internal/gocore/object.go - debug - Git at Google

 // Copyright 2017 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 gocore

 import (
 	"math/bits"
 	"strings"

 	"golang.org/x/debug/internal/core"
 )

 // An Object represents a single reachable object in the Go heap.
 // Unreachable (garbage) objects are not represented as Objects.
 type Object core.Address

 // markObjects finds all the live objects in the heap and marks them
 // in the p.heapInfo mark fields.
 func (p *Process) markObjects() {
 	ptrSize := p.proc.PtrSize()

 	// number of live objects found so far
 	n := 0
 	// total size of live objects
 	var live int64

 	var q []Object

 	// Function to call when we find a new pointer.
 	add := func(x core.Address) {
 		h := p.findHeapInfo(x)
 		if h == nil { // not in heap or not in a valid span
 			// Invalid spans can happen with intra-stack pointers.
 			return
 		}
 		// Round down to object start.
 		x = h.base.Add(x.Sub(h.base) / h.size * h.size)
 		// Object start may map to a different info. Reload heap info.
 		h = p.findHeapInfo(x)
 		// Find mark bit
 		b := uint64(x) % heapInfoSize / 8
 		if h.mark&(uint64(1)<<b) != 0 { // already found
 			return
 		}
 		h.mark |= uint64(1) << b
 		n++
 		live += h.size
 		q = append(q, Object(x))
 	}

 	// Start with scanning all the roots.
 	// Note that we don't just use the DWARF roots, just in case DWARF isn't complete.
 	// Instead we use exactly what the runtime uses.

 	// Goroutine roots
 	for _, g := range p.goroutines {
 		for _, f := range g.frames {
 			for a := range f.Live {
 				add(p.proc.ReadPtr(a))
 			}
 		}
 	}

 	// Global roots
 	for _, m := range p.modules {
 		for _, s := range [2]string{"data", "bss"} {
 			min := core.Address(m.r.Field(s).Uintptr())
 			max := core.Address(m.r.Field("e" + s).Uintptr())
 			gc := m.r.Field("gc" + s + "mask").Field("bytedata").Address()
 			num := max.Sub(min) / ptrSize
 			for i := int64(0); i < num; i++ {
 				if p.proc.ReadUint8(gc.Add(i/8))>>uint(i%8)&1 != 0 {
 					add(p.proc.ReadPtr(min.Add(i * ptrSize)))
 				}
 			}
 		}
 	}

 	// Finalizers
 	for _, r := range p.globals {
 		if !strings.HasPrefix(r.Name, "finalizer for ") {
 			continue
 		}
 		for _, f := range r.Type.Fields {
 			if f.Type.Kind == KindPtr {
 				add(p.proc.ReadPtr(r.Addr.Add(f.Off)))
 			}
 		}
 	}

 	// Expand root set to all reachable objects.
 	for len(q) > 0 {
 		x := q[len(q)-1]
 		q = q[:len(q)-1]

 		// Scan object for pointers.
 		size := p.Size(x)
 		for i := int64(0); i < size; i += ptrSize {
 			a := core.Address(x).Add(i)
 			if p.isPtrFromHeap(a) {
 				add(p.proc.ReadPtr(a))
 			}
 		}
 	}

 	p.nObj = n

 	// Initialize firstIdx fields in the heapInfo, for fast object index lookups.
 	n = 0
 	p.ForEachObject(func(x Object) bool {
 		h := p.findHeapInfo(p.Addr(x))
 		if h.firstIdx == -1 {
 			h.firstIdx = n
 		}
 		n++
 		return true
 	})
 	if n != p.nObj {
 		panic("object count wrong")
 	}

 	// Update stats to include the live/garbage distinction.
 	alloc := p.Stats().Child("heap").Child("in use spans").Child("alloc")
 	alloc.Children = []*Stats{
 		&Stats{"live", live, nil},
 		&Stats{"garbage", alloc.Size - live, nil},
 	}
 }

 // isPtrFromHeap reports whether the inferior at address a contains a pointer.
 // a must be somewhere in the heap.
 func (p *Process) isPtrFromHeap(a core.Address) bool {
 	return p.findHeapInfo(a).IsPtr(a, p.proc.PtrSize())
 }

 // IsPtr reports whether the inferior at address a contains a pointer.
 func (p *Process) IsPtr(a core.Address) bool {
 	h := p.findHeapInfo(a)
 	if h != nil {
 		return h.IsPtr(a, p.proc.PtrSize())
 	}
 	for _, m := range p.modules {
 		for _, s := range [2]string{"data", "bss"} {
 			min := core.Address(m.r.Field(s).Uintptr())
 			max := core.Address(m.r.Field("e" + s).Uintptr())
 			if a < min || a >= max {
 				continue
 			}
 			gc := m.r.Field("gc" + s + "mask").Field("bytedata").Address()
 			i := a.Sub(min)
 			return p.proc.ReadUint8(gc.Add(i/8))>>uint(i%8) != 0
 		}
 	}
 	// Everywhere else can't be a pointer. At least, not a pointer into the Go heap.
 	// TODO: stacks?
 	// TODO: finalizers?
 	return false
 }

 // FindObject finds the object containing a.  Returns that object and the offset within
 // that object to which a points.
 // Returns 0,0 if a doesn't point to a live heap object.
 func (p *Process) FindObject(a core.Address) (Object, int64) {
 	// Round down to the start of an object.
 	h := p.findHeapInfo(a)
 	if h == nil {
 		// Not in Go heap, or in a span
 		// that doesn't hold Go objects (freed, stacks, ...)
 		return 0, 0
 	}
 	x := h.base.Add(a.Sub(h.base) / h.size * h.size)
 	// Check if object is marked.
 	h = p.findHeapInfo(x)
 	if h.mark>>(uint64(x)%heapInfoSize/8)&1 == 0 { // free or garbage
 		return 0, 0
 	}
 	return Object(x), a.Sub(x)
 }

 func (p *Process) findObjectIndex(a core.Address) (int, int64) {
 	x, off := p.FindObject(a)
 	if x == 0 {
 		return -1, 0
 	}
 	h := p.findHeapInfo(core.Address(x))
 	return h.firstIdx + bits.OnesCount64(h.mark&(uint64(1)<<(uint64(x)%heapInfoSize/8)-1)), off
 }

 // ForEachObject calls fn with each object in the Go heap.
 // If fn returns false, ForEachObject returns immediately.
 func (p *Process) ForEachObject(fn func(x Object) bool) {
 	for _, k := range p.pages {
 		pt := p.pageTable[k]
 		for i := range pt {
 			h := &pt[i]
 			m := h.mark
 			for m != 0 {
 				j := bits.TrailingZeros64(m)
 				m &= m - 1
 				x := Object(k)*pageTableSize*heapInfoSize + Object(i)*heapInfoSize + Object(j)*8
 				if !fn(x) {
 					return
 				}
 			}
 		}
 	}
 }

 // ForEachRoot calls fn with each garbage collection root.
 // If fn returns false, ForEachRoot returns immediately.
 func (p *Process) ForEachRoot(fn func(r *Root) bool) {
 	for _, r := range p.globals {
 		if !fn(r) {
 			return
 		}
 	}
 	for _, g := range p.goroutines {
 		for _, f := range g.frames {
 			for _, r := range f.roots {
 				if !fn(r) {
 					return
 				}
 			}
 		}
 	}
 }

 // Addr returns the starting address of x.
 func (p *Process) Addr(x Object) core.Address {
 	return core.Address(x)
 }

 // Size returns the size of x in bytes.
 func (p *Process) Size(x Object) int64 {
 	return p.findHeapInfo(core.Address(x)).size
 }

 // Type returns the type and repeat count for the object x.
 // x contains at least repeat copies of the returned type.
 func (p *Process) Type(x Object) (*Type, int64) {
 	p.typeHeap()

 	i, _ := p.findObjectIndex(core.Address(x))
 	return p.types[i].t, p.types[i].r
 }

 // ForEachPtr calls fn for all heap pointers it finds in x.
 // It calls fn with:
 //   the offset of the pointer slot in x
 //   the pointed-to object y
 //   the offset in y where the pointer points.
 // If fn returns false, ForEachPtr returns immediately.
 // For an edge from an object to its finalizer, the first argument
 // passed to fn will be -1. (TODO: implement)
 func (p *Process) ForEachPtr(x Object, fn func(int64, Object, int64) bool) {
 	size := p.Size(x)
 	for i := int64(0); i < size; i += p.proc.PtrSize() {
 		a := core.Address(x).Add(i)
 		if !p.isPtrFromHeap(a) {
 			continue
 		}
 		ptr := p.proc.ReadPtr(a)
 		y, off := p.FindObject(ptr)
 		if y != 0 {
 			if !fn(i, y, off) {
 				return
 			}
 		}
 	}
 }

 // ForEachRootPtr behaves like ForEachPtr but it starts with a Root instead of an Object.
 func (p *Process) ForEachRootPtr(r *Root, fn func(int64, Object, int64) bool) {
 	edges1(p, r, 0, r.Type, fn)
 }

 // edges1 calls fn for the edges found in an object of type t living at offset off in the root r.
 // If fn returns false, return immediately with false.
 func edges1(p *Process, r *Root, off int64, t *Type, fn func(int64, Object, int64) bool) bool {
 	switch t.Kind {
 	case KindBool, KindInt, KindUint, KindFloat, KindComplex:
 		// no edges here
 	case KindIface, KindEface:
 		// The first word is a type or itab.
 		// Itabs are never in the heap.
 		// Types might be, though.
 		a := r.Addr.Add(off)
 		if r.Frame == nil || r.Frame.Live[a] {
 			dst, off2 := p.FindObject(p.proc.ReadPtr(a))
 			if dst != 0 {
 				if !fn(off, dst, off2) {
 					return false
 				}
 			}
 		}
 		// Treat second word like a pointer.
 		off += p.proc.PtrSize()
 		fallthrough
 	case KindPtr, KindString, KindSlice, KindFunc:
 		a := r.Addr.Add(off)
 		if r.Frame == nil || r.Frame.Live[a] {
 			dst, off2 := p.FindObject(p.proc.ReadPtr(a))
 			if dst != 0 {
 				if !fn(off, dst, off2) {
 					return false
 				}
 			}
 		}
 	case KindArray:
 		s := t.Elem.Size
 		for i := int64(0); i < t.Count; i++ {
 			if !edges1(p, r, off+i*s, t.Elem, fn) {
 				return false
 			}
 		}
 	case KindStruct:
 		for _, f := range t.Fields {
 			if !edges1(p, r, off+f.Off, f.Type, fn) {
 				return false
 			}
 		}
 	}
 	return true
 }

 const heapInfoSize = 512

 // Information for heapInfoSize bytes of heap.
 type heapInfo struct {
 	base     core.Address // start of the span containing this heap region
 	size     int64        // size of objects in the span
 	mark     uint64       // 64 mark bits, one for every 8 bytes
 	firstIdx int          // the index of the first object that starts in this region, or -1 if none
 	// For 64-bit inferiors, ptr[0] contains 64 pointer bits, one
 	// for every 8 bytes.  On 32-bit inferiors, ptr contains 128
 	// pointer bits, one for every 4 bytes.
 	ptr [2]uint64
 }

 func (h *heapInfo) IsPtr(a core.Address, ptrSize int64) bool {
 	if ptrSize == 8 {
 		i := uint(a%heapInfoSize) / 8
 		return h.ptr[0]>>i&1 != 0
 	}
 	i := a % heapInfoSize / 4
 	return h.ptr[i/64]>>(i%64)&1 != 0
 }

 // setHeapPtr records that the memory at heap address a contains a pointer.
 func (p *Process) setHeapPtr(a core.Address) {
 	h := p.allocHeapInfo(a)
 	if p.proc.PtrSize() == 8 {
 		i := uint(a%heapInfoSize) / 8
 		h.ptr[0] |= uint64(1) << i
 		return
 	}
 	i := a % heapInfoSize / 4
 	h.ptr[i/64] |= uint64(1) << (i % 64)
 }

 // Heap info structures cover 9 bits of address.
 // A page table entry covers 20 bits of address (1MB).
 const pageTableSize = 1 << 11

 type pageTableEntry [pageTableSize]heapInfo

 // findHeapInfo finds the heapInfo structure for a.
 // Returns nil if a is not a heap address.
 func (p *Process) findHeapInfo(a core.Address) *heapInfo {
 	k := a / heapInfoSize / pageTableSize
 	i := a / heapInfoSize % pageTableSize
 	t := p.pageTable[k]
 	if t == nil {
 		return nil
 	}
 	h := &t[i]
 	if h.base == 0 {
 		return nil
 	}
 	return h
 }

 // Same as findHeapInfo, but allocates the heapInfo if it
 // hasn't been allocated yet.
 func (p *Process) allocHeapInfo(a core.Address) *heapInfo {
 	k := a / heapInfoSize / pageTableSize
 	i := a / heapInfoSize % pageTableSize
 	t := p.pageTable[k]
 	if t == nil {
 		t = new(pageTableEntry)
 		for j := 0; j < pageTableSize; j++ {
 			t[j].firstIdx = -1
 		}
 		p.pageTable[k] = t
 		p.pages = append(p.pages, k)
 	}
 	return &t[i]
 }
	// Copyright 2017 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 gocore

	import (
	"math/bits"
	"strings"

	"golang.org/x/debug/internal/core"
	)

	// An Object represents a single reachable object in the Go heap.
	// Unreachable (garbage) objects are not represented as Objects.
	type Object core.Address

	// markObjects finds all the live objects in the heap and marks them
	// in the p.heapInfo mark fields.
	func (p *Process) markObjects() {
	ptrSize := p.proc.PtrSize()

	// number of live objects found so far
	n := 0
	// total size of live objects
	var live int64

	var q []Object

	// Function to call when we find a new pointer.
	add := func(x core.Address) {
	h := p.findHeapInfo(x)
	if h == nil { // not in heap or not in a valid span
	// Invalid spans can happen with intra-stack pointers.
	return
	}
	// Round down to object start.
	x = h.base.Add(x.Sub(h.base) / h.size * h.size)
	// Object start may map to a different info. Reload heap info.
	h = p.findHeapInfo(x)
	// Find mark bit
	b := uint64(x) % heapInfoSize / 8
	if h.mark&(uint64(1)<<b) != 0 { // already found
	return
	}
	h.mark \|= uint64(1) << b
	n++
	live += h.size
	q = append(q, Object(x))
	}

	// Start with scanning all the roots.
	// Note that we don't just use the DWARF roots, just in case DWARF isn't complete.
	// Instead we use exactly what the runtime uses.

	// Goroutine roots
	for _, g := range p.goroutines {
	for _, f := range g.frames {
	for a := range f.Live {
	add(p.proc.ReadPtr(a))
	}
	}
	}

	// Global roots
	for _, m := range p.modules {
	for _, s := range [2]string{"data", "bss"} {
	min := core.Address(m.r.Field(s).Uintptr())
	max := core.Address(m.r.Field("e" + s).Uintptr())
	gc := m.r.Field("gc" + s + "mask").Field("bytedata").Address()
	num := max.Sub(min) / ptrSize
	for i := int64(0); i < num; i++ {
	if p.proc.ReadUint8(gc.Add(i/8))>>uint(i%8)&1 != 0 {
	add(p.proc.ReadPtr(min.Add(i * ptrSize)))
	}
	}
	}
	}

	// Finalizers
	for _, r := range p.globals {
	if !strings.HasPrefix(r.Name, "finalizer for ") {
	continue
	}
	for _, f := range r.Type.Fields {
	if f.Type.Kind == KindPtr {
	add(p.proc.ReadPtr(r.Addr.Add(f.Off)))
	}
	}
	}

	// Expand root set to all reachable objects.
	for len(q) > 0 {
	x := q[len(q)-1]
	q = q[:len(q)-1]

	// Scan object for pointers.
	size := p.Size(x)
	for i := int64(0); i < size; i += ptrSize {
	a := core.Address(x).Add(i)
	if p.isPtrFromHeap(a) {
	add(p.proc.ReadPtr(a))
	}
	}
	}

	p.nObj = n

	// Initialize firstIdx fields in the heapInfo, for fast object index lookups.
	n = 0
	p.ForEachObject(func(x Object) bool {
	h := p.findHeapInfo(p.Addr(x))
	if h.firstIdx == -1 {
	h.firstIdx = n
	}
	n++
	return true
	})
	if n != p.nObj {
	panic("object count wrong")
	}

	// Update stats to include the live/garbage distinction.
	alloc := p.Stats().Child("heap").Child("in use spans").Child("alloc")
	alloc.Children = []*Stats{
	&Stats{"live", live, nil},
	&Stats{"garbage", alloc.Size - live, nil},
	}
	}

	// isPtrFromHeap reports whether the inferior at address a contains a pointer.
	// a must be somewhere in the heap.
	func (p *Process) isPtrFromHeap(a core.Address) bool {
	return p.findHeapInfo(a).IsPtr(a, p.proc.PtrSize())
	}

	// IsPtr reports whether the inferior at address a contains a pointer.
	func (p *Process) IsPtr(a core.Address) bool {
	h := p.findHeapInfo(a)
	if h != nil {
	return h.IsPtr(a, p.proc.PtrSize())
	}
	for _, m := range p.modules {
	for _, s := range [2]string{"data", "bss"} {
	min := core.Address(m.r.Field(s).Uintptr())
	max := core.Address(m.r.Field("e" + s).Uintptr())
	if a < min \|\| a >= max {
	continue
	}
	gc := m.r.Field("gc" + s + "mask").Field("bytedata").Address()
	i := a.Sub(min)
	return p.proc.ReadUint8(gc.Add(i/8))>>uint(i%8) != 0
	}
	}
	// Everywhere else can't be a pointer. At least, not a pointer into the Go heap.
	// TODO: stacks?
	// TODO: finalizers?
	return false
	}

	// FindObject finds the object containing a. Returns that object and the offset within
	// that object to which a points.
	// Returns 0,0 if a doesn't point to a live heap object.
	func (p *Process) FindObject(a core.Address) (Object, int64) {
	// Round down to the start of an object.
	h := p.findHeapInfo(a)
	if h == nil {
	// Not in Go heap, or in a span
	// that doesn't hold Go objects (freed, stacks, ...)
	return 0, 0
	}
	x := h.base.Add(a.Sub(h.base) / h.size * h.size)
	// Check if object is marked.
	h = p.findHeapInfo(x)
	if h.mark>>(uint64(x)%heapInfoSize/8)&1 == 0 { // free or garbage
	return 0, 0
	}
	return Object(x), a.Sub(x)
	}

	func (p *Process) findObjectIndex(a core.Address) (int, int64) {
	x, off := p.FindObject(a)
	if x == 0 {
	return -1, 0
	}
	h := p.findHeapInfo(core.Address(x))
	return h.firstIdx + bits.OnesCount64(h.mark&(uint64(1)<<(uint64(x)%heapInfoSize/8)-1)), off
	}

	// ForEachObject calls fn with each object in the Go heap.
	// If fn returns false, ForEachObject returns immediately.
	func (p *Process) ForEachObject(fn func(x Object) bool) {
	for _, k := range p.pages {
	pt := p.pageTable[k]
	for i := range pt {
	h := &pt[i]
	m := h.mark
	for m != 0 {
	j := bits.TrailingZeros64(m)
	m &= m - 1
	x := Object(k)pageTableSizeheapInfoSize + Object(i)heapInfoSize + Object(j)8
	if !fn(x) {
	return
	}
	}
	}
	}
	}

	// ForEachRoot calls fn with each garbage collection root.
	// If fn returns false, ForEachRoot returns immediately.
	func (p Process) ForEachRoot(fn func(r Root) bool) {
	for _, r := range p.globals {
	if !fn(r) {
	return
	}
	}
	for _, g := range p.goroutines {
	for _, f := range g.frames {
	for _, r := range f.roots {
	if !fn(r) {
	return
	}
	}
	}
	}
	}

	// Addr returns the starting address of x.
	func (p *Process) Addr(x Object) core.Address {
	return core.Address(x)
	}

	// Size returns the size of x in bytes.
	func (p *Process) Size(x Object) int64 {
	return p.findHeapInfo(core.Address(x)).size
	}

	// Type returns the type and repeat count for the object x.
	// x contains at least repeat copies of the returned type.
	func (p Process) Type(x Object) (Type, int64) {
	p.typeHeap()

	i, _ := p.findObjectIndex(core.Address(x))
	return p.types[i].t, p.types[i].r
	}

	// ForEachPtr calls fn for all heap pointers it finds in x.
	// It calls fn with:
	// the offset of the pointer slot in x
	// the pointed-to object y
	// the offset in y where the pointer points.
	// If fn returns false, ForEachPtr returns immediately.
	// For an edge from an object to its finalizer, the first argument
	// passed to fn will be -1. (TODO: implement)
	func (p *Process) ForEachPtr(x Object, fn func(int64, Object, int64) bool) {
	size := p.Size(x)
	for i := int64(0); i < size; i += p.proc.PtrSize() {
	a := core.Address(x).Add(i)
	if !p.isPtrFromHeap(a) {
	continue
	}
	ptr := p.proc.ReadPtr(a)
	y, off := p.FindObject(ptr)
	if y != 0 {
	if !fn(i, y, off) {
	return
	}
	}
	}
	}

	// ForEachRootPtr behaves like ForEachPtr but it starts with a Root instead of an Object.
	func (p Process) ForEachRootPtr(r Root, fn func(int64, Object, int64) bool) {
	edges1(p, r, 0, r.Type, fn)
	}

	// edges1 calls fn for the edges found in an object of type t living at offset off in the root r.
	// If fn returns false, return immediately with false.
	func edges1(p Process, r Root, off int64, t *Type, fn func(int64, Object, int64) bool) bool {
	switch t.Kind {
	case KindBool, KindInt, KindUint, KindFloat, KindComplex:
	// no edges here
	case KindIface, KindEface:
	// The first word is a type or itab.
	// Itabs are never in the heap.
	// Types might be, though.
	a := r.Addr.Add(off)
	if r.Frame == nil \|\| r.Frame.Live[a] {
	dst, off2 := p.FindObject(p.proc.ReadPtr(a))
	if dst != 0 {
	if !fn(off, dst, off2) {
	return false
	}
	}
	}
	// Treat second word like a pointer.
	off += p.proc.PtrSize()
	fallthrough
	case KindPtr, KindString, KindSlice, KindFunc:
	a := r.Addr.Add(off)
	if r.Frame == nil \|\| r.Frame.Live[a] {
	dst, off2 := p.FindObject(p.proc.ReadPtr(a))
	if dst != 0 {
	if !fn(off, dst, off2) {
	return false
	}
	}
	}
	case KindArray:
	s := t.Elem.Size
	for i := int64(0); i < t.Count; i++ {
	if !edges1(p, r, off+i*s, t.Elem, fn) {
	return false
	}
	}
	case KindStruct:
	for _, f := range t.Fields {
	if !edges1(p, r, off+f.Off, f.Type, fn) {
	return false
	}
	}
	}
	return true
	}

	const heapInfoSize = 512

	// Information for heapInfoSize bytes of heap.
	type heapInfo struct {
	base core.Address // start of the span containing this heap region
	size int64 // size of objects in the span
	mark uint64 // 64 mark bits, one for every 8 bytes
	firstIdx int // the index of the first object that starts in this region, or -1 if none
	// For 64-bit inferiors, ptr[0] contains 64 pointer bits, one
	// for every 8 bytes. On 32-bit inferiors, ptr contains 128
	// pointer bits, one for every 4 bytes.
	ptr [2]uint64
	}

	func (h *heapInfo) IsPtr(a core.Address, ptrSize int64) bool {
	if ptrSize == 8 {
	i := uint(a%heapInfoSize) / 8
	return h.ptr[0]>>i&1 != 0
	}
	i := a % heapInfoSize / 4
	return h.ptr[i/64]>>(i%64)&1 != 0
	}

	// setHeapPtr records that the memory at heap address a contains a pointer.
	func (p *Process) setHeapPtr(a core.Address) {
	h := p.allocHeapInfo(a)
	if p.proc.PtrSize() == 8 {
	i := uint(a%heapInfoSize) / 8
	h.ptr[0] \|= uint64(1) << i
	return
	}
	i := a % heapInfoSize / 4
	h.ptr[i/64] \|= uint64(1) << (i % 64)
	}

	// Heap info structures cover 9 bits of address.
	// A page table entry covers 20 bits of address (1MB).
	const pageTableSize = 1 << 11

	type pageTableEntry [pageTableSize]heapInfo

	// findHeapInfo finds the heapInfo structure for a.
	// Returns nil if a is not a heap address.
	func (p Process) findHeapInfo(a core.Address) heapInfo {
	k := a / heapInfoSize / pageTableSize
	i := a / heapInfoSize % pageTableSize
	t := p.pageTable[k]
	if t == nil {
	return nil
	}
	h := &t[i]
	if h.base == 0 {
	return nil
	}
	return h
	}

	// Same as findHeapInfo, but allocates the heapInfo if it
	// hasn't been allocated yet.
	func (p Process) allocHeapInfo(a core.Address) heapInfo {
	k := a / heapInfoSize / pageTableSize
	i := a / heapInfoSize % pageTableSize
	t := p.pageTable[k]
	if t == nil {
	t = new(pageTableEntry)
	for j := 0; j < pageTableSize; j++ {
	t[j].firstIdx = -1
	}
	p.pageTable[k] = t
	p.pages = append(p.pages, k)
	}
	return &t[i]
	}