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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
+// http://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 keep tree probablistically 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
+ // http://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) *mspan {
+ if t.spanKey.npages != t.npagesKey {
+ throw("span and treap node npages do not match")
+ }
+ result := t.spanKey
+
+ // 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))
+ return result
+}
+
+// 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
+ }
+}