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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) pred() *treapNode {
if t.left != nil {
// If it has a left child, its predecessor will be
// its right most left (grand)child.
t = t.left
for t.right != nil {
t = t.right
}
return t
}
// If it has no left child, its predecessor will be
// the first grandparent who's right child is its
// ancestor.
//
// We compute this by walking up the treap until the
// current node's parent is its parent's right child.
//
// If we find at any point walking up the treap
// that the current node doesn't have a parent,
// we've hit the root. This means that t is already
// the left-most node in the treap and therefore
// has no predecessor.
for t.parent != nil && t.parent.right != t {
if t.parent.left != t {
println("runtime: predecessor t=", t, "t.spanKey=", t.spanKey)
throw("node is not its parent's child")
}
t = t.parent
}
return t.parent
}
func (t *treapNode) succ() *treapNode {
if t.right != nil {
// If it has a right child, its successor will be
// its left-most right (grand)child.
t = t.right
for t.left != nil {
t = t.left
}
return t
}
// See pred.
for t.parent != nil && t.parent.left != t {
if t.parent.right != t {
println("runtime: predecessor t=", t, "t.spanKey=", t.spanKey)
throw("node is not its parent's child")
}
t = t.parent
}
return t.parent
}
// 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 t.spanKey.base() < s.base()
}
if t == nil {
return
}
if t.spanKey.next != nil || t.spanKey.prev != nil || t.spanKey.list != nil {
throw("span may be on an mSpanList while simultaneously in the treap")
}
if t.spanKey.npages != t.npagesKey {
println("runtime: checkTreapNode treapNode t=", t, " t.npagesKey=", t.npagesKey,
"t.spanKey.npages=", t.spanKey.npages)
throw("span.npages and treap.npagesKey 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")
}
}
// treapIter is a bidirectional iterator type which may be used to iterate over a
// an mTreap in-order forwards (increasing order) or backwards (decreasing order).
// Its purpose is to hide details about the treap from users when trying to iterate
// over it.
//
// To create iterators over the treap, call start or end on an mTreap.
type treapIter struct {
t *treapNode
}
// span returns the span at the current position in the treap.
// If the treap is not valid, span will panic.
func (i *treapIter) span() *mspan {
return i.t.spanKey
}
// valid returns whether the iterator represents a valid position
// in the mTreap.
func (i *treapIter) valid() bool {
return i.t != nil
}
// next moves the iterator forward by one. Once the iterator
// ceases to be valid, calling next will panic.
func (i treapIter) next() treapIter {
i.t = i.t.succ()
return i
}
// prev moves the iterator backwards by one. Once the iterator
// ceases to be valid, calling prev will panic.
func (i treapIter) prev() treapIter {
i.t = i.t.pred()
return i
}
// start returns an iterator which points to the start of the treap (the
// left-most node in the treap).
func (root *mTreap) start() treapIter {
t := root.treap
if t == nil {
return treapIter{}
}
for t.left != nil {
t = t.left
}
return treapIter{t: t}
}
// end returns an iterator which points to the end of the treap (the
// right-most node in the treap).
func (root *mTreap) end() treapIter {
t := root.treap
if t == nil {
return treapIter{}
}
for t.right != nil {
t = t.right
}
return treapIter{t: t}
}
// 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 t.spanKey.base() < span.base() {
// t.npagesKey == npages, so sort on span addresses.
pt = &t.right
} else if t.spanKey.base() > span.base() {
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.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.
mheap_.treapalloc.free(unsafe.Pointer(t))
}
// find searches for, finds, and returns the treap node containing the
// smallest span that can hold npages. If no span has at least npages
// it returns nil.
// This is a simple binary tree search that tracks the best-fit node found
// so far. The best-fit node is guaranteed to be on the path to a
// (maybe non-existent) lowest-base exact match.
func (root *mTreap) find(npages uintptr) *treapNode {
var best *treapNode
t := root.treap
for t != nil {
if t.spanKey == nil {
throw("treap node with nil spanKey found")
}
// If we found an exact match, try to go left anyway. There could be
// a span there with a lower base address.
//
// Don't bother checking nil-ness of left and right here; even if t
// becomes nil, we already know the other path had nothing better for
// us anyway.
if t.npagesKey >= npages {
best = t
t = t.left
} else {
t = t.right
}
}
return best
}
// 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 t.spanKey.base() < span.base() {
t = t.right
} else if t.spanKey.base() > span.base() {
t = t.left
}
}
root.removeNode(t)
}
// erase removes the element referred to by the current position of the
// iterator. This operation consumes the given iterator, so it should no
// longer be used. It is up to the caller to get the next or previous
// iterator before calling erase, if need be.
func (root *mTreap) erase(i treapIter) {
root.removeNode(i.t)
}
// 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
}
}