libgo/go/runtime/mspanset.go - gofrontend - Git at Google

 // Copyright 2020 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.

 package runtime

 import (
 	"internal/cpu"
 	"internal/goarch"
 	"runtime/internal/atomic"
 	"unsafe"
 )

 // A spanSet is a set of *mspans.
 //
 // spanSet is safe for concurrent push and pop operations.
 type spanSet struct {
 	// A spanSet is a two-level data structure consisting of a
 	// growable spine that points to fixed-sized blocks. The spine
 	// can be accessed without locks, but adding a block or
 	// growing it requires taking the spine lock.
 	//
 	// Because each mspan covers at least 8K of heap and takes at
 	// most 8 bytes in the spanSet, the growth of the spine is
 	// quite limited.
 	//
 	// The spine and all blocks are allocated off-heap, which
 	// allows this to be used in the memory manager and avoids the
 	// need for write barriers on all of these. spanSetBlocks are
 	// managed in a pool, though never freed back to the operating
 	// system. We never release spine memory because there could be
 	// concurrent lock-free access and we're likely to reuse it
 	// anyway. (In principle, we could do this during STW.)

 	spineLock mutex
 	spine     unsafe.Pointer // *[N]*spanSetBlock, accessed atomically
 	spineLen  uintptr        // Spine array length, accessed atomically
 	spineCap  uintptr        // Spine array cap, accessed under lock

 	// index is the head and tail of the spanSet in a single field.
 	// The head and the tail both represent an index into the logical
 	// concatenation of all blocks, with the head always behind or
 	// equal to the tail (indicating an empty set). This field is
 	// always accessed atomically.
 	//
 	// The head and the tail are only 32 bits wide, which means we
 	// can only support up to 2^32 pushes before a reset. If every
 	// span in the heap were stored in this set, and each span were
 	// the minimum size (1 runtime page, 8 KiB), then roughly the
 	// smallest heap which would be unrepresentable is 32 TiB in size.
 	index headTailIndex
 }

 const (
 	spanSetBlockEntries = 512 // 4KB on 64-bit
 	spanSetInitSpineCap = 256 // Enough for 1GB heap on 64-bit
 )

 type spanSetBlock struct {
 	// Free spanSetBlocks are managed via a lock-free stack.
 	lfnode

 	// popped is the number of pop operations that have occurred on
 	// this block. This number is used to help determine when a block
 	// may be safely recycled.
 	popped uint32

 	// spans is the set of spans in this block.
 	spans [spanSetBlockEntries]*mspan
 }

 // push adds span s to buffer b. push is safe to call concurrently
 // with other push and pop operations.
 func (b *spanSet) push(s *mspan) {
 	// Obtain our slot.
 	cursor := uintptr(b.index.incTail().tail() - 1)
 	top, bottom := cursor/spanSetBlockEntries, cursor%spanSetBlockEntries

 	// Do we need to add a block?
 	spineLen := atomic.Loaduintptr(&b.spineLen)
 	var block *spanSetBlock
 retry:
 	if top < spineLen {
 		spine := atomic.Loadp(unsafe.Pointer(&b.spine))
 		blockp := add(spine, goarch.PtrSize*top)
 		block = (*spanSetBlock)(atomic.Loadp(blockp))
 	} else {
 		// Add a new block to the spine, potentially growing
 		// the spine.
 		lock(&b.spineLock)
 		// spineLen cannot change until we release the lock,
 		// but may have changed while we were waiting.
 		spineLen = atomic.Loaduintptr(&b.spineLen)
 		if top < spineLen {
 			unlock(&b.spineLock)
 			goto retry
 		}

 		if spineLen == b.spineCap {
 			// Grow the spine.
 			newCap := b.spineCap * 2
 			if newCap == 0 {
 				newCap = spanSetInitSpineCap
 			}
 			newSpine := persistentalloc(newCap*goarch.PtrSize, cpu.CacheLineSize, &memstats.gcMiscSys)
 			if b.spineCap != 0 {
 				// Blocks are allocated off-heap, so
 				// no write barriers.
 				memmove(newSpine, b.spine, b.spineCap*goarch.PtrSize)
 			}
 			// Spine is allocated off-heap, so no write barrier.
 			atomic.StorepNoWB(unsafe.Pointer(&b.spine), newSpine)
 			b.spineCap = newCap
 			// We can't immediately free the old spine
 			// since a concurrent push with a lower index
 			// could still be reading from it. We let it
 			// leak because even a 1TB heap would waste
 			// less than 2MB of memory on old spines. If
 			// this is a problem, we could free old spines
 			// during STW.
 		}

 		// Allocate a new block from the pool.
 		block = spanSetBlockPool.alloc()

 		// Add it to the spine.
 		blockp := add(b.spine, goarch.PtrSize*top)
 		// Blocks are allocated off-heap, so no write barrier.
 		atomic.StorepNoWB(blockp, unsafe.Pointer(block))
 		atomic.Storeuintptr(&b.spineLen, spineLen+1)
 		unlock(&b.spineLock)
 	}

 	// We have a block. Insert the span atomically, since there may be
 	// concurrent readers via the block API.
 	atomic.StorepNoWB(unsafe.Pointer(&block.spans[bottom]), unsafe.Pointer(s))
 }

 // pop removes and returns a span from buffer b, or nil if b is empty.
 // pop is safe to call concurrently with other pop and push operations.
 func (b *spanSet) pop() *mspan {
 	var head, tail uint32
 claimLoop:
 	for {
 		headtail := b.index.load()
 		head, tail = headtail.split()
 		if head >= tail {
 			// The buf is empty, as far as we can tell.
 			return nil
 		}
 		// Check if the head position we want to claim is actually
 		// backed by a block.
 		spineLen := atomic.Loaduintptr(&b.spineLen)
 		if spineLen <= uintptr(head)/spanSetBlockEntries {
 			// We're racing with a spine growth and the allocation of
 			// a new block (and maybe a new spine!), and trying to grab
 			// the span at the index which is currently being pushed.
 			// Instead of spinning, let's just notify the caller that
 			// there's nothing currently here. Spinning on this is
 			// almost definitely not worth it.
 			return nil
 		}
 		// Try to claim the current head by CASing in an updated head.
 		// This may fail transiently due to a push which modifies the
 		// tail, so keep trying while the head isn't changing.
 		want := head
 		for want == head {
 			if b.index.cas(headtail, makeHeadTailIndex(want+1, tail)) {
 				break claimLoop
 			}
 			headtail = b.index.load()
 			head, tail = headtail.split()
 		}
 		// We failed to claim the spot we were after and the head changed,
 		// meaning a popper got ahead of us. Try again from the top because
 		// the buf may not be empty.
 	}
 	top, bottom := head/spanSetBlockEntries, head%spanSetBlockEntries

 	// We may be reading a stale spine pointer, but because the length
 	// grows monotonically and we've already verified it, we'll definitely
 	// be reading from a valid block.
 	spine := atomic.Loadp(unsafe.Pointer(&b.spine))
 	blockp := add(spine, goarch.PtrSize*uintptr(top))

 	// Given that the spine length is correct, we know we will never
 	// see a nil block here, since the length is always updated after
 	// the block is set.
 	block := (*spanSetBlock)(atomic.Loadp(blockp))
 	s := (*mspan)(atomic.Loadp(unsafe.Pointer(&block.spans[bottom])))
 	for s == nil {
 		// We raced with the span actually being set, but given that we
 		// know a block for this span exists, the race window here is
 		// extremely small. Try again.
 		s = (*mspan)(atomic.Loadp(unsafe.Pointer(&block.spans[bottom])))
 	}
 	// Clear the pointer. This isn't strictly necessary, but defensively
 	// avoids accidentally re-using blocks which could lead to memory
 	// corruption. This way, we'll get a nil pointer access instead.
 	atomic.StorepNoWB(unsafe.Pointer(&block.spans[bottom]), nil)

 	// Increase the popped count. If we are the last possible popper
 	// in the block (note that bottom need not equal spanSetBlockEntries-1
 	// due to races) then it's our resposibility to free the block.
 	//
 	// If we increment popped to spanSetBlockEntries, we can be sure that
 	// we're the last popper for this block, and it's thus safe to free it.
 	// Every other popper must have crossed this barrier (and thus finished
 	// popping its corresponding mspan) by the time we get here. Because
 	// we're the last popper, we also don't have to worry about concurrent
 	// pushers (there can't be any). Note that we may not be the popper
 	// which claimed the last slot in the block, we're just the last one
 	// to finish popping.
 	if atomic.Xadd(&block.popped, 1) == spanSetBlockEntries {
 		// Clear the block's pointer.
 		atomic.StorepNoWB(blockp, nil)

 		// Return the block to the block pool.
 		spanSetBlockPool.free(block)
 	}
 	return s
 }

 // reset resets a spanSet which is empty. It will also clean up
 // any left over blocks.
 //
 // Throws if the buf is not empty.
 //
 // reset may not be called concurrently with any other operations
 // on the span set.
 func (b *spanSet) reset() {
 	head, tail := b.index.load().split()
 	if head < tail {
 		print("head = ", head, ", tail = ", tail, "\n")
 		throw("attempt to clear non-empty span set")
 	}
 	top := head / spanSetBlockEntries
 	if uintptr(top) < b.spineLen {
 		// If the head catches up to the tail and the set is empty,
 		// we may not clean up the block containing the head and tail
 		// since it may be pushed into again. In order to avoid leaking
 		// memory since we're going to reset the head and tail, clean
 		// up such a block now, if it exists.
 		blockp := (**spanSetBlock)(add(b.spine, goarch.PtrSize*uintptr(top)))
 		block := *blockp
 		if block != nil {
 			// Sanity check the popped value.
 			if block.popped == 0 {
 				// popped should never be zero because that means we have
 				// pushed at least one value but not yet popped if this
 				// block pointer is not nil.
 				throw("span set block with unpopped elements found in reset")
 			}
 			if block.popped == spanSetBlockEntries {
 				// popped should also never be equal to spanSetBlockEntries
 				// because the last popper should have made the block pointer
 				// in this slot nil.
 				throw("fully empty unfreed span set block found in reset")
 			}

 			// Clear the pointer to the block.
 			atomic.StorepNoWB(unsafe.Pointer(blockp), nil)

 			// Return the block to the block pool.
 			spanSetBlockPool.free(block)
 		}
 	}
 	b.index.reset()
 	atomic.Storeuintptr(&b.spineLen, 0)
 }

 // gccgoAlignment is used to get spanSetBlockPool aligned on a 64-bit
 // boundary on 32-bit x86.
 var gccgoAlignment uint64

 // spanSetBlockPool is a global pool of spanSetBlocks.
 var spanSetBlockPool = (*spanSetBlockAlloc)(unsafe.Pointer(&gccgoAlignment))

 // spanSetBlockAlloc represents a concurrent pool of spanSetBlocks.
 type spanSetBlockAlloc struct {
 	stack lfstack
 }

 // alloc tries to grab a spanSetBlock out of the pool, and if it fails
 // persistentallocs a new one and returns it.
 func (p *spanSetBlockAlloc) alloc() *spanSetBlock {
 	if s := (*spanSetBlock)(p.stack.pop()); s != nil {
 		return s
 	}
 	return (*spanSetBlock)(persistentalloc(unsafe.Sizeof(spanSetBlock{}), cpu.CacheLineSize, &memstats.gcMiscSys))
 }

 // free returns a spanSetBlock back to the pool.
 func (p *spanSetBlockAlloc) free(block *spanSetBlock) {
 	atomic.Store(&block.popped, 0)
 	p.stack.push(&block.lfnode)
 }

 // haidTailIndex represents a combined 32-bit head and 32-bit tail
 // of a queue into a single 64-bit value.
 type headTailIndex uint64

 // makeHeadTailIndex creates a headTailIndex value from a separate
 // head and tail.
 func makeHeadTailIndex(head, tail uint32) headTailIndex {
 	return headTailIndex(uint64(head)<<32 | uint64(tail))
 }

 // head returns the head of a headTailIndex value.
 func (h headTailIndex) head() uint32 {
 	return uint32(h >> 32)
 }

 // tail returns the tail of a headTailIndex value.
 func (h headTailIndex) tail() uint32 {
 	return uint32(h)
 }

 // split splits the headTailIndex value into its parts.
 func (h headTailIndex) split() (head uint32, tail uint32) {
 	return h.head(), h.tail()
 }

 // load atomically reads a headTailIndex value.
 func (h *headTailIndex) load() headTailIndex {
 	return headTailIndex(atomic.Load64((*uint64)(h)))
 }

 // cas atomically compares-and-swaps a headTailIndex value.
 func (h *headTailIndex) cas(old, new headTailIndex) bool {
 	return atomic.Cas64((*uint64)(h), uint64(old), uint64(new))
 }

 // incHead atomically increments the head of a headTailIndex.
 func (h *headTailIndex) incHead() headTailIndex {
 	return headTailIndex(atomic.Xadd64((*uint64)(h), (1 << 32)))
 }

 // decHead atomically decrements the head of a headTailIndex.
 func (h *headTailIndex) decHead() headTailIndex {
 	return headTailIndex(atomic.Xadd64((*uint64)(h), -(1 << 32)))
 }

 // incTail atomically increments the tail of a headTailIndex.
 func (h *headTailIndex) incTail() headTailIndex {
 	ht := headTailIndex(atomic.Xadd64((*uint64)(h), +1))
 	// Check for overflow.
 	if ht.tail() == 0 {
 		print("runtime: head = ", ht.head(), ", tail = ", ht.tail(), "\n")
 		throw("headTailIndex overflow")
 	}
 	return ht
 }

 // reset clears the headTailIndex to (0, 0).
 func (h *headTailIndex) reset() {
 	atomic.Store64((*uint64)(h), 0)
 }
	// Copyright 2020 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.

	package runtime

	import (
	"internal/cpu"
	"internal/goarch"
	"runtime/internal/atomic"
	"unsafe"
	)

	// A spanSet is a set of *mspans.
	//
	// spanSet is safe for concurrent push and pop operations.
	type spanSet struct {
	// A spanSet is a two-level data structure consisting of a
	// growable spine that points to fixed-sized blocks. The spine
	// can be accessed without locks, but adding a block or
	// growing it requires taking the spine lock.
	//
	// Because each mspan covers at least 8K of heap and takes at
	// most 8 bytes in the spanSet, the growth of the spine is
	// quite limited.
	//
	// The spine and all blocks are allocated off-heap, which
	// allows this to be used in the memory manager and avoids the
	// need for write barriers on all of these. spanSetBlocks are
	// managed in a pool, though never freed back to the operating
	// system. We never release spine memory because there could be
	// concurrent lock-free access and we're likely to reuse it
	// anyway. (In principle, we could do this during STW.)

	spineLock mutex
	spine unsafe.Pointer // [N]spanSetBlock, accessed atomically
	spineLen uintptr // Spine array length, accessed atomically
	spineCap uintptr // Spine array cap, accessed under lock

	// index is the head and tail of the spanSet in a single field.
	// The head and the tail both represent an index into the logical
	// concatenation of all blocks, with the head always behind or
	// equal to the tail (indicating an empty set). This field is
	// always accessed atomically.
	//
	// The head and the tail are only 32 bits wide, which means we
	// can only support up to 2^32 pushes before a reset. If every
	// span in the heap were stored in this set, and each span were
	// the minimum size (1 runtime page, 8 KiB), then roughly the
	// smallest heap which would be unrepresentable is 32 TiB in size.
	index headTailIndex
	}

	const (
	spanSetBlockEntries = 512 // 4KB on 64-bit
	spanSetInitSpineCap = 256 // Enough for 1GB heap on 64-bit
	)

	type spanSetBlock struct {
	// Free spanSetBlocks are managed via a lock-free stack.
	lfnode

	// popped is the number of pop operations that have occurred on
	// this block. This number is used to help determine when a block
	// may be safely recycled.
	popped uint32

	// spans is the set of spans in this block.
	spans [spanSetBlockEntries]*mspan
	}

	// push adds span s to buffer b. push is safe to call concurrently
	// with other push and pop operations.
	func (b spanSet) push(s mspan) {
	// Obtain our slot.
	cursor := uintptr(b.index.incTail().tail() - 1)
	top, bottom := cursor/spanSetBlockEntries, cursor%spanSetBlockEntries

	// Do we need to add a block?
	spineLen := atomic.Loaduintptr(&b.spineLen)
	var block *spanSetBlock
	retry:
	if top < spineLen {
	spine := atomic.Loadp(unsafe.Pointer(&b.spine))
	blockp := add(spine, goarch.PtrSize*top)
	block = (*spanSetBlock)(atomic.Loadp(blockp))
	} else {
	// Add a new block to the spine, potentially growing
	// the spine.
	lock(&b.spineLock)
	// spineLen cannot change until we release the lock,
	// but may have changed while we were waiting.
	spineLen = atomic.Loaduintptr(&b.spineLen)
	if top < spineLen {
	unlock(&b.spineLock)
	goto retry
	}

	if spineLen == b.spineCap {
	// Grow the spine.
	newCap := b.spineCap * 2
	if newCap == 0 {
	newCap = spanSetInitSpineCap
	}
	newSpine := persistentalloc(newCap*goarch.PtrSize, cpu.CacheLineSize, &memstats.gcMiscSys)
	if b.spineCap != 0 {
	// Blocks are allocated off-heap, so
	// no write barriers.
	memmove(newSpine, b.spine, b.spineCap*goarch.PtrSize)
	}
	// Spine is allocated off-heap, so no write barrier.
	atomic.StorepNoWB(unsafe.Pointer(&b.spine), newSpine)
	b.spineCap = newCap
	// We can't immediately free the old spine
	// since a concurrent push with a lower index
	// could still be reading from it. We let it
	// leak because even a 1TB heap would waste
	// less than 2MB of memory on old spines. If
	// this is a problem, we could free old spines
	// during STW.
	}

	// Allocate a new block from the pool.
	block = spanSetBlockPool.alloc()

	// Add it to the spine.
	blockp := add(b.spine, goarch.PtrSize*top)
	// Blocks are allocated off-heap, so no write barrier.
	atomic.StorepNoWB(blockp, unsafe.Pointer(block))
	atomic.Storeuintptr(&b.spineLen, spineLen+1)
	unlock(&b.spineLock)
	}

	// We have a block. Insert the span atomically, since there may be
	// concurrent readers via the block API.
	atomic.StorepNoWB(unsafe.Pointer(&block.spans[bottom]), unsafe.Pointer(s))
	}

	// pop removes and returns a span from buffer b, or nil if b is empty.
	// pop is safe to call concurrently with other pop and push operations.
	func (b spanSet) pop() mspan {
	var head, tail uint32
	claimLoop:
	for {
	headtail := b.index.load()
	head, tail = headtail.split()
	if head >= tail {
	// The buf is empty, as far as we can tell.
	return nil
	}
	// Check if the head position we want to claim is actually
	// backed by a block.
	spineLen := atomic.Loaduintptr(&b.spineLen)
	if spineLen <= uintptr(head)/spanSetBlockEntries {
	// We're racing with a spine growth and the allocation of
	// a new block (and maybe a new spine!), and trying to grab
	// the span at the index which is currently being pushed.
	// Instead of spinning, let's just notify the caller that
	// there's nothing currently here. Spinning on this is
	// almost definitely not worth it.
	return nil
	}
	// Try to claim the current head by CASing in an updated head.
	// This may fail transiently due to a push which modifies the
	// tail, so keep trying while the head isn't changing.
	want := head
	for want == head {
	if b.index.cas(headtail, makeHeadTailIndex(want+1, tail)) {
	break claimLoop
	}
	headtail = b.index.load()
	head, tail = headtail.split()
	}
	// We failed to claim the spot we were after and the head changed,
	// meaning a popper got ahead of us. Try again from the top because
	// the buf may not be empty.
	}
	top, bottom := head/spanSetBlockEntries, head%spanSetBlockEntries

	// We may be reading a stale spine pointer, but because the length
	// grows monotonically and we've already verified it, we'll definitely
	// be reading from a valid block.
	spine := atomic.Loadp(unsafe.Pointer(&b.spine))
	blockp := add(spine, goarch.PtrSize*uintptr(top))

	// Given that the spine length is correct, we know we will never
	// see a nil block here, since the length is always updated after
	// the block is set.
	block := (*spanSetBlock)(atomic.Loadp(blockp))
	s := (*mspan)(atomic.Loadp(unsafe.Pointer(&block.spans[bottom])))
	for s == nil {
	// We raced with the span actually being set, but given that we
	// know a block for this span exists, the race window here is
	// extremely small. Try again.
	s = (*mspan)(atomic.Loadp(unsafe.Pointer(&block.spans[bottom])))
	}
	// Clear the pointer. This isn't strictly necessary, but defensively
	// avoids accidentally re-using blocks which could lead to memory
	// corruption. This way, we'll get a nil pointer access instead.
	atomic.StorepNoWB(unsafe.Pointer(&block.spans[bottom]), nil)

	// Increase the popped count. If we are the last possible popper
	// in the block (note that bottom need not equal spanSetBlockEntries-1
	// due to races) then it's our resposibility to free the block.
	//
	// If we increment popped to spanSetBlockEntries, we can be sure that
	// we're the last popper for this block, and it's thus safe to free it.
	// Every other popper must have crossed this barrier (and thus finished
	// popping its corresponding mspan) by the time we get here. Because
	// we're the last popper, we also don't have to worry about concurrent
	// pushers (there can't be any). Note that we may not be the popper
	// which claimed the last slot in the block, we're just the last one
	// to finish popping.
	if atomic.Xadd(&block.popped, 1) == spanSetBlockEntries {
	// Clear the block's pointer.
	atomic.StorepNoWB(blockp, nil)

	// Return the block to the block pool.
	spanSetBlockPool.free(block)
	}
	return s
	}

	// reset resets a spanSet which is empty. It will also clean up
	// any left over blocks.
	//
	// Throws if the buf is not empty.
	//
	// reset may not be called concurrently with any other operations
	// on the span set.
	func (b *spanSet) reset() {
	head, tail := b.index.load().split()
	if head < tail {
	print("head = ", head, ", tail = ", tail, "\n")
	throw("attempt to clear non-empty span set")
	}
	top := head / spanSetBlockEntries
	if uintptr(top) < b.spineLen {
	// If the head catches up to the tail and the set is empty,
	// we may not clean up the block containing the head and tail
	// since it may be pushed into again. In order to avoid leaking
	// memory since we're going to reset the head and tail, clean
	// up such a block now, if it exists.
	blockp := (*spanSetBlock)(add(b.spine, goarch.PtrSizeuintptr(top)))
	block := *blockp
	if block != nil {
	// Sanity check the popped value.
	if block.popped == 0 {
	// popped should never be zero because that means we have
	// pushed at least one value but not yet popped if this
	// block pointer is not nil.
	throw("span set block with unpopped elements found in reset")
	}
	if block.popped == spanSetBlockEntries {
	// popped should also never be equal to spanSetBlockEntries
	// because the last popper should have made the block pointer
	// in this slot nil.
	throw("fully empty unfreed span set block found in reset")
	}

	// Clear the pointer to the block.
	atomic.StorepNoWB(unsafe.Pointer(blockp), nil)

	// Return the block to the block pool.
	spanSetBlockPool.free(block)
	}
	}
	b.index.reset()
	atomic.Storeuintptr(&b.spineLen, 0)
	}

	// gccgoAlignment is used to get spanSetBlockPool aligned on a 64-bit
	// boundary on 32-bit x86.
	var gccgoAlignment uint64

	// spanSetBlockPool is a global pool of spanSetBlocks.
	var spanSetBlockPool = (*spanSetBlockAlloc)(unsafe.Pointer(&gccgoAlignment))

	// spanSetBlockAlloc represents a concurrent pool of spanSetBlocks.
	type spanSetBlockAlloc struct {
	stack lfstack
	}

	// alloc tries to grab a spanSetBlock out of the pool, and if it fails
	// persistentallocs a new one and returns it.
	func (p spanSetBlockAlloc) alloc() spanSetBlock {
	if s := (*spanSetBlock)(p.stack.pop()); s != nil {
	return s
	}
	return (*spanSetBlock)(persistentalloc(unsafe.Sizeof(spanSetBlock{}), cpu.CacheLineSize, &memstats.gcMiscSys))
	}

	// free returns a spanSetBlock back to the pool.
	func (p spanSetBlockAlloc) free(block spanSetBlock) {
	atomic.Store(&block.popped, 0)
	p.stack.push(&block.lfnode)
	}

	// haidTailIndex represents a combined 32-bit head and 32-bit tail
	// of a queue into a single 64-bit value.
	type headTailIndex uint64

	// makeHeadTailIndex creates a headTailIndex value from a separate
	// head and tail.
	func makeHeadTailIndex(head, tail uint32) headTailIndex {
	return headTailIndex(uint64(head)<<32 \| uint64(tail))
	}

	// head returns the head of a headTailIndex value.
	func (h headTailIndex) head() uint32 {
	return uint32(h >> 32)
	}

	// tail returns the tail of a headTailIndex value.
	func (h headTailIndex) tail() uint32 {
	return uint32(h)
	}

	// split splits the headTailIndex value into its parts.
	func (h headTailIndex) split() (head uint32, tail uint32) {
	return h.head(), h.tail()
	}

	// load atomically reads a headTailIndex value.
	func (h *headTailIndex) load() headTailIndex {
	return headTailIndex(atomic.Load64((*uint64)(h)))
	}

	// cas atomically compares-and-swaps a headTailIndex value.
	func (h *headTailIndex) cas(old, new headTailIndex) bool {
	return atomic.Cas64((*uint64)(h), uint64(old), uint64(new))
	}

	// incHead atomically increments the head of a headTailIndex.
	func (h *headTailIndex) incHead() headTailIndex {
	return headTailIndex(atomic.Xadd64((*uint64)(h), (1 << 32)))
	}

	// decHead atomically decrements the head of a headTailIndex.
	func (h *headTailIndex) decHead() headTailIndex {
	return headTailIndex(atomic.Xadd64((*uint64)(h), -(1 << 32)))
	}

	// incTail atomically increments the tail of a headTailIndex.
	func (h *headTailIndex) incTail() headTailIndex {
	ht := headTailIndex(atomic.Xadd64((*uint64)(h), +1))
	// Check for overflow.
	if ht.tail() == 0 {
	print("runtime: head = ", ht.head(), ", tail = ", ht.tail(), "\n")
	throw("headTailIndex overflow")
	}
	return ht
	}

	// reset clears the headTailIndex to (0, 0).
	func (h *headTailIndex) reset() {
	atomic.Store64((*uint64)(h), 0)
	}