| 1 | // Copyright 2021 The Go Authors. All rights reserved. |
|---|---|
| 2 | // Use of this source code is governed by a BSD-style |
| 3 | // license that can be found in the LICENSE file. |
| 4 | |
| 5 | package trie |
| 6 | |
| 7 | // Collision functions combine a left and right hand side (lhs and rhs) values |
| 8 | // the two values are associated with the same key and produces the value that |
| 9 | // will be stored for the key. |
| 10 | // |
| 11 | // Collision functions must be idempotent: |
| 12 | // |
| 13 | // collision(x, x) == x for all x. |
| 14 | // |
| 15 | // Collisions functions may be applied whenever a value is inserted |
| 16 | // or two maps are merged, or intersected. |
| 17 | type Collision func(lhs interface{}, rhs interface{}) interface{} |
| 18 | |
| 19 | // TakeLhs always returns the left value in a collision. |
| 20 | func TakeLhs(lhs, rhs interface{}) interface{} { return lhs } |
| 21 | |
| 22 | // TakeRhs always returns the right hand side in a collision. |
| 23 | func TakeRhs(lhs, rhs interface{}) interface{} { return rhs } |
| 24 | |
| 25 | // Builder creates new Map. Each Builder has a unique Scope. |
| 26 | // |
| 27 | // IMPORTANT: Nodes are hash-consed internally to reduce memory consumption. To |
| 28 | // support hash-consing Builders keep an internal Map of all of the Maps that they |
| 29 | // have created. To GC any of the Maps created by the Builder, all references to |
| 30 | // the Builder must be dropped. This includes MutMaps. |
| 31 | type Builder struct { |
| 32 | scope Scope |
| 33 | |
| 34 | // hash-consing maps for each node type. |
| 35 | empty *empty |
| 36 | leaves map[leaf]*leaf |
| 37 | branches map[branch]*branch |
| 38 | // It may be possible to support more types of patricia tries |
| 39 | // (e.g. non-hash-consed) by making Builder an interface and abstracting |
| 40 | // the mkLeaf and mkBranch functions. |
| 41 | } |
| 42 | |
| 43 | // NewBuilder creates a new Builder with a unique Scope. |
| 44 | func NewBuilder() *Builder { |
| 45 | s := newScope() |
| 46 | return &Builder{ |
| 47 | scope: s, |
| 48 | empty: &empty{s}, |
| 49 | leaves: make(map[leaf]*leaf), |
| 50 | branches: make(map[branch]*branch), |
| 51 | } |
| 52 | } |
| 53 | |
| 54 | func (b *Builder) Scope() Scope { return b.scope } |
| 55 | |
| 56 | // Rescope changes the builder's scope to a new unique Scope. |
| 57 | // |
| 58 | // Any Maps created using the previous scope need to be Cloned |
| 59 | // before any operation. |
| 60 | // |
| 61 | // This makes the old internals of the Builder eligible to be GC'ed. |
| 62 | func (b *Builder) Rescope() { |
| 63 | s := newScope() |
| 64 | b.scope = s |
| 65 | b.empty = &empty{s} |
| 66 | b.leaves = make(map[leaf]*leaf) |
| 67 | b.branches = make(map[branch]*branch) |
| 68 | } |
| 69 | |
| 70 | // Empty is the empty map. |
| 71 | func (b *Builder) Empty() Map { return Map{b.Scope(), b.empty} } |
| 72 | |
| 73 | // InsertWith inserts a new association from k to v into the Map m to create a new map |
| 74 | // in the current scope and handle collisions using the collision function c. |
| 75 | // |
| 76 | // This is roughly corresponds to updating a map[uint64]interface{} by: |
| 77 | // |
| 78 | // if _, ok := m[k]; ok { m[k] = c(m[k], v} else { m[k] = v} |
| 79 | // |
| 80 | // An insertion or update happened whenever Insert(m, ...) != m . |
| 81 | func (b *Builder) InsertWith(c Collision, m Map, k uint64, v interface{}) Map { |
| 82 | m = b.Clone(m) |
| 83 | return Map{b.Scope(), b.insert(c, m.n, b.mkLeaf(key(k), v), false)} |
| 84 | } |
| 85 | |
| 86 | // Inserts a new association from key to value into the Map m to create |
| 87 | // a new map in the current scope. |
| 88 | // |
| 89 | // If there was a previous value mapped by key, keep the previously mapped value. |
| 90 | // This is roughly corresponds to updating a map[uint64]interface{} by: |
| 91 | // |
| 92 | // if _, ok := m[k]; ok { m[k] = val } |
| 93 | // |
| 94 | // This is equivalent to b.Merge(m, b.Create({k: v})). |
| 95 | func (b *Builder) Insert(m Map, k uint64, v interface{}) Map { |
| 96 | return b.InsertWith(TakeLhs, m, k, v) |
| 97 | } |
| 98 | |
| 99 | // Updates a (key, value) in the map. This is roughly corresponds to |
| 100 | // updating a map[uint64]interface{} by: |
| 101 | // |
| 102 | // m[key] = val |
| 103 | func (b *Builder) Update(m Map, key uint64, val interface{}) Map { |
| 104 | return b.InsertWith(TakeRhs, m, key, val) |
| 105 | } |
| 106 | |
| 107 | // Merge two maps lhs and rhs to create a new map in the current scope. |
| 108 | // |
| 109 | // Whenever there is a key in both maps (a collision), the resulting value mapped by |
| 110 | // the key will be `c(lhs[key], rhs[key])`. |
| 111 | func (b *Builder) MergeWith(c Collision, lhs, rhs Map) Map { |
| 112 | lhs, rhs = b.Clone(lhs), b.Clone(rhs) |
| 113 | return Map{b.Scope(), b.merge(c, lhs.n, rhs.n)} |
| 114 | } |
| 115 | |
| 116 | // Merge two maps lhs and rhs to create a new map in the current scope. |
| 117 | // |
| 118 | // Whenever there is a key in both maps (a collision), the resulting value mapped by |
| 119 | // the key will be the value in lhs `b.Collision(lhs[key], rhs[key])`. |
| 120 | func (b *Builder) Merge(lhs, rhs Map) Map { |
| 121 | return b.MergeWith(TakeLhs, lhs, rhs) |
| 122 | } |
| 123 | |
| 124 | // Clone returns a Map that contains the same (key, value) elements |
| 125 | // within b.Scope(), i.e. return m if m.Scope() == b.Scope() or return |
| 126 | // a deep copy of m within b.Scope() otherwise. |
| 127 | func (b *Builder) Clone(m Map) Map { |
| 128 | if m.Scope() == b.Scope() { |
| 129 | return m |
| 130 | } else if m.n == nil { |
| 131 | return Map{b.Scope(), b.empty} |
| 132 | } |
| 133 | return Map{b.Scope(), b.clone(m.n)} |
| 134 | } |
| 135 | func (b *Builder) clone(n node) node { |
| 136 | switch n := n.(type) { |
| 137 | case *empty: |
| 138 | return b.empty |
| 139 | case *leaf: |
| 140 | return b.mkLeaf(n.k, n.v) |
| 141 | case *branch: |
| 142 | return b.mkBranch(n.prefix, n.branching, b.clone(n.left), b.clone(n.right)) |
| 143 | default: |
| 144 | panic("unreachable") |
| 145 | } |
| 146 | } |
| 147 | |
| 148 | // Remove a key from a Map m and return the resulting Map. |
| 149 | func (b *Builder) Remove(m Map, k uint64) Map { |
| 150 | m = b.Clone(m) |
| 151 | return Map{b.Scope(), b.remove(m.n, key(k))} |
| 152 | } |
| 153 | |
| 154 | // Intersect Maps lhs and rhs and returns a map with all of the keys in |
| 155 | // both lhs and rhs and the value comes from lhs, i.e. |
| 156 | // |
| 157 | // {(k, lhs[k]) | k in lhs, k in rhs}. |
| 158 | func (b *Builder) Intersect(lhs, rhs Map) Map { |
| 159 | return b.IntersectWith(TakeLhs, lhs, rhs) |
| 160 | } |
| 161 | |
| 162 | // IntersectWith take lhs and rhs and returns the intersection |
| 163 | // with the value coming from the collision function, i.e. |
| 164 | // |
| 165 | // {(k, c(lhs[k], rhs[k]) ) | k in lhs, k in rhs}. |
| 166 | // |
| 167 | // The elements of the resulting map are always { <k, c(lhs[k], rhs[k]) > } |
| 168 | // for each key k that a key in both lhs and rhs. |
| 169 | func (b *Builder) IntersectWith(c Collision, lhs, rhs Map) Map { |
| 170 | l, r := b.Clone(lhs), b.Clone(rhs) |
| 171 | return Map{b.Scope(), b.intersect(c, l.n, r.n)} |
| 172 | } |
| 173 | |
| 174 | // MutMap is a convenient wrapper for a Map and a *Builder that will be used to create |
| 175 | // new Maps from it. |
| 176 | type MutMap struct { |
| 177 | B *Builder |
| 178 | M Map |
| 179 | } |
| 180 | |
| 181 | // MutEmpty is an empty MutMap for a builder. |
| 182 | func (b *Builder) MutEmpty() MutMap { |
| 183 | return MutMap{b, b.Empty()} |
| 184 | } |
| 185 | |
| 186 | // Insert an element into the map using the collision function for the builder. |
| 187 | // Returns true if the element was inserted. |
| 188 | func (mm *MutMap) Insert(k uint64, v interface{}) bool { |
| 189 | old := mm.M |
| 190 | mm.M = mm.B.Insert(old, k, v) |
| 191 | return old != mm.M |
| 192 | } |
| 193 | |
| 194 | // Updates an element in the map. Returns true if the map was updated. |
| 195 | func (mm *MutMap) Update(k uint64, v interface{}) bool { |
| 196 | old := mm.M |
| 197 | mm.M = mm.B.Update(old, k, v) |
| 198 | return old != mm.M |
| 199 | } |
| 200 | |
| 201 | // Removes a key from the map. Returns true if the element was removed. |
| 202 | func (mm *MutMap) Remove(k uint64) bool { |
| 203 | old := mm.M |
| 204 | mm.M = mm.B.Remove(old, k) |
| 205 | return old != mm.M |
| 206 | } |
| 207 | |
| 208 | // Merge another map into the current one using the collision function |
| 209 | // for the builder. Returns true if the map changed. |
| 210 | func (mm *MutMap) Merge(other Map) bool { |
| 211 | old := mm.M |
| 212 | mm.M = mm.B.Merge(old, other) |
| 213 | return old != mm.M |
| 214 | } |
| 215 | |
| 216 | // Intersect another map into the current one using the collision function |
| 217 | // for the builder. Returns true if the map changed. |
| 218 | func (mm *MutMap) Intersect(other Map) bool { |
| 219 | old := mm.M |
| 220 | mm.M = mm.B.Intersect(old, other) |
| 221 | return old != mm.M |
| 222 | } |
| 223 | |
| 224 | func (b *Builder) Create(m map[uint64]interface{}) Map { |
| 225 | var leaves []*leaf |
| 226 | for k, v := range m { |
| 227 | leaves = append(leaves, b.mkLeaf(key(k), v)) |
| 228 | } |
| 229 | return Map{b.Scope(), b.create(leaves)} |
| 230 | } |
| 231 | |
| 232 | // Merge another map into the current one using the collision function |
| 233 | // for the builder. Returns true if the map changed. |
| 234 | func (mm *MutMap) MergeWith(c Collision, other Map) bool { |
| 235 | old := mm.M |
| 236 | mm.M = mm.B.MergeWith(c, old, other) |
| 237 | return old != mm.M |
| 238 | } |
| 239 | |
| 240 | // creates a map for a collection of leaf nodes. |
| 241 | func (b *Builder) create(leaves []*leaf) node { |
| 242 | n := len(leaves) |
| 243 | if n == 0 { |
| 244 | return b.empty |
| 245 | } else if n == 1 { |
| 246 | return leaves[0] |
| 247 | } |
| 248 | // Note: we can do a more sophisicated algorithm by: |
| 249 | // - sorting the leaves ahead of time, |
| 250 | // - taking the prefix and branching bit of the min and max key, |
| 251 | // - binary searching for the branching bit, |
| 252 | // - splitting exactly where the branch will be, and |
| 253 | // - making the branch node for this prefix + branching bit. |
| 254 | // Skipping until this is a performance bottleneck. |
| 255 | |
| 256 | m := n / 2 // (n >= 2) ==> 1 <= m < n |
| 257 | l, r := leaves[:m], leaves[m:] |
| 258 | return b.merge(nil, b.create(l), b.create(r)) |
| 259 | } |
| 260 | |
| 261 | // mkLeaf returns the hash-consed representative of (k, v) in the current scope. |
| 262 | func (b *Builder) mkLeaf(k key, v interface{}) *leaf { |
| 263 | l := &leaf{k: k, v: v} |
| 264 | if rep, ok := b.leaves[*l]; ok { |
| 265 | return rep |
| 266 | } |
| 267 | b.leaves[*l] = l |
| 268 | return l |
| 269 | } |
| 270 | |
| 271 | // mkBranch returns the hash-consed representative of the tuple |
| 272 | // |
| 273 | // (prefix, branch, left, right) |
| 274 | // |
| 275 | // in the current scope. |
| 276 | func (b *Builder) mkBranch(p prefix, bp bitpos, left node, right node) *branch { |
| 277 | br := &branch{ |
| 278 | sz: left.size() + right.size(), |
| 279 | prefix: p, |
| 280 | branching: bp, |
| 281 | left: left, |
| 282 | right: right, |
| 283 | } |
| 284 | if rep, ok := b.branches[*br]; ok { |
| 285 | return rep |
| 286 | } |
| 287 | b.branches[*br] = br |
| 288 | return br |
| 289 | } |
| 290 | |
| 291 | // join two maps with prefixes p0 and p1 that are *known* to disagree. |
| 292 | func (b *Builder) join(p0 prefix, t0 node, p1 prefix, t1 node) *branch { |
| 293 | m := branchingBit(p0, p1) |
| 294 | var left, right node |
| 295 | if zeroBit(p0, m) { |
| 296 | left, right = t0, t1 |
| 297 | } else { |
| 298 | left, right = t1, t0 |
| 299 | } |
| 300 | prefix := mask(p0, m) |
| 301 | return b.mkBranch(prefix, m, left, right) |
| 302 | } |
| 303 | |
| 304 | // collide two leaves with the same key to create a leaf |
| 305 | // with the collided value. |
| 306 | func (b *Builder) collide(c Collision, left, right *leaf) *leaf { |
| 307 | if left == right { |
| 308 | return left // c is idempotent: c(x, x) == x |
| 309 | } |
| 310 | val := left.v // keep the left value by default if c is nil |
| 311 | if c != nil { |
| 312 | val = c(left.v, right.v) |
| 313 | } |
| 314 | switch val { |
| 315 | case left.v: |
| 316 | return left |
| 317 | case right.v: |
| 318 | return right |
| 319 | default: |
| 320 | return b.mkLeaf(left.k, val) |
| 321 | } |
| 322 | } |
| 323 | |
| 324 | // inserts a leaf l into a map m and returns the resulting map. |
| 325 | // When lhs is true, l is the left hand side in a collision. |
| 326 | // Both l and m are in the current scope. |
| 327 | func (b *Builder) insert(c Collision, m node, l *leaf, lhs bool) node { |
| 328 | switch m := m.(type) { |
| 329 | case *empty: |
| 330 | return l |
| 331 | case *leaf: |
| 332 | if m.k == l.k { |
| 333 | left, right := l, m |
| 334 | if !lhs { |
| 335 | left, right = right, left |
| 336 | } |
| 337 | return b.collide(c, left, right) |
| 338 | } |
| 339 | return b.join(prefix(l.k), l, prefix(m.k), m) |
| 340 | case *branch: |
| 341 | // fallthrough |
| 342 | } |
| 343 | // m is a branch |
| 344 | br := m.(*branch) |
| 345 | if !matchPrefix(prefix(l.k), br.prefix, br.branching) { |
| 346 | return b.join(prefix(l.k), l, br.prefix, br) |
| 347 | } |
| 348 | var left, right node |
| 349 | if zeroBit(prefix(l.k), br.branching) { |
| 350 | left, right = b.insert(c, br.left, l, lhs), br.right |
| 351 | } else { |
| 352 | left, right = br.left, b.insert(c, br.right, l, lhs) |
| 353 | } |
| 354 | if left == br.left && right == br.right { |
| 355 | return m |
| 356 | } |
| 357 | return b.mkBranch(br.prefix, br.branching, left, right) |
| 358 | } |
| 359 | |
| 360 | // merge two maps in the current scope. |
| 361 | func (b *Builder) merge(c Collision, lhs, rhs node) node { |
| 362 | if lhs == rhs { |
| 363 | return lhs |
| 364 | } |
| 365 | switch lhs := lhs.(type) { |
| 366 | case *empty: |
| 367 | return rhs |
| 368 | case *leaf: |
| 369 | return b.insert(c, rhs, lhs, true) |
| 370 | case *branch: |
| 371 | switch rhs := rhs.(type) { |
| 372 | case *empty: |
| 373 | return lhs |
| 374 | case *leaf: |
| 375 | return b.insert(c, lhs, rhs, false) |
| 376 | case *branch: |
| 377 | // fallthrough |
| 378 | } |
| 379 | } |
| 380 | |
| 381 | // Last remaining case is branch branch merging. |
| 382 | // For brevity, we adopt the Okasaki and Gill naming conventions |
| 383 | // for branching and prefixes. |
| 384 | s, t := lhs.(*branch), rhs.(*branch) |
| 385 | p, m := s.prefix, s.branching |
| 386 | q, n := t.prefix, t.branching |
| 387 | |
| 388 | if m == n && p == q { // prefixes are identical. |
| 389 | left, right := b.merge(c, s.left, t.left), b.merge(c, s.right, t.right) |
| 390 | return b.mkBranch(p, m, left, right) |
| 391 | } |
| 392 | if !prefixesOverlap(p, m, q, n) { |
| 393 | return b.join(p, s, q, t) // prefixes are disjoint. |
| 394 | } |
| 395 | // prefixesOverlap(p, m, q, n) && !(m ==n && p == q) |
| 396 | // By prefixesOverlap(...), either: |
| 397 | // higher(m, n) && matchPrefix(q, p, m), or |
| 398 | // higher(n, m) && matchPrefix(p, q, n) |
| 399 | // So either s or t may can be merged with one branch or the other. |
| 400 | switch { |
| 401 | case ord(m, n) && zeroBit(q, m): |
| 402 | return b.mkBranch(p, m, b.merge(c, s.left, t), s.right) |
| 403 | case ord(m, n) && !zeroBit(q, m): |
| 404 | return b.mkBranch(p, m, s.left, b.merge(c, s.right, t)) |
| 405 | case ord(n, m) && zeroBit(p, n): |
| 406 | return b.mkBranch(q, n, b.merge(c, s, t.left), t.right) |
| 407 | default: |
| 408 | return b.mkBranch(q, n, t.left, b.merge(c, s, t.right)) |
| 409 | } |
| 410 | } |
| 411 | |
| 412 | func (b *Builder) remove(m node, k key) node { |
| 413 | switch m := m.(type) { |
| 414 | case *empty: |
| 415 | return m |
| 416 | case *leaf: |
| 417 | if m.k == k { |
| 418 | return b.empty |
| 419 | } |
| 420 | return m |
| 421 | case *branch: |
| 422 | // fallthrough |
| 423 | } |
| 424 | br := m.(*branch) |
| 425 | kp := prefix(k) |
| 426 | if !matchPrefix(kp, br.prefix, br.branching) { |
| 427 | // The prefix does not match. kp is not in br. |
| 428 | return br |
| 429 | } |
| 430 | // the prefix matches. try to remove from the left or right branch. |
| 431 | left, right := br.left, br.right |
| 432 | if zeroBit(kp, br.branching) { |
| 433 | left = b.remove(left, k) // k may be in the left branch. |
| 434 | } else { |
| 435 | right = b.remove(right, k) // k may be in the right branch. |
| 436 | } |
| 437 | if left == br.left && right == br.right { |
| 438 | return br // no update |
| 439 | } else if _, ok := left.(*empty); ok { |
| 440 | return right // left updated and is empty. |
| 441 | } else if _, ok := right.(*empty); ok { |
| 442 | return left // right updated and is empty. |
| 443 | } |
| 444 | // Either left or right updated. Both left and right are not empty. |
| 445 | // The left and right branches still share the same prefix and disagree |
| 446 | // on the same branching bit. It is safe to directly create the branch. |
| 447 | return b.mkBranch(br.prefix, br.branching, left, right) |
| 448 | } |
| 449 | |
| 450 | func (b *Builder) intersect(c Collision, l, r node) node { |
| 451 | if l == r { |
| 452 | return l |
| 453 | } |
| 454 | switch l := l.(type) { |
| 455 | case *empty: |
| 456 | return b.empty |
| 457 | case *leaf: |
| 458 | if rleaf := r.find(l.k); rleaf != nil { |
| 459 | return b.collide(c, l, rleaf) |
| 460 | } |
| 461 | return b.empty |
| 462 | case *branch: |
| 463 | switch r := r.(type) { |
| 464 | case *empty: |
| 465 | return b.empty |
| 466 | case *leaf: |
| 467 | if lleaf := l.find(r.k); lleaf != nil { |
| 468 | return b.collide(c, lleaf, r) |
| 469 | } |
| 470 | return b.empty |
| 471 | case *branch: |
| 472 | // fallthrough |
| 473 | } |
| 474 | } |
| 475 | // Last remaining case is branch branch intersection. |
| 476 | s, t := l.(*branch), r.(*branch) |
| 477 | p, m := s.prefix, s.branching |
| 478 | q, n := t.prefix, t.branching |
| 479 | |
| 480 | if m == n && p == q { |
| 481 | // prefixes are identical. |
| 482 | left, right := b.intersect(c, s.left, t.left), b.intersect(c, s.right, t.right) |
| 483 | if _, ok := left.(*empty); ok { |
| 484 | return right |
| 485 | } else if _, ok := right.(*empty); ok { |
| 486 | return left |
| 487 | } |
| 488 | // The left and right branches are both non-empty. |
| 489 | // They still share the same prefix and disagree on the same branching bit. |
| 490 | // It is safe to directly create the branch. |
| 491 | return b.mkBranch(p, m, left, right) |
| 492 | } |
| 493 | |
| 494 | if !prefixesOverlap(p, m, q, n) { |
| 495 | return b.empty // The prefixes share no keys. |
| 496 | } |
| 497 | // prefixesOverlap(p, m, q, n) && !(m ==n && p == q) |
| 498 | // By prefixesOverlap(...), either: |
| 499 | // ord(m, n) && matchPrefix(q, p, m), or |
| 500 | // ord(n, m) && matchPrefix(p, q, n) |
| 501 | // So either s or t may be a strict subtree of the other. |
| 502 | var lhs, rhs node |
| 503 | switch { |
| 504 | case ord(m, n) && zeroBit(q, m): |
| 505 | lhs, rhs = s.left, t |
| 506 | case ord(m, n) && !zeroBit(q, m): |
| 507 | lhs, rhs = s.right, t |
| 508 | case ord(n, m) && zeroBit(p, n): |
| 509 | lhs, rhs = s, t.left |
| 510 | default: |
| 511 | lhs, rhs = s, t.right |
| 512 | } |
| 513 | return b.intersect(c, lhs, rhs) |
| 514 | } |
| 515 |
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