* NOTE: codewise *identical* to {@link #transformAndFilter(Object[], Function)}
*/
public static Object[] transformAndFilter(Object[] tree, BiFunction apply, I2 param)
{
if (isEmpty(tree))
return tree;
if (isLeaf(tree))
return transformAndFilterLeaf(tree, apply, param);
try (BiTransformer transformer = BiTransformer.get(apply, param))
{
return transformer.apply(tree);
}
}
/**
* Takes a tree and transforms it using the provided function, filtering out any null results.
* The result of any transformation must sort identically as their originals, wrt other results.
*
* If no modifications are made, the original is returned.
*
* An efficient transformAndFilter implementation suitable for a tree consisting of a single leaf root
* NOTE: codewise *identical* to {@link #transformAndFilter(Object[], BiFunction, Object)}
*/
public static Object[] transformAndFilter(Object[] tree, Function apply)
{
if (isEmpty(tree))
return tree;
if (isLeaf(tree))
return transformAndFilterLeaf(tree, apply);
try (Transformer transformer = Transformer.get(apply))
{
return transformer.apply(tree);
}
}
/**
* An efficient transformAndFilter implementation suitable for a tree consisting of a single leaf root
* NOTE: codewise *identical* to {@link #transformAndFilterLeaf(Object[], Function)}
*/
private static Object[] transformAndFilterLeaf(Object[] leaf, BiFunction apply, I2 param)
{
int i = 0, sz = sizeOfLeaf(leaf);
I in;
O out;
do // optimistic loop, looking for first point transformation modifies the input (if any)
{
in = (I) leaf[i];
out = apply.apply(in, param);
} while (in == out && ++i < sz);
// in == out -> i == sz
// otherwise in == leaf[i]
int identicalUntil = i;
if (out == null && ++i < sz)
{
// optimistic loop, looking for first key {@code apply} modifies without removing it (if any)
do
{
in = (I) leaf[i];
out = apply.apply(in, param);
} while (null == out && ++i < sz);
}
// out == null -> i == sz
// otherwise out == apply.apply(leaf[i])
if (i == sz)
{
// if we have reached the end of the input, we're either:
// 1) returning input unmodified; or
// 2) copying some (possibly empty) prefix of it
if (identicalUntil == sz)
return leaf;
if (identicalUntil == 0)
return empty();
Object[] copy = new Object[identicalUntil | 1];
System.arraycopy(leaf, 0, copy, 0, identicalUntil);
return copy;
}
try (FastBuilder builder = fastBuilder())
{
// otherwise copy the initial part that was unmodified, insert the non-null modified key, and continue
if (identicalUntil > 0)
builder.leaf().copyNoOverflow(leaf, 0, identicalUntil);
builder.leaf().addKeyNoOverflow(out);
while (++i < sz)
{
in = (I) leaf[i];
out = apply.apply(in, param);
if (out != null)
builder.leaf().addKeyNoOverflow(out);
}
return builder.build();
}
}
/**
* Takes a tree and transforms it using the provided function.
* The result of any transformation must sort identically as their originals, wrt other results.
*
* If no modifications are made, the original is returned.
*/
public static Object[] transform(Object[] tree, Function function)
{
if (isEmpty(tree)) // isEmpty determined by identity; must return input
return tree;
if (isLeaf(tree)) // escape hatch for fast leaf transformation
return transformLeaf(tree, function);
Object[] result = tree; // optimistically assume we'll return our input unmodified
int keyCount = shallowSizeOfBranch(tree);
for (int i = 0; i < keyCount; ++i)
{
// operate on a pair of (child,key) each loop
Object[] curChild = (Object[]) tree[keyCount + i];
Object[] updChild = transform(curChild, function);
Object curKey = tree[i];
Object updKey = function.apply((I) curKey);
if (result == tree)
{
if (curChild == updChild && curKey == updKey)
continue; // if output still same as input, loop
// otherwise initialise output to a copy of input up to this point
result = transformCopyBranchHelper(tree, keyCount, i, i);
}
result[keyCount + i] = updChild;
result[i] = updKey;
}
// final unrolled copy of loop for last child only (unbalanced with keys)
Object[] curChild = (Object[]) tree[2 * keyCount];
Object[] updChild = transform(curChild, function);
if (result == tree)
{
if (curChild == updChild)
return tree;
result = transformCopyBranchHelper(tree, keyCount, keyCount, keyCount);
}
result[2 * keyCount] = updChild;
result[2 * keyCount + 1] = tree[2 * keyCount + 1]; // take the original sizeMap, as we are exactly the same shape
return result;
}
// create a copy of a branch, with the exact same size, copying the specified number of keys and children
private static Object[] transformCopyBranchHelper(Object[] branch, int keyCount, int copyKeyCount, int copyChildCount)
{
Object[] result = new Object[branch.length];
System.arraycopy(branch, 0, result, 0, copyKeyCount);
System.arraycopy(branch, keyCount, result, keyCount, copyChildCount);
return result;
}
// an efficient transformAndFilter implementation suitable for a tree consisting of a single leaf root
private static Object[] transformLeaf(Object[] leaf, Function apply)
{
Object[] result = leaf; // optimistically assume we'll return our input unmodified
int size = sizeOfLeaf(leaf);
for (int i = 0; i < size; ++i)
{
Object current = leaf[i];
Object updated = apply.apply((I) current);
if (result == leaf)
{
if (current == updated)
continue; // if output still same as input, loop
// otherwise initialise output to a copy of input up to this point
result = new Object[leaf.length];
System.arraycopy(leaf, 0, result, 0, i);
}
result[i] = updated;
}
return result;
}
public static boolean equals(Object[] a, Object[] b)
{
return size(a) == size(b) && Iterators.elementsEqual(iterator(a), iterator(b));
}
public static int hashCode(Object[] btree)
{
// we can't just delegate to Arrays.deepHashCode(),
// because two equivalent trees may be represented by differently shaped trees
int result = 1;
for (Object v : iterable(btree))
result = 31 * result + Objects.hashCode(v);
return result;
}
public static String toString(Object[] btree)
{
return appendBranchOrLeaf(new StringBuilder().append('['), btree).append(']').toString();
}
private static StringBuilder appendBranchOrLeaf(StringBuilder builder, Object[] node)
{
return isLeaf(node) ? appendLeaf(builder, node) : appendBranch(builder, node);
}
private static StringBuilder appendBranch(StringBuilder builder, Object[] branch)
{
int childCount = branch.length / 2;
int keyCount = childCount - 1;
// add keys
for (int i = 0; i < keyCount; i++)
{
if (i != 0)
builder.append(", ");
builder.append(branch[i]);
}
// add children
for (int i = keyCount, m = branch.length - 1; i < m; i++)
{
builder.append(", ");
appendBranchOrLeaf(builder, (Object[]) branch[i]);
}
// add sizeMap
builder.append(", ").append(Arrays.toString((int[]) branch[branch.length - 1]));
return builder;
}
private static StringBuilder appendLeaf(StringBuilder builder, Object[] leaf)
{
return builder.append(Arrays.toString(leaf));
}
/**
* tree index => index of key wrt all items in the tree laid out serially
*
* This version of the method permits requesting out-of-bounds indexes, -1 and size
*
* @param root to calculate tree index within
* @param keyIndex root-local index of key to calculate tree-index
* @return the number of items preceding the key in the whole tree of root
*/
public static int treeIndexOfKey(Object[] root, int keyIndex)
{
if (isLeaf(root))
return keyIndex;
int[] sizeMap = getSizeMap(root);
if ((keyIndex >= 0) & (keyIndex < sizeMap.length))
return sizeMap[keyIndex];
// we support asking for -1 or size, so that we can easily use this for iterator bounds checking
if (keyIndex < 0)
return -1;
return sizeMap[keyIndex - 1] + 1;
}
/**
* @param keyIndex node-local index of the key to calculate index of
* @return keyIndex; this method is here only for symmetry and clarity
*/
public static int treeIndexOfLeafKey(int keyIndex)
{
return keyIndex;
}
/**
* @param root to calculate tree-index within
* @param keyIndex root-local index of key to calculate tree-index of
* @return the number of items preceding the key in the whole tree of root
*/
public static int treeIndexOfBranchKey(Object[] root, int keyIndex)
{
return lookupSizeMap(root, keyIndex);
}
/**
* @param root to calculate tree-index within
* @param childIndex root-local index of *child* to calculate tree-index of
* @return the number of items preceding the child in the whole tree of root
*/
public static int treeIndexOffsetOfChild(Object[] root, int childIndex)
{
if (childIndex == 0)
return 0;
return 1 + lookupSizeMap(root, childIndex - 1);
}
public static Builder builder(Comparator comparator)
{
return new Builder<>(comparator);
}
public static Builder builder(Comparator comparator, int initialCapacity)
{
return new Builder<>(comparator, initialCapacity);
}
public static class Builder
{
// a user-defined bulk resolution, to be applied manually via resolve()
public static interface Resolver
{
// can return a different output type to input, so long as sort order is maintained
// if a resolver is present, this method will be called for every sequence of equal inputs
// even those with only one item
Object resolve(Object[] array, int lb, int ub);
}
// a user-defined resolver that is applied automatically on encountering two duplicate values
public static interface QuickResolver
{
// can return a different output type to input, so long as sort order is maintained
// if a resolver is present, this method will be called for every sequence of equal inputs
// even those with only one item
V resolve(V a, V b);
}
Comparator comparator;
Object[] values;
int count;
boolean detected = true; // true if we have managed to cheaply ensure sorted (+ filtered, if resolver == null) as we have added
boolean auto = true; // false if the user has promised to enforce the sort order and resolve any duplicates
QuickResolver quickResolver;
protected Builder(Comparator comparator)
{
this(comparator, 16);
}
protected Builder(Comparator comparator, int initialCapacity)
{
if (initialCapacity == 0)
initialCapacity = 16;
this.comparator = comparator;
this.values = new Object[initialCapacity];
}
@VisibleForTesting
public Builder()
{
this.values = new Object[16];
}
private Builder(Builder builder)
{
this.comparator = builder.comparator;
this.values = Arrays.copyOf(builder.values, builder.values.length);
this.count = builder.count;
this.detected = builder.detected;
this.auto = builder.auto;
this.quickResolver = builder.quickResolver;
}
/**
* Creates a copy of this {@code Builder}.
*
* @return a copy of this {@code Builder}.
*/
public Builder copy()
{
return new Builder<>(this);
}
public Builder setQuickResolver(QuickResolver quickResolver)
{
this.quickResolver = quickResolver;
return this;
}
public void reuse()
{
reuse(comparator);
}
public void reuse(Comparator comparator)
{
this.comparator = comparator;
Arrays.fill(values, null);
count = 0;
detected = true;
}
public Builder auto(boolean auto)
{
this.auto = auto;
return this;
}
public Builder add(V v)
{
if (count == values.length)
values = Arrays.copyOf(values, count * 2);
Object[] values = this.values;
int prevCount = this.count++;
values[prevCount] = v;
if (auto && detected && prevCount > 0)
{
V prev = (V) values[prevCount - 1];
int c = comparator.compare(prev, v);
if (c == 0 && auto)
{
count = prevCount;
if (quickResolver != null)
values[prevCount - 1] = quickResolver.resolve(prev, v);
}
else if (c > 0)
{
detected = false;
}
}
return this;
}
public Builder addAll(Collection add)
{
if (auto && add instanceof SortedSet && equalComparators(comparator, ((SortedSet) add).comparator()))
{
// if we're a SortedSet, permit quick order-preserving addition of items
// if we collect all duplicates, don't bother as merge will necessarily be more expensive than sorting at end
return mergeAll(add, add.size());
}
detected = false;
if (values.length < count + add.size())
values = Arrays.copyOf(values, max(count + add.size(), count * 2));
for (V v : add)
values[count++] = v;
return this;
}
private static boolean equalComparators(Comparator a, Comparator b)
{
return a == b || (isNaturalComparator(a) && isNaturalComparator(b));
}
private static boolean isNaturalComparator(Comparator a)
{
return a == null || a == Comparator.naturalOrder() || a == Ordering.natural();
}
// iter must be in sorted order!
private Builder mergeAll(Iterable add, int addCount)
{
assert auto;
// ensure the existing contents are in order
autoEnforce();
int curCount = count;
// we make room for curCount * 2 + addCount, so that we can copy the current values to the end
// if necessary for continuing the merge, and have the new values directly after the current value range
if (values.length < curCount * 2 + addCount)
values = Arrays.copyOf(values, max(curCount * 2 + addCount, curCount * 3));
if (add instanceof BTreeSet)
{
// use btree set's fast toArray method, to append directly
((BTreeSet) add).toArray(values, curCount);
}
else
{
// consider calling toArray() and System.arraycopy
int i = curCount;
for (V v : add)
values[i++] = v;
}
return mergeAll(addCount);
}
private Builder mergeAll(int addCount)
{
Object[] a = values;
int addOffset = count;
int i = 0, j = addOffset;
int curEnd = addOffset, addEnd = addOffset + addCount;
// save time in cases where we already have a subset, by skipping dir
while (i < curEnd && j < addEnd)
{
V ai = (V) a[i], aj = (V) a[j];
// in some cases, such as Columns, we may have identity supersets, so perform a cheap object-identity check
int c = ai == aj ? 0 : comparator.compare(ai, aj);
if (c > 0)
break;
else if (c == 0)
{
if (quickResolver != null)
a[i] = quickResolver.resolve(ai, aj);
j++;
}
i++;
}
if (j == addEnd)
return this; // already a superset of the new values
// otherwise, copy the remaining existing values to the very end, freeing up space for merge result
int newCount = i;
System.arraycopy(a, i, a, addEnd, count - i);
curEnd = addEnd + (count - i);
i = addEnd;
while (i < curEnd && j < addEnd)
{
V ai = (V) a[i];
V aj = (V) a[j];
// could avoid one comparison if we cared, but would make this ugly
int c = comparator.compare(ai, aj);
if (c == 0)
{
Object newValue = quickResolver == null ? ai : quickResolver.resolve(ai, aj);
a[newCount++] = newValue;
i++;
j++;
}
else
{
a[newCount++] = c < 0 ? a[i++] : a[j++];
}
}
// exhausted one of the inputs; fill in remainder of the other
if (i < curEnd)
{
System.arraycopy(a, i, a, newCount, curEnd - i);
newCount += curEnd - i;
}
else if (j < addEnd)
{
if (j != newCount)
System.arraycopy(a, j, a, newCount, addEnd - j);
newCount += addEnd - j;
}
count = newCount;
return this;
}
public boolean isEmpty()
{
return count == 0;
}
public Builder reverse()
{
assert !auto;
int mid = count / 2;
for (int i = 0; i < mid; i++)
{
Object t = values[i];
values[i] = values[count - (1 + i)];
values[count - (1 + i)] = t;
}
return this;
}
public Builder sort()
{
Arrays.sort((V[]) values, 0, count, comparator);
return this;
}
// automatically enforce sorted+filtered
private void autoEnforce()
{
if (!detected && count > 1)
{
sort();
int prevIdx = 0;
V prev = (V) values[0];
for (int i = 1; i < count; i++)
{
V next = (V) values[i];
if (comparator.compare(prev, next) != 0)
values[++prevIdx] = prev = next;
else if (quickResolver != null)
values[prevIdx] = prev = quickResolver.resolve(prev, next);
}
count = prevIdx + 1;
}
detected = true;
}
public Builder resolve(Resolver resolver)
{
if (count > 0)
{
int c = 0;
int prev = 0;
for (int i = 1; i < count; i++)
{
if (comparator.compare((V) values[i], (V) values[prev]) != 0)
{
values[c++] = resolver.resolve((V[]) values, prev, i);
prev = i;
}
}
values[c++] = resolver.resolve((V[]) values, prev, count);
count = c;
}
return this;
}
public Object[] build()
{
if (auto)
autoEnforce();
try (BulkIterator iterator = BulkIterator.of(values, 0))
{
return BTree.build(iterator, count, UpdateFunction.noOp());
}
}
}
private static void applyValue(V value, BiConsumer function, A argument)
{
function.accept(argument, value);
}
public static void applyLeaf(Object[] btree, BiConsumer function, A argument)
{
Preconditions.checkArgument(isLeaf(btree));
int limit = getLeafKeyEnd(btree);
for (int i = 0; i < limit; i++)
applyValue((V) btree[i], function, argument);
}
/**
* Simple method to walk the btree forwards and apply a function till a stop condition is reached
*
* Private method
*
* @param btree
* @param function
*/
public static void apply(Object[] btree, BiConsumer function, A argument)
{
if (isLeaf(btree))
{
applyLeaf(btree, function, argument);
return;
}
int childOffset = getChildStart(btree);
int limit = btree.length - 1 - childOffset;
for (int i = 0; i < limit; i++)
{
apply((Object[]) btree[childOffset + i], function, argument);
if (i < childOffset)
applyValue((V) btree[i], function, argument);
}
}
/**
* Simple method to walk the btree forwards and apply a function till a stop condition is reached
*
* Private method
*
* @param btree
* @param function
*/
public static void apply(Object[] btree, Consumer function)
{
BTree.>apply(btree, Consumer::accept, function);
}
private static int find(Object[] btree, V from, Comparator comparator)
{
// find the start index in iteration order
Preconditions.checkNotNull(comparator);
int keyEnd = getKeyEnd(btree);
return Arrays.binarySearch((V[]) btree, 0, keyEnd, from, comparator);
}
private static boolean isStopSentinel(long v)
{
return v == Long.MAX_VALUE;
}
private static long accumulateLeaf(Object[] btree, BiLongAccumulator accumulator, A arg, Comparator comparator, V from, long initialValue)
{
Preconditions.checkArgument(isLeaf(btree));
long value = initialValue;
int limit = getLeafKeyEnd(btree);
int startIdx = 0;
if (from != null)
{
int i = find(btree, from, comparator);
boolean isExact = i >= 0;
startIdx = isExact ? i : (-1 - i);
}
for (int i = startIdx; i < limit; i++)
{
value = accumulator.apply(arg, (V) btree[i], value);
if (isStopSentinel(value))
break;
}
return value;
}
/**
* Walk the btree and accumulate a long value using the supplied accumulator function. Iteration will stop if the
* accumulator function returns the sentinel values Long.MIN_VALUE or Long.MAX_VALUE
*
* If the optional from argument is not null, iteration will start from that value (or the one after it's insertion
* point if an exact match isn't found)
*/
public static long accumulate(Object[] btree, BiLongAccumulator accumulator, A arg, Comparator comparator, V from, long initialValue)
{
if (isLeaf(btree))
return accumulateLeaf(btree, accumulator, arg, comparator, from, initialValue);
long value = initialValue;
int childOffset = getChildStart(btree);
int startChild = 0;
if (from != null)
{
int i = find(btree, from, comparator);
boolean isExact = i >= 0;
startChild = isExact ? i + 1 : -1 - i;
if (isExact)
{
value = accumulator.apply(arg, (V) btree[i], value);
if (isStopSentinel(value))
return value;
from = null;
}
}
int limit = btree.length - 1 - childOffset;
for (int i = startChild; i < limit; i++)
{
value = accumulate((Object[]) btree[childOffset + i], accumulator, arg, comparator, from, value);
if (isStopSentinel(value))
break;
if (i < childOffset)
{
value = accumulator.apply(arg, (V) btree[i], value);
// stop if a sentinel stop value was returned
if (isStopSentinel(value))
break;
}
if (from != null)
from = null;
}
return value;
}
public static long accumulate(Object[] btree, LongAccumulator accumulator, Comparator comparator, V from, long initialValue)
{
return accumulate(btree, LongAccumulator::apply, accumulator, comparator, from, initialValue);
}
public static long accumulate(Object[] btree, LongAccumulator accumulator, long initialValue)
{
return accumulate(btree, accumulator, null, null, initialValue);
}
public static long accumulate(Object[] btree, BiLongAccumulator accumulator, A arg, long initialValue)
{
return accumulate(btree, accumulator, arg, null, null, initialValue);
}
/**
* Calculate the minimum height needed for this size of tree
*
* @param size the tree size
* @return the minimum height needed for this size of tree
*/
private static int minHeight(int size)
{
return heightAtSize2n(size, BRANCH_SHIFT);
}
private static int heightAtSize2n(int size, int branchShift)
{
// branch factor = 1 << branchShift
// => full size at height = (1 << (branchShift * height)) - 1
// => full size at height + 1 = 1 << (branchShift * height)
// => shift(full size at height + 1) = branchShift * height
// => shift(full size at height + 1) / branchShift = height
int lengthInBinary = 64 - Long.numberOfLeadingZeros(size);
return (branchShift - 1 + lengthInBinary) / branchShift;
}
private static int[][] buildBalancedSizeMaps(int branchShift)
{
int count = (32 / branchShift) - 1;
int childCount = 1 << branchShift;
int[][] sizeMaps = new int[count][childCount];
for (int height = 0; height < count; ++height)
{
int childSize = treeSize2n(height + 1, branchShift);
int size = 0;
int[] sizeMap = sizeMaps[height];
for (int i = 0; i < childCount; ++i)
{
sizeMap[i] = size += childSize;
size += 1;
}
}
return sizeMaps;
}
// simply utility to reverse the contents of array[from..to)
private static void reverse(Object[] array, int from, int to)
{
int mid = (from + to) / 2;
for (int i = from; i < mid; i++)
{
int j = to - (1 + i - from);
Object tmp = array[i];
array[i] = array[j];
array[j] = tmp;
}
}
// simply utility to reverse the contents of array[from..to)
private static void reverse(int[] array, int from, int to)
{
int mid = (from + to) / 2;
for (int i = from; i < mid; i++)
{
int j = to - (1 + i - from);
int tmp = array[i];
array[i] = array[j];
array[j] = tmp;
}
}
/**
* Mutate an array of child sizes into a cumulative sizeMap, returning the total size
*/
private static int sizesToSizeMap(int[] sizeMap)
{
int total = sizeMap[0];
for (int i = 1; i < sizeMap.length; ++i)
sizeMap[i] = total += 1 + sizeMap[i];
return total;
}
private static int sizesToSizeMap(int[] sizes, int count)
{
int total = sizes[0];
for (int i = 1; i < count; ++i)
sizes[i] = total += 1 + sizes[i];
return total;
}
/**
* Mutate an array of child sizes into a cumulative sizeMap, returning the total size
*/
private static void sizeMapToSizes(int[] sizeMap)
{
for (int i = sizeMap.length; i > 1; --i)
sizeMap[i] -= 1 + sizeMap[i - 1];
}
/**
* A simple utility method to handle a null upper bound that we treat as infinity
*/
private static int compareWithMaybeInfinity(Comparator comparator, Compare key, Compare ub)
{
if (ub == null)
return -1;
return comparator.compare(key, ub);
}
/**
* Perform {@link #exponentialSearch} on {@code in[from..to)}, treating a {@code find} of {@code null} as infinity.
*/
static int exponentialSearchForMaybeInfinity(Comparator comparator, Object[] in, int from, int to, Compare find)
{
if (find == null)
return -(1 + to);
return exponentialSearch(comparator, in, from, to, find);
}
/**
* Equivalent to {@link Arrays#binarySearch}, only more efficient algorithmically for linear merges.
* Binary search has worst case complexity {@code O(n.lg n)} for a linear merge, whereas exponential search
* has a worst case of {@code O(n)}. However compared to a simple linear merge, the best case for exponential
* search is {@code O(lg(n))} instead of {@code O(n)}.
*/
private static int exponentialSearch(Comparator comparator, Object[] in, int from, int to, Compare find)
{
int step = 0;
while (from + step < to)
{
int i = from + step;
int c = comparator.compare(find, (Compare) in[i]);
if (c < 0)
{
to = i;
break;
}
if (c == 0)
return i;
from = i + 1;
step = step * 2 + 1; // jump in perfect binary search increments
}
return Arrays.binarySearch((Compare[]) in, from, to, find, comparator);
}
/**
* Perform {@link #exponentialSearch} on {@code in[from..to)}; if the value falls outside of the range of these
* elements, test against {@code ub} as though it occurred at position {@code to}
*
* @return same as {@link Arrays#binarySearch} if {@code find} occurs in the range {@code [in[from]..in[to])};
* otherwise the insertion position {@code -(1+to)} if {@code find} is less than {@code ub}, and {@code -(2+t)}
* if it is greater than or equal to.
*
* {@code ub} may be {@code null}, representing infinity.
*/
static int exponentialSearchWithUpperBound(Comparator comparator, Object[] in, int from, int to, Compare ub, Compare find)
{
int step = 0;
while (true)
{
int i = from + step;
if (i >= to)
{
int c = compareWithMaybeInfinity(comparator, find, ub);
if (c >= 0)
return -(2 + to);
break;
}
int c = comparator.compare(find, (Compare) in[i]);
if (c < 0)
{
to = i;
break;
}
if (c == 0)
return i;
from = i + 1;
step = step * 2 + 1; // jump in perfect binary search increments
}
return Arrays.binarySearch((Compare[]) in, from, to, find, comparator);
}
/**
* Compute the size-in-bytes of full trees of cardinality {@code branchFactor^height - 1}
*/
private static long[] sizeOnHeapOfPerfectTrees(int branchShift)
{
long[] result = new long[heightAtSize2n(Integer.MAX_VALUE, branchShift)];
int branchFactor = 1 << branchShift;
result[0] = branchFactor - 1;
for (int i = 1; i < result.length; ++i)
result[i] = sizeOnHeapOfPerfectTree(i + 1, branchFactor);
return result;
}
/**
* Compute the size-in-bytes of a full tree of cardinality {@code branchFactor^height - 1}
* TODO: test
*/
private static long sizeOnHeapOfPerfectTree(int height, int branchShift)
{
int branchFactor = 1 << branchShift;
long branchSize = ObjectSizes.sizeOfReferenceArray(branchFactor * 2);
int branchCount = height == 2 ? 1 : 2 + treeSize2n(height - 2, branchShift);
long leafSize = ObjectSizes.sizeOfReferenceArray((branchFactor - 1) | 1);
int leafCount = 1 + treeSize2n(height - 1, branchShift);
return (branchSize * branchCount) + (leafSize * leafCount);
}
/**
* @return the actual height of {@code tree}
*/
public static int height(Object[] tree)
{
if (isLeaf(tree))
return 1;
int height = 1;
while (!isLeaf(tree))
{
height++;
tree = (Object[]) tree[shallowSizeOfBranch(tree)];
}
return height;
}
/**
* @return the maximum representable size at {@code height}.
*/
private static int denseSize(int height)
{
return treeSize2n(height, BRANCH_SHIFT);
}
/**
* @return the maximum representable size at {@code height}.
*/
private static int checkedDenseSize(int height)
{
assert height * BRANCH_SHIFT < 32;
return denseSize(height);
}
/**
* Computes the number of nodes in a full tree of height {@code height}
* and with {@code 2^branchShift} branch factor.
* i.e. computes {@code (2^branchShift)^height - 1}
*/
private static int treeSize2n(int height, int branchShift)
{
return (1 << (branchShift * height)) - 1;
}
// TODO: test
private static int maxRootHeight(int size)
{
if (size <= BRANCH_FACTOR)
return 1;
return 1 + heightAtSize2n((size - 1) / 2, BRANCH_SHIFT - 1);
}
private static int sizeOfBranch(Object[] branch)
{
int length = branch.length;
// length - 1 == getChildEnd == getPositionOfSizeMap
// (length / 2) - 1 == getChildCount - 1 == position of full tree size
// hard code this, as will be used often;
return ((int[]) branch[length - 1])[(length / 2) - 1];
}
/**
* Checks if the UpdateFunction is an instance of {@code UpdateFunction.Simple}.
*/
private static boolean isSimple(UpdateFunction updateF)
{
return updateF instanceof UpdateFunction.Simple;
}
/**
* @return the size map for the branch node
*/
static int[] sizeMap(Object[] branch)
{
return (int[]) branch[branch.length - 1];
}
public static long sizeOnHeapOf(Object[] tree)
{
if (isEmpty(tree))
return 0;
long size = ObjectSizes.sizeOfArray(tree);
if (isLeaf(tree))
return size;
for (int i = childOffset(tree); i < childEndOffset(tree); i++)
size += sizeOnHeapOf((Object[]) tree[i]);
size += ObjectSizes.sizeOfArray(sizeMap(tree)); // may overcount, since we share size maps
return size;
}
private static long sizeOnHeapOfLeaf(Object[] tree)
{
if (isEmpty(tree))
return 0;
return ObjectSizes.sizeOfArray(tree);
}
// Arbitrary boundaries
private static Object POSITIVE_INFINITY = new Object();
private static Object NEGATIVE_INFINITY = new Object();
/**
* simple static wrapper to calls to cmp.compare() which checks if either a or b are Special (i.e. represent an infinity)
*/
private static int compareWellFormed(Comparator cmp, Object a, Object b)
{
if (a == b)
return 0;
if (a == NEGATIVE_INFINITY | b == POSITIVE_INFINITY)
return -1;
if (b == NEGATIVE_INFINITY | a == POSITIVE_INFINITY)
return 1;
return cmp.compare((V) a, (V) b);
}
public static boolean isWellFormed(Object[] btree, Comparator cmp)
{
return isWellFormedReturnHeight(cmp, btree, true, NEGATIVE_INFINITY, POSITIVE_INFINITY) >= 0;
}
private static int isWellFormedReturnHeight(Comparator cmp, Object[] node, boolean isRoot, Object min, Object max)
{
if (isEmpty(node))
return 0;
if (cmp != null && !isNodeWellFormed(cmp, node, min, max))
return -1;
int keyCount = shallowSize(node);
if (keyCount < 1)
return -1;
if (!isRoot && keyCount < BRANCH_FACTOR / 2 - 1)
return -1;
if (keyCount >= BRANCH_FACTOR)
return -1;
if (isLeaf(node))
return 0;
int[] sizeMap = sizeMap(node);
int size = 0;
int childHeight = -1;
// compare each child node with the branch element at the head of this node it corresponds with
for (int i = childOffset(node); i < childEndOffset(node); i++)
{
Object[] child = (Object[]) node[i];
Object localmax = i < node.length - 2 ? node[i - childOffset(node)] : max;
int height = isWellFormedReturnHeight(cmp, child, false, min, localmax);
if (height == -1)
return -1;
if (childHeight == -1)
childHeight = height;
if (childHeight != height)
return -1;
min = localmax;
size += size(child);
if (sizeMap[i - childOffset(node)] != size)
return -1;
size += 1;
}
return childHeight + 1;
}
private static boolean isNodeWellFormed(Comparator cmp, Object[] node, Object min, Object max)
{
Object previous = min;
int end = shallowSize(node);
for (int i = 0; i < end; i++)
{
Object current = node[i];
if (compareWellFormed(cmp, previous, current) >= 0)
return false;
previous = current;
}
return compareWellFormed(cmp, previous, max) < 0;
}
/**
* Build a tree of unknown size, in order.
*
* Can be used with {@link #reverseInSitu} to build a tree in reverse.
*/
public static FastBuilder fastBuilder()
{
TinyThreadLocalPool.TinyPool> pool = FastBuilder.POOL.get();
FastBuilder builder = (FastBuilder) pool.poll();
if (builder == null)
builder = new FastBuilder<>();
builder.pool = pool;
return builder;
}
/**
* Base class for AbstractFastBuilder.BranchBuilder, LeafBuilder and AbstractFastBuilder,
* containing shared behaviour and declaring some useful abstract methods.
*/
private static abstract class LeafOrBranchBuilder
{
final int height;
final LeafOrBranchBuilder child;
BranchBuilder parent;
/**
* The current buffer contents (if any) of the leaf or branch - always sized to contain a complete
* node of the form being constructed. Always non-null, except briefly during overflow.
*/
Object[] buffer;
/**
* The number of keys in our buffer, whether or not we are building a leaf or branch; if we are building
* a branch, we will ordinarily have the same number of children as well, except temporarily when finishing
* the construction of the node.
*/
int count;
/**
* either
* 1) an empty leftover buffer from a past usage, which can be used when we exhaust {@code buffer}; or
* 2) a full {@code buffer} that has been parked until we next overflow, so we can steal some back
* if we finish before reaching MIN_KEYS in {@code buffer}
*/
Object[] savedBuffer;
/**
* The key we overflowed on when populating savedBuffer. If null, {@link #savedBuffer} is logically empty.
*/
Object savedNextKey;
LeafOrBranchBuilder(LeafOrBranchBuilder child)
{
this.height = child == null ? 1 : 1 + child.height;
this.child = child;
}
/**
* Do we have enough keys in the builder to construct at least one balanced node?
* We could have enough to build two.
*/
final boolean isSufficient()
{
return hasOverflow() || count >= MIN_KEYS;
}
/**
* Do we have an already constructed node saved, that we can propagate or redistribute?
* This implies we are building two nodes, since {@link #savedNextKey} would overflow {@link #savedBuffer}
*/
final boolean hasOverflow()
{
return savedNextKey != null;
}
/**
* Do we have an already constructed node saved AND insufficient keys in our buffer, so
* that we need to share the contents of {@link #savedBuffer} with {@link #buffer} to construct
* our results?
*/
final boolean mustRedistribute()
{
return hasOverflow() && count < MIN_KEYS;
}
/**
* Are we empty, i.e. we have no contents in either {@link #buffer} or {@link #savedBuffer}
*/
final boolean isEmpty()
{
return count == 0 && savedNextKey == null;
}
/**
* Drain the contents of this builder and build up to two nodes, as necessary.
* If {@code unode != null} and we are building a single node that is identical to it, use {@code unode} instead.
* If {@code propagateTo != null} propagate any nodes we build to it.
*
* @return the last node we construct
*/
abstract Object[] drainAndPropagate(Object[] unode, BranchBuilder propagateTo);
/**
* Drain the contents of this builder and build at most one node.
* Requires {@code !hasOverflow()}
*
* @return the node we construct
*/
abstract Object[] drain();
/**
* Complete the build. Drains the node and any used or newly-required parent and returns the root of the
* resulting tree.
*
* @return the root of the constructed tree.
*/
public Object[] completeBuild()
{
LeafOrBranchBuilder level = this;
while (true)
{
if (!level.hasOverflow())
return level.drain();
BranchBuilder parent = level.ensureParent();
level.drainAndPropagate(null, parent);
if (level.savedBuffer != null)
Arrays.fill(level.savedBuffer, null);
level = parent;
}
}
/**
* Takes a node that would logically occur directly preceding the current buffer contents,
* and the key that would separate them in a parent node, and prepends their contents
* to the current buffer's contents. This can be used to redistribute already-propagated
* contents to a parent in cases where this is convenient (i.e. when transforming)
*
* @param predecessor directly preceding node
* @param predecessorNextKey key that would have separated predecessor from buffer contents
*/
abstract void prepend(Object[] predecessor, Object predecessorNextKey);
/**
* Indicates if this builder produces dense nodes, i.e. those that are populated with MAX_KEYS
* at every level. Only the last two children of any branch may be non-dense, and in some cases only
* the last two nodes in any tier of the tree.
*
* This flag switches whether or not we maintain a buffer of sizes, or use the globally shared contents of
* DENSE_SIZE_MAPS.
*/
abstract boolean producesOnlyDense();
/**
* Ensure there is a {@code branch.parent}, and return it
*/
final BranchBuilder ensureParent()
{
if (parent == null)
parent = new BranchBuilder(this);
parent.inUse = true;
return parent;
}
/**
* Mark a branch builder as utilised, so that we must clear it when resetting any {@link AbstractFastBuilder}
*
* @return {@code branch}
*/
static BranchBuilder markUsed(BranchBuilder branch)
{
branch.inUse = true;
return branch;
}
/**
* A utility method for comparing a range of two arrays
*/
static boolean areIdentical(Object[] a, int aOffset, Object[] b, int bOffset, int count)
{
for (int i = 0; i < count; ++i)
{
if (a[i + aOffset] != b[i + bOffset])
return false;
}
return true;
}
/**
* A utility method for comparing a range of two arrays
*/
static boolean areIdentical(int[] a, int aOffset, int[] b, int bOffset, int count)
{
for (int i = 0; i < count; ++i)
{
if (a[i + aOffset] != b[i + bOffset])
return false;
}
return true;
}
}
/**
* LeafBuilder for methods pertaining specifically to building a leaf in an {@link AbstractFastBuilder}.
* Note that {@link AbstractFastBuilder} extends this class directly, however it is convenient to maintain
* distinct classes in the hierarchy for clarity of behaviour and intent.
*/
private static abstract class LeafBuilder extends LeafOrBranchBuilder
{
long allocated;
LeafBuilder()
{
super(null);
buffer = new Object[MAX_KEYS];
}
/**
* Add {@code nextKey} to the buffer, overflowing if necessary
*/
public void addKey(Object nextKey)
{
if (count == MAX_KEYS)
overflow(nextKey);
else
buffer[count++] = nextKey;
}
/**
* Add {@code nextKey} to the buffer; the caller specifying overflow is unnecessary
*/
public void addKeyNoOverflow(Object nextKey)
{
buffer[count++] = nextKey;
}
/**
* Add {@code nextKey} to the buffer; the caller specifying overflow is unnecessary
*/
public void maybeAddKeyNoOverflow(Object nextKey)
{
buffer[count] = nextKey;
count += nextKey != null ? 1 : 0;
}
/**
* Add {@code nextKey} to the buffer; the caller specifying overflow is unnecessary
*/
public void maybeAddKey(Object nextKey)
{
if (count == MAX_KEYS)
{
if (nextKey != null)
overflow(nextKey);
}
else
{
buffer[count] = nextKey;
count += nextKey != null ? 1 : 0;
}
}
/**
* Copy the contents of {@code source[from..to)} to {@code buffer}, overflowing as necessary.
*/
void copy(Object[] source, int offset, int length)
{
if (count + length > MAX_KEYS)
{
int copy = MAX_KEYS - count;
System.arraycopy(source, offset, buffer, count, copy);
offset += copy;
// implicitly: count = MAX_KEYS;
overflow(source[offset++]);
length -= 1 + copy;
}
System.arraycopy(source, offset, buffer, count, length);
count += length;
}
/**
* Copy the contents of {@code source[from..to)} to {@code buffer}; the caller specifying overflow is unnecessary
*/
void copyNoOverflow(Object[] source, int offset, int length)
{
System.arraycopy(source, offset, buffer, count, length);
count += length;
}
/**
* Copy the contents of the data to {@code buffer}, overflowing as necessary.
*/
void copy(Object[] source, int offset, int length, UpdateFunction apply)
{
if (isSimple(apply))
{
copy(source, offset, length);
return;
}
if (count + length > MAX_KEYS)
{
int copy = MAX_KEYS - count;
for (int i = 0; i < copy; ++i)
buffer[count + i] = apply.insert((Insert) source[offset + i]);
offset += copy;
// implicitly: leaf().count = MAX_KEYS;
overflow(apply.insert((Insert) source[offset++]));
length -= 1 + copy;
}
for (int i = 0; i < length; ++i)
buffer[count + i] = apply.insert((Insert) source[offset + i]);
count += length;
}
/**
* {@link #buffer} is full, and we need to make room either by populating {@link #savedBuffer},
* propagating its current contents, if any, to {@link #parent}
*/
void overflow(Object nextKey)
{
if (hasOverflow())
propagateOverflow();
// precondition: count == MAX_KEYS and savedNextKey == null
Object[] newBuffer = savedBuffer;
if (newBuffer == null)
newBuffer = new Object[MAX_KEYS];
savedBuffer = buffer;
savedNextKey = nextKey;
buffer = newBuffer;
count = 0;
}
/**
* Redistribute the contents of {@link #savedBuffer} into {@link #buffer}, finalise {@link #savedBuffer} and flush upwards.
* Invoked when we are building from {@link #buffer}, have insufficient values but a complete leaf in {@link #savedBuffer}
*
* @return the size of the leaf we flushed to our parent from {@link #savedBuffer}
*/
Object[] redistributeOverflowAndDrain()
{
Object[] newLeaf = redistributeAndDrain(savedBuffer, MAX_KEYS, savedNextKey);
savedNextKey = null;
return newLeaf;
}
/**
* Redistribute the contents of {@link #buffer} and an immediate predecessor into a new leaf,
* then construct a new predecessor with the remaining contents and propagate up to our parent
* Invoked when we are building from {@link #buffer}, have insufficient values but either a complete
* leaf in {@link #savedBuffer} or can exfiltrate one from our parent to redistribute.
*
* @return the second of the two new leaves
*/
Object[] redistributeAndDrain(Object[] pred, int predSize, Object predNextKey)
{
// precondition: savedLeafCount == MAX_KEYS && leaf().count < MIN_KEYS
// ensure we have at least MIN_KEYS in leaf().buffer
// first shift leaf().buffer and steal some keys from leaf().savedBuffer and leaf().savedBufferNextKey
int steal = MIN_KEYS - count;
Object[] newLeaf = new Object[MIN_KEYS];
System.arraycopy(pred, predSize - (steal - 1), newLeaf, 0, steal - 1);
newLeaf[steal - 1] = predNextKey;
System.arraycopy(buffer, 0, newLeaf, steal, count);
// then create a leaf out of the remainder of savedBuffer
int newPredecessorCount = predSize - steal;
Object[] newPredecessor = new Object[newPredecessorCount | 1];
System.arraycopy(pred, 0, newPredecessor, 0, newPredecessorCount);
if (allocated >= 0)
allocated += ObjectSizes.sizeOfReferenceArray(newPredecessorCount | 1);
ensureParent().addChildAndNextKey(newPredecessor, newPredecessorCount, pred[newPredecessorCount]);
return newLeaf;
}
/**
* Invoked to fill our {@link #buffer} to >= MIN_KEYS with data ocurring before {@link #buffer};
* possibly instead fills {@link #savedBuffer}
*
* @param pred directly preceding node
* @param predNextKey key that would have separated predecessor from buffer contents
*/
void prepend(Object[] pred, Object predNextKey)
{
assert !hasOverflow();
int predSize = sizeOfLeaf(pred);
int newKeys = 1 + predSize;
if (newKeys + count <= MAX_KEYS)
{
System.arraycopy(buffer, 0, buffer, newKeys, count);
System.arraycopy(pred, 0, buffer, 0, predSize);
buffer[predSize] = predNextKey;
count += newKeys;
}
else
{
if (savedBuffer == null)
savedBuffer = new Object[MAX_KEYS];
System.arraycopy(pred, 0, savedBuffer, 0, predSize);
if (predSize == MAX_KEYS)
{
savedNextKey = predNextKey;
}
else
{
int removeKeys = MAX_KEYS - predSize;
count -= removeKeys;
savedBuffer[predSize] = predNextKey;
System.arraycopy(buffer, 0, savedBuffer, predSize + 1, MAX_KEYS - newKeys);
savedNextKey = buffer[MAX_KEYS - newKeys];
System.arraycopy(buffer, removeKeys, buffer, 0, count);
}
}
}
/**
* Invoked when we want to add a key to the leaf buffer, but it is full
*/
void propagateOverflow()
{
// propagate the leaf we have saved in savedBuffer
// precondition: savedLeafCount == MAX_KEYS
if (allocated >= 0)
allocated += ObjectSizes.sizeOfReferenceArray(MAX_KEYS);
ensureParent().addChildAndNextKey(savedBuffer, MAX_KEYS, savedNextKey);
savedBuffer = null;
savedNextKey = null;
}
/**
* Construct a new leaf from the contents of {@link #buffer}, unless the contents have not changed
* from {@code unode}, in which case return {@code unode} to avoid allocating unnecessary objects.
*
* This is only called when we have enough data to complete the node, i.e. we have MIN_KEYS or more items added
* or the node is the BTree's root.
*/
Object[] drainAndPropagate(Object[] unode, BranchBuilder propagateTo)
{
Object[] leaf;
int sizeOfLeaf;
if (mustRedistribute())
{
// we have too few items, so spread the two buffers across two new nodes
leaf = redistributeOverflowAndDrain();
sizeOfLeaf = MIN_KEYS;
}
else if (!hasOverflow() && unode != null && count == sizeOfLeaf(unode) && areIdentical(buffer, 0, unode, 0, count))
{
// we have exactly the same contents as the original node, so reuse it
leaf = unode;
sizeOfLeaf = count;
}
else
{
// we have maybe one saved full buffer, and one buffer with sufficient contents to copy
if (hasOverflow())
propagateOverflow();
sizeOfLeaf = count;
leaf = drain();
if (allocated >= 0 && sizeOfLeaf > 0)
allocated += ObjectSizes.sizeOfReferenceArray(sizeOfLeaf | 1) - (unode == null ? 0 : sizeOnHeapOfLeaf(unode));
}
count = 0;
if (propagateTo != null)
propagateTo.addChild(leaf, sizeOfLeaf);
return leaf;
}
/**
* Construct a new leaf from the contents of {@code leaf().buffer}, assuming that the node does not overflow.
*/
Object[] drain()
{
// the number of children here may be smaller than MIN_KEYS if this is the root node
assert !hasOverflow();
if (count == 0)
return empty();
Object[] newLeaf = new Object[count | 1];
System.arraycopy(buffer, 0, newLeaf, 0, count);
count = 0;
return newLeaf;
}
}
static class BranchBuilder extends LeafOrBranchBuilder
{
final LeafBuilder leaf;
/**
* sizes of the children in {@link #buffer}. If null, we only produce dense nodes.
*/
int[] sizes;
/**
* sizes of the children in {@link #savedBuffer}
*/
int[] savedSizes;
/**
* marker to limit unnecessary work with unused levels, esp. on reset
*/
boolean inUse;
BranchBuilder(LeafOrBranchBuilder child)
{
super(child);
buffer = new Object[2 * (MAX_KEYS + 1)];
if (!child.producesOnlyDense())
sizes = new int[MAX_KEYS + 1];
this.leaf = child instanceof LeafBuilder ? (LeafBuilder) child : ((BranchBuilder) child).leaf;
}
/**
* Ensure there is room to add another key to {@code branchBuffers[branchIndex]}, and add it;
* invoke {@link #overflow} if necessary
*/
void addKey(Object key)
{
if (count == MAX_KEYS)
overflow(key);
else
buffer[count++] = key;
}
/**
* To be invoked when there's a key already inserted to the buffer that requires a corresponding
* right-hand child, for which the buffers are sized to ensure there is always room.
*/
void addChild(Object[] child, int sizeOfChild)
{
buffer[MAX_KEYS + count] = child;
recordSizeOfChild(sizeOfChild);
}
void recordSizeOfChild(int sizeOfChild)
{
if (sizes != null)
sizes[count] = sizeOfChild;
}
/**
* See {@link BranchBuilder#addChild(Object[], int)}
*/
void addChild(Object[] child)
{
addChild(child, sizes == null ? 0 : size(child));
}
/**
* Insert a new child into a parent branch, when triggered by {@code overflowLeaf} or {@code overflowBranch}
*/
void addChildAndNextKey(Object[] newChild, int newChildSize, Object nextKey)
{
// we should always have room for a child to the right of any key we have previously inserted
buffer[MAX_KEYS + count] = newChild;
recordSizeOfChild(newChildSize);
// but there may not be room for another key
addKey(nextKey);
}
/**
* Invoked when we want to add a key to the leaf buffer, but it is full
*/
void propagateOverflow()
{
// propagate the leaf we have saved in leaf().savedBuffer
if (leaf.allocated >= 0)
leaf.allocated += ObjectSizes.sizeOfReferenceArray(2 * (1 + MAX_KEYS));
int size = setOverflowSizeMap(savedBuffer, MAX_KEYS);
ensureParent().addChildAndNextKey(savedBuffer, size, savedNextKey);
savedBuffer = null;
savedNextKey = null;
}
/**
* Invoked when a branch already contains {@code MAX_KEYS}, and another child is ready to be added.
* Creates a new neighbouring node containing MIN_KEYS items, shifting back the remaining MIN_KEYS+1
* items to the start of the buffer(s).
*/
void overflow(Object nextKey)
{
if (hasOverflow())
propagateOverflow();
Object[] restoreBuffer = savedBuffer;
int[] restoreSizes = savedSizes;
savedBuffer = buffer;
savedSizes = sizes;
savedNextKey = nextKey;
sizes = restoreSizes == null && savedSizes != null ? new int[MAX_KEYS + 1] : restoreSizes;
buffer = restoreBuffer == null ? new Object[2 * (MAX_KEYS + 1)] : restoreBuffer;
count = 0;
}
/**
* Redistribute the contents of branch.savedBuffer into branch.buffer, finalise savedBuffer and flush upwards.
* Invoked when we are building from branch, have insufficient values but a complete branch in savedBuffer.
*
* @return the size of the branch we flushed to our parent from savedBuffer
*/
Object[] redistributeOverflowAndDrain()
{
// now ensure we have at least MIN_KEYS in buffer
// both buffer and savedBuffer should be balanced, so that we have count+1 and MAX_KEYS+1 children respectively
// we need to utilise savedNextKey, so we want to take {@code steal-1} keys from savedBuffer, {@code steal) children
// and the dangling key we use in place of savedNextKey for our parent key.
int steal = MIN_KEYS - count;
Object[] newBranch = new Object[2 * (MIN_KEYS + 1)];
System.arraycopy(savedBuffer, MAX_KEYS - (steal - 1), newBranch, 0, steal - 1);
newBranch[steal - 1] = savedNextKey;
System.arraycopy(buffer, 0, newBranch, steal, count);
System.arraycopy(savedBuffer, 2 * MAX_KEYS + 1 - steal, newBranch, MIN_KEYS, steal);
System.arraycopy(buffer, MAX_KEYS, newBranch, MIN_KEYS + steal, count + 1);
setRedistributedSizeMap(newBranch, steal);
// then create a branch out of the remainder of savedBuffer
int savedBranchCount = MAX_KEYS - steal;
Object[] savedBranch = new Object[2 * (savedBranchCount + 1)];
System.arraycopy(savedBuffer, 0, savedBranch, 0, savedBranchCount);
System.arraycopy(savedBuffer, MAX_KEYS, savedBranch, savedBranchCount, savedBranchCount + 1);
int savedBranchSize = setOverflowSizeMap(savedBranch, savedBranchCount);
if (leaf.allocated >= 0)
leaf.allocated += ObjectSizes.sizeOfReferenceArray(2 * (1 + savedBranchCount));
ensureParent().addChildAndNextKey(savedBranch, savedBranchSize, savedBuffer[savedBranchCount]);
savedNextKey = null;
return newBranch;
}
/**
* See {@link LeafOrBranchBuilder#prepend(Object[], Object)}
*/
void prepend(Object[] pred, Object predNextKey)
{
assert !hasOverflow();
// assumes sizes != null, since only makes sense to use this method in that context
int predKeys = shallowSizeOfBranch(pred);
int[] sizeMap = (int[]) pred[2 * predKeys + 1];
int newKeys = 1 + predKeys;
if (newKeys + count <= MAX_KEYS)
{
System.arraycopy(buffer, 0, buffer, newKeys, count);
System.arraycopy(sizes, 0, sizes, newKeys, count + 1);
System.arraycopy(buffer, MAX_KEYS, buffer, MAX_KEYS + newKeys, count + 1);
System.arraycopy(pred, 0, buffer, 0, predKeys);
buffer[predKeys] = predNextKey;
System.arraycopy(pred, predKeys, buffer, MAX_KEYS, predKeys + 1);
copySizeMapToSizes(sizeMap, 0, sizes, 0, predKeys + 1);
count += newKeys;
}
else
{
if (savedBuffer == null)
{
savedBuffer = new Object[2 * (1 + MAX_KEYS)];
savedSizes = new int[1 + MAX_KEYS];
}
System.arraycopy(pred, 0, savedBuffer, 0, predKeys);
System.arraycopy(pred, predKeys, savedBuffer, MAX_KEYS, predKeys + 1);
copySizeMapToSizes(sizeMap, 0, savedSizes, 0, predKeys + 1);
if (newKeys == MAX_KEYS + 1)
{
savedNextKey = predNextKey;
}
else
{
int removeKeys = (1 + MAX_KEYS - newKeys);
int remainingKeys = count - removeKeys;
savedBuffer[predKeys] = predNextKey;
System.arraycopy(buffer, 0, savedBuffer, newKeys, MAX_KEYS - newKeys);
savedNextKey = buffer[MAX_KEYS - newKeys];
System.arraycopy(sizes, 0, savedSizes, newKeys, MAX_KEYS + 1 - newKeys);
System.arraycopy(buffer, MAX_KEYS, savedBuffer, MAX_KEYS + newKeys, MAX_KEYS + 1 - newKeys);
System.arraycopy(buffer, removeKeys, buffer, 0, remainingKeys);
System.arraycopy(buffer, MAX_KEYS + removeKeys, buffer, MAX_KEYS, remainingKeys + 1);
System.arraycopy(sizes, removeKeys, sizes, 0, remainingKeys + 1);
count = remainingKeys;
}
}
}
boolean producesOnlyDense()
{
return sizes == null;
}
/**
* Construct a new branch from the contents of {@code branchBuffers[branchIndex]}, unless the contents have
* not changed from {@code unode}, in which case return {@code unode} to avoid allocating unnecessary objects.
*
* This is only called when we have enough data to complete the node, i.e. we have MIN_KEYS or more items added
* or the node is the BTree's root.
*/
Object[] drainAndPropagate(Object[] unode, BranchBuilder propagateTo)
{
int sizeOfBranch;
Object[] branch;
if (mustRedistribute())
{
branch = redistributeOverflowAndDrain();
sizeOfBranch = sizeOfBranch(branch);
}
else
{
int usz = unode != null ? shallowSizeOfBranch(unode) : -1;
if (!hasOverflow() && usz == count
&& areIdentical(buffer, 0, unode, 0, usz)
&& areIdentical(buffer, MAX_KEYS, unode, usz, usz + 1))
{
branch = unode;
sizeOfBranch = sizeOfBranch(branch);
}
else
{
if (hasOverflow())
propagateOverflow();
// the number of children here may be smaller than MIN_KEYS if this is the root node, but there must
// be at least one key / two children.
assert count > 0;
branch = new Object[2 * (count + 1)];
System.arraycopy(buffer, 0, branch, 0, count);
System.arraycopy(buffer, MAX_KEYS, branch, count, count + 1);
sizeOfBranch = setDrainSizeMap(unode, usz, branch, count);
}
}
count = 0;
if (propagateTo != null)
propagateTo.addChild(branch, sizeOfBranch);
return branch;
}
/**
* Construct a new branch from the contents of {@code buffer}, assuming that the node does not overflow.
*/
Object[] drain()
{
assert !hasOverflow();
int keys = count;
count = 0;
Object[] branch = new Object[2 * (keys + 1)];
if (keys == MAX_KEYS)
{
Object[] tmp = buffer;
buffer = branch;
branch = tmp;
}
else
{
System.arraycopy(buffer, 0, branch, 0, keys);
System.arraycopy(buffer, MAX_KEYS, branch, keys, keys + 1);
}
setDrainSizeMap(null, -1, branch, keys);
return branch;
}
/**
* Compute (or fetch from cache) and set the sizeMap in {@code branch}, knowing that it
* was constructed from for the contents of {@code buffer}.
*
* For {@link FastBuilder} these are mostly the same, so they are fetched from a global cache and
* resized accordingly, but for {@link AbstractUpdater} we maintain a buffer of sizes.
*/
int setDrainSizeMap(Object[] original, int keysInOriginal, Object[] branch, int keysInBranch)
{
if (producesOnlyDense())
return setImperfectSizeMap(branch, keysInBranch);
// first convert our buffer contents of sizes to represent a sizeMap
int size = sizesToSizeMap(this.sizes, keysInBranch + 1);
// then attempt to reuse the sizeMap from the original node, by comparing the buffer's contents with it
int[] sizeMap;
if (keysInOriginal != keysInBranch || !areIdentical(sizeMap = sizeMap(original), 0, this.sizes, 0, keysInBranch + 1))
{
// if we cannot, then we either take the buffer wholesale and replace its buffer, or copy a prefix
sizeMap = this.sizes;
if (keysInBranch < MAX_KEYS)
sizeMap = Arrays.copyOf(sizeMap, keysInBranch + 1);
else
this.sizes = new int[MAX_KEYS + 1];
}
branch[2 * keysInBranch + 1] = sizeMap;
return size;
}
/**
* Compute (or fetch from cache) and set the sizeMap in {@code branch}, knowing that it
* was constructed from for the contents of {@code savedBuffer}.
*
* For {@link FastBuilder} these are always the same size, so they are fetched from a global cache,
* but for {@link AbstractUpdater} we maintain a buffer of sizes.
*
* @return the size of {@code branch}
*/
int setOverflowSizeMap(Object[] branch, int keys)
{
if (producesOnlyDense())
{
int[] sizeMap = DENSE_SIZE_MAPS[height - 2];
if (keys < MAX_KEYS)
sizeMap = Arrays.copyOf(sizeMap, keys + 1);
branch[2 * keys + 1] = sizeMap;
return keys < MAX_KEYS ? sizeMap[keys] : checkedDenseSize(height + 1);
}
else
{
int[] sizes = savedSizes;
if (keys < MAX_KEYS)
sizes = Arrays.copyOf(sizes, keys + 1);
else
savedSizes = null;
branch[2 * keys + 1] = sizes;
return sizesToSizeMap(sizes);
}
}
/**
* Compute (or fetch from cache) and set the sizeMap in {@code branch}, knowing that it
* was constructed from the contents of both {@code savedBuffer} and {@code buffer}
*
* For {@link FastBuilder} these are mostly the same size, so they are fetched from a global cache
* and only the last items updated, but for {@link AbstractUpdater} we maintain a buffer of sizes.
*/
void setRedistributedSizeMap(Object[] branch, int steal)
{
if (producesOnlyDense())
{
setImperfectSizeMap(branch, MIN_KEYS);
}
else
{
int[] sizeMap = new int[MIN_KEYS + 1];
System.arraycopy(sizes, 0, sizeMap, steal, count + 1);
System.arraycopy(savedSizes, MAX_KEYS + 1 - steal, sizeMap, 0, steal);
branch[2 * MIN_KEYS + 1] = sizeMap;
sizesToSizeMap(sizeMap);
}
}
/**
* Like {@link #setOverflowSizeMap}, but used for building the sizeMap of a node whose
* last two children may have had their contents redistributed; uses the perfect size map
* for all but the final two children, and queries the size of the last children directly
*/
private int setImperfectSizeMap(Object[] branch, int keys)
{
int[] sizeMap = Arrays.copyOf(DENSE_SIZE_MAPS[height - 2], keys + 1);
int size = keys == 1 ? 0 : 1 + sizeMap[keys - 2];
sizeMap[keys - 1] = size += size((Object[]) branch[2 * keys - 1]);
sizeMap[keys] = size += 1 + size((Object[]) branch[2 * keys]);
branch[2 * keys + 1] = sizeMap;
return size;
}
/**
* Copy the contents of {@code unode} into {@code branchBuffers[branchIndex]},
* starting at the child before key with index {@code offset} up to and
* including the key with index {@code offset + length - 1}.
*/
void copyPreceding(Object[] unode, int usz, int offset, int length)
{
int[] uszmap = sizeMap(unode);
if (count + length > MAX_KEYS)
{
// we will overflow, so copy to MAX_KEYS and trigger overflow
int copy = MAX_KEYS - count;
copyPrecedingNoOverflow(unode, usz, uszmap, offset, copy);
offset += copy;
// copy last child that fits
buffer[MAX_KEYS + MAX_KEYS] = unode[usz + offset];
sizes[MAX_KEYS] = uszmap[offset] - (offset > 0 ? (1 + uszmap[offset - 1]) : 0);
overflow(unode[offset]);
length -= 1 + copy;
++offset;
}
copyPrecedingNoOverflow(unode, usz, uszmap, offset, length);
}
/**
* Copy the contents of {@code unode} into {@code branchBuffers[branchIndex]},
* between keys {@code from} and {@code to}, with the caller declaring overflow is unnecessary.
* {@code from} may be {@code -1}, representing the first child only;
* all other indices represent the key/child pairs that follow (i.e. a key and its right-hand child).
*/
private void copyPrecedingNoOverflow(Object[] unode, int usz, int[] uszmap, int offset, int length)
{
if (length <= 1)
{
if (length == 0)
return;
buffer[count] = unode[offset];
buffer[MAX_KEYS + count] = unode[usz + offset];
sizes[count] = uszmap[offset] - (offset > 0 ? (1 + uszmap[offset - 1]) : 0);
++count;
}
else
{
System.arraycopy(unode, offset, buffer, count, length);
System.arraycopy(unode, usz + offset, buffer, MAX_KEYS + count, length);
copySizeMapToSizes(uszmap, offset, sizes, count, length);
count += length;
}
}
/**
* Copy a region of a cumulative sizeMap into an array of plain sizes
*/
static void copySizeMapToSizes(int[] in, int inOffset, int[] out, int outOffset, int count)
{
assert count > 0;
if (inOffset == 0)
{
// we don't need to subtract anything from the first node, so just copy it so we can keep the rest of the loop simple
out[outOffset++] = in[inOffset++];
--count;
}
for (int i = 0; i < count; ++i)
out[outOffset + i] = in[inOffset + i] - (1 + in[inOffset + i - 1]);
}
}
/**
* Shared parent of {@link FastBuilder} and {@link Updater}, both of which
* construct their trees in order without knowing the resultant size upfront.
*
* Maintains a simple stack of buffers that we provide utilities to navigate and update.
*/
private static abstract class AbstractFastBuilder extends LeafBuilder
{
final boolean producesOnlyDense()
{
return getClass() == FastBuilder.class;
}
/**
* An aesthetic convenience for declaring when we are interacting with the leaf, instead of invoking {@code this} directly
*/
final LeafBuilder leaf()
{
return this;
}
/**
* Clear any references we might still retain, to avoid holding onto memory.
*
* While this method is not strictly necessary, it exists to
* ensure the implementing classes are aware they must handle it.
*/
abstract void reset();
}
/**
* A pooled builder for constructing a tree in-order, and without needing any reconciliation.
*
* Constructs whole nodes in place, so that a flush of a complete node can take its buffer entirely.
* Since we build trees of a predictable shape (i.e. perfectly dense) we do not construct a size map.
*/
public static class FastBuilder extends AbstractFastBuilder implements AutoCloseable
{
private static final TinyThreadLocalPool> POOL = new TinyThreadLocalPool<>();
private TinyThreadLocalPool.TinyPool> pool;
FastBuilder()
{
allocated = -1;
} // disable allocation tracking
public void add(V value)
{
leaf().addKey(value);
}
public void add(Object[] from, int offset, int count)
{
leaf().copy(from, offset, count);
}
public Object[] build()
{
return leaf().completeBuild();
}
public Object[] buildReverse()
{
Object[] result = build();
reverseInSitu(result, height(result), false);
return result;
}
@Override
public void close()
{
reset();
pool.offer(this);
pool = null;
}
@Override
void reset()
{
// we clear precisely to leaf().count and branch.count because, in the case of a builder,
// if we ever fill the buffer we will consume it entirely for the tree we are building
// so the last count should match the number of non-null entries
Arrays.fill(leaf().buffer, 0, leaf().count, null);
leaf().count = 0;
BranchBuilder branch = leaf().parent;
while (branch != null && branch.inUse)
{
Arrays.fill(branch.buffer, 0, branch.count, null);
Arrays.fill(branch.buffer, MAX_KEYS, MAX_KEYS + 1 + branch.count, null);
branch.count = 0;
branch.inUse = false;
branch = branch.parent;
}
}
}
private static abstract class AbstractUpdater extends AbstractFastBuilder implements AutoCloseable
{
void reset()
{
assert leaf().count == 0;
clearLeafBuffer(leaf().buffer);
if (leaf().savedBuffer != null)
Arrays.fill(leaf().savedBuffer, null);
BranchBuilder branch = leaf().parent;
while (branch != null && branch.inUse)
{
assert branch.count == 0;
clearBranchBuffer(branch.buffer);
if (branch.savedBuffer != null && branch.savedBuffer[0] != null)
Arrays.fill(branch.savedBuffer, null); // by definition full, if non-empty
branch.inUse = false;
branch = branch.parent;
}
}
/**
* Clear the contents of a branch buffer, aborting once we encounter a null entry
* to save time on small trees
*/
private void clearLeafBuffer(Object[] array)
{
if (array[0] == null)
return;
// find first null entry; loop from beginning, to amortise cost over size of working set
int i = 1;
while (i < array.length && array[i] != null)
++i;
Arrays.fill(array, 0, i, null);
}
/**
* Clear the contents of a branch buffer, aborting once we encounter a null entry
* to save time on small trees
*/
private void clearBranchBuffer(Object[] array)
{
if (array[0] == null)
return;
// find first null entry; loop from beginning, to amortise cost over size of working set
int i = 1;
while (i < MAX_KEYS && array[i] != null)
++i;
Arrays.fill(array, 0, i, null);
Arrays.fill(array, MAX_KEYS, MAX_KEYS + i + 1, null);
}
}
/**
* A pooled object for modifying an existing tree with a new (typically smaller) tree.
*
* Constructs the new tree around the shape of the existing tree, as though we had performed inserts in
* order, copying as much of the original tree as possible. We achieve this by simply merging leaf nodes
* up to the immediately following key in an ancestor, maintaining up to two complete nodes in a buffer until
* this happens, and flushing any nodes we produce in excess of this immediately into the parent buffer.
*
* We construct whole nodes in place, except the size map, so that a flush of a complete node can take its buffer
* entirely.
*
* Searches within both trees to accelerate the process of modification, instead of performing a simple
* iteration over the new tree.
*/
private static class Updater extends AbstractUpdater implements AutoCloseable
{
static final TinyThreadLocalPool POOL = new TinyThreadLocalPool<>();
TinyThreadLocalPool.TinyPool pool;
// the new tree we navigate linearly, and are always on a key or at the end
final SimpleTreeKeysIterator insert = new SimpleTreeKeysIterator<>();
Comparator comparator;
UpdateFunction updateF;
static Updater get()
{
TinyThreadLocalPool.TinyPool pool = POOL.get();
Updater updater = pool.poll();
if (updater == null)
updater = new Updater<>();
updater.pool = pool;
return updater;
}
/**
* Precondition: {@code update} should not be empty.
*
* Inserts {@code insert} into {@code update}, after applying {@code updateF} to each item, or matched item pairs.
*/
Object[] update(Object[] update, Object[] insert, Comparator comparator, UpdateFunction updateF)
{
this.insert.init(insert);
this.updateF = updateF;
this.comparator = comparator;
this.allocated = isSimple(updateF) ? -1 : 0;
int leafDepth = BTree.depth(update) - 1;
LeafOrBranchBuilder builder = leaf();
for (int i = 0; i < leafDepth; ++i)
builder = builder.ensureParent();
Insert ik = this.insert.next();
ik = updateRecursive(ik, update, null, builder);
assert ik == null;
Object[] result = builder.completeBuild();
if (allocated > 0)
updateF.onAllocatedOnHeap(allocated);
return result;
}
/**
* Merge a BTree recursively with the contents of {@code insert} up to the given upper bound.
*
* @param ik The next key from the inserted data.
* @param unode The source branch to update.
* @param uub The branch's upper bound
* @param builder The builder that will receive the data. It needs to be at the same level of the hierarchy
* as the source unode.
* @return The next key from the inserted data, >= uub.
*/
private Insert updateRecursive(Insert ik, Object[] unode, Existing uub, LeafOrBranchBuilder builder)
{
return builder == leaf()
? updateRecursive(ik, unode, uub, (LeafBuilder) builder)
: updateRecursive(ik, unode, uub, (BranchBuilder) builder);
}
private Insert updateRecursive(Insert ik, Object[] unode, Existing uub, BranchBuilder builder)
{
int upos = 0;
int usz = shallowSizeOfBranch(unode);
while (ik != null)
{
int find = exponentialSearchWithUpperBound(comparator, unode, upos, usz, uub, ik);
int c = searchResultToComparison(find);
if (find < 0)
find = -1 - find;
if (find > usz)
break; // nothing else needs to be inserted in this branch
if (find > upos)
builder.copyPreceding(unode, usz, upos, find - upos);
final Existing nextUKey = find < usz ? (Existing) unode[find] : uub;
final Object[] childUNode = (Object[]) unode[find + usz];
// process next child
if (c < 0)
{
// ik fall inside it -- recursively merge the child with the update, using next key as an upper bound
LeafOrBranchBuilder childBuilder = builder.child;
ik = updateRecursive(ik, childUNode, nextUKey, childBuilder);
childBuilder.drainAndPropagate(childUNode, builder);
if (find == usz) // this was the right-most child, branch is complete and we can return immediately
return ik;
c = ik != null ? comparator.compare(nextUKey, ik) : -1;
}
else
builder.addChild(childUNode);
// process next key
if (c == 0)
{
// ik matches next key
builder.addKey(updateF.merge(nextUKey, ik));
ik = insert.next();
}
else
builder.addKey(nextUKey);
upos = find + 1;
}
// copy the rest of the branch and exit
if (upos <= usz)
{
builder.copyPreceding(unode, usz, upos, usz - upos);
builder.addChild((Object[]) unode[usz + usz]);
}
return ik;
}
private Insert updateRecursive(Insert ik, Object[] unode, Existing uub, LeafBuilder builder)
{
int upos = 0;
int usz = sizeOfLeaf(unode);
Existing uk = (Existing) unode[upos];
int c = comparator.compare(uk, ik);
while (true)
{
if (c == 0)
{
leaf().addKey(updateF.merge(uk, ik));
if (++upos < usz)
uk = (Existing) unode[upos];
ik = insert.next();
if (ik == null)
{
builder.copy(unode, upos, usz - upos);
return null;
}
if (upos == usz)
break;
c = comparator.compare(uk, ik);
}
else if (c < 0)
{
int ulim = exponentialSearch(comparator, unode, upos + 1, usz, ik);
c = -searchResultToComparison(ulim); // 0 if match, 1 otherwise
if (ulim < 0)
ulim = -(1 + ulim);
builder.copy(unode, upos, ulim - upos);
if ((upos = ulim) == usz)
break;
uk = (Existing) unode[upos];
}
else
{
builder.addKey(isSimple(updateF) ? ik : updateF.insert(ik));
c = insert.copyKeysSmallerThan(uk, comparator, builder, updateF); // 0 on match, -1 otherwise
ik = insert.next();
if (ik == null)
{
builder.copy(unode, upos, usz - upos);
return null;
}
}
}
if (uub == null || comparator.compare(ik, uub) < 0)
{
builder.addKey(isSimple(updateF) ? ik : updateF.insert(ik));
insert.copyKeysSmallerThan(uub, comparator, builder, updateF); // 0 on match, -1 otherwise
ik = insert.next();
}
return ik;
}
public void close()
{
reset();
pool.offer(this);
pool = null;
}
void reset()
{
super.reset();
insert.reset();
}
}
static int searchResultToComparison(int searchResult)
{
return searchResult >> 31;
}
/**
* Attempts to perform a clean transformation of the original tree into a new tree,
* by replicating its original shape as far as possible.
*
* We do this by attempting to flush our buffers whenever we finish a source-branch at the given level;
* if there are too few contents, we wait until we finish another node at the same level.
*
* This way, we are always resetting at the earliest point we might be able to reuse more parts of the original
* tree, maximising potential reuse.
*
* This can permit us to build unbalanced right-most nodes at each level, in which case we simply rebalance
* when done.
*
* The approach taken here hopefully balances simplicity, garbage generation and execution time.
*/
private static abstract class AbstractTransformer extends AbstractUpdater implements AutoCloseable
{
/**
* An iterator over the tree we are updating
*/
final SimpleTreeIterator update = new SimpleTreeIterator();
/**
* A queue of nodes from update that we are ready to "finish" if we have buffered enough data from them
* The stack pointer is maintained inside of {@link #apply()}
*/
Object[][] queuedToFinish = new Object[1][];
AbstractTransformer()
{
allocated = -1;
ensureParent();
parent.inUse = false;
}
abstract O apply(I v);
Object[] apply(Object[] update)
{
int height = this.update.init(update);
if (queuedToFinish.length < height - 1)
queuedToFinish = new Object[height - 1][];
return apply();
}
/**
* We base our operation on the shape of {@code update}, trying to steal as much of the original tree as
* possible for our new tree
*/
private Object[] apply()
{
Object[] unode = update.node();
int upos = update.position(), usz = sizeOfLeaf(unode);
while (true)
{
// we always start the loop on a leaf node, for both input and output
boolean propagatedOriginalLeaf = false;
if (leaf().count == 0)
{
if (upos == 0)
{ // fast path - buffer is empty and input unconsumed, so may be able to propagate original
I in;
O out;
do
{ // optimistic loop - find first point the transformation modified our input
in = (I) unode[upos];
out = apply(in);
} while (in == out && ++upos < usz);
if ((propagatedOriginalLeaf = (upos == usz)))
{
// if input is unmodified by transformation, propagate the input node
markUsed(parent).addChild(unode, usz);
}
else
{
// otherwise copy up to the first modified portion,
// and fall-through to our below condition for transforming the remainder
leaf().copyNoOverflow(unode, 0, upos++);
if (out != null)
leaf().addKeyNoOverflow(out);
}
}
if (!propagatedOriginalLeaf)
transformLeafNoOverflow(unode, upos, usz);
}
else
{
transformLeaf(unode, upos, usz);
}
// we've finished a leaf, and have to hand it to a parent alongside its right-hand key
// so now we try to do two things:
// 1) find the next unfiltered key from our unfinished parent
// 2) determine how many parents are "finished" and whose buffers we should also attempt to propagate
// we do (1) unconditionally, because:
// a) we need to handle the branch keys somewhere, and it may as well happen in one place
// b) we either need more keys for our incomplete leaf; or
// c) we need a key to go after our last propagated node in any unfinished parent
int finishToHeight = 0;
O nextKey;
do
{
update.ascendToParent(); // always have a node above leaf level, else we'd invoke transformLeaf
BranchBuilder level = parent;
unode = update.node();
upos = update.position();
usz = shallowSizeOfBranch(unode);
while (upos == usz)
{
queuedToFinish[level.height - 2] = unode;
finishToHeight = max(finishToHeight, level.height);
if (!update.ascendToParent())
return finishAndDrain(propagatedOriginalLeaf);
level = level.ensureParent();
unode = update.node();
upos = update.position();
usz = shallowSizeOfBranch(unode);
}
nextKey = apply((I) unode[upos]);
if (nextKey == null && leaf().count > MIN_KEYS) // if we don't have a key, try to steal from leaf().buffer
nextKey = (O) leaf().buffer[--leaf().count];
update.descendIntoNextLeaf(unode, upos, usz);
unode = update.node();
upos = update.position();
usz = sizeOfLeaf(unode);
// nextKey might have been filtered, so we may need to look in this next leaf for it
while (nextKey == null && upos < usz)
nextKey = apply((I) unode[upos++]);
// if we still found no key loop and try again on the next parent, leaf, parent... ad infinitum
} while (nextKey == null);
// we always end with unode a leaf, though it may be that upos == usz and that we will do nothing with it
// we've found a non-null key, now decide what to do with it:
// 1) if we have insufficient keys in our leaf, simply append to the leaf and continue;
// 2) otherwise, walk our parent branches finishing those *before* {@code finishTo}
// 2a) if any cannot be finished, append our new key to it and stop finishing further parents; they
// will be finished the next time we ascend to their level with a complete chain of finishable branches
// 2b) otherwise, add our new key to {@code finishTo}
if (!propagatedOriginalLeaf && !finish(leaf(), null))
{
leaf().addKeyNoOverflow(nextKey);
continue;
}
BranchBuilder finish = parent;
while (true)
{
if (finish.height <= finishToHeight)
{
Object[] originalNode = queuedToFinish[finish.height - 2];
if (finish(finish, originalNode))
{
finish = finish.parent;
continue;
}
}
// add our key to the last unpropagated parent branch buffer
finish.addKey(nextKey);
break;
}
}
}
private void transformLeafNoOverflow(Object[] unode, int upos, int usz)
{
while (upos < usz)
{
O v = apply((I) unode[upos++]);
leaf().maybeAddKeyNoOverflow(v);
}
}
private void transformLeaf(Object[] unode, int upos, int usz)
{
while (upos < usz)
{
O v = apply((I) unode[upos++]);
leaf().maybeAddKey(v);
}
}
/**
* Invoked when we are finished transforming a branch. If the buffer contains insufficient elements,
* we refuse to construct a leaf and return null. Otherwise we propagate the branch to its parent's buffer
* and return the branch we have constructed.
*/
private boolean finish(LeafOrBranchBuilder level, Object[] unode)
{
if (!level.isSufficient())
return false;
level.drainAndPropagate(unode, level.ensureParent());
return true;
}
/**
* Invoked once we have consumed all input.
*
* Completes all unfinished buffers. If they do not contain enough keys, data is stolen from the preceding
* node to the left on the same level. This is easy if our parent already contains a completed child; if it
* does not, we recursively apply the stealing procedure to obtain a non-empty parent. If this process manages
* to reach the root and still find no preceding branch, this will result in making this branch the new root.
*/
private Object[] finishAndDrain(boolean skipLeaf)
{
LeafOrBranchBuilder level = leaf();
if (skipLeaf)
{
level = nonEmptyParentMaybeSteal(level);
// handle an edge case, where we have propagated a single complete leaf but have no other contents in any parent
if (level == null)
return (Object[]) leaf().parent.buffer[MAX_KEYS];
}
while (true)
{
BranchBuilder parent = nonEmptyParentMaybeSteal(level);
if (parent != null && !level.isSufficient())
{
Object[] result = stealAndMaybeRepropagate(level, parent);
if (result != null)
return result;
}
else
{
Object[] originalNode = level == leaf() ? null : queuedToFinish[level.height - 2];
Object[] result = level.drainAndPropagate(originalNode, parent);
if (parent == null)
return result;
}
level = parent;
}
}
BranchBuilder nonEmptyParentMaybeSteal(LeafOrBranchBuilder level)
{
if (level.hasOverflow())
return level.ensureParent();
BranchBuilder parent = level.parent;
if (parent == null || !parent.inUse || (parent.isEmpty() && !tryPrependFromParent(parent)))
return null;
return parent;
}
/**
* precondition: {@code fill.parentInUse()} must return {@code fill.parent}
*
* Steal some data from our ancestors, if possible.
* 1) If no ancestor has any data to steal, simply drain and return the current contents.
* 2) If we exhaust all of our ancestors, and are not now ourselves overflowing, drain and return
* 3) Otherwise propagate the redistributed contents to our parent and return null, indicating we can continue to parent
*
* @return {@code null} if {@code parent} is still logicallly in use after we execute;
* otherwise the return value is the final result
*/
private Object[] stealAndMaybeRepropagate(LeafOrBranchBuilder fill, BranchBuilder parent)
{
// parent already stole, we steal one from it
prependFromParent(fill, parent);
// if we've emptied our parent, attempt to restore it from our grandparent,
// this is so that we can determine an accurate exhausted status
boolean exhausted = !fill.hasOverflow() && parent.isEmpty() && !tryPrependFromParent(parent);
if (exhausted)
return fill.drain();
fill.drainAndPropagate(null, parent);
return null;
}
private boolean tryPrependFromParent(BranchBuilder parent)
{
BranchBuilder grandparent = nonEmptyParentMaybeSteal(parent);
if (grandparent == null)
return false;
prependFromParent(parent, grandparent);
return true;
}
// should only be invoked with parent = parentIfStillInUse(fill), if non-null result
private void prependFromParent(LeafOrBranchBuilder fill, BranchBuilder parent)
{
assert !parent.isEmpty();
Object[] predecessor;
Object predecessorNextKey;
// parent will have same number of children as shallow key count (and may be empty)
if (parent.count == 0 && parent.hasOverflow())
{
// use the saved buffer instead of going to our parent
predecessorNextKey = parent.savedNextKey;
predecessor = (Object[]) parent.savedBuffer[2 * MAX_KEYS];
Object[] tmpBuffer = parent.savedBuffer;
int[] tmpSizes = parent.savedSizes;
parent.savedBuffer = parent.buffer;
parent.savedSizes = parent.sizes;
parent.buffer = tmpBuffer;
parent.sizes = tmpSizes;
parent.savedNextKey = null;
parent.count = MAX_KEYS;
// end with MAX_KEYS keys and children in parent, having stolen MAX_KEYS+1 child and savedNextKey
}
else
{
--parent.count;
predecessor = (Object[]) parent.buffer[MAX_KEYS + parent.count];
predecessorNextKey = parent.buffer[parent.count];
}
fill.prepend(predecessor, predecessorNextKey);
}
void reset()
{
Arrays.fill(queuedToFinish, 0, update.leafDepth, null);
update.reset();
super.reset();
}
}
private static class Transformer extends AbstractTransformer
{
static final TinyThreadLocalPool POOL = new TinyThreadLocalPool<>();
TinyThreadLocalPool.TinyPool pool;
Function apply;
O apply(I v)
{
return apply.apply(v);
}
static Transformer get(Function apply)
{
TinyThreadLocalPool.TinyPool pool = POOL.get();
Transformer transformer = pool.poll();
if (transformer == null)
transformer = new Transformer<>();
transformer.pool = pool;
transformer.apply = apply;
return transformer;
}
public void close()
{
apply = null;
reset();
pool.offer(this);
pool = null;
}
}
private static class BiTransformer extends AbstractTransformer
{
static final TinyThreadLocalPool POOL = new TinyThreadLocalPool<>();
BiFunction apply;
I2 i2;
TinyThreadLocalPool.TinyPool pool;
O apply(I i1)
{
return apply.apply(i1, i2);
}
static BiTransformer get(BiFunction apply, I2 i2)
{
TinyThreadLocalPool.TinyPool pool = POOL.get();
BiTransformer transformer = pool.poll();
if (transformer == null)
transformer = new BiTransformer<>();
transformer.pool = pool;
transformer.apply = apply;
transformer.i2 = i2;
return transformer;
}
public void close()
{
apply = null;
i2 = null;
reset();
pool.offer(this);
pool = null;
}
}
/**
* A base class for very simple walks of a tree without recursion, supporting reuse
*/
private static abstract class SimpleTreeStack
{
// stack we have descended, with 0 the root node
Object[][] nodes;
/**
* the child node we are in, if at lower height, or the key we are on otherwise
* can be < 0, indicating we have not yet entered the contents of the node, and are deliberating
* whether we descend or consume the contents without descending
*/
int[] positions;
int depth, leafDepth;
void reset()
{
Arrays.fill(nodes, 0, leafDepth + 1, null);
// positions gets zero'd during descent
}
Object[] node()
{
return nodes[depth];
}
int position()
{
return positions[depth];
}
}
// Similar to SimpleTreeNavigator, but visits values eagerly
// (the exception being ascendToParent(), which permits iterating through finished parents).
// Begins by immediately descending to first leaf; if empty terminates immediately.
private static class SimpleTreeIterator extends SimpleTreeStack
{
int init(Object[] tree)
{
int maxHeight = maxRootHeight(size(tree));
if (positions == null || maxHeight >= positions.length)
{
positions = new int[maxHeight + 1];
nodes = new Object[maxHeight + 1][];
}
nodes[0] = tree;
if (isEmpty(tree))
{
// already done
leafDepth = 0;
depth = -1;
}
else
{
depth = 0;
positions[0] = 0;
while (!isLeaf(tree))
{
tree = (Object[]) tree[shallowSizeOfBranch(tree)];
nodes[++depth] = tree;
positions[depth] = 0;
}
leafDepth = depth;
}
return leafDepth + 1;
}
void descendIntoNextLeaf(Object[] node, int pos, int sz)
{
positions[depth] = ++pos;
++depth;
nodes[depth] = node = (Object[]) node[sz + pos];
positions[depth] = 0;
while (depth < leafDepth)
{
++depth;
nodes[depth] = node = (Object[]) node[shallowSizeOfBranch(node)];
positions[depth] = 0;
}
}
boolean ascendToParent()
{
if (depth < 0)
return false;
return --depth >= 0;
}
}
private static class SimpleTreeKeysIterator
{
int leafSize;
int leafPos;
Object[] leaf;
Object[][] nodes;
int[] positions;
int depth;
void init(Object[] tree)
{
int maxHeight = maxRootHeight(size(tree));
if (positions == null || maxHeight >= positions.length)
{
positions = new int[maxHeight + 1];
nodes = new Object[maxHeight + 1][];
}
depth = 0;
descendToLeaf(tree);
}
void reset()
{
leaf = null;
Arrays.fill(nodes, 0, nodes.length, null);
}
Insert next()
{
if (leafPos < leafSize) // fast path
return (Insert) leaf[leafPos++];
if (depth == 0)
return null;
Object[] node = nodes[depth - 1];
final int position = positions[depth - 1];
Insert result = (Insert) node[position];
advanceBranch(node, position + 1);
return result;
}
private void advanceBranch(Object[] node, int position)
{
int count = shallowSizeOfBranch(node);
if (position < count)
positions[depth - 1] = position;
else
--depth; // no more children in this branch, remove from stack
descendToLeaf((Object[]) node[count + position]);
}
void descendToLeaf(Object[] node)
{
while (!isLeaf(node))
{
nodes[depth] = node;
positions[depth] = 0;
node = (Object[]) node[shallowSizeOfBranch(node)];
++depth;
}
leaf = node;
leafPos = 0;
leafSize = sizeOfLeaf(node);
}
int copyKeysSmallerThan(Compare bound, Comparator comparator, LeafBuilder builder, UpdateFunction transformer)
{
while (true)
{
int lim = exponentialSearchForMaybeInfinity(comparator, leaf, leafPos, leafSize, bound);
int end = lim >= 0 ? lim : -1 - lim;
if (end > leafPos)
{
builder.copy(leaf, leafPos, end - leafPos, transformer);
leafPos = end;
}
if (end < leafSize)
return searchResultToComparison(lim); // 0 if next is a match for bound, -1 otherwise
if (depth == 0)
return -1;
Object[] node = nodes[depth - 1];
final int position = positions[depth - 1];
Insert branchKey = (Insert) node[position];
int cmp = compareWithMaybeInfinity(comparator, branchKey, bound);
if (cmp >= 0)
return -cmp;
builder.addKey(isSimple(transformer) ? branchKey : transformer.insert(branchKey));
advanceBranch(node, position + 1);
}
}
}
}