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| 1 | +// Copyright 2009 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 | +// Page heap. |
| 6 | +// |
| 7 | +// See malloc.go for the general overview. |
| 8 | +// |
| 9 | +// Large spans are the subject of this file. Spans consisting of less than |
| 10 | +// _MaxMHeapLists are held in lists of like sized spans. Larger spans |
| 11 | +// are held in a treap. See https://en.wikipedia.org/wiki/Treap or |
| 12 | +// http://faculty.washington.edu/aragon/pubs/rst89.pdf for an overview. |
| 13 | +// sema.go also holds an implementation of a treap. |
| 14 | +// |
| 15 | +// Each treapNode holds a single span. The treap is sorted by page size |
| 16 | +// and for spans of the same size a secondary sort based on start address |
| 17 | +// is done. |
| 18 | +// Spans are returned based on a best fit algorithm and for spans of the same |
| 19 | +// size the one at the lowest address is selected. |
| 20 | +// |
| 21 | +// The primary routines are |
| 22 | +// insert: adds a span to the treap |
| 23 | +// remove: removes the span from that treap that best fits the required size |
| 24 | +// removeSpan: which removes a specific span from the treap |
| 25 | +// |
| 26 | +// _mheap.lock must be held when manipulating this data structure. |
| 27 | +// |
| 28 | +package runtime |
| 29 | + |
| 30 | +import ( |
| 31 | + "unsafe" |
| 32 | +) |
| 33 | + |
| 34 | +//go:notinheap |
| 35 | +type mTreap struct { |
| 36 | + treap *treapNode |
| 37 | +} |
| 38 | + |
| 39 | +//go:notinheap |
| 40 | +type treapNode struct { |
| 41 | + right *treapNode // all treapNodes > this treap node |
| 42 | + left *treapNode // all treapNodes < this treap node |
| 43 | + parent *treapNode // direct parent of this node, nil if root |
| 44 | + npagesKey uintptr // number of pages in spanKey, used as primary sort key |
| 45 | + spanKey *mspan // span of size npagesKey, used as secondary sort key |
| 46 | + priority uint32 // random number used by treap algorithm keep tree probablistically balanced |
| 47 | +} |
| 48 | + |
| 49 | +func (t *treapNode) init() { |
| 50 | + t.right = nil |
| 51 | + t.left = nil |
| 52 | + t.parent = nil |
| 53 | + t.spanKey = nil |
| 54 | + t.npagesKey = 0 |
| 55 | + t.priority = 0 |
| 56 | +} |
| 57 | + |
| 58 | +// isSpanInTreap is handy for debugging. One should hold the heap lock, usually |
| 59 | +// mheap_.lock(). |
| 60 | +func (t *treapNode) isSpanInTreap(s *mspan) bool { |
| 61 | + if t == nil { |
| 62 | + return false |
| 63 | + } |
| 64 | + return t.spanKey == s || t.left.isSpanInTreap(s) || t.right.isSpanInTreap(s) |
| 65 | +} |
| 66 | + |
| 67 | +// walkTreap is handy for debugging. |
| 68 | +// Starting at some treapnode t, for example the root, do a depth first preorder walk of |
| 69 | +// the tree executing fn at each treap node. One should hold the heap lock, usually |
| 70 | +// mheap_.lock(). |
| 71 | +func (t *treapNode) walkTreap(fn func(tn *treapNode)) { |
| 72 | + if t == nil { |
| 73 | + return |
| 74 | + } |
| 75 | + fn(t) |
| 76 | + t.left.walkTreap(fn) |
| 77 | + t.right.walkTreap(fn) |
| 78 | +} |
| 79 | + |
| 80 | +// checkTreapNode when used in conjunction with walkTreap can usually detect a |
| 81 | +// poorly formed treap. |
| 82 | +func checkTreapNode(t *treapNode) { |
| 83 | + // lessThan is used to order the treap. |
| 84 | + // npagesKey and npages are the primary keys. |
| 85 | + // spanKey and span are the secondary keys. |
| 86 | + // span == nil (0) will always be lessThan all |
| 87 | + // spans of the same size. |
| 88 | + lessThan := func(npages uintptr, s *mspan) bool { |
| 89 | + if t.npagesKey != npages { |
| 90 | + return t.npagesKey < npages |
| 91 | + } |
| 92 | + // t.npagesKey == npages |
| 93 | + return uintptr(unsafe.Pointer(t.spanKey)) < uintptr(unsafe.Pointer(s)) |
| 94 | + } |
| 95 | + |
| 96 | + if t == nil { |
| 97 | + return |
| 98 | + } |
| 99 | + if t.spanKey.npages != t.npagesKey || t.spanKey.next != nil { |
| 100 | + println("runtime: checkTreapNode treapNode t=", t, " t.npagesKey=", t.npagesKey, |
| 101 | + "t.spanKey.npages=", t.spanKey.npages) |
| 102 | + throw("why does span.npages and treap.ngagesKey do not match?") |
| 103 | + } |
| 104 | + if t.left != nil && lessThan(t.left.npagesKey, t.left.spanKey) { |
| 105 | + throw("t.lessThan(t.left.npagesKey, t.left.spanKey) is not false") |
| 106 | + } |
| 107 | + if t.right != nil && !lessThan(t.right.npagesKey, t.right.spanKey) { |
| 108 | + throw("!t.lessThan(t.left.npagesKey, t.left.spanKey) is not false") |
| 109 | + } |
| 110 | +} |
| 111 | + |
| 112 | +// insert adds span to the large span treap. |
| 113 | +func (root *mTreap) insert(span *mspan) { |
| 114 | + npages := span.npages |
| 115 | + var last *treapNode |
| 116 | + pt := &root.treap |
| 117 | + for t := *pt; t != nil; t = *pt { |
| 118 | + last = t |
| 119 | + if t.npagesKey < npages { |
| 120 | + pt = &t.right |
| 121 | + } else if t.npagesKey > npages { |
| 122 | + pt = &t.left |
| 123 | + } else if uintptr(unsafe.Pointer(t.spanKey)) < uintptr(unsafe.Pointer(span)) { |
| 124 | + // t.npagesKey == npages, so sort on span addresses. |
| 125 | + pt = &t.right |
| 126 | + } else if uintptr(unsafe.Pointer(t.spanKey)) > uintptr(unsafe.Pointer(span)) { |
| 127 | + pt = &t.left |
| 128 | + } else { |
| 129 | + throw("inserting span already in treap") |
| 130 | + } |
| 131 | + } |
| 132 | + |
| 133 | + // Add t as new leaf in tree of span size and unique addrs. |
| 134 | + // The balanced tree is a treap using priority as the random heap priority. |
| 135 | + // That is, it is a binary tree ordered according to the npagesKey, |
| 136 | + // but then among the space of possible binary trees respecting those |
| 137 | + // npagesKeys, it is kept balanced on average by maintaining a heap ordering |
| 138 | + // on the priority: s.priority <= both s.right.priority and s.right.priority. |
| 139 | + // https://en.wikipedia.org/wiki/Treap |
| 140 | + // http://faculty.washington.edu/aragon/pubs/rst89.pdf |
| 141 | + |
| 142 | + t := (*treapNode)(mheap_.treapalloc.alloc()) |
| 143 | + t.init() |
| 144 | + t.npagesKey = span.npages |
| 145 | + t.priority = fastrand() |
| 146 | + t.spanKey = span |
| 147 | + t.parent = last |
| 148 | + *pt = t // t now at a leaf. |
| 149 | + // Rotate up into tree according to priority. |
| 150 | + for t.parent != nil && t.parent.priority > t.priority { |
| 151 | + if t != nil && t.spanKey.npages != t.npagesKey { |
| 152 | + println("runtime: insert t=", t, "t.npagesKey=", t.npagesKey) |
| 153 | + println("runtime: t.spanKey=", t.spanKey, "t.spanKey.npages=", t.spanKey.npages) |
| 154 | + throw("span and treap sizes do not match?") |
| 155 | + } |
| 156 | + if t.parent.left == t { |
| 157 | + root.rotateRight(t.parent) |
| 158 | + } else { |
| 159 | + if t.parent.right != t { |
| 160 | + throw("treap insert finds a broken treap") |
| 161 | + } |
| 162 | + root.rotateLeft(t.parent) |
| 163 | + } |
| 164 | + } |
| 165 | +} |
| 166 | + |
| 167 | +func (root *mTreap) removeNode(t *treapNode) *mspan { |
| 168 | + if t.spanKey.npages != t.npagesKey { |
| 169 | + throw("span and treap node npages do not match") |
| 170 | + } |
| 171 | + result := t.spanKey |
| 172 | + |
| 173 | + // Rotate t down to be leaf of tree for removal, respecting priorities. |
| 174 | + for t.right != nil || t.left != nil { |
| 175 | + if t.right == nil || t.left != nil && t.left.priority < t.right.priority { |
| 176 | + root.rotateRight(t) |
| 177 | + } else { |
| 178 | + root.rotateLeft(t) |
| 179 | + } |
| 180 | + } |
| 181 | + // Remove t, now a leaf. |
| 182 | + if t.parent != nil { |
| 183 | + if t.parent.left == t { |
| 184 | + t.parent.left = nil |
| 185 | + } else { |
| 186 | + t.parent.right = nil |
| 187 | + } |
| 188 | + } else { |
| 189 | + root.treap = nil |
| 190 | + } |
| 191 | + // Return the found treapNode's span after freeing the treapNode. |
| 192 | + t.spanKey = nil |
| 193 | + t.npagesKey = 0 |
| 194 | + mheap_.treapalloc.free(unsafe.Pointer(t)) |
| 195 | + return result |
| 196 | +} |
| 197 | + |
| 198 | +// remove searches for, finds, removes from the treap, and returns the smallest |
| 199 | +// span that can hold npages. If no span has at least npages return nil. |
| 200 | +// This is slightly more complicated than a simple binary tree search |
| 201 | +// since if an exact match is not found the next larger node is |
| 202 | +// returned. |
| 203 | +// If the last node inspected > npagesKey not holding |
| 204 | +// a left node (a smaller npages) is the "best fit" node. |
| 205 | +func (root *mTreap) remove(npages uintptr) *mspan { |
| 206 | + t := root.treap |
| 207 | + for t != nil { |
| 208 | + if t.spanKey == nil { |
| 209 | + throw("treap node with nil spanKey found") |
| 210 | + } |
| 211 | + if t.npagesKey < npages { |
| 212 | + t = t.right |
| 213 | + } else if t.left != nil && t.left.npagesKey >= npages { |
| 214 | + t = t.left |
| 215 | + } else { |
| 216 | + result := t.spanKey |
| 217 | + root.removeNode(t) |
| 218 | + return result |
| 219 | + } |
| 220 | + } |
| 221 | + return nil |
| 222 | +} |
| 223 | + |
| 224 | +// removeSpan searches for, finds, deletes span along with |
| 225 | +// the associated treap node. If the span is not in the treap |
| 226 | +// then t will eventually be set to nil and the t.spanKey |
| 227 | +// will throw. |
| 228 | +func (root *mTreap) removeSpan(span *mspan) { |
| 229 | + npages := span.npages |
| 230 | + t := root.treap |
| 231 | + for t.spanKey != span { |
| 232 | + if t.npagesKey < npages { |
| 233 | + t = t.right |
| 234 | + } else if t.npagesKey > npages { |
| 235 | + t = t.left |
| 236 | + } else if uintptr(unsafe.Pointer(t.spanKey)) < uintptr(unsafe.Pointer(span)) { |
| 237 | + t = t.right |
| 238 | + } else if uintptr(unsafe.Pointer(t.spanKey)) > uintptr(unsafe.Pointer(span)) { |
| 239 | + t = t.left |
| 240 | + } |
| 241 | + } |
| 242 | + root.removeNode(t) |
| 243 | + return |
| 244 | +} |
| 245 | + |
| 246 | +// scavengetreap visits each node in the treap and scavenges the |
| 247 | +// treapNode's span. |
| 248 | +func scavengetreap(treap *treapNode, now, limit uint64) uintptr { |
| 249 | + if treap == nil { |
| 250 | + return 0 |
| 251 | + } |
| 252 | + return scavengeTreapNode(treap, now, limit) + |
| 253 | + scavengetreap(treap.left, now, limit) + |
| 254 | + scavengetreap(treap.right, now, limit) |
| 255 | +} |
| 256 | + |
| 257 | +// rotateLeft rotates the tree rooted at node x. |
| 258 | +// turning (x a (y b c)) into (y (x a b) c). |
| 259 | +func (root *mTreap) rotateLeft(x *treapNode) { |
| 260 | + // p -> (x a (y b c)) |
| 261 | + p := x.parent |
| 262 | + a, y := x.left, x.right |
| 263 | + b, c := y.left, y.right |
| 264 | + |
| 265 | + y.left = x |
| 266 | + x.parent = y |
| 267 | + y.right = c |
| 268 | + if c != nil { |
| 269 | + c.parent = y |
| 270 | + } |
| 271 | + x.left = a |
| 272 | + if a != nil { |
| 273 | + a.parent = x |
| 274 | + } |
| 275 | + x.right = b |
| 276 | + if b != nil { |
| 277 | + b.parent = x |
| 278 | + } |
| 279 | + |
| 280 | + y.parent = p |
| 281 | + if p == nil { |
| 282 | + root.treap = y |
| 283 | + } else if p.left == x { |
| 284 | + p.left = y |
| 285 | + } else { |
| 286 | + if p.right != x { |
| 287 | + throw("large span treap rotateLeft") |
| 288 | + } |
| 289 | + p.right = y |
| 290 | + } |
| 291 | +} |
| 292 | + |
| 293 | +// rotateRight rotates the tree rooted at node y. |
| 294 | +// turning (y (x a b) c) into (x a (y b c)). |
| 295 | +func (root *mTreap) rotateRight(y *treapNode) { |
| 296 | + // p -> (y (x a b) c) |
| 297 | + p := y.parent |
| 298 | + x, c := y.left, y.right |
| 299 | + a, b := x.left, x.right |
| 300 | + |
| 301 | + x.left = a |
| 302 | + if a != nil { |
| 303 | + a.parent = x |
| 304 | + } |
| 305 | + x.right = y |
| 306 | + y.parent = x |
| 307 | + y.left = b |
| 308 | + if b != nil { |
| 309 | + b.parent = y |
| 310 | + } |
| 311 | + y.right = c |
| 312 | + if c != nil { |
| 313 | + c.parent = y |
| 314 | + } |
| 315 | + |
| 316 | + x.parent = p |
| 317 | + if p == nil { |
| 318 | + root.treap = x |
| 319 | + } else if p.left == y { |
| 320 | + p.left = x |
| 321 | + } else { |
| 322 | + if p.right != y { |
| 323 | + throw("large span treap rotateRight") |
| 324 | + } |
| 325 | + p.right = x |
| 326 | + } |
| 327 | +} |
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