ceremonyclient/pebble/internal/manifest/btree.go

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2024-01-03 07:31:42 +00:00
// Copyright 2020 The LevelDB-Go and Pebble Authors. All rights reserved. Use
// of this source code is governed by a BSD-style license that can be found in
// the LICENSE file.
package manifest
import (
"bytes"
"fmt"
"strings"
"sync/atomic"
"unsafe"
"github.com/cockroachdb/errors"
"github.com/cockroachdb/pebble/internal/invariants"
stdcmp "github.com/cockroachdb/pebble/shims/cmp"
)
// The Annotator type defined below is used by other packages to lazily
// compute a value over a B-Tree. Each node of the B-Tree stores one
// `annotation` per annotator, containing the result of the computation over
// the node's subtree.
//
// An annotation is marked as valid if it's current with the current subtree
// state. Annotations are marked as invalid whenever a node will be mutated
// (in mut). Annotators may also return `false` from `Accumulate` to signal
// that a computation for a file is not stable and may change in the future.
// Annotations that include these unstable values are also marked as invalid
// on the node, ensuring that future queries for the annotation will recompute
// the value.
// An Annotator defines a computation over a level's FileMetadata. If the
// computation is stable and uses inputs that are fixed for the lifetime of
// a FileMetadata, the LevelMetadata's internal data structures are annotated
// with the intermediary computations. This allows the computation to be
// computed incrementally as edits are applied to a level.
type Annotator interface {
// Zero returns the zero value of an annotation. This value is returned
// when a LevelMetadata is empty. The dst argument, if non-nil, is an
// obsolete value previously returned by this Annotator and may be
// overwritten and reused to avoid a memory allocation.
Zero(dst interface{}) (v interface{})
// Accumulate computes the annotation for a single file in a level's
// metadata. It merges the file's value into dst and returns a bool flag
// indicating whether or not the value is stable and okay to cache as an
// annotation. If the file's value may change over the life of the file,
// the annotator must return false.
//
// Implementations may modify dst and return it to avoid an allocation.
Accumulate(m *FileMetadata, dst interface{}) (v interface{}, cacheOK bool)
// Merge combines two values src and dst, returning the result.
// Implementations may modify dst and return it to avoid an allocation.
Merge(src interface{}, dst interface{}) interface{}
}
type btreeCmp func(*FileMetadata, *FileMetadata) int
func btreeCmpSeqNum(a, b *FileMetadata) int {
return a.cmpSeqNum(b)
}
func btreeCmpSmallestKey(cmp Compare) btreeCmp {
return func(a, b *FileMetadata) int {
return a.cmpSmallestKey(b, cmp)
}
}
// btreeCmpSpecificOrder is used in tests to construct a B-Tree with a
// specific ordering of FileMetadata within the tree. It's typically used to
// test consistency checking code that needs to construct a malformed B-Tree.
func btreeCmpSpecificOrder(files []*FileMetadata) btreeCmp {
m := map[*FileMetadata]int{}
for i, f := range files {
m[f] = i
}
return func(a, b *FileMetadata) int {
ai, aok := m[a]
bi, bok := m[b]
if !aok || !bok {
panic("btreeCmpSliceOrder called with unknown files")
}
return stdcmp.Compare(ai, bi)
}
}
const (
degree = 16
maxItems = 2*degree - 1
minItems = degree - 1
)
type annotation struct {
annotator Annotator
// v is an annotation value, the output of either
// annotator.Value or annotator.Merge.
v interface{}
// valid indicates whether future reads of the annotation may use v as-is.
// If false, v will be zeroed and recalculated.
valid bool
}
type leafNode struct {
ref atomic.Int32
count int16
leaf bool
// subtreeCount holds the count of files in the entire subtree formed by
// this node. For leaf nodes, subtreeCount is always equal to count. For
// non-leaf nodes, it's the sum of count plus all the children's
// subtreeCounts.
//
// NB: We could move this field to the end of the node struct, since leaf =>
// count=subtreeCount, however the unsafe casting [leafToNode] performs make
// it risky and cumbersome.
subtreeCount int
items [maxItems]*FileMetadata
// annot contains one annotation per annotator, merged over the entire
// node's files (and all descendants for non-leaf nodes).
annot []annotation
}
type node struct {
leafNode
children [maxItems + 1]*node
}
//go:nocheckptr casts a ptr to a smaller struct to a ptr to a larger struct.
func leafToNode(ln *leafNode) *node {
return (*node)(unsafe.Pointer(ln))
}
func newLeafNode() *node {
n := leafToNode(new(leafNode))
n.leaf = true
n.ref.Store(1)
return n
}
func newNode() *node {
n := new(node)
n.ref.Store(1)
return n
}
// mut creates and returns a mutable node reference. If the node is not shared
// with any other trees then it can be modified in place. Otherwise, it must be
// cloned to ensure unique ownership. In this way, we enforce a copy-on-write
// policy which transparently incorporates the idea of local mutations, like
// Clojure's transients or Haskell's ST monad, where nodes are only copied
// during the first time that they are modified between Clone operations.
//
// When a node is cloned, the provided pointer will be redirected to the new
// mutable node.
func mut(n **node) *node {
if (*n).ref.Load() == 1 {
// Exclusive ownership. Can mutate in place.
// Whenever a node will be mutated, reset its annotations to be marked
// as uncached. This ensures any future calls to (*node).annotation
// will recompute annotations on the modified subtree.
for i := range (*n).annot {
(*n).annot[i].valid = false
}
return *n
}
// If we do not have unique ownership over the node then we
// clone it to gain unique ownership. After doing so, we can
// release our reference to the old node. We pass recursive
// as true because even though we just observed the node's
// reference count to be greater than 1, we might be racing
// with another call to decRef on this node.
c := (*n).clone()
(*n).decRef(true /* contentsToo */, nil)
*n = c
// NB: We don't need to clear annotations, because (*node).clone does not
// copy them.
return *n
}
// incRef acquires a reference to the node.
func (n *node) incRef() {
n.ref.Add(1)
}
// decRef releases a reference to the node. If requested, the method will unref
// its items and recurse into child nodes and decrease their refcounts as well.
// Some internal codepaths that manually copy the node's items or children to
// new nodes pass contentsToo=false to preserve existing reference counts during
// operations that should yield a net-zero change to descendant refcounts.
// When a node is released, its contained files are dereferenced.
func (n *node) decRef(contentsToo bool, obsolete *[]*FileBacking) {
if n.ref.Add(-1) > 0 {
// Other references remain. Can't free.
return
}
// Dereference the node's metadata and release child references if
// requested. Some internal callers may not want to propagate the deref
// because they're manually copying the filemetadata and children to other
// nodes, and they want to preserve the existing reference count.
if contentsToo {
for _, f := range n.items[:n.count] {
if f.Unref() == 0 {
// There are two sources of node dereferences: tree mutations
// and Version dereferences. Files should only be made obsolete
// during Version dereferences, during which `obsolete` will be
// non-nil.
if obsolete == nil {
panic(fmt.Sprintf("file metadata %s dereferenced to zero during tree mutation", f.FileNum))
}
// Reference counting is performed on the FileBacking. In the case
// of a virtual sstable, this reference counting is performed on
// a FileBacking which is shared by every single virtual sstable
// with the same backing sstable. If the reference count hits 0,
// then we know that the FileBacking won't be required by any
// sstable in Pebble, and that the backing sstable can be deleted.
*obsolete = append(*obsolete, f.FileBacking)
}
}
if !n.leaf {
for i := int16(0); i <= n.count; i++ {
n.children[i].decRef(true /* contentsToo */, obsolete)
}
}
}
}
// clone creates a clone of the receiver with a single reference count.
func (n *node) clone() *node {
var c *node
if n.leaf {
c = newLeafNode()
} else {
c = newNode()
}
// NB: copy field-by-field without touching n.ref to avoid
// triggering the race detector and looking like a data race.
c.count = n.count
c.items = n.items
c.subtreeCount = n.subtreeCount
// Increase the refcount of each contained item.
for _, f := range n.items[:n.count] {
f.Ref()
}
if !c.leaf {
// Copy children and increase each refcount.
c.children = n.children
for i := int16(0); i <= c.count; i++ {
c.children[i].incRef()
}
}
return c
}
// insertAt inserts the provided file and node at the provided index. This
// function is for use only as a helper function for internal B-Tree code.
// Clients should not invoke it directly.
func (n *node) insertAt(index int, item *FileMetadata, nd *node) {
if index < int(n.count) {
copy(n.items[index+1:n.count+1], n.items[index:n.count])
if !n.leaf {
copy(n.children[index+2:n.count+2], n.children[index+1:n.count+1])
}
}
n.items[index] = item
if !n.leaf {
n.children[index+1] = nd
}
n.count++
}
// pushBack inserts the provided file and node at the tail of the node's items.
// This function is for use only as a helper function for internal B-Tree code.
// Clients should not invoke it directly.
func (n *node) pushBack(item *FileMetadata, nd *node) {
n.items[n.count] = item
if !n.leaf {
n.children[n.count+1] = nd
}
n.count++
}
// pushFront inserts the provided file and node at the head of the
// node's items. This function is for use only as a helper function for internal B-Tree
// code. Clients should not invoke it directly.
func (n *node) pushFront(item *FileMetadata, nd *node) {
if !n.leaf {
copy(n.children[1:n.count+2], n.children[:n.count+1])
n.children[0] = nd
}
copy(n.items[1:n.count+1], n.items[:n.count])
n.items[0] = item
n.count++
}
// removeAt removes a value at a given index, pulling all subsequent values
// back. This function is for use only as a helper function for internal B-Tree
// code. Clients should not invoke it directly.
func (n *node) removeAt(index int) (*FileMetadata, *node) {
var child *node
if !n.leaf {
child = n.children[index+1]
copy(n.children[index+1:n.count], n.children[index+2:n.count+1])
n.children[n.count] = nil
}
n.count--
out := n.items[index]
copy(n.items[index:n.count], n.items[index+1:n.count+1])
n.items[n.count] = nil
return out, child
}
// popBack removes and returns the last element in the list. This function is
// for use only as a helper function for internal B-Tree code. Clients should
// not invoke it directly.
func (n *node) popBack() (*FileMetadata, *node) {
n.count--
out := n.items[n.count]
n.items[n.count] = nil
if n.leaf {
return out, nil
}
child := n.children[n.count+1]
n.children[n.count+1] = nil
return out, child
}
// popFront removes and returns the first element in the list. This function is
// for use only as a helper function for internal B-Tree code. Clients should
// not invoke it directly.
func (n *node) popFront() (*FileMetadata, *node) {
n.count--
var child *node
if !n.leaf {
child = n.children[0]
copy(n.children[:n.count+1], n.children[1:n.count+2])
n.children[n.count+1] = nil
}
out := n.items[0]
copy(n.items[:n.count], n.items[1:n.count+1])
n.items[n.count] = nil
return out, child
}
// find returns the index where the given item should be inserted into this
// list. 'found' is true if the item already exists in the list at the given
// index.
//
// This function is for use only as a helper function for internal B-Tree code.
// Clients should not invoke it directly.
func (n *node) find(cmp btreeCmp, item *FileMetadata) (index int, found bool) {
// Logic copied from sort.Search. Inlining this gave
// an 11% speedup on BenchmarkBTreeDeleteInsert.
i, j := 0, int(n.count)
for i < j {
h := int(uint(i+j) >> 1) // avoid overflow when computing h
// i ≤ h < j
v := cmp(item, n.items[h])
if v == 0 {
return h, true
} else if v > 0 {
i = h + 1
} else {
j = h
}
}
return i, false
}
// split splits the given node at the given index. The current node shrinks,
// and this function returns the item that existed at that index and a new
// node containing all items/children after it.
//
// split is called when we want to perform a transformation like the one
// depicted in the following diagram.
//
// Before:
// +-----------+
// n *node | x y z |
// +--/-/-\-\--+
//
// After:
// +-----------+
// | y | n's parent
// +----/-\----+
// / \
// v v
// +-----------+ +-----------+
// n *node | x | | z | next *node
// +-----------+ +-----------+
//
// split does not perform the complete transformation; the caller is responsible
// for updating the parent appropriately. split splits `n` into two nodes, `n`
// and `next`, returning `next` and the file that separates them. In the diagram
// above, `n.split` removes y and z from `n`, returning y in the first return
// value and `next` in the second return value. The caller is responsible for
// updating n's parent to now contain `y` as the separator between nodes `n` and
// `next`.
//
// This function is for use only as a helper function for internal B-Tree code.
// Clients should not invoke it directly.
func (n *node) split(i int) (*FileMetadata, *node) {
out := n.items[i]
var next *node
if n.leaf {
next = newLeafNode()
} else {
next = newNode()
}
next.count = n.count - int16(i+1)
copy(next.items[:], n.items[i+1:n.count])
for j := int16(i); j < n.count; j++ {
n.items[j] = nil
}
if !n.leaf {
copy(next.children[:], n.children[i+1:n.count+1])
descendantsMoved := 0
for j := int16(i + 1); j <= n.count; j++ {
descendantsMoved += n.children[j].subtreeCount
n.children[j] = nil
}
n.subtreeCount -= descendantsMoved
next.subtreeCount += descendantsMoved
}
n.count = int16(i)
// NB: We subtract one more than `next.count` from n's subtreeCount because
// the item at index `i` was removed from `n.items`. We'll return the item
// at index `i`, and the caller is responsible for updating the subtree
// count of whichever node adopts it.
n.subtreeCount -= int(next.count) + 1
next.subtreeCount += int(next.count)
return out, next
}
// Insert inserts a item into the subtree rooted at this node, making sure no
// nodes in the subtree exceed maxItems items.
func (n *node) Insert(cmp btreeCmp, item *FileMetadata) error {
i, found := n.find(cmp, item)
if found {
// cmp provides a total ordering of the files within a level.
// If we're inserting a metadata that's equal to an existing item
// in the tree, we're inserting a file into a level twice.
return errors.Errorf("files %s and %s collided on sort keys",
errors.Safe(item.FileNum), errors.Safe(n.items[i].FileNum))
}
if n.leaf {
n.insertAt(i, item, nil)
n.subtreeCount++
return nil
}
if n.children[i].count >= maxItems {
splitLa, splitNode := mut(&n.children[i]).split(maxItems / 2)
n.insertAt(i, splitLa, splitNode)
switch cmp := cmp(item, n.items[i]); {
case cmp < 0:
// no change, we want first split node
case cmp > 0:
i++ // we want second split node
default:
// cmp provides a total ordering of the files within a level.
// If we're inserting a metadata that's equal to an existing item
// in the tree, we're inserting a file into a level twice.
return errors.Errorf("files %s and %s collided on sort keys",
errors.Safe(item.FileNum), errors.Safe(n.items[i].FileNum))
}
}
err := mut(&n.children[i]).Insert(cmp, item)
if err == nil {
n.subtreeCount++
}
return err
}
// removeMax removes and returns the maximum item from the subtree rooted at
// this node. This function is for use only as a helper function for internal
// B-Tree code. Clients should not invoke it directly.
func (n *node) removeMax() *FileMetadata {
if n.leaf {
n.count--
n.subtreeCount--
out := n.items[n.count]
n.items[n.count] = nil
return out
}
child := mut(&n.children[n.count])
if child.count <= minItems {
n.rebalanceOrMerge(int(n.count))
return n.removeMax()
}
n.subtreeCount--
return child.removeMax()
}
// Remove removes a item from the subtree rooted at this node. Returns
// the item that was removed or nil if no matching item was found.
func (n *node) Remove(cmp btreeCmp, item *FileMetadata) (out *FileMetadata) {
i, found := n.find(cmp, item)
if n.leaf {
if found {
out, _ = n.removeAt(i)
n.subtreeCount--
return out
}
return nil
}
if n.children[i].count <= minItems {
// Child not large enough to remove from.
n.rebalanceOrMerge(i)
return n.Remove(cmp, item)
}
child := mut(&n.children[i])
if found {
// Replace the item being removed with the max item in our left child.
out = n.items[i]
n.items[i] = child.removeMax()
n.subtreeCount--
return out
}
// File is not in this node and child is large enough to remove from.
out = child.Remove(cmp, item)
if out != nil {
n.subtreeCount--
}
return out
}
// rebalanceOrMerge grows child 'i' to ensure it has sufficient room to remove a
// item from it while keeping it at or above minItems. This function is for use
// only as a helper function for internal B-Tree code. Clients should not invoke
// it directly.
func (n *node) rebalanceOrMerge(i int) {
switch {
case i > 0 && n.children[i-1].count > minItems:
// Rebalance from left sibling.
//
// +-----------+
// | y |
// +----/-\----+
// / \
// v v
// +-----------+ +-----------+
// | x | | |
// +----------\+ +-----------+
// \
// v
// a
//
// After:
//
// +-----------+
// | x |
// +----/-\----+
// / \
// v v
// +-----------+ +-----------+
// | | | y |
// +-----------+ +/----------+
// /
// v
// a
//
left := mut(&n.children[i-1])
child := mut(&n.children[i])
xLa, grandChild := left.popBack()
yLa := n.items[i-1]
child.pushFront(yLa, grandChild)
n.items[i-1] = xLa
child.subtreeCount++
left.subtreeCount--
if grandChild != nil {
child.subtreeCount += grandChild.subtreeCount
left.subtreeCount -= grandChild.subtreeCount
}
case i < int(n.count) && n.children[i+1].count > minItems:
// Rebalance from right sibling.
//
// +-----------+
// | y |
// +----/-\----+
// / \
// v v
// +-----------+ +-----------+
// | | | x |
// +-----------+ +/----------+
// /
// v
// a
//
// After:
//
// +-----------+
// | x |
// +----/-\----+
// / \
// v v
// +-----------+ +-----------+
// | y | | |
// +----------\+ +-----------+
// \
// v
// a
//
right := mut(&n.children[i+1])
child := mut(&n.children[i])
xLa, grandChild := right.popFront()
yLa := n.items[i]
child.pushBack(yLa, grandChild)
child.subtreeCount++
right.subtreeCount--
if grandChild != nil {
child.subtreeCount += grandChild.subtreeCount
right.subtreeCount -= grandChild.subtreeCount
}
n.items[i] = xLa
default:
// Merge with either the left or right sibling.
//
// +-----------+
// | u y v |
// +----/-\----+
// / \
// v v
// +-----------+ +-----------+
// | x | | z |
// +-----------+ +-----------+
//
// After:
//
// +-----------+
// | u v |
// +-----|-----+
// |
// v
// +-----------+
// | x y z |
// +-----------+
//
if i >= int(n.count) {
i = int(n.count - 1)
}
child := mut(&n.children[i])
// Make mergeChild mutable, bumping the refcounts on its children if necessary.
_ = mut(&n.children[i+1])
mergeLa, mergeChild := n.removeAt(i)
child.items[child.count] = mergeLa
copy(child.items[child.count+1:], mergeChild.items[:mergeChild.count])
if !child.leaf {
copy(child.children[child.count+1:], mergeChild.children[:mergeChild.count+1])
}
child.count += mergeChild.count + 1
child.subtreeCount += mergeChild.subtreeCount + 1
mergeChild.decRef(false /* contentsToo */, nil)
}
}
// InvalidateAnnotation removes any existing cached annotations for the provided
// annotator from this node's subtree.
func (n *node) InvalidateAnnotation(a Annotator) {
// Find this annotator's annotation on this node.
var annot *annotation
for i := range n.annot {
if n.annot[i].annotator == a {
annot = &n.annot[i]
}
}
if annot != nil && annot.valid {
annot.valid = false
annot.v = a.Zero(annot.v)
}
if !n.leaf {
for i := int16(0); i <= n.count; i++ {
n.children[i].InvalidateAnnotation(a)
}
}
}
// Annotation retrieves, computing if not already computed, the provided
// annotator's annotation of this node. The second return value indicates
// whether the future reads of this annotation may use the first return value
// as-is. If false, the annotation is not stable and may change on a subsequent
// computation.
func (n *node) Annotation(a Annotator) (interface{}, bool) {
// Find this annotator's annotation on this node.
var annot *annotation
for i := range n.annot {
if n.annot[i].annotator == a {
annot = &n.annot[i]
}
}
// If it exists and is marked as valid, we can return it without
// recomputing anything.
if annot != nil && annot.valid {
return annot.v, true
}
if annot == nil {
// This is n's first time being annotated by a.
// Create a new zeroed annotation.
n.annot = append(n.annot, annotation{
annotator: a,
v: a.Zero(nil),
})
annot = &n.annot[len(n.annot)-1]
} else {
// There's an existing annotation that must be recomputed.
// Zero its value.
annot.v = a.Zero(annot.v)
}
annot.valid = true
for i := int16(0); i <= n.count; i++ {
if !n.leaf {
v, ok := n.children[i].Annotation(a)
annot.v = a.Merge(v, annot.v)
annot.valid = annot.valid && ok
}
if i < n.count {
v, ok := a.Accumulate(n.items[i], annot.v)
annot.v = v
annot.valid = annot.valid && ok
}
}
return annot.v, annot.valid
}
func (n *node) verifyInvariants() {
recomputedSubtreeCount := int(n.count)
if !n.leaf {
for i := int16(0); i <= n.count; i++ {
n.children[i].verifyInvariants()
recomputedSubtreeCount += n.children[i].subtreeCount
}
}
if recomputedSubtreeCount != n.subtreeCount {
panic(fmt.Sprintf("recomputed subtree count (%d) ≠ n.subtreeCount (%d)",
recomputedSubtreeCount, n.subtreeCount))
}
}
// btree is an implementation of a B-Tree.
//
// btree stores FileMetadata in an ordered structure, allowing easy insertion,
// removal, and iteration. The B-Tree stores items in order based on cmp. The
// first level of the LSM uses a cmp function that compares sequence numbers.
// All other levels compare using the FileMetadata.Smallest.
//
// Write operations are not safe for concurrent mutation by multiple
// goroutines, but Read operations are.
type btree struct {
root *node
cmp btreeCmp
}
// Release dereferences and clears the root node of the btree, removing all
// items from the btree. In doing so, it decrements contained file counts.
// It returns a slice of newly obsolete backing files, if any.
func (t *btree) Release() (obsolete []*FileBacking) {
if t.root != nil {
t.root.decRef(true /* contentsToo */, &obsolete)
t.root = nil
}
return obsolete
}
// Clone clones the btree, lazily. It does so in constant time.
func (t *btree) Clone() btree {
c := *t
if c.root != nil {
// Incrementing the reference count on the root node is sufficient to
// ensure that no node in the cloned tree can be mutated by an actor
// holding a reference to the original tree and vice versa. This
// property is upheld because the root node in the receiver btree and
// the returned btree will both necessarily have a reference count of at
// least 2 when this method returns. All tree mutations recursively
// acquire mutable node references (see mut) as they traverse down the
// tree. The act of acquiring a mutable node reference performs a clone
// if a node's reference count is greater than one. Cloning a node (see
// clone) increases the reference count on each of its children,
// ensuring that they have a reference count of at least 2. This, in
// turn, ensures that any of the child nodes that are modified will also
// be copied-on-write, recursively ensuring the immutability property
// over the entire tree.
c.root.incRef()
}
return c
}
// Delete removes the provided file from the tree.
// It returns true if the file now has a zero reference count.
func (t *btree) Delete(item *FileMetadata) (obsolete bool) {
if t.root == nil || t.root.count == 0 {
return false
}
if out := mut(&t.root).Remove(t.cmp, item); out != nil {
obsolete = out.Unref() == 0
}
if invariants.Enabled {
t.root.verifyInvariants()
}
if t.root.count == 0 {
old := t.root
if t.root.leaf {
t.root = nil
} else {
t.root = t.root.children[0]
}
old.decRef(false /* contentsToo */, nil)
}
return obsolete
}
// Insert adds the given item to the tree. If a item in the tree already
// equals the given one, Insert panics.
func (t *btree) Insert(item *FileMetadata) error {
if t.root == nil {
t.root = newLeafNode()
} else if t.root.count >= maxItems {
splitLa, splitNode := mut(&t.root).split(maxItems / 2)
newRoot := newNode()
newRoot.count = 1
newRoot.items[0] = splitLa
newRoot.children[0] = t.root
newRoot.children[1] = splitNode
newRoot.subtreeCount = t.root.subtreeCount + splitNode.subtreeCount + 1
t.root = newRoot
}
item.Ref()
err := mut(&t.root).Insert(t.cmp, item)
if invariants.Enabled {
t.root.verifyInvariants()
}
return err
}
// Iter returns a new iterator object. It is not safe to continue using an
// iterator after modifications are made to the tree. If modifications are made,
// create a new iterator.
func (t *btree) Iter() iterator {
return iterator{r: t.root, pos: -1, cmp: t.cmp}
}
// Count returns the number of files contained within the B-Tree.
func (t *btree) Count() int {
if t.root == nil {
return 0
}
return t.root.subtreeCount
}
// String returns a string description of the tree. The format is
// similar to the https://en.wikipedia.org/wiki/Newick_format.
func (t *btree) String() string {
if t.Count() == 0 {
return ";"
}
var b strings.Builder
t.root.writeString(&b)
return b.String()
}
func (n *node) writeString(b *strings.Builder) {
if n.leaf {
for i := int16(0); i < n.count; i++ {
if i != 0 {
b.WriteString(",")
}
b.WriteString(n.items[i].String())
}
return
}
for i := int16(0); i <= n.count; i++ {
b.WriteString("(")
n.children[i].writeString(b)
b.WriteString(")")
if i < n.count {
b.WriteString(n.items[i].String())
}
}
}
// iterStack represents a stack of (node, pos) tuples, which captures
// iteration state as an iterator descends a btree.
type iterStack struct {
// a contains aLen stack frames when an iterator stack is short enough.
// If the iterator stack overflows the capacity of iterStackArr, the stack
// is moved to s and aLen is set to -1.
a iterStackArr
aLen int16 // -1 when using s
s []iterFrame
}
// Used to avoid allocations for stacks below a certain size.
type iterStackArr [3]iterFrame
type iterFrame struct {
n *node
pos int16
}
func (is *iterStack) push(f iterFrame) {
if is.aLen == -1 {
is.s = append(is.s, f)
} else if int(is.aLen) == len(is.a) {
is.s = make([]iterFrame, int(is.aLen)+1, 2*int(is.aLen))
copy(is.s, is.a[:])
is.s[int(is.aLen)] = f
is.aLen = -1
} else {
is.a[is.aLen] = f
is.aLen++
}
}
func (is *iterStack) pop() iterFrame {
if is.aLen == -1 {
f := is.s[len(is.s)-1]
is.s = is.s[:len(is.s)-1]
return f
}
is.aLen--
return is.a[is.aLen]
}
func (is *iterStack) len() int {
if is.aLen == -1 {
return len(is.s)
}
return int(is.aLen)
}
func (is *iterStack) clone() iterStack {
// If the iterator is using the embedded iterStackArr, we only need to
// copy the struct itself.
if is.s == nil {
return *is
}
clone := *is
clone.s = make([]iterFrame, len(is.s))
copy(clone.s, is.s)
return clone
}
func (is *iterStack) nth(n int) (f iterFrame, ok bool) {
if is.aLen == -1 {
if n >= len(is.s) {
return f, false
}
return is.s[n], true
}
if int16(n) >= is.aLen {
return f, false
}
return is.a[n], true
}
func (is *iterStack) reset() {
if is.aLen == -1 {
is.s = is.s[:0]
} else {
is.aLen = 0
}
}
// iterator is responsible for search and traversal within a btree.
type iterator struct {
// the root node of the B-Tree.
r *node
// n and pos make up the current position of the iterator.
// If valid, n.items[pos] is the current value of the iterator.
//
// n may be nil iff i.r is nil.
n *node
pos int16
// cmp dictates the ordering of the FileMetadata.
cmp func(*FileMetadata, *FileMetadata) int
// a stack of n's ancestors within the B-Tree, alongside the position
// taken to arrive at n. If non-empty, the bottommost frame of the stack
// will always contain the B-Tree root.
s iterStack
}
// countLeft returns the count of files that are to the left of the current
// iterator position.
func (i *iterator) countLeft() int {
if i.r == nil {
return 0
}
// Each iterator has a stack of frames marking the path from the root node
// to the current iterator position. All files (n.items) and all subtrees
// (n.children) with indexes less than [pos] are to the left of the current
// iterator position.
//
// +------------------------+ -
// | Root pos:5 | |
// +------------------------+ | stack
// | Root/5 pos:3 | | frames
// +------------------------+ | [i.s]
// | Root/5/3 pos:9 | |
// +========================+ -
// | |
// | i.n: Root/5/3/9 i.pos:2|
// +------------------------+
//
var count int
// Walk all the ancestors in the iterator stack [i.s], tallying up all the
// files and subtrees to the left of the stack frame's position.
f, ok := i.s.nth(0)
for fi := 0; ok; fi++ {
// There are [f.pos] files contained within [f.n.items] that sort to the
// left of the subtree the iterator has descended.
count += int(f.pos)
// Any subtrees that fall before the stack frame's position are entirely
// to the left of the iterator's current position.
for j := int16(0); j < f.pos; j++ {
count += f.n.children[j].subtreeCount
}
f, ok = i.s.nth(fi + 1)
}
// The bottommost stack frame is inlined within the iterator struct. Again,
// [i.pos] files fall to the left of the current iterator position.
count += int(i.pos)
if !i.n.leaf {
// NB: Unlike above, we use a `<= i.pos` comparison. The iterator is
// positioned at item `i.n.items[i.pos]`, which sorts after everything
// in the subtree at `i.n.children[i.pos]`.
for j := int16(0); j <= i.pos; j++ {
count += i.n.children[j].subtreeCount
}
}
return count
}
func (i *iterator) clone() iterator {
c := *i
c.s = i.s.clone()
return c
}
func (i *iterator) reset() {
i.n = i.r
i.pos = -1
i.s.reset()
}
func (i iterator) String() string {
var buf bytes.Buffer
for n := 0; ; n++ {
f, ok := i.s.nth(n)
if !ok {
break
}
fmt.Fprintf(&buf, "%p: %02d/%02d\n", f.n, f.pos, f.n.count)
}
if i.r == nil {
fmt.Fprintf(&buf, "<nil>: %02d", i.pos)
} else {
fmt.Fprintf(&buf, "%p: %02d/%02d", i.n, i.pos, i.n.count)
}
return buf.String()
}
func cmpIter(a, b iterator) int {
if a.r != b.r {
panic("compared iterators from different btrees")
}
// Each iterator has a stack of frames marking the path from the root node
// to the current iterator position. We walk both paths formed by the
// iterators' stacks simultaneously, descending from the shared root node,
// always comparing nodes at the same level in the tree.
//
// If the iterators' paths ever diverge and point to different nodes, the
// iterators are not equal and we use the node positions to evaluate the
// comparison.
//
// If an iterator's stack ends, we stop descending and use its current
// node and position for the final comparison. One iterator's stack may
// end before another's if one iterator is positioned deeper in the tree.
//
// a b
// +------------------------+ +--------------------------+ -
// | Root pos:5 | = | Root pos:5 | |
// +------------------------+ +--------------------------+ | stack
// | Root/5 pos:3 | = | Root/5 pos:3 | | frames
// +------------------------+ +--------------------------+ |
// | Root/5/3 pos:9 | > | Root/5/3 pos:1 | |
// +========================+ +==========================+ -
// | | | |
// | a.n: Root/5/3/9 a.pos:2| | b.n: Root/5/3/1, b.pos:5 |
// +------------------------+ +--------------------------+
// Initialize with the iterator's current node and position. These are
// conceptually the most-recent/current frame of the iterator stack.
an, apos := a.n, a.pos
bn, bpos := b.n, b.pos
// aok, bok are set while traversing the iterator's path down the B-Tree.
// They're declared in the outer scope because they help distinguish the
// sentinel case when both iterators' first frame points to the last child
// of the root. If an iterator has no other frames in its stack, it's the
// end sentinel state which sorts after everything else.
var aok, bok bool
for i := 0; ; i++ {
var af, bf iterFrame
af, aok = a.s.nth(i)
bf, bok = b.s.nth(i)
if !aok || !bok {
if aok {
// Iterator a, unlike iterator b, still has a frame. Set an,
// apos so we compare using the frame from the stack.
an, apos = af.n, af.pos
}
if bok {
// Iterator b, unlike iterator a, still has a frame. Set bn,
// bpos so we compare using the frame from the stack.
bn, bpos = bf.n, bf.pos
}
break
}
// aok && bok
if af.n != bf.n {
panic("nonmatching nodes during btree iterator comparison")
}
if v := stdcmp.Compare(af.pos, bf.pos); v != 0 {
return v
}
// Otherwise continue up both iterators' stacks (equivalently, down the
// B-Tree away from the root).
}
if aok && bok {
panic("expected one or more stacks to have been exhausted")
}
if an != bn {
panic("nonmatching nodes during btree iterator comparison")
}
if v := stdcmp.Compare(apos, bpos); v != 0 {
return v
}
switch {
case aok:
// a is positioned at a leaf child at this position and b is at an
// end sentinel state.
return -1
case bok:
// b is positioned at a leaf child at this position and a is at an
// end sentinel state.
return +1
default:
return 0
}
}
func (i *iterator) descend(n *node, pos int16) {
i.s.push(iterFrame{n: n, pos: pos})
i.n = n.children[pos]
i.pos = 0
}
// ascend ascends up to the current node's parent and resets the position
// to the one previously set for this parent node.
func (i *iterator) ascend() {
f := i.s.pop()
i.n = f.n
i.pos = f.pos
}
// seek repositions the iterator over the first file for which fn returns
// true, mirroring the semantics of the standard library's sort.Search
// function. Like sort.Search, seek requires the iterator's B-Tree to be
// ordered such that fn returns false for some (possibly empty) prefix of the
// tree's files, and then true for the (possibly empty) remainder.
func (i *iterator) seek(fn func(*FileMetadata) bool) {
i.reset()
if i.r == nil {
return
}
for {
// Logic copied from sort.Search.
j, k := 0, int(i.n.count)
for j < k {
h := int(uint(j+k) >> 1) // avoid overflow when computing h
// j ≤ h < k
if !fn(i.n.items[h]) {
j = h + 1 // preserves f(j-1) == false
} else {
k = h // preserves f(k) == true
}
}
i.pos = int16(j)
if i.n.leaf {
if i.pos == i.n.count {
i.next()
}
return
}
i.descend(i.n, i.pos)
}
}
// first seeks to the first item in the btree.
func (i *iterator) first() {
i.reset()
if i.r == nil {
return
}
for !i.n.leaf {
i.descend(i.n, 0)
}
i.pos = 0
}
// last seeks to the last item in the btree.
func (i *iterator) last() {
i.reset()
if i.r == nil {
return
}
for !i.n.leaf {
i.descend(i.n, i.n.count)
}
i.pos = i.n.count - 1
}
// next positions the iterator to the item immediately following
// its current position.
func (i *iterator) next() {
if i.r == nil {
return
}
if i.n.leaf {
if i.pos < i.n.count {
i.pos++
}
if i.pos < i.n.count {
return
}
for i.s.len() > 0 && i.pos >= i.n.count {
i.ascend()
}
return
}
i.descend(i.n, i.pos+1)
for !i.n.leaf {
i.descend(i.n, 0)
}
i.pos = 0
}
// prev positions the iterator to the item immediately preceding
// its current position.
func (i *iterator) prev() {
if i.r == nil {
return
}
if i.n.leaf {
i.pos--
if i.pos >= 0 {
return
}
for i.s.len() > 0 && i.pos < 0 {
i.ascend()
i.pos--
}
return
}
i.descend(i.n, i.pos)
for !i.n.leaf {
i.descend(i.n, i.n.count)
}
i.pos = i.n.count - 1
}
// valid returns whether the iterator is positioned at a valid position.
func (i *iterator) valid() bool {
return i.r != nil && i.pos >= 0 && i.pos < i.n.count
}
// cur returns the item at the iterator's current position. It is illegal
// to call cur if the iterator is not valid.
func (i *iterator) cur() *FileMetadata {
if invariants.Enabled && !i.valid() {
panic("btree iterator.cur invoked on invalid iterator")
}
return i.n.items[i.pos]
}