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// Copyright 2009 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.
// Page heap.
//
// See malloc.go for the general overview.
//
// Large spans are the subject of this file. Spans consisting of less than
// _MaxMHeapLists are held in lists of like sized spans. Larger spans
// are held in a treap. See https://en.wikipedia.org/wiki/Treap or
// https://faculty.washington.edu/aragon/pubs/rst89.pdf for an overview.
// sema.go also holds an implementation of a treap.
//
// Each treapNode holds a single span. The treap is sorted by page size
// and for spans of the same size a secondary sort based on start address
// is done.
// Spans are returned based on a best fit algorithm and for spans of the same
// size the one at the lowest address is selected.
//
// The primary routines are
// insert: adds a span to the treap
// remove: removes the span from that treap that best fits the required size
// removeSpan: which removes a specific span from the treap
//
// _mheap.lock must be held when manipulating this data structure.
package runtime
import (
"unsafe"
)
//go:notinheap
type mTreap struct {
treap *treapNode
}
//go:notinheap
type treapNode struct {
right *treapNode // all treapNodes > this treap node
left *treapNode // all treapNodes < this treap node
parent *treapNode // direct parent of this node, nil if root
npagesKey uintptr // number of pages in spanKey, used as primary sort key
spanKey *mspan // span of size npagesKey, used as secondary sort key
priority uint32 // random number used by treap algorithm to keep tree probabilistically balanced
}
func (t *treapNode) init() {
t.right = nil
t.left = nil
t.parent = nil
t.spanKey = nil
t.npagesKey = 0
t.priority = 0
}
// isSpanInTreap is handy for debugging. One should hold the heap lock, usually
// mheap_.lock().
func (t *treapNode) isSpanInTreap(s *mspan) bool {
if t == nil {
return false
}
return t.spanKey == s || t.left.isSpanInTreap(s) || t.right.isSpanInTreap(s)
}
// walkTreap is handy for debugging.
// Starting at some treapnode t, for example the root, do a depth first preorder walk of
// the tree executing fn at each treap node. One should hold the heap lock, usually
// mheap_.lock().
func (t *treapNode) walkTreap(fn func(tn *treapNode)) {
if t == nil {
return
}
fn(t)
t.left.walkTreap(fn)
t.right.walkTreap(fn)
}
// checkTreapNode when used in conjunction with walkTreap can usually detect a
// poorly formed treap.
func checkTreapNode(t *treapNode) {
// lessThan is used to order the treap.
// npagesKey and npages are the primary keys.
// spanKey and span are the secondary keys.
// span == nil (0) will always be lessThan all
// spans of the same size.
lessThan := func(npages uintptr, s *mspan) bool {
if t.npagesKey != npages {
return t.npagesKey < npages
}
// t.npagesKey == npages
return uintptr(unsafe.Pointer(t.spanKey)) < uintptr(unsafe.Pointer(s))
}
if t == nil {
return
}
if t.spanKey.npages != t.npagesKey || t.spanKey.next != nil {
println("runtime: checkTreapNode treapNode t=", t, " t.npagesKey=", t.npagesKey,
"t.spanKey.npages=", t.spanKey.npages)
throw("why does span.npages and treap.ngagesKey do not match?")
}
if t.left != nil && lessThan(t.left.npagesKey, t.left.spanKey) {
throw("t.lessThan(t.left.npagesKey, t.left.spanKey) is not false")
}
if t.right != nil && !lessThan(t.right.npagesKey, t.right.spanKey) {
throw("!t.lessThan(t.left.npagesKey, t.left.spanKey) is not false")
}
}
// insert adds span to the large span treap.
func (root *mTreap) insert(span *mspan) {
npages := span.npages
var last *treapNode
pt := &root.treap
for t := *pt; t != nil; t = *pt {
last = t
if t.npagesKey < npages {
pt = &t.right
} else if t.npagesKey > npages {
pt = &t.left
} else if uintptr(unsafe.Pointer(t.spanKey)) < uintptr(unsafe.Pointer(span)) {
// t.npagesKey == npages, so sort on span addresses.
pt = &t.right
} else if uintptr(unsafe.Pointer(t.spanKey)) > uintptr(unsafe.Pointer(span)) {
pt = &t.left
} else {
throw("inserting span already in treap")
}
}
// Add t as new leaf in tree of span size and unique addrs.
// The balanced tree is a treap using priority as the random heap priority.
// That is, it is a binary tree ordered according to the npagesKey,
// but then among the space of possible binary trees respecting those
// npagesKeys, it is kept balanced on average by maintaining a heap ordering
// on the priority: s.priority <= both s.right.priority and s.right.priority.
// https://en.wikipedia.org/wiki/Treap
// https://faculty.washington.edu/aragon/pubs/rst89.pdf
t := (*treapNode)(mheap_.treapalloc.alloc())
t.init()
t.npagesKey = span.npages
t.priority = fastrand()
t.spanKey = span
t.parent = last
*pt = t // t now at a leaf.
// Rotate up into tree according to priority.
for t.parent != nil && t.parent.priority > t.priority {
if t != nil && t.spanKey.npages != t.npagesKey {
println("runtime: insert t=", t, "t.npagesKey=", t.npagesKey)
println("runtime: t.spanKey=", t.spanKey, "t.spanKey.npages=", t.spanKey.npages)
throw("span and treap sizes do not match?")
}
if t.parent.left == t {
root.rotateRight(t.parent)
} else {
if t.parent.right != t {
throw("treap insert finds a broken treap")
}
root.rotateLeft(t.parent)
}
}
}
func (root *mTreap) removeNode(t *treapNode) {
if t.spanKey.npages != t.npagesKey {
throw("span and treap node npages do not match")
}
// Rotate t down to be leaf of tree for removal, respecting priorities.
for t.right != nil || t.left != nil {
if t.right == nil || t.left != nil && t.left.priority < t.right.priority {
root.rotateRight(t)
} else {
root.rotateLeft(t)
}
}
// Remove t, now a leaf.
if t.parent != nil {
if t.parent.left == t {
t.parent.left = nil
} else {
t.parent.right = nil
}
} else {
root.treap = nil
}
// Return the found treapNode's span after freeing the treapNode.
t.spanKey = nil
t.npagesKey = 0
mheap_.treapalloc.free(unsafe.Pointer(t))
}
// remove searches for, finds, removes from the treap, and returns the smallest
// span that can hold npages. If no span has at least npages return nil.
// This is slightly more complicated than a simple binary tree search
// since if an exact match is not found the next larger node is
// returned.
// If the last node inspected > npagesKey not holding
// a left node (a smaller npages) is the "best fit" node.
func (root *mTreap) remove(npages uintptr) *mspan {
t := root.treap
for t != nil {
if t.spanKey == nil {
throw("treap node with nil spanKey found")
}
if t.npagesKey < npages {
t = t.right
} else if t.left != nil && t.left.npagesKey >= npages {
t = t.left
} else {
result := t.spanKey
root.removeNode(t)
return result
}
}
return nil
}
// removeSpan searches for, finds, deletes span along with
// the associated treap node. If the span is not in the treap
// then t will eventually be set to nil and the t.spanKey
// will throw.
func (root *mTreap) removeSpan(span *mspan) {
npages := span.npages
t := root.treap
for t.spanKey != span {
if t.npagesKey < npages {
t = t.right
} else if t.npagesKey > npages {
t = t.left
} else if uintptr(unsafe.Pointer(t.spanKey)) < uintptr(unsafe.Pointer(span)) {
t = t.right
} else if uintptr(unsafe.Pointer(t.spanKey)) > uintptr(unsafe.Pointer(span)) {
t = t.left
}
}
root.removeNode(t)
}
// scavengetreap visits each node in the treap and scavenges the
// treapNode's span.
func scavengetreap(treap *treapNode, now, limit uint64) uintptr {
if treap == nil {
return 0
}
return scavengeTreapNode(treap, now, limit) +
scavengetreap(treap.left, now, limit) +
scavengetreap(treap.right, now, limit)
}
// rotateLeft rotates the tree rooted at node x.
// turning (x a (y b c)) into (y (x a b) c).
func (root *mTreap) rotateLeft(x *treapNode) {
// p -> (x a (y b c))
p := x.parent
a, y := x.left, x.right
b, c := y.left, y.right
y.left = x
x.parent = y
y.right = c
if c != nil {
c.parent = y
}
x.left = a
if a != nil {
a.parent = x
}
x.right = b
if b != nil {
b.parent = x
}
y.parent = p
if p == nil {
root.treap = y
} else if p.left == x {
p.left = y
} else {
if p.right != x {
throw("large span treap rotateLeft")
}
p.right = y
}
}
// rotateRight rotates the tree rooted at node y.
// turning (y (x a b) c) into (x a (y b c)).
func (root *mTreap) rotateRight(y *treapNode) {
// p -> (y (x a b) c)
p := y.parent
x, c := y.left, y.right
a, b := x.left, x.right
x.left = a
if a != nil {
a.parent = x
}
x.right = y
y.parent = x
y.left = b
if b != nil {
b.parent = y
}
y.right = c
if c != nil {
c.parent = y
}
x.parent = p
if p == nil {
root.treap = x
} else if p.left == y {
p.left = x
} else {
if p.right != y {
throw("large span treap rotateRight")
}
p.right = x
}
}