| // Copyright 2021 The Go 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 trie |
| |
| // Collision functions combine a left and right hand side (lhs and rhs) values |
| // the two values are associated with the same key and produces the value that |
| // will be stored for the key. |
| // |
| // Collision functions must be idempotent: |
| // collision(x, x) == x for all x. |
| // Collisions functions may be applied whenever a value is inserted |
| // or two maps are merged, or intersected. |
| type Collision func(lhs interface{}, rhs interface{}) interface{} |
| |
| // TakeLhs always returns the left value in a collision. |
| func TakeLhs(lhs, rhs interface{}) interface{} { return lhs } |
| |
| // TakeRhs always returns the right hand side in a collision. |
| func TakeRhs(lhs, rhs interface{}) interface{} { return rhs } |
| |
| // Builder creates new Map. Each Builder has a unique Scope. |
| // |
| // IMPORTANT: Nodes are hash-consed internally to reduce memory consumption. To |
| // support hash-consing Builders keep an internal Map of all of the Maps that they |
| // have created. To GC any of the Maps created by the Builder, all references to |
| // the Builder must be dropped. This includes MutMaps. |
| type Builder struct { |
| scope Scope |
| |
| // hash-consing maps for each node type. |
| empty *empty |
| leaves map[leaf]*leaf |
| branches map[branch]*branch |
| // It may be possible to support more types of patricia tries |
| // (e.g. non-hash-consed) by making Builder an interface and abstracting |
| // the mkLeaf and mkBranch functions. |
| } |
| |
| // NewBuilder creates a new Builder with a unique Scope. |
| func NewBuilder() *Builder { |
| s := newScope() |
| return &Builder{ |
| scope: s, |
| empty: &empty{s}, |
| leaves: make(map[leaf]*leaf), |
| branches: make(map[branch]*branch), |
| } |
| } |
| |
| func (b *Builder) Scope() Scope { return b.scope } |
| |
| // Rescope changes the builder's scope to a new unique Scope. |
| // |
| // Any Maps created using the previous scope need to be Cloned |
| // before any operation. |
| // |
| // This makes the old internals of the Builder eligible to be GC'ed. |
| func (b *Builder) Rescope() { |
| s := newScope() |
| b.scope = s |
| b.empty = &empty{s} |
| b.leaves = make(map[leaf]*leaf) |
| b.branches = make(map[branch]*branch) |
| } |
| |
| // Empty is the empty map. |
| func (b *Builder) Empty() Map { return Map{b.Scope(), b.empty} } |
| |
| // InsertWith inserts a new association from k to v into the Map m to create a new map |
| // in the current scope and handle collisions using the collision function c. |
| // |
| // This is roughly corresponds to updating a map[uint64]interface{} by: |
| // if _, ok := m[k]; ok { m[k] = c(m[k], v} else { m[k] = v} |
| // |
| // An insertion or update happened whenever Insert(m, ...) != m . |
| func (b *Builder) InsertWith(c Collision, m Map, k uint64, v interface{}) Map { |
| m = b.Clone(m) |
| return Map{b.Scope(), b.insert(c, m.n, b.mkLeaf(key(k), v), false)} |
| } |
| |
| // Inserts a new association from key to value into the Map m to create |
| // a new map in the current scope. |
| // |
| // If there was a previous value mapped by key, keep the previously mapped value. |
| // This is roughly corresponds to updating a map[uint64]interface{} by: |
| // if _, ok := m[k]; ok { m[k] = val } |
| // |
| // This is equivalent to b.Merge(m, b.Create({k: v})). |
| func (b *Builder) Insert(m Map, k uint64, v interface{}) Map { |
| return b.InsertWith(TakeLhs, m, k, v) |
| } |
| |
| // Updates a (key, value) in the map. This is roughly corresponds to |
| // updating a map[uint64]interface{} by: |
| // m[key] = val |
| func (b *Builder) Update(m Map, key uint64, val interface{}) Map { |
| return b.InsertWith(TakeRhs, m, key, val) |
| } |
| |
| // Merge two maps lhs and rhs to create a new map in the current scope. |
| // |
| // Whenever there is a key in both maps (a collision), the resulting value mapped by |
| // the key will be `c(lhs[key], rhs[key])`. |
| func (b *Builder) MergeWith(c Collision, lhs, rhs Map) Map { |
| lhs, rhs = b.Clone(lhs), b.Clone(rhs) |
| return Map{b.Scope(), b.merge(c, lhs.n, rhs.n)} |
| } |
| |
| // Merge two maps lhs and rhs to create a new map in the current scope. |
| // |
| // Whenever there is a key in both maps (a collision), the resulting value mapped by |
| // the key will be the value in lhs `b.Collision(lhs[key], rhs[key])`. |
| func (b *Builder) Merge(lhs, rhs Map) Map { |
| return b.MergeWith(TakeLhs, lhs, rhs) |
| } |
| |
| // Clone returns a Map that contains the same (key, value) elements |
| // within b.Scope(), i.e. return m if m.Scope() == b.Scope() or return |
| // a deep copy of m within b.Scope() otherwise. |
| func (b *Builder) Clone(m Map) Map { |
| if m.Scope() == b.Scope() { |
| return m |
| } else if m.n == nil { |
| return Map{b.Scope(), b.empty} |
| } |
| return Map{b.Scope(), b.clone(m.n)} |
| } |
| func (b *Builder) clone(n node) node { |
| switch n := n.(type) { |
| case *empty: |
| return b.empty |
| case *leaf: |
| return b.mkLeaf(n.k, n.v) |
| case *branch: |
| return b.mkBranch(n.prefix, n.branching, b.clone(n.left), b.clone(n.right)) |
| default: |
| panic("unreachable") |
| } |
| } |
| |
| // Remove a key from a Map m and return the resulting Map. |
| func (b *Builder) Remove(m Map, k uint64) Map { |
| m = b.Clone(m) |
| return Map{b.Scope(), b.remove(m.n, key(k))} |
| } |
| |
| // Intersect Maps lhs and rhs and returns a map with all of the keys in |
| // both lhs and rhs and the value comes from lhs, i.e. |
| // {(k, lhs[k]) | k in lhs, k in rhs}. |
| func (b *Builder) Intersect(lhs, rhs Map) Map { |
| return b.IntersectWith(TakeLhs, lhs, rhs) |
| } |
| |
| // IntersectWith take lhs and rhs and returns the intersection |
| // with the value coming from the collision function, i.e. |
| // {(k, c(lhs[k], rhs[k]) ) | k in lhs, k in rhs}. |
| // The elements of the resulting map are always { <k, c(lhs[k], rhs[k]) > } |
| // for each key k that a key in both lhs and rhs. |
| func (b *Builder) IntersectWith(c Collision, lhs, rhs Map) Map { |
| l, r := b.Clone(lhs), b.Clone(rhs) |
| return Map{b.Scope(), b.intersect(c, l.n, r.n)} |
| } |
| |
| // MutMap is a convenient wrapper for a Map and a *Builder that will be used to create |
| // new Maps from it. |
| type MutMap struct { |
| B *Builder |
| M Map |
| } |
| |
| // MutEmpty is an empty MutMap for a builder. |
| func (b *Builder) MutEmpty() MutMap { |
| return MutMap{b, b.Empty()} |
| } |
| |
| // Insert an element into the map using the collision function for the builder. |
| // Returns true if the element was inserted. |
| func (mm *MutMap) Insert(k uint64, v interface{}) bool { |
| old := mm.M |
| mm.M = mm.B.Insert(old, k, v) |
| return old != mm.M |
| } |
| |
| // Updates an element in the map. Returns true if the map was updated. |
| func (mm *MutMap) Update(k uint64, v interface{}) bool { |
| old := mm.M |
| mm.M = mm.B.Update(old, k, v) |
| return old != mm.M |
| } |
| |
| // Removes a key from the map. Returns true if the element was removed. |
| func (mm *MutMap) Remove(k uint64) bool { |
| old := mm.M |
| mm.M = mm.B.Remove(old, k) |
| return old != mm.M |
| } |
| |
| // Merge another map into the current one using the collision function |
| // for the builder. Returns true if the map changed. |
| func (mm *MutMap) Merge(other Map) bool { |
| old := mm.M |
| mm.M = mm.B.Merge(old, other) |
| return old != mm.M |
| } |
| |
| // Intersect another map into the current one using the collision function |
| // for the builder. Returns true if the map changed. |
| func (mm *MutMap) Intersect(other Map) bool { |
| old := mm.M |
| mm.M = mm.B.Intersect(old, other) |
| return old != mm.M |
| } |
| |
| func (b *Builder) Create(m map[uint64]interface{}) Map { |
| var leaves []*leaf |
| for k, v := range m { |
| leaves = append(leaves, b.mkLeaf(key(k), v)) |
| } |
| return Map{b.Scope(), b.create(leaves)} |
| } |
| |
| // Merge another map into the current one using the collision function |
| // for the builder. Returns true if the map changed. |
| func (mm *MutMap) MergeWith(c Collision, other Map) bool { |
| old := mm.M |
| mm.M = mm.B.MergeWith(c, old, other) |
| return old != mm.M |
| } |
| |
| // creates a map for a collection of leaf nodes. |
| func (b *Builder) create(leaves []*leaf) node { |
| n := len(leaves) |
| if n == 0 { |
| return b.empty |
| } else if n == 1 { |
| return leaves[0] |
| } |
| // Note: we can do a more sophisicated algorithm by: |
| // - sorting the leaves ahead of time, |
| // - taking the prefix and branching bit of the min and max key, |
| // - binary searching for the branching bit, |
| // - splitting exactly where the branch will be, and |
| // - making the branch node for this prefix + branching bit. |
| // Skipping until this is a performance bottleneck. |
| |
| m := n / 2 // (n >= 2) ==> 1 <= m < n |
| l, r := leaves[:m], leaves[m:] |
| return b.merge(nil, b.create(l), b.create(r)) |
| } |
| |
| // mkLeaf returns the hash-consed representative of (k, v) in the current scope. |
| func (b *Builder) mkLeaf(k key, v interface{}) *leaf { |
| l := &leaf{k: k, v: v} |
| if rep, ok := b.leaves[*l]; ok { |
| return rep |
| } |
| b.leaves[*l] = l |
| return l |
| } |
| |
| // mkBranch returns the hash-consed representative of the tuple |
| // (prefix, branch, left, right) |
| // in the current scope. |
| func (b *Builder) mkBranch(p prefix, bp bitpos, left node, right node) *branch { |
| br := &branch{ |
| sz: left.size() + right.size(), |
| prefix: p, |
| branching: bp, |
| left: left, |
| right: right, |
| } |
| if rep, ok := b.branches[*br]; ok { |
| return rep |
| } |
| b.branches[*br] = br |
| return br |
| } |
| |
| // join two maps with prefixes p0 and p1 that are *known* to disagree. |
| func (b *Builder) join(p0 prefix, t0 node, p1 prefix, t1 node) *branch { |
| m := branchingBit(p0, p1) |
| var left, right node |
| if zeroBit(p0, m) { |
| left, right = t0, t1 |
| } else { |
| left, right = t1, t0 |
| } |
| prefix := mask(p0, m) |
| return b.mkBranch(prefix, m, left, right) |
| } |
| |
| // collide two leaves with the same key to create a leaf |
| // with the collided value. |
| func (b *Builder) collide(c Collision, left, right *leaf) *leaf { |
| if left == right { |
| return left // c is idempotent: c(x, x) == x |
| } |
| val := left.v // keep the left value by default if c is nil |
| if c != nil { |
| val = c(left.v, right.v) |
| } |
| switch val { |
| case left.v: |
| return left |
| case right.v: |
| return right |
| default: |
| return b.mkLeaf(left.k, val) |
| } |
| } |
| |
| // inserts a leaf l into a map m and returns the resulting map. |
| // When lhs is true, l is the left hand side in a collision. |
| // Both l and m are in the current scope. |
| func (b *Builder) insert(c Collision, m node, l *leaf, lhs bool) node { |
| switch m := m.(type) { |
| case *empty: |
| return l |
| case *leaf: |
| if m.k == l.k { |
| left, right := l, m |
| if !lhs { |
| left, right = right, left |
| } |
| return b.collide(c, left, right) |
| } |
| return b.join(prefix(l.k), l, prefix(m.k), m) |
| case *branch: |
| // fallthrough |
| } |
| // m is a branch |
| br := m.(*branch) |
| if !matchPrefix(prefix(l.k), br.prefix, br.branching) { |
| return b.join(prefix(l.k), l, br.prefix, br) |
| } |
| var left, right node |
| if zeroBit(prefix(l.k), br.branching) { |
| left, right = b.insert(c, br.left, l, lhs), br.right |
| } else { |
| left, right = br.left, b.insert(c, br.right, l, lhs) |
| } |
| if left == br.left && right == br.right { |
| return m |
| } |
| return b.mkBranch(br.prefix, br.branching, left, right) |
| } |
| |
| // merge two maps in the current scope. |
| func (b *Builder) merge(c Collision, lhs, rhs node) node { |
| if lhs == rhs { |
| return lhs |
| } |
| switch lhs := lhs.(type) { |
| case *empty: |
| return rhs |
| case *leaf: |
| return b.insert(c, rhs, lhs, true) |
| case *branch: |
| switch rhs := rhs.(type) { |
| case *empty: |
| return lhs |
| case *leaf: |
| return b.insert(c, lhs, rhs, false) |
| case *branch: |
| // fallthrough |
| } |
| } |
| |
| // Last remaining case is branch branch merging. |
| // For brevity, we adopt the Okasaki and Gill naming conventions |
| // for branching and prefixes. |
| s, t := lhs.(*branch), rhs.(*branch) |
| p, m := s.prefix, s.branching |
| q, n := t.prefix, t.branching |
| |
| if m == n && p == q { // prefixes are identical. |
| left, right := b.merge(c, s.left, t.left), b.merge(c, s.right, t.right) |
| return b.mkBranch(p, m, left, right) |
| } |
| if !prefixesOverlap(p, m, q, n) { |
| return b.join(p, s, q, t) // prefixes are disjoint. |
| } |
| // prefixesOverlap(p, m, q, n) && !(m ==n && p == q) |
| // By prefixesOverlap(...), either: |
| // higher(m, n) && matchPrefix(q, p, m), or |
| // higher(n, m) && matchPrefix(p, q, n) |
| // So either s or t may can be merged with one branch or the other. |
| switch { |
| case ord(m, n) && zeroBit(q, m): |
| return b.mkBranch(p, m, b.merge(c, s.left, t), s.right) |
| case ord(m, n) && !zeroBit(q, m): |
| return b.mkBranch(p, m, s.left, b.merge(c, s.right, t)) |
| case ord(n, m) && zeroBit(p, n): |
| return b.mkBranch(q, n, b.merge(c, s, t.left), t.right) |
| default: |
| return b.mkBranch(q, n, t.left, b.merge(c, s, t.right)) |
| } |
| } |
| |
| func (b *Builder) remove(m node, k key) node { |
| switch m := m.(type) { |
| case *empty: |
| return m |
| case *leaf: |
| if m.k == k { |
| return b.empty |
| } |
| return m |
| case *branch: |
| // fallthrough |
| } |
| br := m.(*branch) |
| kp := prefix(k) |
| if !matchPrefix(kp, br.prefix, br.branching) { |
| // The prefix does not match. kp is not in br. |
| return br |
| } |
| // the prefix matches. try to remove from the left or right branch. |
| left, right := br.left, br.right |
| if zeroBit(kp, br.branching) { |
| left = b.remove(left, k) // k may be in the left branch. |
| } else { |
| right = b.remove(right, k) // k may be in the right branch. |
| } |
| if left == br.left && right == br.right { |
| return br // no update |
| } else if _, ok := left.(*empty); ok { |
| return right // left updated and is empty. |
| } else if _, ok := right.(*empty); ok { |
| return left // right updated and is empty. |
| } |
| // Either left or right updated. Both left and right are not empty. |
| // The left and right branches still share the same prefix and disagree |
| // on the same branching bit. It is safe to directly create the branch. |
| return b.mkBranch(br.prefix, br.branching, left, right) |
| } |
| |
| func (b *Builder) intersect(c Collision, l, r node) node { |
| if l == r { |
| return l |
| } |
| switch l := l.(type) { |
| case *empty: |
| return b.empty |
| case *leaf: |
| if rleaf := r.find(l.k); rleaf != nil { |
| return b.collide(c, l, rleaf) |
| } |
| return b.empty |
| case *branch: |
| switch r := r.(type) { |
| case *empty: |
| return b.empty |
| case *leaf: |
| if lleaf := l.find(r.k); lleaf != nil { |
| return b.collide(c, lleaf, r) |
| } |
| return b.empty |
| case *branch: |
| // fallthrough |
| } |
| } |
| // Last remaining case is branch branch intersection. |
| s, t := l.(*branch), r.(*branch) |
| p, m := s.prefix, s.branching |
| q, n := t.prefix, t.branching |
| |
| if m == n && p == q { |
| // prefixes are identical. |
| left, right := b.intersect(c, s.left, t.left), b.intersect(c, s.right, t.right) |
| if _, ok := left.(*empty); ok { |
| return right |
| } else if _, ok := right.(*empty); ok { |
| return left |
| } |
| // The left and right branches are both non-empty. |
| // They still share the same prefix and disagree on the same branching bit. |
| // It is safe to directly create the branch. |
| return b.mkBranch(p, m, left, right) |
| } |
| |
| if !prefixesOverlap(p, m, q, n) { |
| return b.empty // The prefixes share no keys. |
| } |
| // prefixesOverlap(p, m, q, n) && !(m ==n && p == q) |
| // By prefixesOverlap(...), either: |
| // ord(m, n) && matchPrefix(q, p, m), or |
| // ord(n, m) && matchPrefix(p, q, n) |
| // So either s or t may be a strict subtree of the other. |
| var lhs, rhs node |
| switch { |
| case ord(m, n) && zeroBit(q, m): |
| lhs, rhs = s.left, t |
| case ord(m, n) && !zeroBit(q, m): |
| lhs, rhs = s.right, t |
| case ord(n, m) && zeroBit(p, n): |
| lhs, rhs = s, t.left |
| default: |
| lhs, rhs = s, t.right |
| } |
| return b.intersect(c, lhs, rhs) |
| } |