src/runtime/mranges.go - go - Git at Google

 // Copyright 2019 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.

 // Address range data structure.
 //
 // This file contains an implementation of a data structure which
 // manages ordered address ranges.

 package runtime

 import (
 	"runtime/internal/sys"
 	"unsafe"
 )

 // addrRange represents a region of address space.
 //
 // An addrRange must never span a gap in the address space.
 type addrRange struct {
 	// base and limit together represent the region of address space
 	// [base, limit). That is, base is inclusive, limit is exclusive.
 	// These are address over an offset view of the address space on
 	// platforms with a segmented address space, that is, on platforms
 	// where arenaBaseOffset != 0.
 	base, limit offAddr
 }

 // makeAddrRange creates a new address range from two virtual addresses.
 //
 // Throws if the base and limit are not in the same memory segment.
 func makeAddrRange(base, limit uintptr) addrRange {
 	r := addrRange{offAddr{base}, offAddr{limit}}
 	if (base-arenaBaseOffset >= base) != (limit-arenaBaseOffset >= limit) {
 		throw("addr range base and limit are not in the same memory segment")
 	}
 	return r
 }

 // size returns the size of the range represented in bytes.
 func (a addrRange) size() uintptr {
 	if !a.base.lessThan(a.limit) {
 		return 0
 	}
 	// Subtraction is safe because limit and base must be in the same
 	// segment of the address space.
 	return a.limit.diff(a.base)
 }

 // contains returns whether or not the range contains a given address.
 func (a addrRange) contains(addr uintptr) bool {
 	return a.base.lessEqual(offAddr{addr}) && (offAddr{addr}).lessThan(a.limit)
 }

 // subtract takes the addrRange toPrune and cuts out any overlap with
 // from, then returns the new range. subtract assumes that a and b
 // either don't overlap at all, only overlap on one side, or are equal.
 // If b is strictly contained in a, thus forcing a split, it will throw.
 func (a addrRange) subtract(b addrRange) addrRange {
 	if b.base.lessEqual(a.base) && a.limit.lessEqual(b.limit) {
 		return addrRange{}
 	} else if a.base.lessThan(b.base) && b.limit.lessThan(a.limit) {
 		throw("bad prune")
 	} else if b.limit.lessThan(a.limit) && a.base.lessThan(b.limit) {
 		a.base = b.limit
 	} else if a.base.lessThan(b.base) && b.base.lessThan(a.limit) {
 		a.limit = b.base
 	}
 	return a
 }

 // removeGreaterEqual removes all addresses in a greater than or equal
 // to addr and returns the new range.
 func (a addrRange) removeGreaterEqual(addr uintptr) addrRange {
 	if (offAddr{addr}).lessEqual(a.base) {
 		return addrRange{}
 	}
 	if a.limit.lessEqual(offAddr{addr}) {
 		return a
 	}
 	return makeAddrRange(a.base.addr(), addr)
 }

 var (
 	// minOffAddr is the minimum address in the offset space, and
 	// it corresponds to the virtual address arenaBaseOffset.
 	minOffAddr = offAddr{arenaBaseOffset}

 	// maxOffAddr is the maximum address in the offset address
 	// space. It corresponds to the highest virtual address representable
 	// by the page alloc chunk and heap arena maps.
 	maxOffAddr = offAddr{(((1 << heapAddrBits) - 1) + arenaBaseOffset) & uintptrMask}
 )

 // offAddr represents an address in a contiguous view
 // of the address space on systems where the address space is
 // segmented. On other systems, it's just a normal address.
 type offAddr struct {
 	// a is just the virtual address, but should never be used
 	// directly. Call addr() to get this value instead.
 	a uintptr
 }

 // add adds a uintptr offset to the offAddr.
 func (l offAddr) add(bytes uintptr) offAddr {
 	return offAddr{a: l.a + bytes}
 }

 // sub subtracts a uintptr offset from the offAddr.
 func (l offAddr) sub(bytes uintptr) offAddr {
 	return offAddr{a: l.a - bytes}
 }

 // diff returns the amount of bytes in between the
 // two offAddrs.
 func (l1 offAddr) diff(l2 offAddr) uintptr {
 	return l1.a - l2.a
 }

 // lessThan returns true if l1 is less than l2 in the offset
 // address space.
 func (l1 offAddr) lessThan(l2 offAddr) bool {
 	return (l1.a - arenaBaseOffset) < (l2.a - arenaBaseOffset)
 }

 // lessEqual returns true if l1 is less than or equal to l2 in
 // the offset address space.
 func (l1 offAddr) lessEqual(l2 offAddr) bool {
 	return (l1.a - arenaBaseOffset) <= (l2.a - arenaBaseOffset)
 }

 // equal returns true if the two offAddr values are equal.
 func (l1 offAddr) equal(l2 offAddr) bool {
 	// No need to compare in the offset space, it
 	// means the same thing.
 	return l1 == l2
 }

 // addr returns the virtual address for this offset address.
 func (l offAddr) addr() uintptr {
 	return l.a
 }

 // addrRanges is a data structure holding a collection of ranges of
 // address space.
 //
 // The ranges are coalesced eagerly to reduce the
 // number ranges it holds.
 //
 // The slice backing store for this field is persistentalloc'd
 // and thus there is no way to free it.
 //
 // addrRanges is not thread-safe.
 type addrRanges struct {
 	// ranges is a slice of ranges sorted by base.
 	ranges []addrRange

 	// totalBytes is the total amount of address space in bytes counted by
 	// this addrRanges.
 	totalBytes uintptr

 	// sysStat is the stat to track allocations by this type
 	sysStat *sysMemStat
 }

 func (a *addrRanges) init(sysStat *sysMemStat) {
 	ranges := (*notInHeapSlice)(unsafe.Pointer(&a.ranges))
 	ranges.len = 0
 	ranges.cap = 16
 	ranges.array = (*notInHeap)(persistentalloc(unsafe.Sizeof(addrRange{})*uintptr(ranges.cap), sys.PtrSize, sysStat))
 	a.sysStat = sysStat
 	a.totalBytes = 0
 }

 // findSucc returns the first index in a such that addr is
 // less than the base of the addrRange at that index.
 func (a *addrRanges) findSucc(addr uintptr) int {
 	base := offAddr{addr}

 	// Narrow down the search space via a binary search
 	// for large addrRanges until we have at most iterMax
 	// candidates left.
 	const iterMax = 8
 	bot, top := 0, len(a.ranges)
 	for top-bot > iterMax {
 		i := ((top - bot) / 2) + bot
 		if a.ranges[i].contains(base.addr()) {
 			// a.ranges[i] contains base, so
 			// its successor is the next index.
 			return i + 1
 		}
 		if base.lessThan(a.ranges[i].base) {
 			// In this case i might actually be
 			// the successor, but we can't be sure
 			// until we check the ones before it.
 			top = i
 		} else {
 			// In this case we know base is
 			// greater than or equal to a.ranges[i].limit-1,
 			// so i is definitely not the successor.
 			// We already checked i, so pick the next
 			// one.
 			bot = i + 1
 		}
 	}
 	// There are top-bot candidates left, so
 	// iterate over them and find the first that
 	// base is strictly less than.
 	for i := bot; i < top; i++ {
 		if base.lessThan(a.ranges[i].base) {
 			return i
 		}
 	}
 	return top
 }

 // findAddrGreaterEqual returns the smallest address represented by a
 // that is >= addr. Thus, if the address is represented by a,
 // then it returns addr. The second return value indicates whether
 // such an address exists for addr in a. That is, if addr is larger than
 // any address known to a, the second return value will be false.
 func (a *addrRanges) findAddrGreaterEqual(addr uintptr) (uintptr, bool) {
 	i := a.findSucc(addr)
 	if i == 0 {
 		return a.ranges[0].base.addr(), true
 	}
 	if a.ranges[i-1].contains(addr) {
 		return addr, true
 	}
 	if i < len(a.ranges) {
 		return a.ranges[i].base.addr(), true
 	}
 	return 0, false
 }

 // contains returns true if a covers the address addr.
 func (a *addrRanges) contains(addr uintptr) bool {
 	i := a.findSucc(addr)
 	if i == 0 {
 		return false
 	}
 	return a.ranges[i-1].contains(addr)
 }

 // add inserts a new address range to a.
 //
 // r must not overlap with any address range in a and r.size() must be > 0.
 func (a *addrRanges) add(r addrRange) {
 	// The copies in this function are potentially expensive, but this data
 	// structure is meant to represent the Go heap. At worst, copying this
 	// would take ~160µs assuming a conservative copying rate of 25 GiB/s (the
 	// copy will almost never trigger a page fault) for a 1 TiB heap with 4 MiB
 	// arenas which is completely discontiguous. ~160µs is still a lot, but in
 	// practice most platforms have 64 MiB arenas (which cuts this by a factor
 	// of 16) and Go heaps are usually mostly contiguous, so the chance that
 	// an addrRanges even grows to that size is extremely low.

 	// An empty range has no effect on the set of addresses represented
 	// by a, but passing a zero-sized range is almost always a bug.
 	if r.size() == 0 {
 		print("runtime: range = {", hex(r.base.addr()), ", ", hex(r.limit.addr()), "}\n")
 		throw("attempted to add zero-sized address range")
 	}
 	// Because we assume r is not currently represented in a,
 	// findSucc gives us our insertion index.
 	i := a.findSucc(r.base.addr())
 	coalescesDown := i > 0 && a.ranges[i-1].limit.equal(r.base)
 	coalescesUp := i < len(a.ranges) && r.limit.equal(a.ranges[i].base)
 	if coalescesUp && coalescesDown {
 		// We have neighbors and they both border us.
 		// Merge a.ranges[i-1], r, and a.ranges[i] together into a.ranges[i-1].
 		a.ranges[i-1].limit = a.ranges[i].limit

 		// Delete a.ranges[i].
 		copy(a.ranges[i:], a.ranges[i+1:])
 		a.ranges = a.ranges[:len(a.ranges)-1]
 	} else if coalescesDown {
 		// We have a neighbor at a lower address only and it borders us.
 		// Merge the new space into a.ranges[i-1].
 		a.ranges[i-1].limit = r.limit
 	} else if coalescesUp {
 		// We have a neighbor at a higher address only and it borders us.
 		// Merge the new space into a.ranges[i].
 		a.ranges[i].base = r.base
 	} else {
 		// We may or may not have neighbors which don't border us.
 		// Add the new range.
 		if len(a.ranges)+1 > cap(a.ranges) {
 			// Grow the array. Note that this leaks the old array, but since
 			// we're doubling we have at most 2x waste. For a 1 TiB heap and
 			// 4 MiB arenas which are all discontiguous (both very conservative
 			// assumptions), this would waste at most 4 MiB of memory.
 			oldRanges := a.ranges
 			ranges := (*notInHeapSlice)(unsafe.Pointer(&a.ranges))
 			ranges.len = len(oldRanges) + 1
 			ranges.cap = cap(oldRanges) * 2
 			ranges.array = (*notInHeap)(persistentalloc(unsafe.Sizeof(addrRange{})*uintptr(ranges.cap), sys.PtrSize, a.sysStat))

 			// Copy in the old array, but make space for the new range.
 			copy(a.ranges[:i], oldRanges[:i])
 			copy(a.ranges[i+1:], oldRanges[i:])
 		} else {
 			a.ranges = a.ranges[:len(a.ranges)+1]
 			copy(a.ranges[i+1:], a.ranges[i:])
 		}
 		a.ranges[i] = r
 	}
 	a.totalBytes += r.size()
 }

 // removeLast removes and returns the highest-addressed contiguous range
 // of a, or the last nBytes of that range, whichever is smaller. If a is
 // empty, it returns an empty range.
 func (a *addrRanges) removeLast(nBytes uintptr) addrRange {
 	if len(a.ranges) == 0 {
 		return addrRange{}
 	}
 	r := a.ranges[len(a.ranges)-1]
 	size := r.size()
 	if size > nBytes {
 		newEnd := r.limit.sub(nBytes)
 		a.ranges[len(a.ranges)-1].limit = newEnd
 		a.totalBytes -= nBytes
 		return addrRange{newEnd, r.limit}
 	}
 	a.ranges = a.ranges[:len(a.ranges)-1]
 	a.totalBytes -= size
 	return r
 }

 // removeGreaterEqual removes the ranges of a which are above addr, and additionally
 // splits any range containing addr.
 func (a *addrRanges) removeGreaterEqual(addr uintptr) {
 	pivot := a.findSucc(addr)
 	if pivot == 0 {
 		// addr is before all ranges in a.
 		a.totalBytes = 0
 		a.ranges = a.ranges[:0]
 		return
 	}
 	removed := uintptr(0)
 	for _, r := range a.ranges[pivot:] {
 		removed += r.size()
 	}
 	if r := a.ranges[pivot-1]; r.contains(addr) {
 		removed += r.size()
 		r = r.removeGreaterEqual(addr)
 		if r.size() == 0 {
 			pivot--
 		} else {
 			removed -= r.size()
 			a.ranges[pivot-1] = r
 		}
 	}
 	a.ranges = a.ranges[:pivot]
 	a.totalBytes -= removed
 }

 // cloneInto makes a deep clone of a's state into b, re-using
 // b's ranges if able.
 func (a *addrRanges) cloneInto(b *addrRanges) {
 	if len(a.ranges) > cap(b.ranges) {
 		// Grow the array.
 		ranges := (*notInHeapSlice)(unsafe.Pointer(&b.ranges))
 		ranges.len = 0
 		ranges.cap = cap(a.ranges)
 		ranges.array = (*notInHeap)(persistentalloc(unsafe.Sizeof(addrRange{})*uintptr(ranges.cap), sys.PtrSize, b.sysStat))
 	}
 	b.ranges = b.ranges[:len(a.ranges)]
 	b.totalBytes = a.totalBytes
 	copy(b.ranges, a.ranges)
 }
	// Copyright 2019 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.

	// Address range data structure.
	//
	// This file contains an implementation of a data structure which
	// manages ordered address ranges.

	package runtime

	import (
	"runtime/internal/sys"
	"unsafe"
	)

	// addrRange represents a region of address space.
	//
	// An addrRange must never span a gap in the address space.
	type addrRange struct {
	// base and limit together represent the region of address space
	// [base, limit). That is, base is inclusive, limit is exclusive.
	// These are address over an offset view of the address space on
	// platforms with a segmented address space, that is, on platforms
	// where arenaBaseOffset != 0.
	base, limit offAddr
	}

	// makeAddrRange creates a new address range from two virtual addresses.
	//
	// Throws if the base and limit are not in the same memory segment.
	func makeAddrRange(base, limit uintptr) addrRange {
	r := addrRange{offAddr{base}, offAddr{limit}}
	if (base-arenaBaseOffset >= base) != (limit-arenaBaseOffset >= limit) {
	throw("addr range base and limit are not in the same memory segment")
	}
	return r
	}

	// size returns the size of the range represented in bytes.
	func (a addrRange) size() uintptr {
	if !a.base.lessThan(a.limit) {
	return 0
	}
	// Subtraction is safe because limit and base must be in the same
	// segment of the address space.
	return a.limit.diff(a.base)
	}

	// contains returns whether or not the range contains a given address.
	func (a addrRange) contains(addr uintptr) bool {
	return a.base.lessEqual(offAddr{addr}) && (offAddr{addr}).lessThan(a.limit)
	}

	// subtract takes the addrRange toPrune and cuts out any overlap with
	// from, then returns the new range. subtract assumes that a and b
	// either don't overlap at all, only overlap on one side, or are equal.
	// If b is strictly contained in a, thus forcing a split, it will throw.
	func (a addrRange) subtract(b addrRange) addrRange {
	if b.base.lessEqual(a.base) && a.limit.lessEqual(b.limit) {
	return addrRange{}
	} else if a.base.lessThan(b.base) && b.limit.lessThan(a.limit) {
	throw("bad prune")
	} else if b.limit.lessThan(a.limit) && a.base.lessThan(b.limit) {
	a.base = b.limit
	} else if a.base.lessThan(b.base) && b.base.lessThan(a.limit) {
	a.limit = b.base
	}
	return a
	}

	// removeGreaterEqual removes all addresses in a greater than or equal
	// to addr and returns the new range.
	func (a addrRange) removeGreaterEqual(addr uintptr) addrRange {
	if (offAddr{addr}).lessEqual(a.base) {
	return addrRange{}
	}
	if a.limit.lessEqual(offAddr{addr}) {
	return a
	}
	return makeAddrRange(a.base.addr(), addr)
	}

	var (
	// minOffAddr is the minimum address in the offset space, and
	// it corresponds to the virtual address arenaBaseOffset.
	minOffAddr = offAddr{arenaBaseOffset}

	// maxOffAddr is the maximum address in the offset address
	// space. It corresponds to the highest virtual address representable
	// by the page alloc chunk and heap arena maps.
	maxOffAddr = offAddr{(((1 << heapAddrBits) - 1) + arenaBaseOffset) & uintptrMask}
	)

	// offAddr represents an address in a contiguous view
	// of the address space on systems where the address space is
	// segmented. On other systems, it's just a normal address.
	type offAddr struct {
	// a is just the virtual address, but should never be used
	// directly. Call addr() to get this value instead.
	a uintptr
	}

	// add adds a uintptr offset to the offAddr.
	func (l offAddr) add(bytes uintptr) offAddr {
	return offAddr{a: l.a + bytes}
	}

	// sub subtracts a uintptr offset from the offAddr.
	func (l offAddr) sub(bytes uintptr) offAddr {
	return offAddr{a: l.a - bytes}
	}

	// diff returns the amount of bytes in between the
	// two offAddrs.
	func (l1 offAddr) diff(l2 offAddr) uintptr {
	return l1.a - l2.a
	}

	// lessThan returns true if l1 is less than l2 in the offset
	// address space.
	func (l1 offAddr) lessThan(l2 offAddr) bool {
	return (l1.a - arenaBaseOffset) < (l2.a - arenaBaseOffset)
	}

	// lessEqual returns true if l1 is less than or equal to l2 in
	// the offset address space.
	func (l1 offAddr) lessEqual(l2 offAddr) bool {
	return (l1.a - arenaBaseOffset) <= (l2.a - arenaBaseOffset)
	}

	// equal returns true if the two offAddr values are equal.
	func (l1 offAddr) equal(l2 offAddr) bool {
	// No need to compare in the offset space, it
	// means the same thing.
	return l1 == l2
	}

	// addr returns the virtual address for this offset address.
	func (l offAddr) addr() uintptr {
	return l.a
	}

	// addrRanges is a data structure holding a collection of ranges of
	// address space.
	//
	// The ranges are coalesced eagerly to reduce the
	// number ranges it holds.
	//
	// The slice backing store for this field is persistentalloc'd
	// and thus there is no way to free it.
	//
	// addrRanges is not thread-safe.
	type addrRanges struct {
	// ranges is a slice of ranges sorted by base.
	ranges []addrRange

	// totalBytes is the total amount of address space in bytes counted by
	// this addrRanges.
	totalBytes uintptr

	// sysStat is the stat to track allocations by this type
	sysStat *sysMemStat
	}

	func (a addrRanges) init(sysStat sysMemStat) {
	ranges := (*notInHeapSlice)(unsafe.Pointer(&a.ranges))
	ranges.len = 0
	ranges.cap = 16
	ranges.array = (notInHeap)(persistentalloc(unsafe.Sizeof(addrRange{})uintptr(ranges.cap), sys.PtrSize, sysStat))
	a.sysStat = sysStat
	a.totalBytes = 0
	}

	// findSucc returns the first index in a such that addr is
	// less than the base of the addrRange at that index.
	func (a *addrRanges) findSucc(addr uintptr) int {
	base := offAddr{addr}

	// Narrow down the search space via a binary search
	// for large addrRanges until we have at most iterMax
	// candidates left.
	const iterMax = 8
	bot, top := 0, len(a.ranges)
	for top-bot > iterMax {
	i := ((top - bot) / 2) + bot
	if a.ranges[i].contains(base.addr()) {
	// a.ranges[i] contains base, so
	// its successor is the next index.
	return i + 1
	}
	if base.lessThan(a.ranges[i].base) {
	// In this case i might actually be
	// the successor, but we can't be sure
	// until we check the ones before it.
	top = i
	} else {
	// In this case we know base is
	// greater than or equal to a.ranges[i].limit-1,
	// so i is definitely not the successor.
	// We already checked i, so pick the next
	// one.
	bot = i + 1
	}
	}
	// There are top-bot candidates left, so
	// iterate over them and find the first that
	// base is strictly less than.
	for i := bot; i < top; i++ {
	if base.lessThan(a.ranges[i].base) {
	return i
	}
	}
	return top
	}

	// findAddrGreaterEqual returns the smallest address represented by a
	// that is >= addr. Thus, if the address is represented by a,
	// then it returns addr. The second return value indicates whether
	// such an address exists for addr in a. That is, if addr is larger than
	// any address known to a, the second return value will be false.
	func (a *addrRanges) findAddrGreaterEqual(addr uintptr) (uintptr, bool) {
	i := a.findSucc(addr)
	if i == 0 {
	return a.ranges[0].base.addr(), true
	}
	if a.ranges[i-1].contains(addr) {
	return addr, true
	}
	if i < len(a.ranges) {
	return a.ranges[i].base.addr(), true
	}
	return 0, false
	}

	// contains returns true if a covers the address addr.
	func (a *addrRanges) contains(addr uintptr) bool {
	i := a.findSucc(addr)
	if i == 0 {
	return false
	}
	return a.ranges[i-1].contains(addr)
	}

	// add inserts a new address range to a.
	//
	// r must not overlap with any address range in a and r.size() must be > 0.
	func (a *addrRanges) add(r addrRange) {
	// The copies in this function are potentially expensive, but this data
	// structure is meant to represent the Go heap. At worst, copying this
	// would take ~160µs assuming a conservative copying rate of 25 GiB/s (the
	// copy will almost never trigger a page fault) for a 1 TiB heap with 4 MiB
	// arenas which is completely discontiguous. ~160µs is still a lot, but in
	// practice most platforms have 64 MiB arenas (which cuts this by a factor
	// of 16) and Go heaps are usually mostly contiguous, so the chance that
	// an addrRanges even grows to that size is extremely low.

	// An empty range has no effect on the set of addresses represented
	// by a, but passing a zero-sized range is almost always a bug.
	if r.size() == 0 {
	print("runtime: range = {", hex(r.base.addr()), ", ", hex(r.limit.addr()), "}\n")
	throw("attempted to add zero-sized address range")
	}
	// Because we assume r is not currently represented in a,
	// findSucc gives us our insertion index.
	i := a.findSucc(r.base.addr())
	coalescesDown := i > 0 && a.ranges[i-1].limit.equal(r.base)
	coalescesUp := i < len(a.ranges) && r.limit.equal(a.ranges[i].base)
	if coalescesUp && coalescesDown {
	// We have neighbors and they both border us.
	// Merge a.ranges[i-1], r, and a.ranges[i] together into a.ranges[i-1].
	a.ranges[i-1].limit = a.ranges[i].limit

	// Delete a.ranges[i].
	copy(a.ranges[i:], a.ranges[i+1:])
	a.ranges = a.ranges[:len(a.ranges)-1]
	} else if coalescesDown {
	// We have a neighbor at a lower address only and it borders us.
	// Merge the new space into a.ranges[i-1].
	a.ranges[i-1].limit = r.limit
	} else if coalescesUp {
	// We have a neighbor at a higher address only and it borders us.
	// Merge the new space into a.ranges[i].
	a.ranges[i].base = r.base
	} else {
	// We may or may not have neighbors which don't border us.
	// Add the new range.
	if len(a.ranges)+1 > cap(a.ranges) {
	// Grow the array. Note that this leaks the old array, but since
	// we're doubling we have at most 2x waste. For a 1 TiB heap and
	// 4 MiB arenas which are all discontiguous (both very conservative
	// assumptions), this would waste at most 4 MiB of memory.
	oldRanges := a.ranges
	ranges := (*notInHeapSlice)(unsafe.Pointer(&a.ranges))
	ranges.len = len(oldRanges) + 1
	ranges.cap = cap(oldRanges) * 2
	ranges.array = (notInHeap)(persistentalloc(unsafe.Sizeof(addrRange{})uintptr(ranges.cap), sys.PtrSize, a.sysStat))

	// Copy in the old array, but make space for the new range.
	copy(a.ranges[:i], oldRanges[:i])
	copy(a.ranges[i+1:], oldRanges[i:])
	} else {
	a.ranges = a.ranges[:len(a.ranges)+1]
	copy(a.ranges[i+1:], a.ranges[i:])
	}
	a.ranges[i] = r
	}
	a.totalBytes += r.size()
	}

	// removeLast removes and returns the highest-addressed contiguous range
	// of a, or the last nBytes of that range, whichever is smaller. If a is
	// empty, it returns an empty range.
	func (a *addrRanges) removeLast(nBytes uintptr) addrRange {
	if len(a.ranges) == 0 {
	return addrRange{}
	}
	r := a.ranges[len(a.ranges)-1]
	size := r.size()
	if size > nBytes {
	newEnd := r.limit.sub(nBytes)
	a.ranges[len(a.ranges)-1].limit = newEnd
	a.totalBytes -= nBytes
	return addrRange{newEnd, r.limit}
	}
	a.ranges = a.ranges[:len(a.ranges)-1]
	a.totalBytes -= size
	return r
	}

	// removeGreaterEqual removes the ranges of a which are above addr, and additionally
	// splits any range containing addr.
	func (a *addrRanges) removeGreaterEqual(addr uintptr) {
	pivot := a.findSucc(addr)
	if pivot == 0 {
	// addr is before all ranges in a.
	a.totalBytes = 0
	a.ranges = a.ranges[:0]
	return
	}
	removed := uintptr(0)
	for _, r := range a.ranges[pivot:] {
	removed += r.size()
	}
	if r := a.ranges[pivot-1]; r.contains(addr) {
	removed += r.size()
	r = r.removeGreaterEqual(addr)
	if r.size() == 0 {
	pivot--
	} else {
	removed -= r.size()
	a.ranges[pivot-1] = r
	}
	}
	a.ranges = a.ranges[:pivot]
	a.totalBytes -= removed
	}

	// cloneInto makes a deep clone of a's state into b, re-using
	// b's ranges if able.
	func (a addrRanges) cloneInto(b addrRanges) {
	if len(a.ranges) > cap(b.ranges) {
	// Grow the array.
	ranges := (*notInHeapSlice)(unsafe.Pointer(&b.ranges))
	ranges.len = 0
	ranges.cap = cap(a.ranges)
	ranges.array = (notInHeap)(persistentalloc(unsafe.Sizeof(addrRange{})uintptr(ranges.cap), sys.PtrSize, b.sysStat))
	}
	b.ranges = b.ranges[:len(a.ranges)]
	b.totalBytes = a.totalBytes
	copy(b.ranges, a.ranges)
	}