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Diffstat (limited to 'pkg/segment/set.go')
| -rw-r--r-- | pkg/segment/set.go | 1359 |
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diff --git a/pkg/segment/set.go b/pkg/segment/set.go new file mode 100644 index 000000000..6eed1d930 --- /dev/null +++ b/pkg/segment/set.go @@ -0,0 +1,1359 @@ +// Copyright 2018 Google Inc. +// +// Licensed 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 segment provides tools for working with collections of segments. A +// segment is a key-value mapping, where the key is a non-empty contiguous +// range of values of type Key, and the value is a single value of type Value. +// +// Clients using this package must use the go_template_instance rule in +// tools/go_generics/defs.bzl to create an instantiation of this +// template package, providing types to use in place of Key, Range, Value, and +// Functions. See pkg/segment/test/BUILD for a usage example. +package segment + +import ( + "bytes" + "fmt" +) + +// Key is a required type parameter that must be an integral type. +type Key uint64 + +// Range is a required type parameter equivalent to Range<Key>. +type Range interface{} + +// Value is a required type parameter. +type Value interface{} + +// Functions is a required type parameter that must be a struct implementing +// the methods defined by Functions. +type Functions interface { + // MinKey returns the minimum allowed key. + MinKey() Key + + // MaxKey returns the maximum allowed key + 1. + MaxKey() Key + + // ClearValue deinitializes the given value. (For example, if Value is a + // pointer or interface type, ClearValue should set it to nil.) + ClearValue(*Value) + + // Merge attempts to merge the values corresponding to two consecutive + // segments. If successful, Merge returns (merged value, true). Otherwise, + // it returns (unspecified, false). + // + // Preconditions: r1.End == r2.Start. + // + // Postconditions: If merging succeeds, val1 and val2 are invalidated. + Merge(r1 Range, val1 Value, r2 Range, val2 Value) (Value, bool) + + // Split splits a segment's value at a key within its range, such that the + // first returned value corresponds to the range [r.Start, split) and the + // second returned value corresponds to the range [split, r.End). + // + // Preconditions: r.Start < split < r.End. + // + // Postconditions: The original value val is invalidated. + Split(r Range, val Value, split Key) (Value, Value) +} + +const ( + // minDegree is the minimum degree of an internal node in a Set B-tree. + // + // - Any non-root node has at least minDegree-1 segments. + // + // - Any non-root internal (non-leaf) node has at least minDegree children. + // + // - The root node may have fewer than minDegree-1 segments, but it may + // only have 0 segments if the tree is empty. + // + // Our implementation requires minDegree >= 3. Higher values of minDegree + // usually improve performance, but increase memory usage for small sets. + minDegree = 3 + + maxDegree = 2 * minDegree +) + +// A Set is a mapping of segments with non-overlapping Range keys. The zero +// value for a Set is an empty set. Set values are not safely movable nor +// copyable. Set is thread-compatible. +type Set struct { + root node `state:".(*SegmentDataSlices)"` +} + +// IsEmpty returns true if the set contains no segments. +func (s *Set) IsEmpty() bool { + return s.root.nrSegments == 0 +} + +// IsEmptyRange returns true iff no segments in the set overlap the given +// range. This is semantically equivalent to s.SpanRange(r) == 0, but may be +// more efficient. +func (s *Set) IsEmptyRange(r Range) bool { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return true + } + _, gap := s.Find(r.Start) + if !gap.Ok() { + return false + } + return r.End <= gap.End() +} + +// Span returns the total size of all segments in the set. +func (s *Set) Span() Key { + var sz Key + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sz += seg.Range().Length() + } + return sz +} + +// SpanRange returns the total size of the intersection of segments in the set +// with the given range. +func (s *Set) SpanRange(r Range) Key { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return 0 + } + var sz Key + for seg := s.LowerBoundSegment(r.Start); seg.Ok() && seg.Start() < r.End; seg = seg.NextSegment() { + sz += seg.Range().Intersect(r).Length() + } + return sz +} + +// FirstSegment returns the first segment in the set. If the set is empty, +// FirstSegment returns a terminal iterator. +func (s *Set) FirstSegment() Iterator { + if s.root.nrSegments == 0 { + return Iterator{} + } + return s.root.firstSegment() +} + +// LastSegment returns the last segment in the set. If the set is empty, +// LastSegment returns a terminal iterator. +func (s *Set) LastSegment() Iterator { + if s.root.nrSegments == 0 { + return Iterator{} + } + return s.root.lastSegment() +} + +// FirstGap returns the first gap in the set. +func (s *Set) FirstGap() GapIterator { + n := &s.root + for n.hasChildren { + n = n.children[0] + } + return GapIterator{n, 0} +} + +// LastGap returns the last gap in the set. +func (s *Set) LastGap() GapIterator { + n := &s.root + for n.hasChildren { + n = n.children[n.nrSegments] + } + return GapIterator{n, n.nrSegments} +} + +// Find returns the segment or gap whose range contains the given key. If a +// segment is found, the returned Iterator is non-terminal and the +// returned GapIterator is terminal. Otherwise, the returned Iterator is +// terminal and the returned GapIterator is non-terminal. +func (s *Set) Find(key Key) (Iterator, GapIterator) { + n := &s.root + for { + // Binary search invariant: the correct value of i lies within [lower, + // upper]. + lower := 0 + upper := n.nrSegments + for lower < upper { + i := lower + (upper-lower)/2 + if r := n.keys[i]; key < r.End { + if key >= r.Start { + return Iterator{n, i}, GapIterator{} + } + upper = i + } else { + lower = i + 1 + } + } + i := lower + if !n.hasChildren { + return Iterator{}, GapIterator{n, i} + } + n = n.children[i] + } +} + +// FindSegment returns the segment whose range contains the given key. If no +// such segment exists, FindSegment returns a terminal iterator. +func (s *Set) FindSegment(key Key) Iterator { + seg, _ := s.Find(key) + return seg +} + +// LowerBoundSegment returns the segment with the lowest range that contains a +// key greater than or equal to min. If no such segment exists, +// LowerBoundSegment returns a terminal iterator. +func (s *Set) LowerBoundSegment(min Key) Iterator { + seg, gap := s.Find(min) + if seg.Ok() { + return seg + } + return gap.NextSegment() +} + +// UpperBoundSegment returns the segment with the highest range that contains a +// key less than or equal to max. If no such segment exists, UpperBoundSegment +// returns a terminal iterator. +func (s *Set) UpperBoundSegment(max Key) Iterator { + seg, gap := s.Find(max) + if seg.Ok() { + return seg + } + return gap.PrevSegment() +} + +// FindGap returns the gap containing the given key. If no such gap exists +// (i.e. the set contains a segment containing that key), FindGap returns a +// terminal iterator. +func (s *Set) FindGap(key Key) GapIterator { + _, gap := s.Find(key) + return gap +} + +// LowerBoundGap returns the gap with the lowest range that is greater than or +// equal to min. +func (s *Set) LowerBoundGap(min Key) GapIterator { + seg, gap := s.Find(min) + if gap.Ok() { + return gap + } + return seg.NextGap() +} + +// UpperBoundGap returns the gap with the highest range that is less than or +// equal to max. +func (s *Set) UpperBoundGap(max Key) GapIterator { + seg, gap := s.Find(max) + if gap.Ok() { + return gap + } + return seg.PrevGap() +} + +// Add inserts the given segment into the set and returns true. If the new +// segment can be merged with adjacent segments, Add will do so. If the new +// segment would overlap an existing segment, Add returns false. If Add +// succeeds, all existing iterators are invalidated. +func (s *Set) Add(r Range, val Value) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.Insert(gap, r, val) + return true +} + +// AddWithoutMerging inserts the given segment into the set and returns true. +// If it would overlap an existing segment, AddWithoutMerging does nothing and +// returns false. If AddWithoutMerging succeeds, all existing iterators are +// invalidated. +func (s *Set) AddWithoutMerging(r Range, val Value) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.InsertWithoutMergingUnchecked(gap, r, val) + return true +} + +// Insert inserts the given segment into the given gap. If the new segment can +// be merged with adjacent segments, Insert will do so. Insert returns an +// iterator to the segment containing the inserted value (which may have been +// merged with other values). All existing iterators (including gap, but not +// including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, Insert panics. +// +// Insert is semantically equivalent to a InsertWithoutMerging followed by a +// Merge, but may be more efficient. Note that there is no unchecked variant of +// Insert since Insert must retrieve and inspect gap's predecessor and +// successor segments regardless. +func (s *Set) Insert(gap GapIterator, r Range, val Value) Iterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + prev, next := gap.PrevSegment(), gap.NextSegment() + if prev.Ok() && prev.End() > r.Start { + panic(fmt.Sprintf("new segment %v overlaps predecessor %v", r, prev.Range())) + } + if next.Ok() && next.Start() < r.End { + panic(fmt.Sprintf("new segment %v overlaps successor %v", r, next.Range())) + } + if prev.Ok() && prev.End() == r.Start { + if mval, ok := (Functions{}).Merge(prev.Range(), prev.Value(), r, val); ok { + prev.SetEndUnchecked(r.End) + prev.SetValue(mval) + if next.Ok() && next.Start() == r.End { + val = mval + if mval, ok := (Functions{}).Merge(prev.Range(), val, next.Range(), next.Value()); ok { + prev.SetEndUnchecked(next.End()) + prev.SetValue(mval) + return s.Remove(next).PrevSegment() + } + } + return prev + } + } + if next.Ok() && next.Start() == r.End { + if mval, ok := (Functions{}).Merge(r, val, next.Range(), next.Value()); ok { + next.SetStartUnchecked(r.Start) + next.SetValue(mval) + return next + } + } + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMerging inserts the given segment into the given gap and +// returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, +// InsertWithoutMerging panics. +func (s *Set) InsertWithoutMerging(gap GapIterator, r Range, val Value) Iterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if gr := gap.Range(); !gr.IsSupersetOf(r) { + panic(fmt.Sprintf("cannot insert segment range %v into gap range %v", r, gr)) + } + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMergingUnchecked inserts the given segment into the given gap +// and returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// Preconditions: r.Start >= gap.Start(); r.End <= gap.End(). +func (s *Set) InsertWithoutMergingUnchecked(gap GapIterator, r Range, val Value) Iterator { + gap = gap.node.rebalanceBeforeInsert(gap) + copy(gap.node.keys[gap.index+1:], gap.node.keys[gap.index:gap.node.nrSegments]) + copy(gap.node.values[gap.index+1:], gap.node.values[gap.index:gap.node.nrSegments]) + gap.node.keys[gap.index] = r + gap.node.values[gap.index] = val + gap.node.nrSegments++ + return Iterator{gap.node, gap.index} +} + +// Remove removes the given segment and returns an iterator to the vacated gap. +// All existing iterators (including seg, but not including the returned +// iterator) are invalidated. +func (s *Set) Remove(seg Iterator) GapIterator { + // We only want to remove directly from a leaf node. + if seg.node.hasChildren { + // Since seg.node has children, the removed segment must have a + // predecessor (at the end of the rightmost leaf of its left child + // subtree). Move the contents of that predecessor into the removed + // segment's position, and remove that predecessor instead. (We choose + // to steal the predecessor rather than the successor because removing + // from the end of a leaf node doesn't involve any copying unless + // merging is required.) + victim := seg.PrevSegment() + // This must be unchecked since until victim is removed, seg and victim + // overlap. + seg.SetRangeUnchecked(victim.Range()) + seg.SetValue(victim.Value()) + return s.Remove(victim).NextGap() + } + copy(seg.node.keys[seg.index:], seg.node.keys[seg.index+1:seg.node.nrSegments]) + copy(seg.node.values[seg.index:], seg.node.values[seg.index+1:seg.node.nrSegments]) + Functions{}.ClearValue(&seg.node.values[seg.node.nrSegments-1]) + seg.node.nrSegments-- + return seg.node.rebalanceAfterRemove(GapIterator{seg.node, seg.index}) +} + +// RemoveAll removes all segments from the set. All existing iterators are +// invalidated. +func (s *Set) RemoveAll() { + s.root = node{} +} + +// RemoveRange removes all segments in the given range. An iterator to the +// newly formed gap is returned, and all existing iterators are invalidated. +func (s *Set) RemoveRange(r Range) GapIterator { + seg, gap := s.Find(r.Start) + if seg.Ok() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + for seg = gap.NextSegment(); seg.Ok() && seg.Start() < r.End; seg = gap.NextSegment() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + return gap +} + +// Merge attempts to merge two neighboring segments. If successful, Merge +// returns an iterator to the merged segment, and all existing iterators are +// invalidated. Otherwise, Merge returns a terminal iterator. +// +// If first is not the predecessor of second, Merge panics. +func (s *Set) Merge(first, second Iterator) Iterator { + if first.NextSegment() != second { + panic(fmt.Sprintf("attempt to merge non-neighboring segments %v, %v", first.Range(), second.Range())) + } + return s.MergeUnchecked(first, second) +} + +// MergeUnchecked attempts to merge two neighboring segments. If successful, +// MergeUnchecked returns an iterator to the merged segment, and all existing +// iterators are invalidated. Otherwise, MergeUnchecked returns a terminal +// iterator. +// +// Precondition: first is the predecessor of second: first.NextSegment() == +// second, first == second.PrevSegment(). +func (s *Set) MergeUnchecked(first, second Iterator) Iterator { + if first.End() == second.Start() { + if mval, ok := (Functions{}).Merge(first.Range(), first.Value(), second.Range(), second.Value()); ok { + // N.B. This must be unchecked because until s.Remove(second), first + // overlaps second. + first.SetEndUnchecked(second.End()) + first.SetValue(mval) + return s.Remove(second).PrevSegment() + } + } + return Iterator{} +} + +// MergeAll attempts to merge all adjacent segments in the set. All existing +// iterators are invalidated. +func (s *Set) MergeAll() { + seg := s.FirstSegment() + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeRange attempts to merge all adjacent segments that contain a key in the +// specific range. All existing iterators are invalidated. +func (s *Set) MergeRange(r Range) { + seg := s.LowerBoundSegment(r.Start) + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() && next.Range().Start < r.End { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeAdjacent attempts to merge the segment containing r.Start with its +// predecessor, and the segment containing r.End-1 with its successor. +func (s *Set) MergeAdjacent(r Range) { + first := s.FindSegment(r.Start) + if first.Ok() { + if prev := first.PrevSegment(); prev.Ok() { + s.Merge(prev, first) + } + } + last := s.FindSegment(r.End - 1) + if last.Ok() { + if next := last.NextSegment(); next.Ok() { + s.Merge(last, next) + } + } +} + +// Split splits the given segment at the given key and returns iterators to the +// two resulting segments. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +// +// If the segment cannot be split at split (because split is at the start or +// end of the segment's range, so splitting would produce a segment with zero +// length, or because split falls outside the segment's range altogether), +// Split panics. +func (s *Set) Split(seg Iterator, split Key) (Iterator, Iterator) { + if !seg.Range().CanSplitAt(split) { + panic(fmt.Sprintf("can't split %v at %v", seg.Range(), split)) + } + return s.SplitUnchecked(seg, split) +} + +// SplitUnchecked splits the given segment at the given key and returns +// iterators to the two resulting segments. All existing iterators (including +// seg, but not including the returned iterators) are invalidated. +// +// Preconditions: seg.Start() < key < seg.End(). +func (s *Set) SplitUnchecked(seg Iterator, split Key) (Iterator, Iterator) { + val1, val2 := (Functions{}).Split(seg.Range(), seg.Value(), split) + end2 := seg.End() + seg.SetEndUnchecked(split) + seg.SetValue(val1) + seg2 := s.InsertWithoutMergingUnchecked(seg.NextGap(), Range{split, end2}, val2) + // seg may now be invalid due to the Insert. + return seg2.PrevSegment(), seg2 +} + +// SplitAt splits the segment straddling split, if one exists. SplitAt returns +// true if a segment was split and false otherwise. If SplitAt splits a +// segment, all existing iterators are invalidated. +func (s *Set) SplitAt(split Key) bool { + if seg := s.FindSegment(split); seg.Ok() && seg.Range().CanSplitAt(split) { + s.SplitUnchecked(seg, split) + return true + } + return false +} + +// Isolate ensures that the given segment's range does not escape r by +// splitting at r.Start and r.End if necessary, and returns an updated iterator +// to the bounded segment. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +func (s *Set) Isolate(seg Iterator, r Range) Iterator { + if seg.Range().CanSplitAt(r.Start) { + _, seg = s.SplitUnchecked(seg, r.Start) + } + if seg.Range().CanSplitAt(r.End) { + seg, _ = s.SplitUnchecked(seg, r.End) + } + return seg +} + +// ApplyContiguous applies a function to a contiguous range of segments, +// splitting if necessary. The function is applied until the first gap is +// encountered, at which point the gap is returned. If the function is applied +// across the entire range, a terminal gap is returned. All existing iterators +// are invalidated. +// +// N.B. The Iterator must not be invalidated by the function. +func (s *Set) ApplyContiguous(r Range, fn func(seg Iterator)) GapIterator { + seg, gap := s.Find(r.Start) + if !seg.Ok() { + return gap + } + for { + seg = s.Isolate(seg, r) + fn(seg) + if seg.End() >= r.End { + return GapIterator{} + } + gap = seg.NextGap() + if !gap.IsEmpty() { + return gap + } + seg = gap.NextSegment() + if !seg.Ok() { + // This implies that the last segment extended all the + // way to the maximum value, since the gap was empty. + return GapIterator{} + } + } +} + +type node struct { + // An internal binary tree node looks like: + // + // K + // / \ + // Cl Cr + // + // where all keys in the subtree rooted by Cl (the left subtree) are less + // than K (the key of the parent node), and all keys in the subtree rooted + // by Cr (the right subtree) are greater than K. + // + // An internal B-tree node's indexes work out to look like: + // + // K0 K1 K2 ... Kn-1 + // / \/ \/ \ ... / \ + // C0 C1 C2 C3 ... Cn-1 Cn + // + // where n is nrSegments. + nrSegments int + + // parent is a pointer to this node's parent. If this node is root, parent + // is nil. + parent *node + + // parentIndex is the index of this node in parent.children. + parentIndex int + + // Flag for internal nodes that is technically redundant with "children[0] + // != nil", but is stored in the first cache line. "hasChildren" rather + // than "isLeaf" because false must be the correct value for an empty root. + hasChildren bool + + // Nodes store keys and values in separate arrays to maximize locality in + // the common case (scanning keys for lookup). + keys [maxDegree - 1]Range + values [maxDegree - 1]Value + children [maxDegree]*node +} + +// firstSegment returns the first segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *node) firstSegment() Iterator { + for n.hasChildren { + n = n.children[0] + } + return Iterator{n, 0} +} + +// lastSegment returns the last segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *node) lastSegment() Iterator { + for n.hasChildren { + n = n.children[n.nrSegments] + } + return Iterator{n, n.nrSegments - 1} +} + +func (n *node) prevSibling() *node { + if n.parent == nil || n.parentIndex == 0 { + return nil + } + return n.parent.children[n.parentIndex-1] +} + +func (n *node) nextSibling() *node { + if n.parent == nil || n.parentIndex == n.parent.nrSegments { + return nil + } + return n.parent.children[n.parentIndex+1] +} + +// rebalanceBeforeInsert splits n and its ancestors if they are full, as +// required for insertion, and returns an updated iterator to the position +// represented by gap. +func (n *node) rebalanceBeforeInsert(gap GapIterator) GapIterator { + if n.parent != nil { + gap = n.parent.rebalanceBeforeInsert(gap) + } + if n.nrSegments < maxDegree-1 { + return gap + } + if n.parent == nil { + // n is root. Move all segments before and after n's median segment + // into new child nodes adjacent to the median segment, which is now + // the only segment in root. + left := &node{ + nrSegments: minDegree - 1, + parent: n, + parentIndex: 0, + hasChildren: n.hasChildren, + } + right := &node{ + nrSegments: minDegree - 1, + parent: n, + parentIndex: 1, + hasChildren: n.hasChildren, + } + copy(left.keys[:minDegree-1], n.keys[:minDegree-1]) + copy(left.values[:minDegree-1], n.values[:minDegree-1]) + copy(right.keys[:minDegree-1], n.keys[minDegree:]) + copy(right.values[:minDegree-1], n.values[minDegree:]) + n.keys[0], n.values[0] = n.keys[minDegree-1], n.values[minDegree-1] + zeroValueSlice(n.values[1:]) + if n.hasChildren { + copy(left.children[:minDegree], n.children[:minDegree]) + copy(right.children[:minDegree], n.children[minDegree:]) + zeroNodeSlice(n.children[2:]) + for i := 0; i < minDegree; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + right.children[i].parent = right + right.children[i].parentIndex = i + } + } + n.nrSegments = 1 + n.hasChildren = true + n.children[0] = left + n.children[1] = right + if gap.node != n { + return gap + } + if gap.index < minDegree { + return GapIterator{left, gap.index} + } + return GapIterator{right, gap.index - minDegree} + } + // n is non-root. Move n's median segment into its parent node (which can't + // be full because we've already invoked n.parent.rebalanceBeforeInsert) + // and move all segments after n's median into a new sibling node (the + // median segment's right child subtree). + copy(n.parent.keys[n.parentIndex+1:], n.parent.keys[n.parentIndex:n.parent.nrSegments]) + copy(n.parent.values[n.parentIndex+1:], n.parent.values[n.parentIndex:n.parent.nrSegments]) + n.parent.keys[n.parentIndex], n.parent.values[n.parentIndex] = n.keys[minDegree-1], n.values[minDegree-1] + copy(n.parent.children[n.parentIndex+2:], n.parent.children[n.parentIndex+1:n.parent.nrSegments+1]) + for i := n.parentIndex + 2; i < n.parent.nrSegments+2; i++ { + n.parent.children[i].parentIndex = i + } + sibling := &node{ + nrSegments: minDegree - 1, + parent: n.parent, + parentIndex: n.parentIndex + 1, + hasChildren: n.hasChildren, + } + n.parent.children[n.parentIndex+1] = sibling + n.parent.nrSegments++ + copy(sibling.keys[:minDegree-1], n.keys[minDegree:]) + copy(sibling.values[:minDegree-1], n.values[minDegree:]) + zeroValueSlice(n.values[minDegree-1:]) + if n.hasChildren { + copy(sibling.children[:minDegree], n.children[minDegree:]) + zeroNodeSlice(n.children[minDegree:]) + for i := 0; i < minDegree; i++ { + sibling.children[i].parent = sibling + sibling.children[i].parentIndex = i + } + } + n.nrSegments = minDegree - 1 + // gap.node can't be n.parent because gaps are always in leaf nodes. + if gap.node != n { + return gap + } + if gap.index < minDegree { + return gap + } + return GapIterator{sibling, gap.index - minDegree} +} + +// rebalanceAfterRemove "unsplits" n and its ancestors if they are deficient +// (contain fewer segments than required by B-tree invariants), as required for +// removal, and returns an updated iterator to the position represented by gap. +// +// Precondition: n is the only node in the tree that may currently violate a +// B-tree invariant. +func (n *node) rebalanceAfterRemove(gap GapIterator) GapIterator { + for { + if n.nrSegments >= minDegree-1 { + return gap + } + if n.parent == nil { + // Root is allowed to be deficient. + return gap + } + // There's one other thing we can do before resorting to unsplitting. + // If either sibling node has at least minDegree segments, rotate that + // sibling's closest segment through the segment in the parent that + // separates us. That is, given: + // + // ... D ... + // / \ + // ... B C] [E ... + // + // where the node containing E is deficient, end up with: + // + // ... C ... + // / \ + // ... B] [D E ... + // + // As in Set.Remove, prefer rotating from the end of the sibling to the + // left: by precondition, n.node has fewer segments (to memcpy) than + // the sibling does. + if sibling := n.prevSibling(); sibling != nil && sibling.nrSegments >= minDegree { + copy(n.keys[1:], n.keys[:n.nrSegments]) + copy(n.values[1:], n.values[:n.nrSegments]) + n.keys[0] = n.parent.keys[n.parentIndex-1] + n.values[0] = n.parent.values[n.parentIndex-1] + n.parent.keys[n.parentIndex-1] = sibling.keys[sibling.nrSegments-1] + n.parent.values[n.parentIndex-1] = sibling.values[sibling.nrSegments-1] + Functions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + copy(n.children[1:], n.children[:n.nrSegments+1]) + n.children[0] = sibling.children[sibling.nrSegments] + sibling.children[sibling.nrSegments] = nil + n.children[0].parent = n + n.children[0].parentIndex = 0 + for i := 1; i < n.nrSegments+2; i++ { + n.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + if gap.node == sibling && gap.index == sibling.nrSegments { + return GapIterator{n, 0} + } + if gap.node == n { + return GapIterator{n, gap.index + 1} + } + return gap + } + if sibling := n.nextSibling(); sibling != nil && sibling.nrSegments >= minDegree { + n.keys[n.nrSegments] = n.parent.keys[n.parentIndex] + n.values[n.nrSegments] = n.parent.values[n.parentIndex] + n.parent.keys[n.parentIndex] = sibling.keys[0] + n.parent.values[n.parentIndex] = sibling.values[0] + copy(sibling.keys[:sibling.nrSegments-1], sibling.keys[1:]) + copy(sibling.values[:sibling.nrSegments-1], sibling.values[1:]) + Functions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + n.children[n.nrSegments+1] = sibling.children[0] + copy(sibling.children[:sibling.nrSegments], sibling.children[1:]) + sibling.children[sibling.nrSegments] = nil + n.children[n.nrSegments+1].parent = n + n.children[n.nrSegments+1].parentIndex = n.nrSegments + 1 + for i := 0; i < sibling.nrSegments; i++ { + sibling.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + if gap.node == sibling { + if gap.index == 0 { + return GapIterator{n, n.nrSegments} + } + return GapIterator{sibling, gap.index - 1} + } + return gap + } + // Otherwise, we must unsplit. + p := n.parent + if p.nrSegments == 1 { + // Merge all segments in both n and its sibling back into n.parent. + // This is the reverse of the root splitting case in + // node.rebalanceBeforeInsert. (Because we require minDegree >= 3, + // only root can have 1 segment in this path, so this reduces the + // height of the tree by 1, without violating the constraint that + // all leaf nodes remain at the same depth.) + left, right := p.children[0], p.children[1] + p.nrSegments = left.nrSegments + right.nrSegments + 1 + p.hasChildren = left.hasChildren + p.keys[left.nrSegments] = p.keys[0] + p.values[left.nrSegments] = p.values[0] + copy(p.keys[:left.nrSegments], left.keys[:left.nrSegments]) + copy(p.values[:left.nrSegments], left.values[:left.nrSegments]) + copy(p.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(p.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(p.children[:left.nrSegments+1], left.children[:left.nrSegments+1]) + copy(p.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := 0; i < p.nrSegments+1; i++ { + p.children[i].parent = p + p.children[i].parentIndex = i + } + } else { + p.children[0] = nil + p.children[1] = nil + } + if gap.node == left { + return GapIterator{p, gap.index} + } + if gap.node == right { + return GapIterator{p, gap.index + left.nrSegments + 1} + } + return gap + } + // Merge n and either sibling, along with the segment separating the + // two, into whichever of the two nodes comes first. This is the + // reverse of the non-root splitting case in + // node.rebalanceBeforeInsert. + var left, right *node + if n.parentIndex > 0 { + left = n.prevSibling() + right = n + } else { + left = n + right = n.nextSibling() + } + // Fix up gap first since we need the old left.nrSegments, which + // merging will change. + if gap.node == right { + gap = GapIterator{left, gap.index + left.nrSegments + 1} + } + left.keys[left.nrSegments] = p.keys[left.parentIndex] + left.values[left.nrSegments] = p.values[left.parentIndex] + copy(left.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(left.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(left.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := left.nrSegments + 1; i < left.nrSegments+right.nrSegments+2; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + } + } + left.nrSegments += right.nrSegments + 1 + copy(p.keys[left.parentIndex:], p.keys[left.parentIndex+1:p.nrSegments]) + copy(p.values[left.parentIndex:], p.values[left.parentIndex+1:p.nrSegments]) + Functions{}.ClearValue(&p.values[p.nrSegments-1]) + copy(p.children[left.parentIndex+1:], p.children[left.parentIndex+2:p.nrSegments+1]) + for i := 0; i < p.nrSegments; i++ { + p.children[i].parentIndex = i + } + p.children[p.nrSegments] = nil + p.nrSegments-- + // This process robs p of one segment, so recurse into rebalancing p. + n = p + } +} + +// A Iterator is conceptually one of: +// +// - A pointer to a segment in a set; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Iterators are copyable values and are meaningfully equality-comparable. The +// zero value of Iterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type Iterator struct { + // node is the node containing the iterated segment. If the iterator is + // terminal, node is nil. + node *node + + // index is the index of the segment in node.keys/values. + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (seg Iterator) Ok() bool { + return seg.node != nil +} + +// Range returns the iterated segment's range key. +func (seg Iterator) Range() Range { + return seg.node.keys[seg.index] +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (seg Iterator) Start() Key { + return seg.node.keys[seg.index].Start +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (seg Iterator) End() Key { + return seg.node.keys[seg.index].End +} + +// SetRangeUnchecked mutates the iterated segment's range key. This operation +// does not invalidate any iterators. +// +// Preconditions: +// +// - r.Length() > 0. +// +// - The new range must not overlap an existing one: If seg.NextSegment().Ok(), +// then r.end <= seg.NextSegment().Start(); if seg.PrevSegment().Ok(), then +// r.start >= seg.PrevSegment().End(). +func (seg Iterator) SetRangeUnchecked(r Range) { + seg.node.keys[seg.index] = r +} + +// SetRange mutates the iterated segment's range key. If the new range would +// cause the iterated segment to overlap another segment, or if the new range +// is invalid, SetRange panics. This operation does not invalidate any +// iterators. +func (seg Iterator) SetRange(r Range) { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if prev := seg.PrevSegment(); prev.Ok() && r.Start < prev.End() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, prev.Range())) + } + if next := seg.NextSegment(); next.Ok() && r.End > next.Start() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, next.Range())) + } + seg.SetRangeUnchecked(r) +} + +// SetStartUnchecked mutates the iterated segment's start. This operation does +// not invalidate any iterators. +// +// Preconditions: The new start must be valid: start < seg.End(); if +// seg.PrevSegment().Ok(), then start >= seg.PrevSegment().End(). +func (seg Iterator) SetStartUnchecked(start Key) { + seg.node.keys[seg.index].Start = start +} + +// SetStart mutates the iterated segment's start. If the new start value would +// cause the iterated segment to overlap another segment, or would result in an +// invalid range, SetStart panics. This operation does not invalidate any +// iterators. +func (seg Iterator) SetStart(start Key) { + if start >= seg.End() { + panic(fmt.Sprintf("new start %v would invalidate segment range %v", start, seg.Range())) + } + if prev := seg.PrevSegment(); prev.Ok() && start < prev.End() { + panic(fmt.Sprintf("new start %v would cause segment range %v to overlap segment range %v", start, seg.Range(), prev.Range())) + } + seg.SetStartUnchecked(start) +} + +// SetEndUnchecked mutates the iterated segment's end. This operation does not +// invalidate any iterators. +// +// Preconditions: The new end must be valid: end > seg.Start(); if +// seg.NextSegment().Ok(), then end <= seg.NextSegment().Start(). +func (seg Iterator) SetEndUnchecked(end Key) { + seg.node.keys[seg.index].End = end +} + +// SetEnd mutates the iterated segment's end. If the new end value would cause +// the iterated segment to overlap another segment, or would result in an +// invalid range, SetEnd panics. This operation does not invalidate any +// iterators. +func (seg Iterator) SetEnd(end Key) { + if end <= seg.Start() { + panic(fmt.Sprintf("new end %v would invalidate segment range %v", end, seg.Range())) + } + if next := seg.NextSegment(); next.Ok() && end > next.Start() { + panic(fmt.Sprintf("new end %v would cause segment range %v to overlap segment range %v", end, seg.Range(), next.Range())) + } + seg.SetEndUnchecked(end) +} + +// Value returns a copy of the iterated segment's value. +func (seg Iterator) Value() Value { + return seg.node.values[seg.index] +} + +// ValuePtr returns a pointer to the iterated segment's value. The pointer is +// invalidated if the iterator is invalidated. This operation does not +// invalidate any iterators. +func (seg Iterator) ValuePtr() *Value { + return &seg.node.values[seg.index] +} + +// SetValue mutates the iterated segment's value. This operation does not +// invalidate any iterators. +func (seg Iterator) SetValue(val Value) { + seg.node.values[seg.index] = val +} + +// PrevSegment returns the iterated segment's predecessor. If there is no +// preceding segment, PrevSegment returns a terminal iterator. +func (seg Iterator) PrevSegment() Iterator { + if seg.node.hasChildren { + return seg.node.children[seg.index].lastSegment() + } + if seg.index > 0 { + return Iterator{seg.node, seg.index - 1} + } + if seg.node.parent == nil { + return Iterator{} + } + return segmentBeforePosition(seg.node.parent, seg.node.parentIndex) +} + +// NextSegment returns the iterated segment's successor. If there is no +// succeeding segment, NextSegment returns a terminal iterator. +func (seg Iterator) NextSegment() Iterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment() + } + if seg.index < seg.node.nrSegments-1 { + return Iterator{seg.node, seg.index + 1} + } + if seg.node.parent == nil { + return Iterator{} + } + return segmentAfterPosition(seg.node.parent, seg.node.parentIndex) +} + +// PrevGap returns the gap immediately before the iterated segment. +func (seg Iterator) PrevGap() GapIterator { + if seg.node.hasChildren { + // Note that this isn't recursive because the last segment in a subtree + // must be in a leaf node. + return seg.node.children[seg.index].lastSegment().NextGap() + } + return GapIterator{seg.node, seg.index} +} + +// NextGap returns the gap immediately after the iterated segment. +func (seg Iterator) NextGap() GapIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment().PrevGap() + } + return GapIterator{seg.node, seg.index + 1} +} + +// PrevNonEmpty returns the iterated segment's predecessor if it is adjacent, +// or the gap before the iterated segment otherwise. If seg.Start() == +// Functions.MinKey(), PrevNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by PrevNonEmpty will be +// non-terminal. +func (seg Iterator) PrevNonEmpty() (Iterator, GapIterator) { + gap := seg.PrevGap() + if gap.Range().Length() != 0 { + return Iterator{}, gap + } + return gap.PrevSegment(), GapIterator{} +} + +// NextNonEmpty returns the iterated segment's successor if it is adjacent, or +// the gap after the iterated segment otherwise. If seg.End() == +// Functions.MaxKey(), NextNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by NextNonEmpty will be +// non-terminal. +func (seg Iterator) NextNonEmpty() (Iterator, GapIterator) { + gap := seg.NextGap() + if gap.Range().Length() != 0 { + return Iterator{}, gap + } + return gap.NextSegment(), GapIterator{} +} + +// A GapIterator is conceptually one of: +// +// - A pointer to a position between two segments, before the first segment, or +// after the last segment in a set, called a *gap*; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Note that the gap between two adjacent segments exists (iterators to it are +// non-terminal), but has a length of zero. GapIterator.IsEmpty returns true +// for such gaps. An empty set contains a single gap, spanning the entire range +// of the set's keys. +// +// GapIterators are copyable values and are meaningfully equality-comparable. +// The zero value of GapIterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type GapIterator struct { + // The representation of a GapIterator is identical to that of an Iterator, + // except that index corresponds to positions between segments in the same + // way as for node.children (see comment for node.nrSegments). + node *node + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (gap GapIterator) Ok() bool { + return gap.node != nil +} + +// Range returns the range spanned by the iterated gap. +func (gap GapIterator) Range() Range { + return Range{gap.Start(), gap.End()} +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (gap GapIterator) Start() Key { + if ps := gap.PrevSegment(); ps.Ok() { + return ps.End() + } + return Functions{}.MinKey() +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (gap GapIterator) End() Key { + if ns := gap.NextSegment(); ns.Ok() { + return ns.Start() + } + return Functions{}.MaxKey() +} + +// IsEmpty returns true if the iterated gap is empty (that is, the "gap" is +// between two adjacent segments.) +func (gap GapIterator) IsEmpty() bool { + return gap.Range().Length() == 0 +} + +// PrevSegment returns the segment immediately before the iterated gap. If no +// such segment exists, PrevSegment returns a terminal iterator. +func (gap GapIterator) PrevSegment() Iterator { + return segmentBeforePosition(gap.node, gap.index) +} + +// NextSegment returns the segment immediately after the iterated gap. If no +// such segment exists, NextSegment returns a terminal iterator. +func (gap GapIterator) NextSegment() Iterator { + return segmentAfterPosition(gap.node, gap.index) +} + +// PrevGap returns the iterated gap's predecessor. If no such gap exists, +// PrevGap returns a terminal iterator. +func (gap GapIterator) PrevGap() GapIterator { + seg := gap.PrevSegment() + if !seg.Ok() { + return GapIterator{} + } + return seg.PrevGap() +} + +// NextGap returns the iterated gap's successor. If no such gap exists, NextGap +// returns a terminal iterator. +func (gap GapIterator) NextGap() GapIterator { + seg := gap.NextSegment() + if !seg.Ok() { + return GapIterator{} + } + return seg.NextGap() +} + +// segmentBeforePosition returns the predecessor segment of the position given +// by n.children[i], which may or may not contain a child. If no such segment +// exists, segmentBeforePosition returns a terminal iterator. +func segmentBeforePosition(n *node, i int) Iterator { + for i == 0 { + if n.parent == nil { + return Iterator{} + } + n, i = n.parent, n.parentIndex + } + return Iterator{n, i - 1} +} + +// segmentAfterPosition returns the successor segment of the position given by +// n.children[i], which may or may not contain a child. If no such segment +// exists, segmentAfterPosition returns a terminal iterator. +func segmentAfterPosition(n *node, i int) Iterator { + for i == n.nrSegments { + if n.parent == nil { + return Iterator{} + } + n, i = n.parent, n.parentIndex + } + return Iterator{n, i} +} + +func zeroValueSlice(slice []Value) { + // TODO: check if Go is actually smart enough to optimize a + // ClearValue that assigns nil to a memset here + for i := range slice { + Functions{}.ClearValue(&slice[i]) + } +} + +func zeroNodeSlice(slice []*node) { + for i := range slice { + slice[i] = nil + } +} + +// String stringifies a Set for debugging. +func (s *Set) String() string { + return s.root.String() +} + +// String stringifes a node (and all of its children) for debugging. +func (n *node) String() string { + var buf bytes.Buffer + n.writeDebugString(&buf, "") + return buf.String() +} + +func (n *node) writeDebugString(buf *bytes.Buffer, prefix string) { + if n.hasChildren != (n.nrSegments > 0 && n.children[0] != nil) { + buf.WriteString(prefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent value of hasChildren: got %v, want %v\n", n.hasChildren, !n.hasChildren)) + } + for i := 0; i < n.nrSegments; i++ { + if child := n.children[i]; child != nil { + cprefix := fmt.Sprintf("%s- % 3d ", prefix, i) + if child.parent != n || child.parentIndex != i { + buf.WriteString(cprefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent linkage to parent: got (%p, %d), want (%p, %d)\n", child.parent, child.parentIndex, n, i)) + } + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, i)) + } + buf.WriteString(prefix) + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + if child := n.children[n.nrSegments]; child != nil { + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, n.nrSegments)) + } +} + +// SegmentDataSlices represents segments from a set as slices of start, end, and +// values. SegmentDataSlices is primarily used as an intermediate representation +// for save/restore and the layout here is optimized for that. +type SegmentDataSlices struct { + Start []Key + End []Key + Values []Value +} + +// ExportSortedSlice returns a copy of all segments in the given set, in ascending +// key order. +func (s *Set) ExportSortedSlices() *SegmentDataSlices { + var sds SegmentDataSlices + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sds.Start = append(sds.Start, seg.Start()) + sds.End = append(sds.End, seg.End()) + sds.Values = append(sds.Values, seg.Value()) + } + sds.Start = sds.Start[:len(sds.Start):len(sds.Start)] + sds.End = sds.End[:len(sds.End):len(sds.End)] + sds.Values = sds.Values[:len(sds.Values):len(sds.Values)] + return &sds +} + +// ImportSortedSlice initializes the given set from the given slice. +// +// Preconditions: s must be empty. sds must represent a valid set (the segments +// in sds must have valid lengths that do not overlap). The segments in sds +// must be sorted in ascending key order. +func (s *Set) ImportSortedSlices(sds *SegmentDataSlices) error { + if !s.IsEmpty() { + return fmt.Errorf("cannot import into non-empty set %v", s) + } + gap := s.FirstGap() + for i := range sds.Start { + r := Range{sds.Start[i], sds.End[i]} + if !gap.Range().IsSupersetOf(r) { + return fmt.Errorf("segment overlaps a preceding segment or is incorrectly sorted: [%d, %d) => %v", sds.Start[i], sds.End[i], sds.Values[i]) + } + gap = s.InsertWithoutMerging(gap, r, sds.Values[i]).NextGap() + } + return nil +} |