diff options
Diffstat (limited to 'pkg/sentry/mm')
| -rw-r--r-- | pkg/sentry/mm/BUILD | 142 | ||||
| -rw-r--r-- | pkg/sentry/mm/README.md | 280 | ||||
| -rw-r--r-- | pkg/sentry/mm/file_refcount_set.go | 1643 | ||||
| -rw-r--r-- | pkg/sentry/mm/io_list.go | 193 | ||||
| -rw-r--r-- | pkg/sentry/mm/mm_state_autogen.go | 404 | ||||
| -rw-r--r-- | pkg/sentry/mm/mm_test.go | 230 | ||||
| -rw-r--r-- | pkg/sentry/mm/pma_set.go | 1643 | ||||
| -rw-r--r-- | pkg/sentry/mm/vma_set.go | 1643 |
8 files changed, 5526 insertions, 652 deletions
diff --git a/pkg/sentry/mm/BUILD b/pkg/sentry/mm/BUILD deleted file mode 100644 index a036ce53c..000000000 --- a/pkg/sentry/mm/BUILD +++ /dev/null @@ -1,142 +0,0 @@ -load("//tools:defs.bzl", "go_library", "go_test") -load("//tools/go_generics:defs.bzl", "go_template_instance") - -package(licenses = ["notice"]) - -go_template_instance( - name = "file_refcount_set", - out = "file_refcount_set.go", - imports = { - "platform": "gvisor.dev/gvisor/pkg/sentry/platform", - }, - package = "mm", - prefix = "fileRefcount", - template = "//pkg/segment:generic_set", - types = { - "Key": "uint64", - "Range": "platform.FileRange", - "Value": "int32", - "Functions": "fileRefcountSetFunctions", - }, -) - -go_template_instance( - name = "vma_set", - out = "vma_set.go", - consts = { - "minDegree": "8", - "trackGaps": "1", - }, - imports = { - "usermem": "gvisor.dev/gvisor/pkg/usermem", - }, - package = "mm", - prefix = "vma", - template = "//pkg/segment:generic_set", - types = { - "Key": "usermem.Addr", - "Range": "usermem.AddrRange", - "Value": "vma", - "Functions": "vmaSetFunctions", - }, -) - -go_template_instance( - name = "pma_set", - out = "pma_set.go", - consts = { - "minDegree": "8", - }, - imports = { - "usermem": "gvisor.dev/gvisor/pkg/usermem", - }, - package = "mm", - prefix = "pma", - template = "//pkg/segment:generic_set", - types = { - "Key": "usermem.Addr", - "Range": "usermem.AddrRange", - "Value": "pma", - "Functions": "pmaSetFunctions", - }, -) - -go_template_instance( - name = "io_list", - out = "io_list.go", - package = "mm", - prefix = "io", - template = "//pkg/ilist:generic_list", - types = { - "Element": "*ioResult", - "Linker": "*ioResult", - }, -) - -go_library( - name = "mm", - srcs = [ - "address_space.go", - "aio_context.go", - "aio_context_state.go", - "debug.go", - "file_refcount_set.go", - "io.go", - "io_list.go", - "lifecycle.go", - "metadata.go", - "mm.go", - "pma.go", - "pma_set.go", - "procfs.go", - "save_restore.go", - "shm.go", - "special_mappable.go", - "syscalls.go", - "vma.go", - "vma_set.go", - ], - visibility = ["//pkg/sentry:internal"], - deps = [ - "//pkg/abi/linux", - "//pkg/atomicbitops", - "//pkg/context", - "//pkg/log", - "//pkg/refs", - "//pkg/safecopy", - "//pkg/safemem", - "//pkg/sentry/arch", - "//pkg/sentry/fs/proc/seqfile", - "//pkg/sentry/fsbridge", - "//pkg/sentry/kernel/auth", - "//pkg/sentry/kernel/futex", - "//pkg/sentry/kernel/shm", - "//pkg/sentry/limits", - "//pkg/sentry/memmap", - "//pkg/sentry/pgalloc", - "//pkg/sentry/platform", - "//pkg/sentry/usage", - "//pkg/sync", - "//pkg/syserror", - "//pkg/tcpip/buffer", - "//pkg/usermem", - ], -) - -go_test( - name = "mm_test", - size = "small", - srcs = ["mm_test.go"], - library = ":mm", - deps = [ - "//pkg/context", - "//pkg/sentry/arch", - "//pkg/sentry/contexttest", - "//pkg/sentry/limits", - "//pkg/sentry/memmap", - "//pkg/sentry/pgalloc", - "//pkg/sentry/platform", - "//pkg/syserror", - "//pkg/usermem", - ], -) diff --git a/pkg/sentry/mm/README.md b/pkg/sentry/mm/README.md deleted file mode 100644 index f4d43d927..000000000 --- a/pkg/sentry/mm/README.md +++ /dev/null @@ -1,280 +0,0 @@ -This package provides an emulation of Linux semantics for application virtual -memory mappings. - -For completeness, this document also describes aspects of the memory management -subsystem defined outside this package. - -# Background - -We begin by describing semantics for virtual memory in Linux. - -A virtual address space is defined as a collection of mappings from virtual -addresses to physical memory. However, userspace applications do not configure -mappings to physical memory directly. Instead, applications configure memory -mappings from virtual addresses to offsets into a file using the `mmap` system -call.[^mmap-anon] For example, a call to: - - mmap( - /* addr = */ 0x400000, - /* length = */ 0x1000, - PROT_READ | PROT_WRITE, - MAP_SHARED, - /* fd = */ 3, - /* offset = */ 0); - -creates a mapping of length 0x1000 bytes, starting at virtual address (VA) -0x400000, to offset 0 in the file represented by file descriptor (FD) 3. Within -the Linux kernel, virtual memory mappings are represented by *virtual memory -areas* (VMAs). Supposing that FD 3 represents file /tmp/foo, the state of the -virtual memory subsystem after the `mmap` call may be depicted as: - - VMA: VA:0x400000 -> /tmp/foo:0x0 - -Establishing a virtual memory area does not necessarily establish a mapping to a -physical address, because Linux has not necessarily provisioned physical memory -to store the file's contents. Thus, if the application attempts to read the -contents of VA 0x400000, it may incur a *page fault*, a CPU exception that -forces the kernel to create such a mapping to service the read. - -For a file, doing so consists of several logical phases: - -1. The kernel allocates physical memory to store the contents of the required - part of the file, and copies file contents to the allocated memory. - Supposing that the kernel chooses the physical memory at physical address - (PA) 0x2fb000, the resulting state of the system is: - - VMA: VA:0x400000 -> /tmp/foo:0x0 - Filemap: /tmp/foo:0x0 -> PA:0x2fb000 - - (In Linux the state of the mapping from file offset to physical memory is - stored in `struct address_space`, but to avoid confusion with other notions - of address space we will refer to this system as filemap, named after Linux - kernel source file `mm/filemap.c`.) - -2. The kernel stores the effective mapping from virtual to physical address in - a *page table entry* (PTE) in the application's *page tables*, which are - used by the CPU's virtual memory hardware to perform address translation. - The resulting state of the system is: - - VMA: VA:0x400000 -> /tmp/foo:0x0 - Filemap: /tmp/foo:0x0 -> PA:0x2fb000 - PTE: VA:0x400000 -----------------> PA:0x2fb000 - - The PTE is required for the application to actually use the contents of the - mapped file as virtual memory. However, the PTE is derived from the VMA and - filemap state, both of which are independently mutable, such that mutations - to either will affect the PTE. For example: - - - The application may remove the VMA using the `munmap` system call. This - breaks the mapping from VA:0x400000 to /tmp/foo:0x0, and consequently - the mapping from VA:0x400000 to PA:0x2fb000. However, it does not - necessarily break the mapping from /tmp/foo:0x0 to PA:0x2fb000, so a - future mapping of the same file offset may reuse this physical memory. - - - The application may invalidate the file's contents by passing a length - of 0 to the `ftruncate` system call. This breaks the mapping from - /tmp/foo:0x0 to PA:0x2fb000, and consequently the mapping from - VA:0x400000 to PA:0x2fb000. However, it does not break the mapping from - VA:0x400000 to /tmp/foo:0x0, so future changes to the file's contents - may again be made visible at VA:0x400000 after another page fault - results in the allocation of a new physical address. - - Note that, in order to correctly break the mapping from VA:0x400000 to - PA:0x2fb000 in the latter case, filemap must also store a *reverse mapping* - from /tmp/foo:0x0 to VA:0x400000 so that it can locate and remove the PTE. - -[^mmap-anon]: Memory mappings to non-files are discussed in later sections. - -## Private Mappings - -The preceding example considered VMAs created using the `MAP_SHARED` flag, which -means that PTEs derived from the mapping should always use physical memory that -represents the current state of the mapped file.[^mmap-dev-zero] Applications -can alternatively pass the `MAP_PRIVATE` flag to create a *private mapping*. -Private mappings are *copy-on-write*. - -Suppose that the application instead created a private mapping in the previous -example. In Linux, the state of the system after a read page fault would be: - - VMA: VA:0x400000 -> /tmp/foo:0x0 (private) - Filemap: /tmp/foo:0x0 -> PA:0x2fb000 - PTE: VA:0x400000 -----------------> PA:0x2fb000 (read-only) - -Now suppose the application attempts to write to VA:0x400000. For a shared -mapping, the write would be propagated to PA:0x2fb000, and the kernel would be -responsible for ensuring that the write is later propagated to the mapped file. -For a private mapping, the write incurs another page fault since the PTE is -marked read-only. In response, the kernel allocates physical memory to store the -mapping's *private copy* of the file's contents, copies file contents to the -allocated memory, and changes the PTE to map to the private copy. Supposing that -the kernel chooses the physical memory at physical address (PA) 0x5ea000, the -resulting state of the system is: - - VMA: VA:0x400000 -> /tmp/foo:0x0 (private) - Filemap: /tmp/foo:0x0 -> PA:0x2fb000 - PTE: VA:0x400000 -----------------> PA:0x5ea000 - -Note that the filemap mapping from /tmp/foo:0x0 to PA:0x2fb000 may still exist, -but is now irrelevant to this mapping. - -[^mmap-dev-zero]: Modulo files with special mmap semantics such as `/dev/zero`. - -## Anonymous Mappings - -Instead of passing a file to the `mmap` system call, applications can instead -request an *anonymous* mapping by passing the `MAP_ANONYMOUS` flag. -Semantically, an anonymous mapping is essentially a mapping to an ephemeral file -initially filled with zero bytes. Practically speaking, this is how shared -anonymous mappings are implemented, but private anonymous mappings do not result -in the creation of an ephemeral file; since there would be no way to modify the -contents of the underlying file through a private mapping, all private anonymous -mappings use a single shared page filled with zero bytes until copy-on-write -occurs. - -# Virtual Memory in the Sentry - -The sentry implements application virtual memory atop a host kernel, introducing -an additional level of indirection to the above. - -Consider the same scenario as in the previous section. Since the sentry handles -application system calls, the effect of an application `mmap` system call is to -create a VMA in the sentry (as opposed to the host kernel): - - Sentry VMA: VA:0x400000 -> /tmp/foo:0x0 - -When the application first incurs a page fault on this address, the host kernel -delivers information about the page fault to the sentry in a platform-dependent -manner, and the sentry handles the fault: - -1. The sentry allocates memory to store the contents of the required part of - the file, and copies file contents to the allocated memory. However, since - the sentry is implemented atop a host kernel, it does not configure mappings - to physical memory directly. Instead, mappable "memory" in the sentry is - represented by a host file descriptor and offset, since (as noted in - "Background") this is the memory mapping primitive provided by the host - kernel. In general, memory is allocated from a temporary host file using the - `pgalloc` package. Supposing that the sentry allocates offset 0x3000 from - host file "memory-file", the resulting state is: - - Sentry VMA: VA:0x400000 -> /tmp/foo:0x0 - Sentry filemap: /tmp/foo:0x0 -> host:memory-file:0x3000 - -2. The sentry stores the effective mapping from virtual address to host file in - a host VMA by invoking the `mmap` system call: - - Sentry VMA: VA:0x400000 -> /tmp/foo:0x0 - Sentry filemap: /tmp/foo:0x0 -> host:memory-file:0x3000 - Host VMA: VA:0x400000 -----------------> host:memory-file:0x3000 - -3. The sentry returns control to the application, which immediately incurs the - page fault again.[^mmap-populate] However, since a host VMA now exists for - the faulting virtual address, the host kernel now handles the page fault as - described in "Background": - - Sentry VMA: VA:0x400000 -> /tmp/foo:0x0 - Sentry filemap: /tmp/foo:0x0 -> host:memory-file:0x3000 - Host VMA: VA:0x400000 -----------------> host:memory-file:0x3000 - Host filemap: host:memory-file:0x3000 -> PA:0x2fb000 - Host PTE: VA:0x400000 --------------------------------------------> PA:0x2fb000 - -Thus, from an implementation standpoint, host VMAs serve the same purpose in the -sentry that PTEs do in Linux. As in Linux, sentry VMA and filemap state is -independently mutable, and the desired state of host VMAs is derived from that -state. - -[^mmap-populate]: The sentry could force the host kernel to establish PTEs when - it creates the host VMA by passing the `MAP_POPULATE` flag to - the `mmap` system call, but usually does not. This is because, - to reduce the number of page faults that require handling by - the sentry and (correspondingly) the number of host `mmap` - system calls, the sentry usually creates host VMAs that are - much larger than the single faulting page. - -## Private Mappings - -The sentry implements private mappings consistently with Linux. Before -copy-on-write, the private mapping example given in the Background results in: - - Sentry VMA: VA:0x400000 -> /tmp/foo:0x0 (private) - Sentry filemap: /tmp/foo:0x0 -> host:memory-file:0x3000 - Host VMA: VA:0x400000 -----------------> host:memory-file:0x3000 (read-only) - Host filemap: host:memory-file:0x3000 -> PA:0x2fb000 - Host PTE: VA:0x400000 --------------------------------------------> PA:0x2fb000 (read-only) - -When the application attempts to write to this address, the host kernel delivers -information about the resulting page fault to the sentry. Analogous to Linux, -the sentry allocates memory to store the mapping's private copy of the file's -contents, copies file contents to the allocated memory, and changes the host VMA -to map to the private copy. Supposing that the sentry chooses the offset 0x4000 -in host file `memory-file` to store the private copy, the state of the system -after copy-on-write is: - - Sentry VMA: VA:0x400000 -> /tmp/foo:0x0 (private) - Sentry filemap: /tmp/foo:0x0 -> host:memory-file:0x3000 - Host VMA: VA:0x400000 -----------------> host:memory-file:0x4000 - Host filemap: host:memory-file:0x4000 -> PA:0x5ea000 - Host PTE: VA:0x400000 --------------------------------------------> PA:0x5ea000 - -However, this highlights an important difference between Linux and the sentry. -In Linux, page tables are concrete (architecture-dependent) data structures -owned by the kernel. Conversely, the sentry has the ability to create and -destroy host VMAs using host system calls, but it does not have direct access to -their state. Thus, as written, if the application invokes the `munmap` system -call to remove the sentry VMA, it is non-trivial for the sentry to determine -that it should deallocate `host:memory-file:0x4000`. This implies that the -sentry must retain information about the host VMAs that it has created. - -## Anonymous Mappings - -The sentry implements anonymous mappings consistently with Linux, except that -there is no shared zero page. - -# Implementation Constructs - -In Linux: - -- A virtual address space is represented by `struct mm_struct`. - -- VMAs are represented by `struct vm_area_struct`, stored in `struct - mm_struct::mmap`. - -- Mappings from file offsets to physical memory are stored in `struct - address_space`. - -- Reverse mappings from file offsets to virtual mappings are stored in `struct - address_space::i_mmap`. - -- Physical memory pages are represented by a pointer to `struct page` or an - index called a *page frame number* (PFN), represented by `pfn_t`. - -- PTEs are represented by architecture-dependent type `pte_t`, stored in a - table hierarchy rooted at `struct mm_struct::pgd`. - -In the sentry: - -- A virtual address space is represented by type [`mm.MemoryManager`][mm]. - -- Sentry VMAs are represented by type [`mm.vma`][mm], stored in - `mm.MemoryManager.vmas`. - -- Mappings from sentry file offsets to host file offsets are abstracted - through interface method [`memmap.Mappable.Translate`][memmap]. - -- Reverse mappings from sentry file offsets to virtual mappings are abstracted - through interface methods - [`memmap.Mappable.AddMapping` and `memmap.Mappable.RemoveMapping`][memmap]. - -- Host files that may be mapped into host VMAs are represented by type - [`platform.File`][platform]. - -- Host VMAs are represented in the sentry by type [`mm.pma`][mm] ("platform - mapping area"), stored in `mm.MemoryManager.pmas`. - -- Creation and destruction of host VMAs is abstracted through interface - methods - [`platform.AddressSpace.MapFile` and `platform.AddressSpace.Unmap`][platform]. - -[memmap]: https://github.com/google/gvisor/blob/master/pkg/sentry/memmap/memmap.go -[mm]: https://github.com/google/gvisor/blob/master/pkg/sentry/mm/mm.go -[pgalloc]: https://github.com/google/gvisor/blob/master/pkg/sentry/pgalloc/pgalloc.go -[platform]: https://github.com/google/gvisor/blob/master/pkg/sentry/platform/platform.go diff --git a/pkg/sentry/mm/file_refcount_set.go b/pkg/sentry/mm/file_refcount_set.go new file mode 100644 index 000000000..475c73fee --- /dev/null +++ b/pkg/sentry/mm/file_refcount_set.go @@ -0,0 +1,1643 @@ +package mm + +import ( + __generics_imported0 "gvisor.dev/gvisor/pkg/sentry/platform" +) + +import ( + "bytes" + "fmt" +) + +// trackGaps is an optional parameter. +// +// If trackGaps is 1, the Set will track maximum gap size recursively, +// enabling the GapIterator.{Prev,Next}LargeEnoughGap functions. In this +// case, Key must be an unsigned integer. +// +// trackGaps must be 0 or 1. +const fileRefcounttrackGaps = 0 + +var _ = uint8(fileRefcounttrackGaps << 7) // Will fail if not zero or one. + +// dynamicGap is a type that disappears if trackGaps is 0. +type fileRefcountdynamicGap [fileRefcounttrackGaps]uint64 + +// Get returns the value of the gap. +// +// Precondition: trackGaps must be non-zero. +func (d *fileRefcountdynamicGap) Get() uint64 { + return d[:][0] +} + +// Set sets the value of the gap. +// +// Precondition: trackGaps must be non-zero. +func (d *fileRefcountdynamicGap) Set(v uint64) { + d[:][0] = v +} + +const ( + // minDegree is the minimum degree of an internal node in a Set B-tree. + // + // - Any non-root node has at least minDegree-1 segments. + // + // - Any non-root internal (non-leaf) node has at least minDegree children. + // + // - The root node may have fewer than minDegree-1 segments, but it may + // only have 0 segments if the tree is empty. + // + // Our implementation requires minDegree >= 3. Higher values of minDegree + // usually improve performance, but increase memory usage for small sets. + fileRefcountminDegree = 3 + + fileRefcountmaxDegree = 2 * fileRefcountminDegree +) + +// A Set is a mapping of segments with non-overlapping Range keys. The zero +// value for a Set is an empty set. Set values are not safely movable nor +// copyable. Set is thread-compatible. +// +// +stateify savable +type fileRefcountSet struct { + root fileRefcountnode `state:".(*fileRefcountSegmentDataSlices)"` +} + +// IsEmpty returns true if the set contains no segments. +func (s *fileRefcountSet) IsEmpty() bool { + return s.root.nrSegments == 0 +} + +// IsEmptyRange returns true iff no segments in the set overlap the given +// range. This is semantically equivalent to s.SpanRange(r) == 0, but may be +// more efficient. +func (s *fileRefcountSet) IsEmptyRange(r __generics_imported0.FileRange) bool { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return true + } + _, gap := s.Find(r.Start) + if !gap.Ok() { + return false + } + return r.End <= gap.End() +} + +// Span returns the total size of all segments in the set. +func (s *fileRefcountSet) Span() uint64 { + var sz uint64 + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sz += seg.Range().Length() + } + return sz +} + +// SpanRange returns the total size of the intersection of segments in the set +// with the given range. +func (s *fileRefcountSet) SpanRange(r __generics_imported0.FileRange) uint64 { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return 0 + } + var sz uint64 + for seg := s.LowerBoundSegment(r.Start); seg.Ok() && seg.Start() < r.End; seg = seg.NextSegment() { + sz += seg.Range().Intersect(r).Length() + } + return sz +} + +// FirstSegment returns the first segment in the set. If the set is empty, +// FirstSegment returns a terminal iterator. +func (s *fileRefcountSet) FirstSegment() fileRefcountIterator { + if s.root.nrSegments == 0 { + return fileRefcountIterator{} + } + return s.root.firstSegment() +} + +// LastSegment returns the last segment in the set. If the set is empty, +// LastSegment returns a terminal iterator. +func (s *fileRefcountSet) LastSegment() fileRefcountIterator { + if s.root.nrSegments == 0 { + return fileRefcountIterator{} + } + return s.root.lastSegment() +} + +// FirstGap returns the first gap in the set. +func (s *fileRefcountSet) FirstGap() fileRefcountGapIterator { + n := &s.root + for n.hasChildren { + n = n.children[0] + } + return fileRefcountGapIterator{n, 0} +} + +// LastGap returns the last gap in the set. +func (s *fileRefcountSet) LastGap() fileRefcountGapIterator { + n := &s.root + for n.hasChildren { + n = n.children[n.nrSegments] + } + return fileRefcountGapIterator{n, n.nrSegments} +} + +// Find returns the segment or gap whose range contains the given key. If a +// segment is found, the returned Iterator is non-terminal and the +// returned GapIterator is terminal. Otherwise, the returned Iterator is +// terminal and the returned GapIterator is non-terminal. +func (s *fileRefcountSet) Find(key uint64) (fileRefcountIterator, fileRefcountGapIterator) { + n := &s.root + for { + + lower := 0 + upper := n.nrSegments + for lower < upper { + i := lower + (upper-lower)/2 + if r := n.keys[i]; key < r.End { + if key >= r.Start { + return fileRefcountIterator{n, i}, fileRefcountGapIterator{} + } + upper = i + } else { + lower = i + 1 + } + } + i := lower + if !n.hasChildren { + return fileRefcountIterator{}, fileRefcountGapIterator{n, i} + } + n = n.children[i] + } +} + +// FindSegment returns the segment whose range contains the given key. If no +// such segment exists, FindSegment returns a terminal iterator. +func (s *fileRefcountSet) FindSegment(key uint64) fileRefcountIterator { + seg, _ := s.Find(key) + return seg +} + +// LowerBoundSegment returns the segment with the lowest range that contains a +// key greater than or equal to min. If no such segment exists, +// LowerBoundSegment returns a terminal iterator. +func (s *fileRefcountSet) LowerBoundSegment(min uint64) fileRefcountIterator { + seg, gap := s.Find(min) + if seg.Ok() { + return seg + } + return gap.NextSegment() +} + +// UpperBoundSegment returns the segment with the highest range that contains a +// key less than or equal to max. If no such segment exists, UpperBoundSegment +// returns a terminal iterator. +func (s *fileRefcountSet) UpperBoundSegment(max uint64) fileRefcountIterator { + seg, gap := s.Find(max) + if seg.Ok() { + return seg + } + return gap.PrevSegment() +} + +// FindGap returns the gap containing the given key. If no such gap exists +// (i.e. the set contains a segment containing that key), FindGap returns a +// terminal iterator. +func (s *fileRefcountSet) FindGap(key uint64) fileRefcountGapIterator { + _, gap := s.Find(key) + return gap +} + +// LowerBoundGap returns the gap with the lowest range that is greater than or +// equal to min. +func (s *fileRefcountSet) LowerBoundGap(min uint64) fileRefcountGapIterator { + seg, gap := s.Find(min) + if gap.Ok() { + return gap + } + return seg.NextGap() +} + +// UpperBoundGap returns the gap with the highest range that is less than or +// equal to max. +func (s *fileRefcountSet) UpperBoundGap(max uint64) fileRefcountGapIterator { + seg, gap := s.Find(max) + if gap.Ok() { + return gap + } + return seg.PrevGap() +} + +// Add inserts the given segment into the set and returns true. If the new +// segment can be merged with adjacent segments, Add will do so. If the new +// segment would overlap an existing segment, Add returns false. If Add +// succeeds, all existing iterators are invalidated. +func (s *fileRefcountSet) Add(r __generics_imported0.FileRange, val int32) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.Insert(gap, r, val) + return true +} + +// AddWithoutMerging inserts the given segment into the set and returns true. +// If it would overlap an existing segment, AddWithoutMerging does nothing and +// returns false. If AddWithoutMerging succeeds, all existing iterators are +// invalidated. +func (s *fileRefcountSet) AddWithoutMerging(r __generics_imported0.FileRange, val int32) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.InsertWithoutMergingUnchecked(gap, r, val) + return true +} + +// Insert inserts the given segment into the given gap. If the new segment can +// be merged with adjacent segments, Insert will do so. Insert returns an +// iterator to the segment containing the inserted value (which may have been +// merged with other values). All existing iterators (including gap, but not +// including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, Insert panics. +// +// Insert is semantically equivalent to a InsertWithoutMerging followed by a +// Merge, but may be more efficient. Note that there is no unchecked variant of +// Insert since Insert must retrieve and inspect gap's predecessor and +// successor segments regardless. +func (s *fileRefcountSet) Insert(gap fileRefcountGapIterator, r __generics_imported0.FileRange, val int32) fileRefcountIterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + prev, next := gap.PrevSegment(), gap.NextSegment() + if prev.Ok() && prev.End() > r.Start { + panic(fmt.Sprintf("new segment %v overlaps predecessor %v", r, prev.Range())) + } + if next.Ok() && next.Start() < r.End { + panic(fmt.Sprintf("new segment %v overlaps successor %v", r, next.Range())) + } + if prev.Ok() && prev.End() == r.Start { + if mval, ok := (fileRefcountSetFunctions{}).Merge(prev.Range(), prev.Value(), r, val); ok { + shrinkMaxGap := fileRefcounttrackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get() + prev.SetEndUnchecked(r.End) + prev.SetValue(mval) + if shrinkMaxGap { + gap.node.updateMaxGapLeaf() + } + if next.Ok() && next.Start() == r.End { + val = mval + if mval, ok := (fileRefcountSetFunctions{}).Merge(prev.Range(), val, next.Range(), next.Value()); ok { + prev.SetEndUnchecked(next.End()) + prev.SetValue(mval) + return s.Remove(next).PrevSegment() + } + } + return prev + } + } + if next.Ok() && next.Start() == r.End { + if mval, ok := (fileRefcountSetFunctions{}).Merge(r, val, next.Range(), next.Value()); ok { + shrinkMaxGap := fileRefcounttrackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get() + next.SetStartUnchecked(r.Start) + next.SetValue(mval) + if shrinkMaxGap { + gap.node.updateMaxGapLeaf() + } + return next + } + } + + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMerging inserts the given segment into the given gap and +// returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, +// InsertWithoutMerging panics. +func (s *fileRefcountSet) InsertWithoutMerging(gap fileRefcountGapIterator, r __generics_imported0.FileRange, val int32) fileRefcountIterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if gr := gap.Range(); !gr.IsSupersetOf(r) { + panic(fmt.Sprintf("cannot insert segment range %v into gap range %v", r, gr)) + } + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMergingUnchecked inserts the given segment into the given gap +// and returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// Preconditions: r.Start >= gap.Start(); r.End <= gap.End(). +func (s *fileRefcountSet) InsertWithoutMergingUnchecked(gap fileRefcountGapIterator, r __generics_imported0.FileRange, val int32) fileRefcountIterator { + gap = gap.node.rebalanceBeforeInsert(gap) + splitMaxGap := fileRefcounttrackGaps != 0 && (gap.node.nrSegments == 0 || gap.Range().Length() == gap.node.maxGap.Get()) + copy(gap.node.keys[gap.index+1:], gap.node.keys[gap.index:gap.node.nrSegments]) + copy(gap.node.values[gap.index+1:], gap.node.values[gap.index:gap.node.nrSegments]) + gap.node.keys[gap.index] = r + gap.node.values[gap.index] = val + gap.node.nrSegments++ + if splitMaxGap { + gap.node.updateMaxGapLeaf() + } + return fileRefcountIterator{gap.node, gap.index} +} + +// Remove removes the given segment and returns an iterator to the vacated gap. +// All existing iterators (including seg, but not including the returned +// iterator) are invalidated. +func (s *fileRefcountSet) Remove(seg fileRefcountIterator) fileRefcountGapIterator { + + if seg.node.hasChildren { + + victim := seg.PrevSegment() + + seg.SetRangeUnchecked(victim.Range()) + seg.SetValue(victim.Value()) + + nextAdjacentNode := seg.NextSegment().node + if fileRefcounttrackGaps != 0 { + nextAdjacentNode.updateMaxGapLeaf() + } + return s.Remove(victim).NextGap() + } + copy(seg.node.keys[seg.index:], seg.node.keys[seg.index+1:seg.node.nrSegments]) + copy(seg.node.values[seg.index:], seg.node.values[seg.index+1:seg.node.nrSegments]) + fileRefcountSetFunctions{}.ClearValue(&seg.node.values[seg.node.nrSegments-1]) + seg.node.nrSegments-- + if fileRefcounttrackGaps != 0 { + seg.node.updateMaxGapLeaf() + } + return seg.node.rebalanceAfterRemove(fileRefcountGapIterator{seg.node, seg.index}) +} + +// RemoveAll removes all segments from the set. All existing iterators are +// invalidated. +func (s *fileRefcountSet) RemoveAll() { + s.root = fileRefcountnode{} +} + +// RemoveRange removes all segments in the given range. An iterator to the +// newly formed gap is returned, and all existing iterators are invalidated. +func (s *fileRefcountSet) RemoveRange(r __generics_imported0.FileRange) fileRefcountGapIterator { + seg, gap := s.Find(r.Start) + if seg.Ok() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + for seg = gap.NextSegment(); seg.Ok() && seg.Start() < r.End; seg = gap.NextSegment() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + return gap +} + +// Merge attempts to merge two neighboring segments. If successful, Merge +// returns an iterator to the merged segment, and all existing iterators are +// invalidated. Otherwise, Merge returns a terminal iterator. +// +// If first is not the predecessor of second, Merge panics. +func (s *fileRefcountSet) Merge(first, second fileRefcountIterator) fileRefcountIterator { + if first.NextSegment() != second { + panic(fmt.Sprintf("attempt to merge non-neighboring segments %v, %v", first.Range(), second.Range())) + } + return s.MergeUnchecked(first, second) +} + +// MergeUnchecked attempts to merge two neighboring segments. If successful, +// MergeUnchecked returns an iterator to the merged segment, and all existing +// iterators are invalidated. Otherwise, MergeUnchecked returns a terminal +// iterator. +// +// Precondition: first is the predecessor of second: first.NextSegment() == +// second, first == second.PrevSegment(). +func (s *fileRefcountSet) MergeUnchecked(first, second fileRefcountIterator) fileRefcountIterator { + if first.End() == second.Start() { + if mval, ok := (fileRefcountSetFunctions{}).Merge(first.Range(), first.Value(), second.Range(), second.Value()); ok { + + first.SetEndUnchecked(second.End()) + first.SetValue(mval) + + return s.Remove(second).PrevSegment() + } + } + return fileRefcountIterator{} +} + +// MergeAll attempts to merge all adjacent segments in the set. All existing +// iterators are invalidated. +func (s *fileRefcountSet) MergeAll() { + seg := s.FirstSegment() + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeRange attempts to merge all adjacent segments that contain a key in the +// specific range. All existing iterators are invalidated. +func (s *fileRefcountSet) MergeRange(r __generics_imported0.FileRange) { + seg := s.LowerBoundSegment(r.Start) + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() && next.Range().Start < r.End { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeAdjacent attempts to merge the segment containing r.Start with its +// predecessor, and the segment containing r.End-1 with its successor. +func (s *fileRefcountSet) MergeAdjacent(r __generics_imported0.FileRange) { + first := s.FindSegment(r.Start) + if first.Ok() { + if prev := first.PrevSegment(); prev.Ok() { + s.Merge(prev, first) + } + } + last := s.FindSegment(r.End - 1) + if last.Ok() { + if next := last.NextSegment(); next.Ok() { + s.Merge(last, next) + } + } +} + +// Split splits the given segment at the given key and returns iterators to the +// two resulting segments. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +// +// If the segment cannot be split at split (because split is at the start or +// end of the segment's range, so splitting would produce a segment with zero +// length, or because split falls outside the segment's range altogether), +// Split panics. +func (s *fileRefcountSet) Split(seg fileRefcountIterator, split uint64) (fileRefcountIterator, fileRefcountIterator) { + if !seg.Range().CanSplitAt(split) { + panic(fmt.Sprintf("can't split %v at %v", seg.Range(), split)) + } + return s.SplitUnchecked(seg, split) +} + +// SplitUnchecked splits the given segment at the given key and returns +// iterators to the two resulting segments. All existing iterators (including +// seg, but not including the returned iterators) are invalidated. +// +// Preconditions: seg.Start() < key < seg.End(). +func (s *fileRefcountSet) SplitUnchecked(seg fileRefcountIterator, split uint64) (fileRefcountIterator, fileRefcountIterator) { + val1, val2 := (fileRefcountSetFunctions{}).Split(seg.Range(), seg.Value(), split) + end2 := seg.End() + seg.SetEndUnchecked(split) + seg.SetValue(val1) + seg2 := s.InsertWithoutMergingUnchecked(seg.NextGap(), __generics_imported0.FileRange{split, end2}, val2) + + return seg2.PrevSegment(), seg2 +} + +// SplitAt splits the segment straddling split, if one exists. SplitAt returns +// true if a segment was split and false otherwise. If SplitAt splits a +// segment, all existing iterators are invalidated. +func (s *fileRefcountSet) SplitAt(split uint64) bool { + if seg := s.FindSegment(split); seg.Ok() && seg.Range().CanSplitAt(split) { + s.SplitUnchecked(seg, split) + return true + } + return false +} + +// Isolate ensures that the given segment's range does not escape r by +// splitting at r.Start and r.End if necessary, and returns an updated iterator +// to the bounded segment. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +func (s *fileRefcountSet) Isolate(seg fileRefcountIterator, r __generics_imported0.FileRange) fileRefcountIterator { + if seg.Range().CanSplitAt(r.Start) { + _, seg = s.SplitUnchecked(seg, r.Start) + } + if seg.Range().CanSplitAt(r.End) { + seg, _ = s.SplitUnchecked(seg, r.End) + } + return seg +} + +// ApplyContiguous applies a function to a contiguous range of segments, +// splitting if necessary. The function is applied until the first gap is +// encountered, at which point the gap is returned. If the function is applied +// across the entire range, a terminal gap is returned. All existing iterators +// are invalidated. +// +// N.B. The Iterator must not be invalidated by the function. +func (s *fileRefcountSet) ApplyContiguous(r __generics_imported0.FileRange, fn func(seg fileRefcountIterator)) fileRefcountGapIterator { + seg, gap := s.Find(r.Start) + if !seg.Ok() { + return gap + } + for { + seg = s.Isolate(seg, r) + fn(seg) + if seg.End() >= r.End { + return fileRefcountGapIterator{} + } + gap = seg.NextGap() + if !gap.IsEmpty() { + return gap + } + seg = gap.NextSegment() + if !seg.Ok() { + + return fileRefcountGapIterator{} + } + } +} + +// +stateify savable +type fileRefcountnode struct { + // An internal binary tree node looks like: + // + // K + // / \ + // Cl Cr + // + // where all keys in the subtree rooted by Cl (the left subtree) are less + // than K (the key of the parent node), and all keys in the subtree rooted + // by Cr (the right subtree) are greater than K. + // + // An internal B-tree node's indexes work out to look like: + // + // K0 K1 K2 ... Kn-1 + // / \/ \/ \ ... / \ + // C0 C1 C2 C3 ... Cn-1 Cn + // + // where n is nrSegments. + nrSegments int + + // parent is a pointer to this node's parent. If this node is root, parent + // is nil. + parent *fileRefcountnode + + // parentIndex is the index of this node in parent.children. + parentIndex int + + // Flag for internal nodes that is technically redundant with "children[0] + // != nil", but is stored in the first cache line. "hasChildren" rather + // than "isLeaf" because false must be the correct value for an empty root. + hasChildren bool + + // The longest gap within this node. If the node is a leaf, it's simply the + // maximum gap among all the (nrSegments+1) gaps formed by its nrSegments keys + // including the 0th and nrSegments-th gap possibly shared with its upper-level + // nodes; if it's a non-leaf node, it's the max of all children's maxGap. + maxGap fileRefcountdynamicGap + + // Nodes store keys and values in separate arrays to maximize locality in + // the common case (scanning keys for lookup). + keys [fileRefcountmaxDegree - 1]__generics_imported0.FileRange + values [fileRefcountmaxDegree - 1]int32 + children [fileRefcountmaxDegree]*fileRefcountnode +} + +// firstSegment returns the first segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *fileRefcountnode) firstSegment() fileRefcountIterator { + for n.hasChildren { + n = n.children[0] + } + return fileRefcountIterator{n, 0} +} + +// lastSegment returns the last segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *fileRefcountnode) lastSegment() fileRefcountIterator { + for n.hasChildren { + n = n.children[n.nrSegments] + } + return fileRefcountIterator{n, n.nrSegments - 1} +} + +func (n *fileRefcountnode) prevSibling() *fileRefcountnode { + if n.parent == nil || n.parentIndex == 0 { + return nil + } + return n.parent.children[n.parentIndex-1] +} + +func (n *fileRefcountnode) nextSibling() *fileRefcountnode { + if n.parent == nil || n.parentIndex == n.parent.nrSegments { + return nil + } + return n.parent.children[n.parentIndex+1] +} + +// rebalanceBeforeInsert splits n and its ancestors if they are full, as +// required for insertion, and returns an updated iterator to the position +// represented by gap. +func (n *fileRefcountnode) rebalanceBeforeInsert(gap fileRefcountGapIterator) fileRefcountGapIterator { + if n.nrSegments < fileRefcountmaxDegree-1 { + return gap + } + if n.parent != nil { + gap = n.parent.rebalanceBeforeInsert(gap) + } + if n.parent == nil { + + left := &fileRefcountnode{ + nrSegments: fileRefcountminDegree - 1, + parent: n, + parentIndex: 0, + hasChildren: n.hasChildren, + } + right := &fileRefcountnode{ + nrSegments: fileRefcountminDegree - 1, + parent: n, + parentIndex: 1, + hasChildren: n.hasChildren, + } + copy(left.keys[:fileRefcountminDegree-1], n.keys[:fileRefcountminDegree-1]) + copy(left.values[:fileRefcountminDegree-1], n.values[:fileRefcountminDegree-1]) + copy(right.keys[:fileRefcountminDegree-1], n.keys[fileRefcountminDegree:]) + copy(right.values[:fileRefcountminDegree-1], n.values[fileRefcountminDegree:]) + n.keys[0], n.values[0] = n.keys[fileRefcountminDegree-1], n.values[fileRefcountminDegree-1] + fileRefcountzeroValueSlice(n.values[1:]) + if n.hasChildren { + copy(left.children[:fileRefcountminDegree], n.children[:fileRefcountminDegree]) + copy(right.children[:fileRefcountminDegree], n.children[fileRefcountminDegree:]) + fileRefcountzeroNodeSlice(n.children[2:]) + for i := 0; i < fileRefcountminDegree; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + right.children[i].parent = right + right.children[i].parentIndex = i + } + } + n.nrSegments = 1 + n.hasChildren = true + n.children[0] = left + n.children[1] = right + + if fileRefcounttrackGaps != 0 { + left.updateMaxGapLocal() + right.updateMaxGapLocal() + } + if gap.node != n { + return gap + } + if gap.index < fileRefcountminDegree { + return fileRefcountGapIterator{left, gap.index} + } + return fileRefcountGapIterator{right, gap.index - fileRefcountminDegree} + } + + copy(n.parent.keys[n.parentIndex+1:], n.parent.keys[n.parentIndex:n.parent.nrSegments]) + copy(n.parent.values[n.parentIndex+1:], n.parent.values[n.parentIndex:n.parent.nrSegments]) + n.parent.keys[n.parentIndex], n.parent.values[n.parentIndex] = n.keys[fileRefcountminDegree-1], n.values[fileRefcountminDegree-1] + copy(n.parent.children[n.parentIndex+2:], n.parent.children[n.parentIndex+1:n.parent.nrSegments+1]) + for i := n.parentIndex + 2; i < n.parent.nrSegments+2; i++ { + n.parent.children[i].parentIndex = i + } + sibling := &fileRefcountnode{ + nrSegments: fileRefcountminDegree - 1, + parent: n.parent, + parentIndex: n.parentIndex + 1, + hasChildren: n.hasChildren, + } + n.parent.children[n.parentIndex+1] = sibling + n.parent.nrSegments++ + copy(sibling.keys[:fileRefcountminDegree-1], n.keys[fileRefcountminDegree:]) + copy(sibling.values[:fileRefcountminDegree-1], n.values[fileRefcountminDegree:]) + fileRefcountzeroValueSlice(n.values[fileRefcountminDegree-1:]) + if n.hasChildren { + copy(sibling.children[:fileRefcountminDegree], n.children[fileRefcountminDegree:]) + fileRefcountzeroNodeSlice(n.children[fileRefcountminDegree:]) + for i := 0; i < fileRefcountminDegree; i++ { + sibling.children[i].parent = sibling + sibling.children[i].parentIndex = i + } + } + n.nrSegments = fileRefcountminDegree - 1 + + if fileRefcounttrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + + if gap.node != n { + return gap + } + if gap.index < fileRefcountminDegree { + return gap + } + return fileRefcountGapIterator{sibling, gap.index - fileRefcountminDegree} +} + +// rebalanceAfterRemove "unsplits" n and its ancestors if they are deficient +// (contain fewer segments than required by B-tree invariants), as required for +// removal, and returns an updated iterator to the position represented by gap. +// +// Precondition: n is the only node in the tree that may currently violate a +// B-tree invariant. +func (n *fileRefcountnode) rebalanceAfterRemove(gap fileRefcountGapIterator) fileRefcountGapIterator { + for { + if n.nrSegments >= fileRefcountminDegree-1 { + return gap + } + if n.parent == nil { + + return gap + } + + if sibling := n.prevSibling(); sibling != nil && sibling.nrSegments >= fileRefcountminDegree { + copy(n.keys[1:], n.keys[:n.nrSegments]) + copy(n.values[1:], n.values[:n.nrSegments]) + n.keys[0] = n.parent.keys[n.parentIndex-1] + n.values[0] = n.parent.values[n.parentIndex-1] + n.parent.keys[n.parentIndex-1] = sibling.keys[sibling.nrSegments-1] + n.parent.values[n.parentIndex-1] = sibling.values[sibling.nrSegments-1] + fileRefcountSetFunctions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + copy(n.children[1:], n.children[:n.nrSegments+1]) + n.children[0] = sibling.children[sibling.nrSegments] + sibling.children[sibling.nrSegments] = nil + n.children[0].parent = n + n.children[0].parentIndex = 0 + for i := 1; i < n.nrSegments+2; i++ { + n.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + + if fileRefcounttrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + if gap.node == sibling && gap.index == sibling.nrSegments { + return fileRefcountGapIterator{n, 0} + } + if gap.node == n { + return fileRefcountGapIterator{n, gap.index + 1} + } + return gap + } + if sibling := n.nextSibling(); sibling != nil && sibling.nrSegments >= fileRefcountminDegree { + n.keys[n.nrSegments] = n.parent.keys[n.parentIndex] + n.values[n.nrSegments] = n.parent.values[n.parentIndex] + n.parent.keys[n.parentIndex] = sibling.keys[0] + n.parent.values[n.parentIndex] = sibling.values[0] + copy(sibling.keys[:sibling.nrSegments-1], sibling.keys[1:]) + copy(sibling.values[:sibling.nrSegments-1], sibling.values[1:]) + fileRefcountSetFunctions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + n.children[n.nrSegments+1] = sibling.children[0] + copy(sibling.children[:sibling.nrSegments], sibling.children[1:]) + sibling.children[sibling.nrSegments] = nil + n.children[n.nrSegments+1].parent = n + n.children[n.nrSegments+1].parentIndex = n.nrSegments + 1 + for i := 0; i < sibling.nrSegments; i++ { + sibling.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + + if fileRefcounttrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + if gap.node == sibling { + if gap.index == 0 { + return fileRefcountGapIterator{n, n.nrSegments} + } + return fileRefcountGapIterator{sibling, gap.index - 1} + } + return gap + } + + p := n.parent + if p.nrSegments == 1 { + + left, right := p.children[0], p.children[1] + p.nrSegments = left.nrSegments + right.nrSegments + 1 + p.hasChildren = left.hasChildren + p.keys[left.nrSegments] = p.keys[0] + p.values[left.nrSegments] = p.values[0] + copy(p.keys[:left.nrSegments], left.keys[:left.nrSegments]) + copy(p.values[:left.nrSegments], left.values[:left.nrSegments]) + copy(p.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(p.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(p.children[:left.nrSegments+1], left.children[:left.nrSegments+1]) + copy(p.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := 0; i < p.nrSegments+1; i++ { + p.children[i].parent = p + p.children[i].parentIndex = i + } + } else { + p.children[0] = nil + p.children[1] = nil + } + + if gap.node == left { + return fileRefcountGapIterator{p, gap.index} + } + if gap.node == right { + return fileRefcountGapIterator{p, gap.index + left.nrSegments + 1} + } + return gap + } + // Merge n and either sibling, along with the segment separating the + // two, into whichever of the two nodes comes first. This is the + // reverse of the non-root splitting case in + // node.rebalanceBeforeInsert. + var left, right *fileRefcountnode + if n.parentIndex > 0 { + left = n.prevSibling() + right = n + } else { + left = n + right = n.nextSibling() + } + + if gap.node == right { + gap = fileRefcountGapIterator{left, gap.index + left.nrSegments + 1} + } + left.keys[left.nrSegments] = p.keys[left.parentIndex] + left.values[left.nrSegments] = p.values[left.parentIndex] + copy(left.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(left.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(left.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := left.nrSegments + 1; i < left.nrSegments+right.nrSegments+2; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + } + } + left.nrSegments += right.nrSegments + 1 + copy(p.keys[left.parentIndex:], p.keys[left.parentIndex+1:p.nrSegments]) + copy(p.values[left.parentIndex:], p.values[left.parentIndex+1:p.nrSegments]) + fileRefcountSetFunctions{}.ClearValue(&p.values[p.nrSegments-1]) + copy(p.children[left.parentIndex+1:], p.children[left.parentIndex+2:p.nrSegments+1]) + for i := 0; i < p.nrSegments; i++ { + p.children[i].parentIndex = i + } + p.children[p.nrSegments] = nil + p.nrSegments-- + + if fileRefcounttrackGaps != 0 { + left.updateMaxGapLocal() + } + + n = p + } +} + +// updateMaxGapLeaf updates maxGap bottom-up from the calling leaf until no +// necessary update. +// +// Preconditions: n must be a leaf node, trackGaps must be 1. +func (n *fileRefcountnode) updateMaxGapLeaf() { + if n.hasChildren { + panic(fmt.Sprintf("updateMaxGapLeaf should always be called on leaf node: %v", n)) + } + max := n.calculateMaxGapLeaf() + if max == n.maxGap.Get() { + + return + } + oldMax := n.maxGap.Get() + n.maxGap.Set(max) + if max > oldMax { + + for p := n.parent; p != nil; p = p.parent { + if p.maxGap.Get() >= max { + + break + } + + p.maxGap.Set(max) + } + return + } + + for p := n.parent; p != nil; p = p.parent { + if p.maxGap.Get() > oldMax { + + break + } + + parentNewMax := p.calculateMaxGapInternal() + if p.maxGap.Get() == parentNewMax { + + break + } + + p.maxGap.Set(parentNewMax) + } +} + +// updateMaxGapLocal updates maxGap of the calling node solely with no +// propagation to ancestor nodes. +// +// Precondition: trackGaps must be 1. +func (n *fileRefcountnode) updateMaxGapLocal() { + if !n.hasChildren { + + n.maxGap.Set(n.calculateMaxGapLeaf()) + } else { + + n.maxGap.Set(n.calculateMaxGapInternal()) + } +} + +// calculateMaxGapLeaf iterates the gaps within a leaf node and calculate the +// max. +// +// Preconditions: n must be a leaf node. +func (n *fileRefcountnode) calculateMaxGapLeaf() uint64 { + max := fileRefcountGapIterator{n, 0}.Range().Length() + for i := 1; i <= n.nrSegments; i++ { + if current := (fileRefcountGapIterator{n, i}).Range().Length(); current > max { + max = current + } + } + return max +} + +// calculateMaxGapInternal iterates children's maxGap within an internal node n +// and calculate the max. +// +// Preconditions: n must be a non-leaf node. +func (n *fileRefcountnode) calculateMaxGapInternal() uint64 { + max := n.children[0].maxGap.Get() + for i := 1; i <= n.nrSegments; i++ { + if current := n.children[i].maxGap.Get(); current > max { + max = current + } + } + return max +} + +// searchFirstLargeEnoughGap returns the first gap having at least minSize length +// in the subtree rooted by n. If not found, return a terminal gap iterator. +func (n *fileRefcountnode) searchFirstLargeEnoughGap(minSize uint64) fileRefcountGapIterator { + if n.maxGap.Get() < minSize { + return fileRefcountGapIterator{} + } + if n.hasChildren { + for i := 0; i <= n.nrSegments; i++ { + if largeEnoughGap := n.children[i].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } + } else { + for i := 0; i <= n.nrSegments; i++ { + currentGap := fileRefcountGapIterator{n, i} + if currentGap.Range().Length() >= minSize { + return currentGap + } + } + } + panic(fmt.Sprintf("invalid maxGap in %v", n)) +} + +// searchLastLargeEnoughGap returns the last gap having at least minSize length +// in the subtree rooted by n. If not found, return a terminal gap iterator. +func (n *fileRefcountnode) searchLastLargeEnoughGap(minSize uint64) fileRefcountGapIterator { + if n.maxGap.Get() < minSize { + return fileRefcountGapIterator{} + } + if n.hasChildren { + for i := n.nrSegments; i >= 0; i-- { + if largeEnoughGap := n.children[i].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } + } else { + for i := n.nrSegments; i >= 0; i-- { + currentGap := fileRefcountGapIterator{n, i} + if currentGap.Range().Length() >= minSize { + return currentGap + } + } + } + panic(fmt.Sprintf("invalid maxGap in %v", n)) +} + +// A Iterator is conceptually one of: +// +// - A pointer to a segment in a set; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Iterators are copyable values and are meaningfully equality-comparable. The +// zero value of Iterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type fileRefcountIterator struct { + // node is the node containing the iterated segment. If the iterator is + // terminal, node is nil. + node *fileRefcountnode + + // index is the index of the segment in node.keys/values. + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (seg fileRefcountIterator) Ok() bool { + return seg.node != nil +} + +// Range returns the iterated segment's range key. +func (seg fileRefcountIterator) Range() __generics_imported0.FileRange { + return seg.node.keys[seg.index] +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (seg fileRefcountIterator) Start() uint64 { + return seg.node.keys[seg.index].Start +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (seg fileRefcountIterator) End() uint64 { + return seg.node.keys[seg.index].End +} + +// SetRangeUnchecked mutates the iterated segment's range key. This operation +// does not invalidate any iterators. +// +// Preconditions: +// +// - r.Length() > 0. +// +// - The new range must not overlap an existing one: If seg.NextSegment().Ok(), +// then r.end <= seg.NextSegment().Start(); if seg.PrevSegment().Ok(), then +// r.start >= seg.PrevSegment().End(). +func (seg fileRefcountIterator) SetRangeUnchecked(r __generics_imported0.FileRange) { + seg.node.keys[seg.index] = r +} + +// SetRange mutates the iterated segment's range key. If the new range would +// cause the iterated segment to overlap another segment, or if the new range +// is invalid, SetRange panics. This operation does not invalidate any +// iterators. +func (seg fileRefcountIterator) SetRange(r __generics_imported0.FileRange) { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if prev := seg.PrevSegment(); prev.Ok() && r.Start < prev.End() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, prev.Range())) + } + if next := seg.NextSegment(); next.Ok() && r.End > next.Start() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, next.Range())) + } + seg.SetRangeUnchecked(r) +} + +// SetStartUnchecked mutates the iterated segment's start. This operation does +// not invalidate any iterators. +// +// Preconditions: The new start must be valid: start < seg.End(); if +// seg.PrevSegment().Ok(), then start >= seg.PrevSegment().End(). +func (seg fileRefcountIterator) SetStartUnchecked(start uint64) { + seg.node.keys[seg.index].Start = start +} + +// SetStart mutates the iterated segment's start. If the new start value would +// cause the iterated segment to overlap another segment, or would result in an +// invalid range, SetStart panics. This operation does not invalidate any +// iterators. +func (seg fileRefcountIterator) SetStart(start uint64) { + if start >= seg.End() { + panic(fmt.Sprintf("new start %v would invalidate segment range %v", start, seg.Range())) + } + if prev := seg.PrevSegment(); prev.Ok() && start < prev.End() { + panic(fmt.Sprintf("new start %v would cause segment range %v to overlap segment range %v", start, seg.Range(), prev.Range())) + } + seg.SetStartUnchecked(start) +} + +// SetEndUnchecked mutates the iterated segment's end. This operation does not +// invalidate any iterators. +// +// Preconditions: The new end must be valid: end > seg.Start(); if +// seg.NextSegment().Ok(), then end <= seg.NextSegment().Start(). +func (seg fileRefcountIterator) SetEndUnchecked(end uint64) { + seg.node.keys[seg.index].End = end +} + +// SetEnd mutates the iterated segment's end. If the new end value would cause +// the iterated segment to overlap another segment, or would result in an +// invalid range, SetEnd panics. This operation does not invalidate any +// iterators. +func (seg fileRefcountIterator) SetEnd(end uint64) { + if end <= seg.Start() { + panic(fmt.Sprintf("new end %v would invalidate segment range %v", end, seg.Range())) + } + if next := seg.NextSegment(); next.Ok() && end > next.Start() { + panic(fmt.Sprintf("new end %v would cause segment range %v to overlap segment range %v", end, seg.Range(), next.Range())) + } + seg.SetEndUnchecked(end) +} + +// Value returns a copy of the iterated segment's value. +func (seg fileRefcountIterator) Value() int32 { + return seg.node.values[seg.index] +} + +// ValuePtr returns a pointer to the iterated segment's value. The pointer is +// invalidated if the iterator is invalidated. This operation does not +// invalidate any iterators. +func (seg fileRefcountIterator) ValuePtr() *int32 { + return &seg.node.values[seg.index] +} + +// SetValue mutates the iterated segment's value. This operation does not +// invalidate any iterators. +func (seg fileRefcountIterator) SetValue(val int32) { + seg.node.values[seg.index] = val +} + +// PrevSegment returns the iterated segment's predecessor. If there is no +// preceding segment, PrevSegment returns a terminal iterator. +func (seg fileRefcountIterator) PrevSegment() fileRefcountIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index].lastSegment() + } + if seg.index > 0 { + return fileRefcountIterator{seg.node, seg.index - 1} + } + if seg.node.parent == nil { + return fileRefcountIterator{} + } + return fileRefcountsegmentBeforePosition(seg.node.parent, seg.node.parentIndex) +} + +// NextSegment returns the iterated segment's successor. If there is no +// succeeding segment, NextSegment returns a terminal iterator. +func (seg fileRefcountIterator) NextSegment() fileRefcountIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment() + } + if seg.index < seg.node.nrSegments-1 { + return fileRefcountIterator{seg.node, seg.index + 1} + } + if seg.node.parent == nil { + return fileRefcountIterator{} + } + return fileRefcountsegmentAfterPosition(seg.node.parent, seg.node.parentIndex) +} + +// PrevGap returns the gap immediately before the iterated segment. +func (seg fileRefcountIterator) PrevGap() fileRefcountGapIterator { + if seg.node.hasChildren { + + return seg.node.children[seg.index].lastSegment().NextGap() + } + return fileRefcountGapIterator{seg.node, seg.index} +} + +// NextGap returns the gap immediately after the iterated segment. +func (seg fileRefcountIterator) NextGap() fileRefcountGapIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment().PrevGap() + } + return fileRefcountGapIterator{seg.node, seg.index + 1} +} + +// PrevNonEmpty returns the iterated segment's predecessor if it is adjacent, +// or the gap before the iterated segment otherwise. If seg.Start() == +// Functions.MinKey(), PrevNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by PrevNonEmpty will be +// non-terminal. +func (seg fileRefcountIterator) PrevNonEmpty() (fileRefcountIterator, fileRefcountGapIterator) { + gap := seg.PrevGap() + if gap.Range().Length() != 0 { + return fileRefcountIterator{}, gap + } + return gap.PrevSegment(), fileRefcountGapIterator{} +} + +// NextNonEmpty returns the iterated segment's successor if it is adjacent, or +// the gap after the iterated segment otherwise. If seg.End() == +// Functions.MaxKey(), NextNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by NextNonEmpty will be +// non-terminal. +func (seg fileRefcountIterator) NextNonEmpty() (fileRefcountIterator, fileRefcountGapIterator) { + gap := seg.NextGap() + if gap.Range().Length() != 0 { + return fileRefcountIterator{}, gap + } + return gap.NextSegment(), fileRefcountGapIterator{} +} + +// A GapIterator is conceptually one of: +// +// - A pointer to a position between two segments, before the first segment, or +// after the last segment in a set, called a *gap*; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Note that the gap between two adjacent segments exists (iterators to it are +// non-terminal), but has a length of zero. GapIterator.IsEmpty returns true +// for such gaps. An empty set contains a single gap, spanning the entire range +// of the set's keys. +// +// GapIterators are copyable values and are meaningfully equality-comparable. +// The zero value of GapIterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type fileRefcountGapIterator struct { + // The representation of a GapIterator is identical to that of an Iterator, + // except that index corresponds to positions between segments in the same + // way as for node.children (see comment for node.nrSegments). + node *fileRefcountnode + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (gap fileRefcountGapIterator) Ok() bool { + return gap.node != nil +} + +// Range returns the range spanned by the iterated gap. +func (gap fileRefcountGapIterator) Range() __generics_imported0.FileRange { + return __generics_imported0.FileRange{gap.Start(), gap.End()} +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (gap fileRefcountGapIterator) Start() uint64 { + if ps := gap.PrevSegment(); ps.Ok() { + return ps.End() + } + return fileRefcountSetFunctions{}.MinKey() +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (gap fileRefcountGapIterator) End() uint64 { + if ns := gap.NextSegment(); ns.Ok() { + return ns.Start() + } + return fileRefcountSetFunctions{}.MaxKey() +} + +// IsEmpty returns true if the iterated gap is empty (that is, the "gap" is +// between two adjacent segments.) +func (gap fileRefcountGapIterator) IsEmpty() bool { + return gap.Range().Length() == 0 +} + +// PrevSegment returns the segment immediately before the iterated gap. If no +// such segment exists, PrevSegment returns a terminal iterator. +func (gap fileRefcountGapIterator) PrevSegment() fileRefcountIterator { + return fileRefcountsegmentBeforePosition(gap.node, gap.index) +} + +// NextSegment returns the segment immediately after the iterated gap. If no +// such segment exists, NextSegment returns a terminal iterator. +func (gap fileRefcountGapIterator) NextSegment() fileRefcountIterator { + return fileRefcountsegmentAfterPosition(gap.node, gap.index) +} + +// PrevGap returns the iterated gap's predecessor. If no such gap exists, +// PrevGap returns a terminal iterator. +func (gap fileRefcountGapIterator) PrevGap() fileRefcountGapIterator { + seg := gap.PrevSegment() + if !seg.Ok() { + return fileRefcountGapIterator{} + } + return seg.PrevGap() +} + +// NextGap returns the iterated gap's successor. If no such gap exists, NextGap +// returns a terminal iterator. +func (gap fileRefcountGapIterator) NextGap() fileRefcountGapIterator { + seg := gap.NextSegment() + if !seg.Ok() { + return fileRefcountGapIterator{} + } + return seg.NextGap() +} + +// NextLargeEnoughGap returns the iterated gap's first next gap with larger +// length than minSize. If not found, return a terminal gap iterator (does NOT +// include this gap itself). +// +// Precondition: trackGaps must be 1. +func (gap fileRefcountGapIterator) NextLargeEnoughGap(minSize uint64) fileRefcountGapIterator { + if fileRefcounttrackGaps != 1 { + panic("set is not tracking gaps") + } + if gap.node != nil && gap.node.hasChildren && gap.index == gap.node.nrSegments { + + gap.node = gap.NextSegment().node + gap.index = 0 + return gap.nextLargeEnoughGapHelper(minSize) + } + return gap.nextLargeEnoughGapHelper(minSize) +} + +// nextLargeEnoughGapHelper is the helper function used by NextLargeEnoughGap +// to do the real recursions. +// +// Preconditions: gap is NOT the trailing gap of a non-leaf node. +func (gap fileRefcountGapIterator) nextLargeEnoughGapHelper(minSize uint64) fileRefcountGapIterator { + + for gap.node != nil && + (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == gap.node.nrSegments)) { + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + + if gap.node == nil { + return fileRefcountGapIterator{} + } + + gap.index++ + for gap.index <= gap.node.nrSegments { + if gap.node.hasChildren { + if largeEnoughGap := gap.node.children[gap.index].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } else { + if gap.Range().Length() >= minSize { + return gap + } + } + gap.index++ + } + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + if gap.node != nil && gap.index == gap.node.nrSegments { + + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + return gap.nextLargeEnoughGapHelper(minSize) +} + +// PrevLargeEnoughGap returns the iterated gap's first prev gap with larger or +// equal length than minSize. If not found, return a terminal gap iterator +// (does NOT include this gap itself). +// +// Precondition: trackGaps must be 1. +func (gap fileRefcountGapIterator) PrevLargeEnoughGap(minSize uint64) fileRefcountGapIterator { + if fileRefcounttrackGaps != 1 { + panic("set is not tracking gaps") + } + if gap.node != nil && gap.node.hasChildren && gap.index == 0 { + + gap.node = gap.PrevSegment().node + gap.index = gap.node.nrSegments + return gap.prevLargeEnoughGapHelper(minSize) + } + return gap.prevLargeEnoughGapHelper(minSize) +} + +// prevLargeEnoughGapHelper is the helper function used by PrevLargeEnoughGap +// to do the real recursions. +// +// Preconditions: gap is NOT the first gap of a non-leaf node. +func (gap fileRefcountGapIterator) prevLargeEnoughGapHelper(minSize uint64) fileRefcountGapIterator { + + for gap.node != nil && + (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == 0)) { + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + + if gap.node == nil { + return fileRefcountGapIterator{} + } + + gap.index-- + for gap.index >= 0 { + if gap.node.hasChildren { + if largeEnoughGap := gap.node.children[gap.index].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } else { + if gap.Range().Length() >= minSize { + return gap + } + } + gap.index-- + } + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + if gap.node != nil && gap.index == 0 { + + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + return gap.prevLargeEnoughGapHelper(minSize) +} + +// segmentBeforePosition returns the predecessor segment of the position given +// by n.children[i], which may or may not contain a child. If no such segment +// exists, segmentBeforePosition returns a terminal iterator. +func fileRefcountsegmentBeforePosition(n *fileRefcountnode, i int) fileRefcountIterator { + for i == 0 { + if n.parent == nil { + return fileRefcountIterator{} + } + n, i = n.parent, n.parentIndex + } + return fileRefcountIterator{n, i - 1} +} + +// segmentAfterPosition returns the successor segment of the position given by +// n.children[i], which may or may not contain a child. If no such segment +// exists, segmentAfterPosition returns a terminal iterator. +func fileRefcountsegmentAfterPosition(n *fileRefcountnode, i int) fileRefcountIterator { + for i == n.nrSegments { + if n.parent == nil { + return fileRefcountIterator{} + } + n, i = n.parent, n.parentIndex + } + return fileRefcountIterator{n, i} +} + +func fileRefcountzeroValueSlice(slice []int32) { + + for i := range slice { + fileRefcountSetFunctions{}.ClearValue(&slice[i]) + } +} + +func fileRefcountzeroNodeSlice(slice []*fileRefcountnode) { + for i := range slice { + slice[i] = nil + } +} + +// String stringifies a Set for debugging. +func (s *fileRefcountSet) String() string { + return s.root.String() +} + +// String stringifies a node (and all of its children) for debugging. +func (n *fileRefcountnode) String() string { + var buf bytes.Buffer + n.writeDebugString(&buf, "") + return buf.String() +} + +func (n *fileRefcountnode) writeDebugString(buf *bytes.Buffer, prefix string) { + if n.hasChildren != (n.nrSegments > 0 && n.children[0] != nil) { + buf.WriteString(prefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent value of hasChildren: got %v, want %v\n", n.hasChildren, !n.hasChildren)) + } + for i := 0; i < n.nrSegments; i++ { + if child := n.children[i]; child != nil { + cprefix := fmt.Sprintf("%s- % 3d ", prefix, i) + if child.parent != n || child.parentIndex != i { + buf.WriteString(cprefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent linkage to parent: got (%p, %d), want (%p, %d)\n", child.parent, child.parentIndex, n, i)) + } + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, i)) + } + buf.WriteString(prefix) + if n.hasChildren { + if fileRefcounttrackGaps != 0 { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v, maxGap: %d\n", i, n.keys[i], n.values[i], n.maxGap.Get())) + } else { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + } else { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + } + if child := n.children[n.nrSegments]; child != nil { + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, n.nrSegments)) + } +} + +// SegmentDataSlices represents segments from a set as slices of start, end, and +// values. SegmentDataSlices is primarily used as an intermediate representation +// for save/restore and the layout here is optimized for that. +// +// +stateify savable +type fileRefcountSegmentDataSlices struct { + Start []uint64 + End []uint64 + Values []int32 +} + +// ExportSortedSlice returns a copy of all segments in the given set, in ascending +// key order. +func (s *fileRefcountSet) ExportSortedSlices() *fileRefcountSegmentDataSlices { + var sds fileRefcountSegmentDataSlices + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sds.Start = append(sds.Start, seg.Start()) + sds.End = append(sds.End, seg.End()) + sds.Values = append(sds.Values, seg.Value()) + } + sds.Start = sds.Start[:len(sds.Start):len(sds.Start)] + sds.End = sds.End[:len(sds.End):len(sds.End)] + sds.Values = sds.Values[:len(sds.Values):len(sds.Values)] + return &sds +} + +// ImportSortedSlice initializes the given set from the given slice. +// +// Preconditions: s must be empty. sds must represent a valid set (the segments +// in sds must have valid lengths that do not overlap). The segments in sds +// must be sorted in ascending key order. +func (s *fileRefcountSet) ImportSortedSlices(sds *fileRefcountSegmentDataSlices) error { + if !s.IsEmpty() { + return fmt.Errorf("cannot import into non-empty set %v", s) + } + gap := s.FirstGap() + for i := range sds.Start { + r := __generics_imported0.FileRange{sds.Start[i], sds.End[i]} + if !gap.Range().IsSupersetOf(r) { + return fmt.Errorf("segment overlaps a preceding segment or is incorrectly sorted: [%d, %d) => %v", sds.Start[i], sds.End[i], sds.Values[i]) + } + gap = s.InsertWithoutMerging(gap, r, sds.Values[i]).NextGap() + } + return nil +} + +// segmentTestCheck returns an error if s is incorrectly sorted, does not +// contain exactly expectedSegments segments, or contains a segment which +// fails the passed check. +// +// This should be used only for testing, and has been added to this package for +// templating convenience. +func (s *fileRefcountSet) segmentTestCheck(expectedSegments int, segFunc func(int, __generics_imported0.FileRange, int32) error) error { + havePrev := false + prev := uint64(0) + nrSegments := 0 + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + next := seg.Start() + if havePrev && prev >= next { + return fmt.Errorf("incorrect order: key %d (segment %d) >= key %d (segment %d)", prev, nrSegments-1, next, nrSegments) + } + if segFunc != nil { + if err := segFunc(nrSegments, seg.Range(), seg.Value()); err != nil { + return err + } + } + prev = next + havePrev = true + nrSegments++ + } + if nrSegments != expectedSegments { + return fmt.Errorf("incorrect number of segments: got %d, wanted %d", nrSegments, expectedSegments) + } + return nil +} + +// countSegments counts the number of segments in the set. +// +// Similar to Check, this should only be used for testing. +func (s *fileRefcountSet) countSegments() (segments int) { + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + segments++ + } + return segments +} +func (s *fileRefcountSet) saveRoot() *fileRefcountSegmentDataSlices { + return s.ExportSortedSlices() +} + +func (s *fileRefcountSet) loadRoot(sds *fileRefcountSegmentDataSlices) { + if err := s.ImportSortedSlices(sds); err != nil { + panic(err) + } +} diff --git a/pkg/sentry/mm/io_list.go b/pkg/sentry/mm/io_list.go new file mode 100644 index 000000000..ae0f19fc5 --- /dev/null +++ b/pkg/sentry/mm/io_list.go @@ -0,0 +1,193 @@ +package mm + +// ElementMapper provides an identity mapping by default. +// +// This can be replaced to provide a struct that maps elements to linker +// objects, if they are not the same. An ElementMapper is not typically +// required if: Linker is left as is, Element is left as is, or Linker and +// Element are the same type. +type ioElementMapper struct{} + +// linkerFor maps an Element to a Linker. +// +// This default implementation should be inlined. +// +//go:nosplit +func (ioElementMapper) linkerFor(elem *ioResult) *ioResult { return elem } + +// List is an intrusive list. Entries can be added to or removed from the list +// in O(1) time and with no additional memory allocations. +// +// The zero value for List is an empty list ready to use. +// +// To iterate over a list (where l is a List): +// for e := l.Front(); e != nil; e = e.Next() { +// // do something with e. +// } +// +// +stateify savable +type ioList struct { + head *ioResult + tail *ioResult +} + +// Reset resets list l to the empty state. +func (l *ioList) Reset() { + l.head = nil + l.tail = nil +} + +// Empty returns true iff the list is empty. +func (l *ioList) Empty() bool { + return l.head == nil +} + +// Front returns the first element of list l or nil. +func (l *ioList) Front() *ioResult { + return l.head +} + +// Back returns the last element of list l or nil. +func (l *ioList) Back() *ioResult { + return l.tail +} + +// Len returns the number of elements in the list. +// +// NOTE: This is an O(n) operation. +func (l *ioList) Len() (count int) { + for e := l.Front(); e != nil; e = e.Next() { + count++ + } + return count +} + +// PushFront inserts the element e at the front of list l. +func (l *ioList) PushFront(e *ioResult) { + linker := ioElementMapper{}.linkerFor(e) + linker.SetNext(l.head) + linker.SetPrev(nil) + if l.head != nil { + ioElementMapper{}.linkerFor(l.head).SetPrev(e) + } else { + l.tail = e + } + + l.head = e +} + +// PushBack inserts the element e at the back of list l. +func (l *ioList) PushBack(e *ioResult) { + linker := ioElementMapper{}.linkerFor(e) + linker.SetNext(nil) + linker.SetPrev(l.tail) + if l.tail != nil { + ioElementMapper{}.linkerFor(l.tail).SetNext(e) + } else { + l.head = e + } + + l.tail = e +} + +// PushBackList inserts list m at the end of list l, emptying m. +func (l *ioList) PushBackList(m *ioList) { + if l.head == nil { + l.head = m.head + l.tail = m.tail + } else if m.head != nil { + ioElementMapper{}.linkerFor(l.tail).SetNext(m.head) + ioElementMapper{}.linkerFor(m.head).SetPrev(l.tail) + + l.tail = m.tail + } + m.head = nil + m.tail = nil +} + +// InsertAfter inserts e after b. +func (l *ioList) InsertAfter(b, e *ioResult) { + bLinker := ioElementMapper{}.linkerFor(b) + eLinker := ioElementMapper{}.linkerFor(e) + + a := bLinker.Next() + + eLinker.SetNext(a) + eLinker.SetPrev(b) + bLinker.SetNext(e) + + if a != nil { + ioElementMapper{}.linkerFor(a).SetPrev(e) + } else { + l.tail = e + } +} + +// InsertBefore inserts e before a. +func (l *ioList) InsertBefore(a, e *ioResult) { + aLinker := ioElementMapper{}.linkerFor(a) + eLinker := ioElementMapper{}.linkerFor(e) + + b := aLinker.Prev() + eLinker.SetNext(a) + eLinker.SetPrev(b) + aLinker.SetPrev(e) + + if b != nil { + ioElementMapper{}.linkerFor(b).SetNext(e) + } else { + l.head = e + } +} + +// Remove removes e from l. +func (l *ioList) Remove(e *ioResult) { + linker := ioElementMapper{}.linkerFor(e) + prev := linker.Prev() + next := linker.Next() + + if prev != nil { + ioElementMapper{}.linkerFor(prev).SetNext(next) + } else { + l.head = next + } + + if next != nil { + ioElementMapper{}.linkerFor(next).SetPrev(prev) + } else { + l.tail = prev + } + + linker.SetNext(nil) + linker.SetPrev(nil) +} + +// Entry is a default implementation of Linker. Users can add anonymous fields +// of this type to their structs to make them automatically implement the +// methods needed by List. +// +// +stateify savable +type ioEntry struct { + next *ioResult + prev *ioResult +} + +// Next returns the entry that follows e in the list. +func (e *ioEntry) Next() *ioResult { + return e.next +} + +// Prev returns the entry that precedes e in the list. +func (e *ioEntry) Prev() *ioResult { + return e.prev +} + +// SetNext assigns 'entry' as the entry that follows e in the list. +func (e *ioEntry) SetNext(elem *ioResult) { + e.next = elem +} + +// SetPrev assigns 'entry' as the entry that precedes e in the list. +func (e *ioEntry) SetPrev(elem *ioResult) { + e.prev = elem +} diff --git a/pkg/sentry/mm/mm_state_autogen.go b/pkg/sentry/mm/mm_state_autogen.go new file mode 100644 index 000000000..fde35bcd8 --- /dev/null +++ b/pkg/sentry/mm/mm_state_autogen.go @@ -0,0 +1,404 @@ +// automatically generated by stateify. + +package mm + +import ( + "gvisor.dev/gvisor/pkg/state" +) + +func (x *aioManager) beforeSave() {} +func (x *aioManager) save(m state.Map) { + x.beforeSave() + m.Save("contexts", &x.contexts) +} + +func (x *aioManager) afterLoad() {} +func (x *aioManager) load(m state.Map) { + m.Load("contexts", &x.contexts) +} + +func (x *ioResult) beforeSave() {} +func (x *ioResult) save(m state.Map) { + x.beforeSave() + m.Save("data", &x.data) + m.Save("ioEntry", &x.ioEntry) +} + +func (x *ioResult) afterLoad() {} +func (x *ioResult) load(m state.Map) { + m.Load("data", &x.data) + m.Load("ioEntry", &x.ioEntry) +} + +func (x *AIOContext) beforeSave() {} +func (x *AIOContext) save(m state.Map) { + x.beforeSave() + if !state.IsZeroValue(&x.dead) { + m.Failf("dead is %#v, expected zero", &x.dead) + } + m.Save("results", &x.results) + m.Save("maxOutstanding", &x.maxOutstanding) + m.Save("outstanding", &x.outstanding) +} + +func (x *AIOContext) load(m state.Map) { + m.Load("results", &x.results) + m.Load("maxOutstanding", &x.maxOutstanding) + m.Load("outstanding", &x.outstanding) + m.AfterLoad(x.afterLoad) +} + +func (x *aioMappable) beforeSave() {} +func (x *aioMappable) save(m state.Map) { + x.beforeSave() + m.Save("AtomicRefCount", &x.AtomicRefCount) + m.Save("mfp", &x.mfp) + m.Save("fr", &x.fr) +} + +func (x *aioMappable) afterLoad() {} +func (x *aioMappable) load(m state.Map) { + m.Load("AtomicRefCount", &x.AtomicRefCount) + m.Load("mfp", &x.mfp) + m.Load("fr", &x.fr) +} + +func (x *fileRefcountSet) beforeSave() {} +func (x *fileRefcountSet) save(m state.Map) { + x.beforeSave() + var root *fileRefcountSegmentDataSlices = x.saveRoot() + m.SaveValue("root", root) +} + +func (x *fileRefcountSet) afterLoad() {} +func (x *fileRefcountSet) load(m state.Map) { + m.LoadValue("root", new(*fileRefcountSegmentDataSlices), func(y interface{}) { x.loadRoot(y.(*fileRefcountSegmentDataSlices)) }) +} + +func (x *fileRefcountnode) beforeSave() {} +func (x *fileRefcountnode) save(m state.Map) { + x.beforeSave() + m.Save("nrSegments", &x.nrSegments) + m.Save("parent", &x.parent) + m.Save("parentIndex", &x.parentIndex) + m.Save("hasChildren", &x.hasChildren) + m.Save("maxGap", &x.maxGap) + m.Save("keys", &x.keys) + m.Save("values", &x.values) + m.Save("children", &x.children) +} + +func (x *fileRefcountnode) afterLoad() {} +func (x *fileRefcountnode) load(m state.Map) { + m.Load("nrSegments", &x.nrSegments) + m.Load("parent", &x.parent) + m.Load("parentIndex", &x.parentIndex) + m.Load("hasChildren", &x.hasChildren) + m.Load("maxGap", &x.maxGap) + m.Load("keys", &x.keys) + m.Load("values", &x.values) + m.Load("children", &x.children) +} + +func (x *fileRefcountSegmentDataSlices) beforeSave() {} +func (x *fileRefcountSegmentDataSlices) save(m state.Map) { + x.beforeSave() + m.Save("Start", &x.Start) + m.Save("End", &x.End) + m.Save("Values", &x.Values) +} + +func (x *fileRefcountSegmentDataSlices) afterLoad() {} +func (x *fileRefcountSegmentDataSlices) load(m state.Map) { + m.Load("Start", &x.Start) + m.Load("End", &x.End) + m.Load("Values", &x.Values) +} + +func (x *ioList) beforeSave() {} +func (x *ioList) save(m state.Map) { + x.beforeSave() + m.Save("head", &x.head) + m.Save("tail", &x.tail) +} + +func (x *ioList) afterLoad() {} +func (x *ioList) load(m state.Map) { + m.Load("head", &x.head) + m.Load("tail", &x.tail) +} + +func (x *ioEntry) beforeSave() {} +func (x *ioEntry) save(m state.Map) { + x.beforeSave() + m.Save("next", &x.next) + m.Save("prev", &x.prev) +} + +func (x *ioEntry) afterLoad() {} +func (x *ioEntry) load(m state.Map) { + m.Load("next", &x.next) + m.Load("prev", &x.prev) +} + +func (x *MemoryManager) save(m state.Map) { + x.beforeSave() + if !state.IsZeroValue(&x.active) { + m.Failf("active is %#v, expected zero", &x.active) + } + if !state.IsZeroValue(&x.captureInvalidations) { + m.Failf("captureInvalidations is %#v, expected zero", &x.captureInvalidations) + } + m.Save("p", &x.p) + m.Save("mfp", &x.mfp) + m.Save("layout", &x.layout) + m.Save("privateRefs", &x.privateRefs) + m.Save("users", &x.users) + m.Save("vmas", &x.vmas) + m.Save("brk", &x.brk) + m.Save("usageAS", &x.usageAS) + m.Save("lockedAS", &x.lockedAS) + m.Save("dataAS", &x.dataAS) + m.Save("defMLockMode", &x.defMLockMode) + m.Save("pmas", &x.pmas) + m.Save("curRSS", &x.curRSS) + m.Save("maxRSS", &x.maxRSS) + m.Save("argv", &x.argv) + m.Save("envv", &x.envv) + m.Save("auxv", &x.auxv) + m.Save("executable", &x.executable) + m.Save("dumpability", &x.dumpability) + m.Save("aioManager", &x.aioManager) + m.Save("sleepForActivation", &x.sleepForActivation) + m.Save("vdsoSigReturnAddr", &x.vdsoSigReturnAddr) +} + +func (x *MemoryManager) load(m state.Map) { + m.Load("p", &x.p) + m.Load("mfp", &x.mfp) + m.Load("layout", &x.layout) + m.Load("privateRefs", &x.privateRefs) + m.Load("users", &x.users) + m.Load("vmas", &x.vmas) + m.Load("brk", &x.brk) + m.Load("usageAS", &x.usageAS) + m.Load("lockedAS", &x.lockedAS) + m.Load("dataAS", &x.dataAS) + m.Load("defMLockMode", &x.defMLockMode) + m.Load("pmas", &x.pmas) + m.Load("curRSS", &x.curRSS) + m.Load("maxRSS", &x.maxRSS) + m.Load("argv", &x.argv) + m.Load("envv", &x.envv) + m.Load("auxv", &x.auxv) + m.Load("executable", &x.executable) + m.Load("dumpability", &x.dumpability) + m.Load("aioManager", &x.aioManager) + m.Load("sleepForActivation", &x.sleepForActivation) + m.Load("vdsoSigReturnAddr", &x.vdsoSigReturnAddr) + m.AfterLoad(x.afterLoad) +} + +func (x *vma) beforeSave() {} +func (x *vma) save(m state.Map) { + x.beforeSave() + var realPerms int = x.saveRealPerms() + m.SaveValue("realPerms", realPerms) + m.Save("mappable", &x.mappable) + m.Save("off", &x.off) + m.Save("dontfork", &x.dontfork) + m.Save("mlockMode", &x.mlockMode) + m.Save("numaPolicy", &x.numaPolicy) + m.Save("numaNodemask", &x.numaNodemask) + m.Save("id", &x.id) + m.Save("hint", &x.hint) +} + +func (x *vma) afterLoad() {} +func (x *vma) load(m state.Map) { + m.Load("mappable", &x.mappable) + m.Load("off", &x.off) + m.Load("dontfork", &x.dontfork) + m.Load("mlockMode", &x.mlockMode) + m.Load("numaPolicy", &x.numaPolicy) + m.Load("numaNodemask", &x.numaNodemask) + m.Load("id", &x.id) + m.Load("hint", &x.hint) + m.LoadValue("realPerms", new(int), func(y interface{}) { x.loadRealPerms(y.(int)) }) +} + +func (x *pma) beforeSave() {} +func (x *pma) save(m state.Map) { + x.beforeSave() + m.Save("off", &x.off) + m.Save("translatePerms", &x.translatePerms) + m.Save("effectivePerms", &x.effectivePerms) + m.Save("maxPerms", &x.maxPerms) + m.Save("needCOW", &x.needCOW) + m.Save("private", &x.private) +} + +func (x *pma) afterLoad() {} +func (x *pma) load(m state.Map) { + m.Load("off", &x.off) + m.Load("translatePerms", &x.translatePerms) + m.Load("effectivePerms", &x.effectivePerms) + m.Load("maxPerms", &x.maxPerms) + m.Load("needCOW", &x.needCOW) + m.Load("private", &x.private) +} + +func (x *privateRefs) beforeSave() {} +func (x *privateRefs) save(m state.Map) { + x.beforeSave() + m.Save("refs", &x.refs) +} + +func (x *privateRefs) afterLoad() {} +func (x *privateRefs) load(m state.Map) { + m.Load("refs", &x.refs) +} + +func (x *pmaSet) beforeSave() {} +func (x *pmaSet) save(m state.Map) { + x.beforeSave() + var root *pmaSegmentDataSlices = x.saveRoot() + m.SaveValue("root", root) +} + +func (x *pmaSet) afterLoad() {} +func (x *pmaSet) load(m state.Map) { + m.LoadValue("root", new(*pmaSegmentDataSlices), func(y interface{}) { x.loadRoot(y.(*pmaSegmentDataSlices)) }) +} + +func (x *pmanode) beforeSave() {} +func (x *pmanode) save(m state.Map) { + x.beforeSave() + m.Save("nrSegments", &x.nrSegments) + m.Save("parent", &x.parent) + m.Save("parentIndex", &x.parentIndex) + m.Save("hasChildren", &x.hasChildren) + m.Save("maxGap", &x.maxGap) + m.Save("keys", &x.keys) + m.Save("values", &x.values) + m.Save("children", &x.children) +} + +func (x *pmanode) afterLoad() {} +func (x *pmanode) load(m state.Map) { + m.Load("nrSegments", &x.nrSegments) + m.Load("parent", &x.parent) + m.Load("parentIndex", &x.parentIndex) + m.Load("hasChildren", &x.hasChildren) + m.Load("maxGap", &x.maxGap) + m.Load("keys", &x.keys) + m.Load("values", &x.values) + m.Load("children", &x.children) +} + +func (x *pmaSegmentDataSlices) beforeSave() {} +func (x *pmaSegmentDataSlices) save(m state.Map) { + x.beforeSave() + m.Save("Start", &x.Start) + m.Save("End", &x.End) + m.Save("Values", &x.Values) +} + +func (x *pmaSegmentDataSlices) afterLoad() {} +func (x *pmaSegmentDataSlices) load(m state.Map) { + m.Load("Start", &x.Start) + m.Load("End", &x.End) + m.Load("Values", &x.Values) +} + +func (x *SpecialMappable) beforeSave() {} +func (x *SpecialMappable) save(m state.Map) { + x.beforeSave() + m.Save("AtomicRefCount", &x.AtomicRefCount) + m.Save("mfp", &x.mfp) + m.Save("fr", &x.fr) + m.Save("name", &x.name) +} + +func (x *SpecialMappable) afterLoad() {} +func (x *SpecialMappable) load(m state.Map) { + m.Load("AtomicRefCount", &x.AtomicRefCount) + m.Load("mfp", &x.mfp) + m.Load("fr", &x.fr) + m.Load("name", &x.name) +} + +func (x *vmaSet) beforeSave() {} +func (x *vmaSet) save(m state.Map) { + x.beforeSave() + var root *vmaSegmentDataSlices = x.saveRoot() + m.SaveValue("root", root) +} + +func (x *vmaSet) afterLoad() {} +func (x *vmaSet) load(m state.Map) { + m.LoadValue("root", new(*vmaSegmentDataSlices), func(y interface{}) { x.loadRoot(y.(*vmaSegmentDataSlices)) }) +} + +func (x *vmanode) beforeSave() {} +func (x *vmanode) save(m state.Map) { + x.beforeSave() + m.Save("nrSegments", &x.nrSegments) + m.Save("parent", &x.parent) + m.Save("parentIndex", &x.parentIndex) + m.Save("hasChildren", &x.hasChildren) + m.Save("maxGap", &x.maxGap) + m.Save("keys", &x.keys) + m.Save("values", &x.values) + m.Save("children", &x.children) +} + +func (x *vmanode) afterLoad() {} +func (x *vmanode) load(m state.Map) { + m.Load("nrSegments", &x.nrSegments) + m.Load("parent", &x.parent) + m.Load("parentIndex", &x.parentIndex) + m.Load("hasChildren", &x.hasChildren) + m.Load("maxGap", &x.maxGap) + m.Load("keys", &x.keys) + m.Load("values", &x.values) + m.Load("children", &x.children) +} + +func (x *vmaSegmentDataSlices) beforeSave() {} +func (x *vmaSegmentDataSlices) save(m state.Map) { + x.beforeSave() + m.Save("Start", &x.Start) + m.Save("End", &x.End) + m.Save("Values", &x.Values) +} + +func (x *vmaSegmentDataSlices) afterLoad() {} +func (x *vmaSegmentDataSlices) load(m state.Map) { + m.Load("Start", &x.Start) + m.Load("End", &x.End) + m.Load("Values", &x.Values) +} + +func init() { + state.Register("pkg/sentry/mm.aioManager", (*aioManager)(nil), state.Fns{Save: (*aioManager).save, Load: (*aioManager).load}) + state.Register("pkg/sentry/mm.ioResult", (*ioResult)(nil), state.Fns{Save: (*ioResult).save, Load: (*ioResult).load}) + state.Register("pkg/sentry/mm.AIOContext", (*AIOContext)(nil), state.Fns{Save: (*AIOContext).save, Load: (*AIOContext).load}) + state.Register("pkg/sentry/mm.aioMappable", (*aioMappable)(nil), state.Fns{Save: (*aioMappable).save, Load: (*aioMappable).load}) + state.Register("pkg/sentry/mm.fileRefcountSet", (*fileRefcountSet)(nil), state.Fns{Save: (*fileRefcountSet).save, Load: (*fileRefcountSet).load}) + state.Register("pkg/sentry/mm.fileRefcountnode", (*fileRefcountnode)(nil), state.Fns{Save: (*fileRefcountnode).save, Load: (*fileRefcountnode).load}) + state.Register("pkg/sentry/mm.fileRefcountSegmentDataSlices", (*fileRefcountSegmentDataSlices)(nil), state.Fns{Save: (*fileRefcountSegmentDataSlices).save, Load: (*fileRefcountSegmentDataSlices).load}) + state.Register("pkg/sentry/mm.ioList", (*ioList)(nil), state.Fns{Save: (*ioList).save, Load: (*ioList).load}) + state.Register("pkg/sentry/mm.ioEntry", (*ioEntry)(nil), state.Fns{Save: (*ioEntry).save, Load: (*ioEntry).load}) + state.Register("pkg/sentry/mm.MemoryManager", (*MemoryManager)(nil), state.Fns{Save: (*MemoryManager).save, Load: (*MemoryManager).load}) + state.Register("pkg/sentry/mm.vma", (*vma)(nil), state.Fns{Save: (*vma).save, Load: (*vma).load}) + state.Register("pkg/sentry/mm.pma", (*pma)(nil), state.Fns{Save: (*pma).save, Load: (*pma).load}) + state.Register("pkg/sentry/mm.privateRefs", (*privateRefs)(nil), state.Fns{Save: (*privateRefs).save, Load: (*privateRefs).load}) + state.Register("pkg/sentry/mm.pmaSet", (*pmaSet)(nil), state.Fns{Save: (*pmaSet).save, Load: (*pmaSet).load}) + state.Register("pkg/sentry/mm.pmanode", (*pmanode)(nil), state.Fns{Save: (*pmanode).save, Load: (*pmanode).load}) + state.Register("pkg/sentry/mm.pmaSegmentDataSlices", (*pmaSegmentDataSlices)(nil), state.Fns{Save: (*pmaSegmentDataSlices).save, Load: (*pmaSegmentDataSlices).load}) + state.Register("pkg/sentry/mm.SpecialMappable", (*SpecialMappable)(nil), state.Fns{Save: (*SpecialMappable).save, Load: (*SpecialMappable).load}) + state.Register("pkg/sentry/mm.vmaSet", (*vmaSet)(nil), state.Fns{Save: (*vmaSet).save, Load: (*vmaSet).load}) + state.Register("pkg/sentry/mm.vmanode", (*vmanode)(nil), state.Fns{Save: (*vmanode).save, Load: (*vmanode).load}) + state.Register("pkg/sentry/mm.vmaSegmentDataSlices", (*vmaSegmentDataSlices)(nil), state.Fns{Save: (*vmaSegmentDataSlices).save, Load: (*vmaSegmentDataSlices).load}) +} diff --git a/pkg/sentry/mm/mm_test.go b/pkg/sentry/mm/mm_test.go deleted file mode 100644 index fdc308542..000000000 --- a/pkg/sentry/mm/mm_test.go +++ /dev/null @@ -1,230 +0,0 @@ -// Copyright 2018 The gVisor Authors. -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -package mm - -import ( - "testing" - - "gvisor.dev/gvisor/pkg/context" - "gvisor.dev/gvisor/pkg/sentry/arch" - "gvisor.dev/gvisor/pkg/sentry/contexttest" - "gvisor.dev/gvisor/pkg/sentry/limits" - "gvisor.dev/gvisor/pkg/sentry/memmap" - "gvisor.dev/gvisor/pkg/sentry/pgalloc" - "gvisor.dev/gvisor/pkg/sentry/platform" - "gvisor.dev/gvisor/pkg/syserror" - "gvisor.dev/gvisor/pkg/usermem" -) - -func testMemoryManager(ctx context.Context) *MemoryManager { - p := platform.FromContext(ctx) - mfp := pgalloc.MemoryFileProviderFromContext(ctx) - mm := NewMemoryManager(p, mfp, false) - mm.layout = arch.MmapLayout{ - MinAddr: p.MinUserAddress(), - MaxAddr: p.MaxUserAddress(), - BottomUpBase: p.MinUserAddress(), - TopDownBase: p.MaxUserAddress(), - } - return mm -} - -func (mm *MemoryManager) realUsageAS() uint64 { - return uint64(mm.vmas.Span()) -} - -func TestUsageASUpdates(t *testing.T) { - ctx := contexttest.Context(t) - mm := testMemoryManager(ctx) - defer mm.DecUsers(ctx) - - addr, err := mm.MMap(ctx, memmap.MMapOpts{ - Length: 2 * usermem.PageSize, - }) - if err != nil { - t.Fatalf("MMap got err %v want nil", err) - } - realUsage := mm.realUsageAS() - if mm.usageAS != realUsage { - t.Fatalf("usageAS believes %v bytes are mapped; %v bytes are actually mapped", mm.usageAS, realUsage) - } - - mm.MUnmap(ctx, addr, usermem.PageSize) - realUsage = mm.realUsageAS() - if mm.usageAS != realUsage { - t.Fatalf("usageAS believes %v bytes are mapped; %v bytes are actually mapped", mm.usageAS, realUsage) - } -} - -func (mm *MemoryManager) realDataAS() uint64 { - var sz uint64 - for seg := mm.vmas.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { - vma := seg.Value() - if vma.isPrivateDataLocked() { - sz += uint64(seg.Range().Length()) - } - } - return sz -} - -func TestDataASUpdates(t *testing.T) { - ctx := contexttest.Context(t) - mm := testMemoryManager(ctx) - defer mm.DecUsers(ctx) - - addr, err := mm.MMap(ctx, memmap.MMapOpts{ - Length: 3 * usermem.PageSize, - Private: true, - Perms: usermem.Write, - MaxPerms: usermem.AnyAccess, - }) - if err != nil { - t.Fatalf("MMap got err %v want nil", err) - } - if mm.dataAS == 0 { - t.Fatalf("dataAS is 0, wanted not 0") - } - realDataAS := mm.realDataAS() - if mm.dataAS != realDataAS { - t.Fatalf("dataAS believes %v bytes are mapped; %v bytes are actually mapped", mm.dataAS, realDataAS) - } - - mm.MUnmap(ctx, addr, usermem.PageSize) - realDataAS = mm.realDataAS() - if mm.dataAS != realDataAS { - t.Fatalf("dataAS believes %v bytes are mapped; %v bytes are actually mapped", mm.dataAS, realDataAS) - } - - mm.MProtect(addr+usermem.PageSize, usermem.PageSize, usermem.Read, false) - realDataAS = mm.realDataAS() - if mm.dataAS != realDataAS { - t.Fatalf("dataAS believes %v bytes are mapped; %v bytes are actually mapped", mm.dataAS, realDataAS) - } - - mm.MRemap(ctx, addr+2*usermem.PageSize, usermem.PageSize, 2*usermem.PageSize, MRemapOpts{ - Move: MRemapMayMove, - }) - realDataAS = mm.realDataAS() - if mm.dataAS != realDataAS { - t.Fatalf("dataAS believes %v bytes are mapped; %v bytes are actually mapped", mm.dataAS, realDataAS) - } -} - -func TestBrkDataLimitUpdates(t *testing.T) { - limitSet := limits.NewLimitSet() - limitSet.Set(limits.Data, limits.Limit{}, true /* privileged */) // zero RLIMIT_DATA - - ctx := contexttest.WithLimitSet(contexttest.Context(t), limitSet) - mm := testMemoryManager(ctx) - defer mm.DecUsers(ctx) - - // Try to extend the brk by one page and expect doing so to fail. - oldBrk, _ := mm.Brk(ctx, 0) - if newBrk, _ := mm.Brk(ctx, oldBrk+usermem.PageSize); newBrk != oldBrk { - t.Errorf("brk() increased data segment above RLIMIT_DATA (old brk = %#x, new brk = %#x", oldBrk, newBrk) - } -} - -// TestIOAfterUnmap ensures that IO fails after unmap. -func TestIOAfterUnmap(t *testing.T) { - ctx := contexttest.Context(t) - mm := testMemoryManager(ctx) - defer mm.DecUsers(ctx) - - addr, err := mm.MMap(ctx, memmap.MMapOpts{ - Length: usermem.PageSize, - Private: true, - Perms: usermem.Read, - MaxPerms: usermem.AnyAccess, - }) - if err != nil { - t.Fatalf("MMap got err %v want nil", err) - } - - // IO works before munmap. - b := make([]byte, 1) - n, err := mm.CopyIn(ctx, addr, b, usermem.IOOpts{}) - if err != nil { - t.Errorf("CopyIn got err %v want nil", err) - } - if n != 1 { - t.Errorf("CopyIn got %d want 1", n) - } - - err = mm.MUnmap(ctx, addr, usermem.PageSize) - if err != nil { - t.Fatalf("MUnmap got err %v want nil", err) - } - - n, err = mm.CopyIn(ctx, addr, b, usermem.IOOpts{}) - if err != syserror.EFAULT { - t.Errorf("CopyIn got err %v want EFAULT", err) - } - if n != 0 { - t.Errorf("CopyIn got %d want 0", n) - } -} - -// TestIOAfterMProtect tests IO interaction with mprotect permissions. -func TestIOAfterMProtect(t *testing.T) { - ctx := contexttest.Context(t) - mm := testMemoryManager(ctx) - defer mm.DecUsers(ctx) - - addr, err := mm.MMap(ctx, memmap.MMapOpts{ - Length: usermem.PageSize, - Private: true, - Perms: usermem.ReadWrite, - MaxPerms: usermem.AnyAccess, - }) - if err != nil { - t.Fatalf("MMap got err %v want nil", err) - } - - // Writing works before mprotect. - b := make([]byte, 1) - n, err := mm.CopyOut(ctx, addr, b, usermem.IOOpts{}) - if err != nil { - t.Errorf("CopyOut got err %v want nil", err) - } - if n != 1 { - t.Errorf("CopyOut got %d want 1", n) - } - - err = mm.MProtect(addr, usermem.PageSize, usermem.Read, false) - if err != nil { - t.Errorf("MProtect got err %v want nil", err) - } - - // Without IgnorePermissions, CopyOut should no longer succeed. - n, err = mm.CopyOut(ctx, addr, b, usermem.IOOpts{}) - if err != syserror.EFAULT { - t.Errorf("CopyOut got err %v want EFAULT", err) - } - if n != 0 { - t.Errorf("CopyOut got %d want 0", n) - } - - // With IgnorePermissions, CopyOut should succeed despite mprotect. - n, err = mm.CopyOut(ctx, addr, b, usermem.IOOpts{ - IgnorePermissions: true, - }) - if err != nil { - t.Errorf("CopyOut got err %v want nil", err) - } - if n != 1 { - t.Errorf("CopyOut got %d want 1", n) - } -} diff --git a/pkg/sentry/mm/pma_set.go b/pkg/sentry/mm/pma_set.go new file mode 100644 index 000000000..d0cc1f9d3 --- /dev/null +++ b/pkg/sentry/mm/pma_set.go @@ -0,0 +1,1643 @@ +package mm + +import ( + __generics_imported0 "gvisor.dev/gvisor/pkg/usermem" +) + +import ( + "bytes" + "fmt" +) + +// trackGaps is an optional parameter. +// +// If trackGaps is 1, the Set will track maximum gap size recursively, +// enabling the GapIterator.{Prev,Next}LargeEnoughGap functions. In this +// case, Key must be an unsigned integer. +// +// trackGaps must be 0 or 1. +const pmatrackGaps = 0 + +var _ = uint8(pmatrackGaps << 7) // Will fail if not zero or one. + +// dynamicGap is a type that disappears if trackGaps is 0. +type pmadynamicGap [pmatrackGaps]__generics_imported0.Addr + +// Get returns the value of the gap. +// +// Precondition: trackGaps must be non-zero. +func (d *pmadynamicGap) Get() __generics_imported0.Addr { + return d[:][0] +} + +// Set sets the value of the gap. +// +// Precondition: trackGaps must be non-zero. +func (d *pmadynamicGap) Set(v __generics_imported0.Addr) { + d[:][0] = v +} + +const ( + // minDegree is the minimum degree of an internal node in a Set B-tree. + // + // - Any non-root node has at least minDegree-1 segments. + // + // - Any non-root internal (non-leaf) node has at least minDegree children. + // + // - The root node may have fewer than minDegree-1 segments, but it may + // only have 0 segments if the tree is empty. + // + // Our implementation requires minDegree >= 3. Higher values of minDegree + // usually improve performance, but increase memory usage for small sets. + pmaminDegree = 8 + + pmamaxDegree = 2 * pmaminDegree +) + +// A Set is a mapping of segments with non-overlapping Range keys. The zero +// value for a Set is an empty set. Set values are not safely movable nor +// copyable. Set is thread-compatible. +// +// +stateify savable +type pmaSet struct { + root pmanode `state:".(*pmaSegmentDataSlices)"` +} + +// IsEmpty returns true if the set contains no segments. +func (s *pmaSet) IsEmpty() bool { + return s.root.nrSegments == 0 +} + +// IsEmptyRange returns true iff no segments in the set overlap the given +// range. This is semantically equivalent to s.SpanRange(r) == 0, but may be +// more efficient. +func (s *pmaSet) IsEmptyRange(r __generics_imported0.AddrRange) bool { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return true + } + _, gap := s.Find(r.Start) + if !gap.Ok() { + return false + } + return r.End <= gap.End() +} + +// Span returns the total size of all segments in the set. +func (s *pmaSet) Span() __generics_imported0.Addr { + var sz __generics_imported0.Addr + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sz += seg.Range().Length() + } + return sz +} + +// SpanRange returns the total size of the intersection of segments in the set +// with the given range. +func (s *pmaSet) SpanRange(r __generics_imported0.AddrRange) __generics_imported0.Addr { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return 0 + } + var sz __generics_imported0.Addr + for seg := s.LowerBoundSegment(r.Start); seg.Ok() && seg.Start() < r.End; seg = seg.NextSegment() { + sz += seg.Range().Intersect(r).Length() + } + return sz +} + +// FirstSegment returns the first segment in the set. If the set is empty, +// FirstSegment returns a terminal iterator. +func (s *pmaSet) FirstSegment() pmaIterator { + if s.root.nrSegments == 0 { + return pmaIterator{} + } + return s.root.firstSegment() +} + +// LastSegment returns the last segment in the set. If the set is empty, +// LastSegment returns a terminal iterator. +func (s *pmaSet) LastSegment() pmaIterator { + if s.root.nrSegments == 0 { + return pmaIterator{} + } + return s.root.lastSegment() +} + +// FirstGap returns the first gap in the set. +func (s *pmaSet) FirstGap() pmaGapIterator { + n := &s.root + for n.hasChildren { + n = n.children[0] + } + return pmaGapIterator{n, 0} +} + +// LastGap returns the last gap in the set. +func (s *pmaSet) LastGap() pmaGapIterator { + n := &s.root + for n.hasChildren { + n = n.children[n.nrSegments] + } + return pmaGapIterator{n, n.nrSegments} +} + +// Find returns the segment or gap whose range contains the given key. If a +// segment is found, the returned Iterator is non-terminal and the +// returned GapIterator is terminal. Otherwise, the returned Iterator is +// terminal and the returned GapIterator is non-terminal. +func (s *pmaSet) Find(key __generics_imported0.Addr) (pmaIterator, pmaGapIterator) { + n := &s.root + for { + + lower := 0 + upper := n.nrSegments + for lower < upper { + i := lower + (upper-lower)/2 + if r := n.keys[i]; key < r.End { + if key >= r.Start { + return pmaIterator{n, i}, pmaGapIterator{} + } + upper = i + } else { + lower = i + 1 + } + } + i := lower + if !n.hasChildren { + return pmaIterator{}, pmaGapIterator{n, i} + } + n = n.children[i] + } +} + +// FindSegment returns the segment whose range contains the given key. If no +// such segment exists, FindSegment returns a terminal iterator. +func (s *pmaSet) FindSegment(key __generics_imported0.Addr) pmaIterator { + seg, _ := s.Find(key) + return seg +} + +// LowerBoundSegment returns the segment with the lowest range that contains a +// key greater than or equal to min. If no such segment exists, +// LowerBoundSegment returns a terminal iterator. +func (s *pmaSet) LowerBoundSegment(min __generics_imported0.Addr) pmaIterator { + seg, gap := s.Find(min) + if seg.Ok() { + return seg + } + return gap.NextSegment() +} + +// UpperBoundSegment returns the segment with the highest range that contains a +// key less than or equal to max. If no such segment exists, UpperBoundSegment +// returns a terminal iterator. +func (s *pmaSet) UpperBoundSegment(max __generics_imported0.Addr) pmaIterator { + seg, gap := s.Find(max) + if seg.Ok() { + return seg + } + return gap.PrevSegment() +} + +// FindGap returns the gap containing the given key. If no such gap exists +// (i.e. the set contains a segment containing that key), FindGap returns a +// terminal iterator. +func (s *pmaSet) FindGap(key __generics_imported0.Addr) pmaGapIterator { + _, gap := s.Find(key) + return gap +} + +// LowerBoundGap returns the gap with the lowest range that is greater than or +// equal to min. +func (s *pmaSet) LowerBoundGap(min __generics_imported0.Addr) pmaGapIterator { + seg, gap := s.Find(min) + if gap.Ok() { + return gap + } + return seg.NextGap() +} + +// UpperBoundGap returns the gap with the highest range that is less than or +// equal to max. +func (s *pmaSet) UpperBoundGap(max __generics_imported0.Addr) pmaGapIterator { + seg, gap := s.Find(max) + if gap.Ok() { + return gap + } + return seg.PrevGap() +} + +// Add inserts the given segment into the set and returns true. If the new +// segment can be merged with adjacent segments, Add will do so. If the new +// segment would overlap an existing segment, Add returns false. If Add +// succeeds, all existing iterators are invalidated. +func (s *pmaSet) Add(r __generics_imported0.AddrRange, val pma) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.Insert(gap, r, val) + return true +} + +// AddWithoutMerging inserts the given segment into the set and returns true. +// If it would overlap an existing segment, AddWithoutMerging does nothing and +// returns false. If AddWithoutMerging succeeds, all existing iterators are +// invalidated. +func (s *pmaSet) AddWithoutMerging(r __generics_imported0.AddrRange, val pma) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.InsertWithoutMergingUnchecked(gap, r, val) + return true +} + +// Insert inserts the given segment into the given gap. If the new segment can +// be merged with adjacent segments, Insert will do so. Insert returns an +// iterator to the segment containing the inserted value (which may have been +// merged with other values). All existing iterators (including gap, but not +// including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, Insert panics. +// +// Insert is semantically equivalent to a InsertWithoutMerging followed by a +// Merge, but may be more efficient. Note that there is no unchecked variant of +// Insert since Insert must retrieve and inspect gap's predecessor and +// successor segments regardless. +func (s *pmaSet) Insert(gap pmaGapIterator, r __generics_imported0.AddrRange, val pma) pmaIterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + prev, next := gap.PrevSegment(), gap.NextSegment() + if prev.Ok() && prev.End() > r.Start { + panic(fmt.Sprintf("new segment %v overlaps predecessor %v", r, prev.Range())) + } + if next.Ok() && next.Start() < r.End { + panic(fmt.Sprintf("new segment %v overlaps successor %v", r, next.Range())) + } + if prev.Ok() && prev.End() == r.Start { + if mval, ok := (pmaSetFunctions{}).Merge(prev.Range(), prev.Value(), r, val); ok { + shrinkMaxGap := pmatrackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get() + prev.SetEndUnchecked(r.End) + prev.SetValue(mval) + if shrinkMaxGap { + gap.node.updateMaxGapLeaf() + } + if next.Ok() && next.Start() == r.End { + val = mval + if mval, ok := (pmaSetFunctions{}).Merge(prev.Range(), val, next.Range(), next.Value()); ok { + prev.SetEndUnchecked(next.End()) + prev.SetValue(mval) + return s.Remove(next).PrevSegment() + } + } + return prev + } + } + if next.Ok() && next.Start() == r.End { + if mval, ok := (pmaSetFunctions{}).Merge(r, val, next.Range(), next.Value()); ok { + shrinkMaxGap := pmatrackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get() + next.SetStartUnchecked(r.Start) + next.SetValue(mval) + if shrinkMaxGap { + gap.node.updateMaxGapLeaf() + } + return next + } + } + + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMerging inserts the given segment into the given gap and +// returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, +// InsertWithoutMerging panics. +func (s *pmaSet) InsertWithoutMerging(gap pmaGapIterator, r __generics_imported0.AddrRange, val pma) pmaIterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if gr := gap.Range(); !gr.IsSupersetOf(r) { + panic(fmt.Sprintf("cannot insert segment range %v into gap range %v", r, gr)) + } + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMergingUnchecked inserts the given segment into the given gap +// and returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// Preconditions: r.Start >= gap.Start(); r.End <= gap.End(). +func (s *pmaSet) InsertWithoutMergingUnchecked(gap pmaGapIterator, r __generics_imported0.AddrRange, val pma) pmaIterator { + gap = gap.node.rebalanceBeforeInsert(gap) + splitMaxGap := pmatrackGaps != 0 && (gap.node.nrSegments == 0 || gap.Range().Length() == gap.node.maxGap.Get()) + copy(gap.node.keys[gap.index+1:], gap.node.keys[gap.index:gap.node.nrSegments]) + copy(gap.node.values[gap.index+1:], gap.node.values[gap.index:gap.node.nrSegments]) + gap.node.keys[gap.index] = r + gap.node.values[gap.index] = val + gap.node.nrSegments++ + if splitMaxGap { + gap.node.updateMaxGapLeaf() + } + return pmaIterator{gap.node, gap.index} +} + +// Remove removes the given segment and returns an iterator to the vacated gap. +// All existing iterators (including seg, but not including the returned +// iterator) are invalidated. +func (s *pmaSet) Remove(seg pmaIterator) pmaGapIterator { + + if seg.node.hasChildren { + + victim := seg.PrevSegment() + + seg.SetRangeUnchecked(victim.Range()) + seg.SetValue(victim.Value()) + + nextAdjacentNode := seg.NextSegment().node + if pmatrackGaps != 0 { + nextAdjacentNode.updateMaxGapLeaf() + } + return s.Remove(victim).NextGap() + } + copy(seg.node.keys[seg.index:], seg.node.keys[seg.index+1:seg.node.nrSegments]) + copy(seg.node.values[seg.index:], seg.node.values[seg.index+1:seg.node.nrSegments]) + pmaSetFunctions{}.ClearValue(&seg.node.values[seg.node.nrSegments-1]) + seg.node.nrSegments-- + if pmatrackGaps != 0 { + seg.node.updateMaxGapLeaf() + } + return seg.node.rebalanceAfterRemove(pmaGapIterator{seg.node, seg.index}) +} + +// RemoveAll removes all segments from the set. All existing iterators are +// invalidated. +func (s *pmaSet) RemoveAll() { + s.root = pmanode{} +} + +// RemoveRange removes all segments in the given range. An iterator to the +// newly formed gap is returned, and all existing iterators are invalidated. +func (s *pmaSet) RemoveRange(r __generics_imported0.AddrRange) pmaGapIterator { + seg, gap := s.Find(r.Start) + if seg.Ok() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + for seg = gap.NextSegment(); seg.Ok() && seg.Start() < r.End; seg = gap.NextSegment() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + return gap +} + +// Merge attempts to merge two neighboring segments. If successful, Merge +// returns an iterator to the merged segment, and all existing iterators are +// invalidated. Otherwise, Merge returns a terminal iterator. +// +// If first is not the predecessor of second, Merge panics. +func (s *pmaSet) Merge(first, second pmaIterator) pmaIterator { + if first.NextSegment() != second { + panic(fmt.Sprintf("attempt to merge non-neighboring segments %v, %v", first.Range(), second.Range())) + } + return s.MergeUnchecked(first, second) +} + +// MergeUnchecked attempts to merge two neighboring segments. If successful, +// MergeUnchecked returns an iterator to the merged segment, and all existing +// iterators are invalidated. Otherwise, MergeUnchecked returns a terminal +// iterator. +// +// Precondition: first is the predecessor of second: first.NextSegment() == +// second, first == second.PrevSegment(). +func (s *pmaSet) MergeUnchecked(first, second pmaIterator) pmaIterator { + if first.End() == second.Start() { + if mval, ok := (pmaSetFunctions{}).Merge(first.Range(), first.Value(), second.Range(), second.Value()); ok { + + first.SetEndUnchecked(second.End()) + first.SetValue(mval) + + return s.Remove(second).PrevSegment() + } + } + return pmaIterator{} +} + +// MergeAll attempts to merge all adjacent segments in the set. All existing +// iterators are invalidated. +func (s *pmaSet) MergeAll() { + seg := s.FirstSegment() + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeRange attempts to merge all adjacent segments that contain a key in the +// specific range. All existing iterators are invalidated. +func (s *pmaSet) MergeRange(r __generics_imported0.AddrRange) { + seg := s.LowerBoundSegment(r.Start) + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() && next.Range().Start < r.End { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeAdjacent attempts to merge the segment containing r.Start with its +// predecessor, and the segment containing r.End-1 with its successor. +func (s *pmaSet) MergeAdjacent(r __generics_imported0.AddrRange) { + first := s.FindSegment(r.Start) + if first.Ok() { + if prev := first.PrevSegment(); prev.Ok() { + s.Merge(prev, first) + } + } + last := s.FindSegment(r.End - 1) + if last.Ok() { + if next := last.NextSegment(); next.Ok() { + s.Merge(last, next) + } + } +} + +// Split splits the given segment at the given key and returns iterators to the +// two resulting segments. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +// +// If the segment cannot be split at split (because split is at the start or +// end of the segment's range, so splitting would produce a segment with zero +// length, or because split falls outside the segment's range altogether), +// Split panics. +func (s *pmaSet) Split(seg pmaIterator, split __generics_imported0.Addr) (pmaIterator, pmaIterator) { + if !seg.Range().CanSplitAt(split) { + panic(fmt.Sprintf("can't split %v at %v", seg.Range(), split)) + } + return s.SplitUnchecked(seg, split) +} + +// SplitUnchecked splits the given segment at the given key and returns +// iterators to the two resulting segments. All existing iterators (including +// seg, but not including the returned iterators) are invalidated. +// +// Preconditions: seg.Start() < key < seg.End(). +func (s *pmaSet) SplitUnchecked(seg pmaIterator, split __generics_imported0.Addr) (pmaIterator, pmaIterator) { + val1, val2 := (pmaSetFunctions{}).Split(seg.Range(), seg.Value(), split) + end2 := seg.End() + seg.SetEndUnchecked(split) + seg.SetValue(val1) + seg2 := s.InsertWithoutMergingUnchecked(seg.NextGap(), __generics_imported0.AddrRange{split, end2}, val2) + + return seg2.PrevSegment(), seg2 +} + +// SplitAt splits the segment straddling split, if one exists. SplitAt returns +// true if a segment was split and false otherwise. If SplitAt splits a +// segment, all existing iterators are invalidated. +func (s *pmaSet) SplitAt(split __generics_imported0.Addr) bool { + if seg := s.FindSegment(split); seg.Ok() && seg.Range().CanSplitAt(split) { + s.SplitUnchecked(seg, split) + return true + } + return false +} + +// Isolate ensures that the given segment's range does not escape r by +// splitting at r.Start and r.End if necessary, and returns an updated iterator +// to the bounded segment. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +func (s *pmaSet) Isolate(seg pmaIterator, r __generics_imported0.AddrRange) pmaIterator { + if seg.Range().CanSplitAt(r.Start) { + _, seg = s.SplitUnchecked(seg, r.Start) + } + if seg.Range().CanSplitAt(r.End) { + seg, _ = s.SplitUnchecked(seg, r.End) + } + return seg +} + +// ApplyContiguous applies a function to a contiguous range of segments, +// splitting if necessary. The function is applied until the first gap is +// encountered, at which point the gap is returned. If the function is applied +// across the entire range, a terminal gap is returned. All existing iterators +// are invalidated. +// +// N.B. The Iterator must not be invalidated by the function. +func (s *pmaSet) ApplyContiguous(r __generics_imported0.AddrRange, fn func(seg pmaIterator)) pmaGapIterator { + seg, gap := s.Find(r.Start) + if !seg.Ok() { + return gap + } + for { + seg = s.Isolate(seg, r) + fn(seg) + if seg.End() >= r.End { + return pmaGapIterator{} + } + gap = seg.NextGap() + if !gap.IsEmpty() { + return gap + } + seg = gap.NextSegment() + if !seg.Ok() { + + return pmaGapIterator{} + } + } +} + +// +stateify savable +type pmanode struct { + // An internal binary tree node looks like: + // + // K + // / \ + // Cl Cr + // + // where all keys in the subtree rooted by Cl (the left subtree) are less + // than K (the key of the parent node), and all keys in the subtree rooted + // by Cr (the right subtree) are greater than K. + // + // An internal B-tree node's indexes work out to look like: + // + // K0 K1 K2 ... Kn-1 + // / \/ \/ \ ... / \ + // C0 C1 C2 C3 ... Cn-1 Cn + // + // where n is nrSegments. + nrSegments int + + // parent is a pointer to this node's parent. If this node is root, parent + // is nil. + parent *pmanode + + // parentIndex is the index of this node in parent.children. + parentIndex int + + // Flag for internal nodes that is technically redundant with "children[0] + // != nil", but is stored in the first cache line. "hasChildren" rather + // than "isLeaf" because false must be the correct value for an empty root. + hasChildren bool + + // The longest gap within this node. If the node is a leaf, it's simply the + // maximum gap among all the (nrSegments+1) gaps formed by its nrSegments keys + // including the 0th and nrSegments-th gap possibly shared with its upper-level + // nodes; if it's a non-leaf node, it's the max of all children's maxGap. + maxGap pmadynamicGap + + // Nodes store keys and values in separate arrays to maximize locality in + // the common case (scanning keys for lookup). + keys [pmamaxDegree - 1]__generics_imported0.AddrRange + values [pmamaxDegree - 1]pma + children [pmamaxDegree]*pmanode +} + +// firstSegment returns the first segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *pmanode) firstSegment() pmaIterator { + for n.hasChildren { + n = n.children[0] + } + return pmaIterator{n, 0} +} + +// lastSegment returns the last segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *pmanode) lastSegment() pmaIterator { + for n.hasChildren { + n = n.children[n.nrSegments] + } + return pmaIterator{n, n.nrSegments - 1} +} + +func (n *pmanode) prevSibling() *pmanode { + if n.parent == nil || n.parentIndex == 0 { + return nil + } + return n.parent.children[n.parentIndex-1] +} + +func (n *pmanode) nextSibling() *pmanode { + if n.parent == nil || n.parentIndex == n.parent.nrSegments { + return nil + } + return n.parent.children[n.parentIndex+1] +} + +// rebalanceBeforeInsert splits n and its ancestors if they are full, as +// required for insertion, and returns an updated iterator to the position +// represented by gap. +func (n *pmanode) rebalanceBeforeInsert(gap pmaGapIterator) pmaGapIterator { + if n.nrSegments < pmamaxDegree-1 { + return gap + } + if n.parent != nil { + gap = n.parent.rebalanceBeforeInsert(gap) + } + if n.parent == nil { + + left := &pmanode{ + nrSegments: pmaminDegree - 1, + parent: n, + parentIndex: 0, + hasChildren: n.hasChildren, + } + right := &pmanode{ + nrSegments: pmaminDegree - 1, + parent: n, + parentIndex: 1, + hasChildren: n.hasChildren, + } + copy(left.keys[:pmaminDegree-1], n.keys[:pmaminDegree-1]) + copy(left.values[:pmaminDegree-1], n.values[:pmaminDegree-1]) + copy(right.keys[:pmaminDegree-1], n.keys[pmaminDegree:]) + copy(right.values[:pmaminDegree-1], n.values[pmaminDegree:]) + n.keys[0], n.values[0] = n.keys[pmaminDegree-1], n.values[pmaminDegree-1] + pmazeroValueSlice(n.values[1:]) + if n.hasChildren { + copy(left.children[:pmaminDegree], n.children[:pmaminDegree]) + copy(right.children[:pmaminDegree], n.children[pmaminDegree:]) + pmazeroNodeSlice(n.children[2:]) + for i := 0; i < pmaminDegree; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + right.children[i].parent = right + right.children[i].parentIndex = i + } + } + n.nrSegments = 1 + n.hasChildren = true + n.children[0] = left + n.children[1] = right + + if pmatrackGaps != 0 { + left.updateMaxGapLocal() + right.updateMaxGapLocal() + } + if gap.node != n { + return gap + } + if gap.index < pmaminDegree { + return pmaGapIterator{left, gap.index} + } + return pmaGapIterator{right, gap.index - pmaminDegree} + } + + copy(n.parent.keys[n.parentIndex+1:], n.parent.keys[n.parentIndex:n.parent.nrSegments]) + copy(n.parent.values[n.parentIndex+1:], n.parent.values[n.parentIndex:n.parent.nrSegments]) + n.parent.keys[n.parentIndex], n.parent.values[n.parentIndex] = n.keys[pmaminDegree-1], n.values[pmaminDegree-1] + copy(n.parent.children[n.parentIndex+2:], n.parent.children[n.parentIndex+1:n.parent.nrSegments+1]) + for i := n.parentIndex + 2; i < n.parent.nrSegments+2; i++ { + n.parent.children[i].parentIndex = i + } + sibling := &pmanode{ + nrSegments: pmaminDegree - 1, + parent: n.parent, + parentIndex: n.parentIndex + 1, + hasChildren: n.hasChildren, + } + n.parent.children[n.parentIndex+1] = sibling + n.parent.nrSegments++ + copy(sibling.keys[:pmaminDegree-1], n.keys[pmaminDegree:]) + copy(sibling.values[:pmaminDegree-1], n.values[pmaminDegree:]) + pmazeroValueSlice(n.values[pmaminDegree-1:]) + if n.hasChildren { + copy(sibling.children[:pmaminDegree], n.children[pmaminDegree:]) + pmazeroNodeSlice(n.children[pmaminDegree:]) + for i := 0; i < pmaminDegree; i++ { + sibling.children[i].parent = sibling + sibling.children[i].parentIndex = i + } + } + n.nrSegments = pmaminDegree - 1 + + if pmatrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + + if gap.node != n { + return gap + } + if gap.index < pmaminDegree { + return gap + } + return pmaGapIterator{sibling, gap.index - pmaminDegree} +} + +// rebalanceAfterRemove "unsplits" n and its ancestors if they are deficient +// (contain fewer segments than required by B-tree invariants), as required for +// removal, and returns an updated iterator to the position represented by gap. +// +// Precondition: n is the only node in the tree that may currently violate a +// B-tree invariant. +func (n *pmanode) rebalanceAfterRemove(gap pmaGapIterator) pmaGapIterator { + for { + if n.nrSegments >= pmaminDegree-1 { + return gap + } + if n.parent == nil { + + return gap + } + + if sibling := n.prevSibling(); sibling != nil && sibling.nrSegments >= pmaminDegree { + copy(n.keys[1:], n.keys[:n.nrSegments]) + copy(n.values[1:], n.values[:n.nrSegments]) + n.keys[0] = n.parent.keys[n.parentIndex-1] + n.values[0] = n.parent.values[n.parentIndex-1] + n.parent.keys[n.parentIndex-1] = sibling.keys[sibling.nrSegments-1] + n.parent.values[n.parentIndex-1] = sibling.values[sibling.nrSegments-1] + pmaSetFunctions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + copy(n.children[1:], n.children[:n.nrSegments+1]) + n.children[0] = sibling.children[sibling.nrSegments] + sibling.children[sibling.nrSegments] = nil + n.children[0].parent = n + n.children[0].parentIndex = 0 + for i := 1; i < n.nrSegments+2; i++ { + n.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + + if pmatrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + if gap.node == sibling && gap.index == sibling.nrSegments { + return pmaGapIterator{n, 0} + } + if gap.node == n { + return pmaGapIterator{n, gap.index + 1} + } + return gap + } + if sibling := n.nextSibling(); sibling != nil && sibling.nrSegments >= pmaminDegree { + n.keys[n.nrSegments] = n.parent.keys[n.parentIndex] + n.values[n.nrSegments] = n.parent.values[n.parentIndex] + n.parent.keys[n.parentIndex] = sibling.keys[0] + n.parent.values[n.parentIndex] = sibling.values[0] + copy(sibling.keys[:sibling.nrSegments-1], sibling.keys[1:]) + copy(sibling.values[:sibling.nrSegments-1], sibling.values[1:]) + pmaSetFunctions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + n.children[n.nrSegments+1] = sibling.children[0] + copy(sibling.children[:sibling.nrSegments], sibling.children[1:]) + sibling.children[sibling.nrSegments] = nil + n.children[n.nrSegments+1].parent = n + n.children[n.nrSegments+1].parentIndex = n.nrSegments + 1 + for i := 0; i < sibling.nrSegments; i++ { + sibling.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + + if pmatrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + if gap.node == sibling { + if gap.index == 0 { + return pmaGapIterator{n, n.nrSegments} + } + return pmaGapIterator{sibling, gap.index - 1} + } + return gap + } + + p := n.parent + if p.nrSegments == 1 { + + left, right := p.children[0], p.children[1] + p.nrSegments = left.nrSegments + right.nrSegments + 1 + p.hasChildren = left.hasChildren + p.keys[left.nrSegments] = p.keys[0] + p.values[left.nrSegments] = p.values[0] + copy(p.keys[:left.nrSegments], left.keys[:left.nrSegments]) + copy(p.values[:left.nrSegments], left.values[:left.nrSegments]) + copy(p.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(p.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(p.children[:left.nrSegments+1], left.children[:left.nrSegments+1]) + copy(p.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := 0; i < p.nrSegments+1; i++ { + p.children[i].parent = p + p.children[i].parentIndex = i + } + } else { + p.children[0] = nil + p.children[1] = nil + } + + if gap.node == left { + return pmaGapIterator{p, gap.index} + } + if gap.node == right { + return pmaGapIterator{p, gap.index + left.nrSegments + 1} + } + return gap + } + // Merge n and either sibling, along with the segment separating the + // two, into whichever of the two nodes comes first. This is the + // reverse of the non-root splitting case in + // node.rebalanceBeforeInsert. + var left, right *pmanode + if n.parentIndex > 0 { + left = n.prevSibling() + right = n + } else { + left = n + right = n.nextSibling() + } + + if gap.node == right { + gap = pmaGapIterator{left, gap.index + left.nrSegments + 1} + } + left.keys[left.nrSegments] = p.keys[left.parentIndex] + left.values[left.nrSegments] = p.values[left.parentIndex] + copy(left.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(left.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(left.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := left.nrSegments + 1; i < left.nrSegments+right.nrSegments+2; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + } + } + left.nrSegments += right.nrSegments + 1 + copy(p.keys[left.parentIndex:], p.keys[left.parentIndex+1:p.nrSegments]) + copy(p.values[left.parentIndex:], p.values[left.parentIndex+1:p.nrSegments]) + pmaSetFunctions{}.ClearValue(&p.values[p.nrSegments-1]) + copy(p.children[left.parentIndex+1:], p.children[left.parentIndex+2:p.nrSegments+1]) + for i := 0; i < p.nrSegments; i++ { + p.children[i].parentIndex = i + } + p.children[p.nrSegments] = nil + p.nrSegments-- + + if pmatrackGaps != 0 { + left.updateMaxGapLocal() + } + + n = p + } +} + +// updateMaxGapLeaf updates maxGap bottom-up from the calling leaf until no +// necessary update. +// +// Preconditions: n must be a leaf node, trackGaps must be 1. +func (n *pmanode) updateMaxGapLeaf() { + if n.hasChildren { + panic(fmt.Sprintf("updateMaxGapLeaf should always be called on leaf node: %v", n)) + } + max := n.calculateMaxGapLeaf() + if max == n.maxGap.Get() { + + return + } + oldMax := n.maxGap.Get() + n.maxGap.Set(max) + if max > oldMax { + + for p := n.parent; p != nil; p = p.parent { + if p.maxGap.Get() >= max { + + break + } + + p.maxGap.Set(max) + } + return + } + + for p := n.parent; p != nil; p = p.parent { + if p.maxGap.Get() > oldMax { + + break + } + + parentNewMax := p.calculateMaxGapInternal() + if p.maxGap.Get() == parentNewMax { + + break + } + + p.maxGap.Set(parentNewMax) + } +} + +// updateMaxGapLocal updates maxGap of the calling node solely with no +// propagation to ancestor nodes. +// +// Precondition: trackGaps must be 1. +func (n *pmanode) updateMaxGapLocal() { + if !n.hasChildren { + + n.maxGap.Set(n.calculateMaxGapLeaf()) + } else { + + n.maxGap.Set(n.calculateMaxGapInternal()) + } +} + +// calculateMaxGapLeaf iterates the gaps within a leaf node and calculate the +// max. +// +// Preconditions: n must be a leaf node. +func (n *pmanode) calculateMaxGapLeaf() __generics_imported0.Addr { + max := pmaGapIterator{n, 0}.Range().Length() + for i := 1; i <= n.nrSegments; i++ { + if current := (pmaGapIterator{n, i}).Range().Length(); current > max { + max = current + } + } + return max +} + +// calculateMaxGapInternal iterates children's maxGap within an internal node n +// and calculate the max. +// +// Preconditions: n must be a non-leaf node. +func (n *pmanode) calculateMaxGapInternal() __generics_imported0.Addr { + max := n.children[0].maxGap.Get() + for i := 1; i <= n.nrSegments; i++ { + if current := n.children[i].maxGap.Get(); current > max { + max = current + } + } + return max +} + +// searchFirstLargeEnoughGap returns the first gap having at least minSize length +// in the subtree rooted by n. If not found, return a terminal gap iterator. +func (n *pmanode) searchFirstLargeEnoughGap(minSize __generics_imported0.Addr) pmaGapIterator { + if n.maxGap.Get() < minSize { + return pmaGapIterator{} + } + if n.hasChildren { + for i := 0; i <= n.nrSegments; i++ { + if largeEnoughGap := n.children[i].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } + } else { + for i := 0; i <= n.nrSegments; i++ { + currentGap := pmaGapIterator{n, i} + if currentGap.Range().Length() >= minSize { + return currentGap + } + } + } + panic(fmt.Sprintf("invalid maxGap in %v", n)) +} + +// searchLastLargeEnoughGap returns the last gap having at least minSize length +// in the subtree rooted by n. If not found, return a terminal gap iterator. +func (n *pmanode) searchLastLargeEnoughGap(minSize __generics_imported0.Addr) pmaGapIterator { + if n.maxGap.Get() < minSize { + return pmaGapIterator{} + } + if n.hasChildren { + for i := n.nrSegments; i >= 0; i-- { + if largeEnoughGap := n.children[i].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } + } else { + for i := n.nrSegments; i >= 0; i-- { + currentGap := pmaGapIterator{n, i} + if currentGap.Range().Length() >= minSize { + return currentGap + } + } + } + panic(fmt.Sprintf("invalid maxGap in %v", n)) +} + +// A Iterator is conceptually one of: +// +// - A pointer to a segment in a set; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Iterators are copyable values and are meaningfully equality-comparable. The +// zero value of Iterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type pmaIterator struct { + // node is the node containing the iterated segment. If the iterator is + // terminal, node is nil. + node *pmanode + + // index is the index of the segment in node.keys/values. + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (seg pmaIterator) Ok() bool { + return seg.node != nil +} + +// Range returns the iterated segment's range key. +func (seg pmaIterator) Range() __generics_imported0.AddrRange { + return seg.node.keys[seg.index] +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (seg pmaIterator) Start() __generics_imported0.Addr { + return seg.node.keys[seg.index].Start +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (seg pmaIterator) End() __generics_imported0.Addr { + return seg.node.keys[seg.index].End +} + +// SetRangeUnchecked mutates the iterated segment's range key. This operation +// does not invalidate any iterators. +// +// Preconditions: +// +// - r.Length() > 0. +// +// - The new range must not overlap an existing one: If seg.NextSegment().Ok(), +// then r.end <= seg.NextSegment().Start(); if seg.PrevSegment().Ok(), then +// r.start >= seg.PrevSegment().End(). +func (seg pmaIterator) SetRangeUnchecked(r __generics_imported0.AddrRange) { + seg.node.keys[seg.index] = r +} + +// SetRange mutates the iterated segment's range key. If the new range would +// cause the iterated segment to overlap another segment, or if the new range +// is invalid, SetRange panics. This operation does not invalidate any +// iterators. +func (seg pmaIterator) SetRange(r __generics_imported0.AddrRange) { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if prev := seg.PrevSegment(); prev.Ok() && r.Start < prev.End() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, prev.Range())) + } + if next := seg.NextSegment(); next.Ok() && r.End > next.Start() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, next.Range())) + } + seg.SetRangeUnchecked(r) +} + +// SetStartUnchecked mutates the iterated segment's start. This operation does +// not invalidate any iterators. +// +// Preconditions: The new start must be valid: start < seg.End(); if +// seg.PrevSegment().Ok(), then start >= seg.PrevSegment().End(). +func (seg pmaIterator) SetStartUnchecked(start __generics_imported0.Addr) { + seg.node.keys[seg.index].Start = start +} + +// SetStart mutates the iterated segment's start. If the new start value would +// cause the iterated segment to overlap another segment, or would result in an +// invalid range, SetStart panics. This operation does not invalidate any +// iterators. +func (seg pmaIterator) SetStart(start __generics_imported0.Addr) { + if start >= seg.End() { + panic(fmt.Sprintf("new start %v would invalidate segment range %v", start, seg.Range())) + } + if prev := seg.PrevSegment(); prev.Ok() && start < prev.End() { + panic(fmt.Sprintf("new start %v would cause segment range %v to overlap segment range %v", start, seg.Range(), prev.Range())) + } + seg.SetStartUnchecked(start) +} + +// SetEndUnchecked mutates the iterated segment's end. This operation does not +// invalidate any iterators. +// +// Preconditions: The new end must be valid: end > seg.Start(); if +// seg.NextSegment().Ok(), then end <= seg.NextSegment().Start(). +func (seg pmaIterator) SetEndUnchecked(end __generics_imported0.Addr) { + seg.node.keys[seg.index].End = end +} + +// SetEnd mutates the iterated segment's end. If the new end value would cause +// the iterated segment to overlap another segment, or would result in an +// invalid range, SetEnd panics. This operation does not invalidate any +// iterators. +func (seg pmaIterator) SetEnd(end __generics_imported0.Addr) { + if end <= seg.Start() { + panic(fmt.Sprintf("new end %v would invalidate segment range %v", end, seg.Range())) + } + if next := seg.NextSegment(); next.Ok() && end > next.Start() { + panic(fmt.Sprintf("new end %v would cause segment range %v to overlap segment range %v", end, seg.Range(), next.Range())) + } + seg.SetEndUnchecked(end) +} + +// Value returns a copy of the iterated segment's value. +func (seg pmaIterator) Value() pma { + return seg.node.values[seg.index] +} + +// ValuePtr returns a pointer to the iterated segment's value. The pointer is +// invalidated if the iterator is invalidated. This operation does not +// invalidate any iterators. +func (seg pmaIterator) ValuePtr() *pma { + return &seg.node.values[seg.index] +} + +// SetValue mutates the iterated segment's value. This operation does not +// invalidate any iterators. +func (seg pmaIterator) SetValue(val pma) { + seg.node.values[seg.index] = val +} + +// PrevSegment returns the iterated segment's predecessor. If there is no +// preceding segment, PrevSegment returns a terminal iterator. +func (seg pmaIterator) PrevSegment() pmaIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index].lastSegment() + } + if seg.index > 0 { + return pmaIterator{seg.node, seg.index - 1} + } + if seg.node.parent == nil { + return pmaIterator{} + } + return pmasegmentBeforePosition(seg.node.parent, seg.node.parentIndex) +} + +// NextSegment returns the iterated segment's successor. If there is no +// succeeding segment, NextSegment returns a terminal iterator. +func (seg pmaIterator) NextSegment() pmaIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment() + } + if seg.index < seg.node.nrSegments-1 { + return pmaIterator{seg.node, seg.index + 1} + } + if seg.node.parent == nil { + return pmaIterator{} + } + return pmasegmentAfterPosition(seg.node.parent, seg.node.parentIndex) +} + +// PrevGap returns the gap immediately before the iterated segment. +func (seg pmaIterator) PrevGap() pmaGapIterator { + if seg.node.hasChildren { + + return seg.node.children[seg.index].lastSegment().NextGap() + } + return pmaGapIterator{seg.node, seg.index} +} + +// NextGap returns the gap immediately after the iterated segment. +func (seg pmaIterator) NextGap() pmaGapIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment().PrevGap() + } + return pmaGapIterator{seg.node, seg.index + 1} +} + +// PrevNonEmpty returns the iterated segment's predecessor if it is adjacent, +// or the gap before the iterated segment otherwise. If seg.Start() == +// Functions.MinKey(), PrevNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by PrevNonEmpty will be +// non-terminal. +func (seg pmaIterator) PrevNonEmpty() (pmaIterator, pmaGapIterator) { + gap := seg.PrevGap() + if gap.Range().Length() != 0 { + return pmaIterator{}, gap + } + return gap.PrevSegment(), pmaGapIterator{} +} + +// NextNonEmpty returns the iterated segment's successor if it is adjacent, or +// the gap after the iterated segment otherwise. If seg.End() == +// Functions.MaxKey(), NextNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by NextNonEmpty will be +// non-terminal. +func (seg pmaIterator) NextNonEmpty() (pmaIterator, pmaGapIterator) { + gap := seg.NextGap() + if gap.Range().Length() != 0 { + return pmaIterator{}, gap + } + return gap.NextSegment(), pmaGapIterator{} +} + +// A GapIterator is conceptually one of: +// +// - A pointer to a position between two segments, before the first segment, or +// after the last segment in a set, called a *gap*; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Note that the gap between two adjacent segments exists (iterators to it are +// non-terminal), but has a length of zero. GapIterator.IsEmpty returns true +// for such gaps. An empty set contains a single gap, spanning the entire range +// of the set's keys. +// +// GapIterators are copyable values and are meaningfully equality-comparable. +// The zero value of GapIterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type pmaGapIterator struct { + // The representation of a GapIterator is identical to that of an Iterator, + // except that index corresponds to positions between segments in the same + // way as for node.children (see comment for node.nrSegments). + node *pmanode + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (gap pmaGapIterator) Ok() bool { + return gap.node != nil +} + +// Range returns the range spanned by the iterated gap. +func (gap pmaGapIterator) Range() __generics_imported0.AddrRange { + return __generics_imported0.AddrRange{gap.Start(), gap.End()} +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (gap pmaGapIterator) Start() __generics_imported0.Addr { + if ps := gap.PrevSegment(); ps.Ok() { + return ps.End() + } + return pmaSetFunctions{}.MinKey() +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (gap pmaGapIterator) End() __generics_imported0.Addr { + if ns := gap.NextSegment(); ns.Ok() { + return ns.Start() + } + return pmaSetFunctions{}.MaxKey() +} + +// IsEmpty returns true if the iterated gap is empty (that is, the "gap" is +// between two adjacent segments.) +func (gap pmaGapIterator) IsEmpty() bool { + return gap.Range().Length() == 0 +} + +// PrevSegment returns the segment immediately before the iterated gap. If no +// such segment exists, PrevSegment returns a terminal iterator. +func (gap pmaGapIterator) PrevSegment() pmaIterator { + return pmasegmentBeforePosition(gap.node, gap.index) +} + +// NextSegment returns the segment immediately after the iterated gap. If no +// such segment exists, NextSegment returns a terminal iterator. +func (gap pmaGapIterator) NextSegment() pmaIterator { + return pmasegmentAfterPosition(gap.node, gap.index) +} + +// PrevGap returns the iterated gap's predecessor. If no such gap exists, +// PrevGap returns a terminal iterator. +func (gap pmaGapIterator) PrevGap() pmaGapIterator { + seg := gap.PrevSegment() + if !seg.Ok() { + return pmaGapIterator{} + } + return seg.PrevGap() +} + +// NextGap returns the iterated gap's successor. If no such gap exists, NextGap +// returns a terminal iterator. +func (gap pmaGapIterator) NextGap() pmaGapIterator { + seg := gap.NextSegment() + if !seg.Ok() { + return pmaGapIterator{} + } + return seg.NextGap() +} + +// NextLargeEnoughGap returns the iterated gap's first next gap with larger +// length than minSize. If not found, return a terminal gap iterator (does NOT +// include this gap itself). +// +// Precondition: trackGaps must be 1. +func (gap pmaGapIterator) NextLargeEnoughGap(minSize __generics_imported0.Addr) pmaGapIterator { + if pmatrackGaps != 1 { + panic("set is not tracking gaps") + } + if gap.node != nil && gap.node.hasChildren && gap.index == gap.node.nrSegments { + + gap.node = gap.NextSegment().node + gap.index = 0 + return gap.nextLargeEnoughGapHelper(minSize) + } + return gap.nextLargeEnoughGapHelper(minSize) +} + +// nextLargeEnoughGapHelper is the helper function used by NextLargeEnoughGap +// to do the real recursions. +// +// Preconditions: gap is NOT the trailing gap of a non-leaf node. +func (gap pmaGapIterator) nextLargeEnoughGapHelper(minSize __generics_imported0.Addr) pmaGapIterator { + + for gap.node != nil && + (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == gap.node.nrSegments)) { + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + + if gap.node == nil { + return pmaGapIterator{} + } + + gap.index++ + for gap.index <= gap.node.nrSegments { + if gap.node.hasChildren { + if largeEnoughGap := gap.node.children[gap.index].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } else { + if gap.Range().Length() >= minSize { + return gap + } + } + gap.index++ + } + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + if gap.node != nil && gap.index == gap.node.nrSegments { + + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + return gap.nextLargeEnoughGapHelper(minSize) +} + +// PrevLargeEnoughGap returns the iterated gap's first prev gap with larger or +// equal length than minSize. If not found, return a terminal gap iterator +// (does NOT include this gap itself). +// +// Precondition: trackGaps must be 1. +func (gap pmaGapIterator) PrevLargeEnoughGap(minSize __generics_imported0.Addr) pmaGapIterator { + if pmatrackGaps != 1 { + panic("set is not tracking gaps") + } + if gap.node != nil && gap.node.hasChildren && gap.index == 0 { + + gap.node = gap.PrevSegment().node + gap.index = gap.node.nrSegments + return gap.prevLargeEnoughGapHelper(minSize) + } + return gap.prevLargeEnoughGapHelper(minSize) +} + +// prevLargeEnoughGapHelper is the helper function used by PrevLargeEnoughGap +// to do the real recursions. +// +// Preconditions: gap is NOT the first gap of a non-leaf node. +func (gap pmaGapIterator) prevLargeEnoughGapHelper(minSize __generics_imported0.Addr) pmaGapIterator { + + for gap.node != nil && + (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == 0)) { + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + + if gap.node == nil { + return pmaGapIterator{} + } + + gap.index-- + for gap.index >= 0 { + if gap.node.hasChildren { + if largeEnoughGap := gap.node.children[gap.index].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } else { + if gap.Range().Length() >= minSize { + return gap + } + } + gap.index-- + } + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + if gap.node != nil && gap.index == 0 { + + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + return gap.prevLargeEnoughGapHelper(minSize) +} + +// segmentBeforePosition returns the predecessor segment of the position given +// by n.children[i], which may or may not contain a child. If no such segment +// exists, segmentBeforePosition returns a terminal iterator. +func pmasegmentBeforePosition(n *pmanode, i int) pmaIterator { + for i == 0 { + if n.parent == nil { + return pmaIterator{} + } + n, i = n.parent, n.parentIndex + } + return pmaIterator{n, i - 1} +} + +// segmentAfterPosition returns the successor segment of the position given by +// n.children[i], which may or may not contain a child. If no such segment +// exists, segmentAfterPosition returns a terminal iterator. +func pmasegmentAfterPosition(n *pmanode, i int) pmaIterator { + for i == n.nrSegments { + if n.parent == nil { + return pmaIterator{} + } + n, i = n.parent, n.parentIndex + } + return pmaIterator{n, i} +} + +func pmazeroValueSlice(slice []pma) { + + for i := range slice { + pmaSetFunctions{}.ClearValue(&slice[i]) + } +} + +func pmazeroNodeSlice(slice []*pmanode) { + for i := range slice { + slice[i] = nil + } +} + +// String stringifies a Set for debugging. +func (s *pmaSet) String() string { + return s.root.String() +} + +// String stringifies a node (and all of its children) for debugging. +func (n *pmanode) String() string { + var buf bytes.Buffer + n.writeDebugString(&buf, "") + return buf.String() +} + +func (n *pmanode) writeDebugString(buf *bytes.Buffer, prefix string) { + if n.hasChildren != (n.nrSegments > 0 && n.children[0] != nil) { + buf.WriteString(prefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent value of hasChildren: got %v, want %v\n", n.hasChildren, !n.hasChildren)) + } + for i := 0; i < n.nrSegments; i++ { + if child := n.children[i]; child != nil { + cprefix := fmt.Sprintf("%s- % 3d ", prefix, i) + if child.parent != n || child.parentIndex != i { + buf.WriteString(cprefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent linkage to parent: got (%p, %d), want (%p, %d)\n", child.parent, child.parentIndex, n, i)) + } + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, i)) + } + buf.WriteString(prefix) + if n.hasChildren { + if pmatrackGaps != 0 { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v, maxGap: %d\n", i, n.keys[i], n.values[i], n.maxGap.Get())) + } else { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + } else { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + } + if child := n.children[n.nrSegments]; child != nil { + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, n.nrSegments)) + } +} + +// SegmentDataSlices represents segments from a set as slices of start, end, and +// values. SegmentDataSlices is primarily used as an intermediate representation +// for save/restore and the layout here is optimized for that. +// +// +stateify savable +type pmaSegmentDataSlices struct { + Start []__generics_imported0.Addr + End []__generics_imported0.Addr + Values []pma +} + +// ExportSortedSlice returns a copy of all segments in the given set, in ascending +// key order. +func (s *pmaSet) ExportSortedSlices() *pmaSegmentDataSlices { + var sds pmaSegmentDataSlices + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sds.Start = append(sds.Start, seg.Start()) + sds.End = append(sds.End, seg.End()) + sds.Values = append(sds.Values, seg.Value()) + } + sds.Start = sds.Start[:len(sds.Start):len(sds.Start)] + sds.End = sds.End[:len(sds.End):len(sds.End)] + sds.Values = sds.Values[:len(sds.Values):len(sds.Values)] + return &sds +} + +// ImportSortedSlice initializes the given set from the given slice. +// +// Preconditions: s must be empty. sds must represent a valid set (the segments +// in sds must have valid lengths that do not overlap). The segments in sds +// must be sorted in ascending key order. +func (s *pmaSet) ImportSortedSlices(sds *pmaSegmentDataSlices) error { + if !s.IsEmpty() { + return fmt.Errorf("cannot import into non-empty set %v", s) + } + gap := s.FirstGap() + for i := range sds.Start { + r := __generics_imported0.AddrRange{sds.Start[i], sds.End[i]} + if !gap.Range().IsSupersetOf(r) { + return fmt.Errorf("segment overlaps a preceding segment or is incorrectly sorted: [%d, %d) => %v", sds.Start[i], sds.End[i], sds.Values[i]) + } + gap = s.InsertWithoutMerging(gap, r, sds.Values[i]).NextGap() + } + return nil +} + +// segmentTestCheck returns an error if s is incorrectly sorted, does not +// contain exactly expectedSegments segments, or contains a segment which +// fails the passed check. +// +// This should be used only for testing, and has been added to this package for +// templating convenience. +func (s *pmaSet) segmentTestCheck(expectedSegments int, segFunc func(int, __generics_imported0.AddrRange, pma) error) error { + havePrev := false + prev := __generics_imported0.Addr(0) + nrSegments := 0 + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + next := seg.Start() + if havePrev && prev >= next { + return fmt.Errorf("incorrect order: key %d (segment %d) >= key %d (segment %d)", prev, nrSegments-1, next, nrSegments) + } + if segFunc != nil { + if err := segFunc(nrSegments, seg.Range(), seg.Value()); err != nil { + return err + } + } + prev = next + havePrev = true + nrSegments++ + } + if nrSegments != expectedSegments { + return fmt.Errorf("incorrect number of segments: got %d, wanted %d", nrSegments, expectedSegments) + } + return nil +} + +// countSegments counts the number of segments in the set. +// +// Similar to Check, this should only be used for testing. +func (s *pmaSet) countSegments() (segments int) { + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + segments++ + } + return segments +} +func (s *pmaSet) saveRoot() *pmaSegmentDataSlices { + return s.ExportSortedSlices() +} + +func (s *pmaSet) loadRoot(sds *pmaSegmentDataSlices) { + if err := s.ImportSortedSlices(sds); err != nil { + panic(err) + } +} diff --git a/pkg/sentry/mm/vma_set.go b/pkg/sentry/mm/vma_set.go new file mode 100644 index 000000000..e515ef105 --- /dev/null +++ b/pkg/sentry/mm/vma_set.go @@ -0,0 +1,1643 @@ +package mm + +import ( + __generics_imported0 "gvisor.dev/gvisor/pkg/usermem" +) + +import ( + "bytes" + "fmt" +) + +// trackGaps is an optional parameter. +// +// If trackGaps is 1, the Set will track maximum gap size recursively, +// enabling the GapIterator.{Prev,Next}LargeEnoughGap functions. In this +// case, Key must be an unsigned integer. +// +// trackGaps must be 0 or 1. +const vmatrackGaps = 1 + +var _ = uint8(vmatrackGaps << 7) // Will fail if not zero or one. + +// dynamicGap is a type that disappears if trackGaps is 0. +type vmadynamicGap [vmatrackGaps]__generics_imported0.Addr + +// Get returns the value of the gap. +// +// Precondition: trackGaps must be non-zero. +func (d *vmadynamicGap) Get() __generics_imported0.Addr { + return d[:][0] +} + +// Set sets the value of the gap. +// +// Precondition: trackGaps must be non-zero. +func (d *vmadynamicGap) Set(v __generics_imported0.Addr) { + d[:][0] = v +} + +const ( + // minDegree is the minimum degree of an internal node in a Set B-tree. + // + // - Any non-root node has at least minDegree-1 segments. + // + // - Any non-root internal (non-leaf) node has at least minDegree children. + // + // - The root node may have fewer than minDegree-1 segments, but it may + // only have 0 segments if the tree is empty. + // + // Our implementation requires minDegree >= 3. Higher values of minDegree + // usually improve performance, but increase memory usage for small sets. + vmaminDegree = 8 + + vmamaxDegree = 2 * vmaminDegree +) + +// A Set is a mapping of segments with non-overlapping Range keys. The zero +// value for a Set is an empty set. Set values are not safely movable nor +// copyable. Set is thread-compatible. +// +// +stateify savable +type vmaSet struct { + root vmanode `state:".(*vmaSegmentDataSlices)"` +} + +// IsEmpty returns true if the set contains no segments. +func (s *vmaSet) IsEmpty() bool { + return s.root.nrSegments == 0 +} + +// IsEmptyRange returns true iff no segments in the set overlap the given +// range. This is semantically equivalent to s.SpanRange(r) == 0, but may be +// more efficient. +func (s *vmaSet) IsEmptyRange(r __generics_imported0.AddrRange) bool { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return true + } + _, gap := s.Find(r.Start) + if !gap.Ok() { + return false + } + return r.End <= gap.End() +} + +// Span returns the total size of all segments in the set. +func (s *vmaSet) Span() __generics_imported0.Addr { + var sz __generics_imported0.Addr + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sz += seg.Range().Length() + } + return sz +} + +// SpanRange returns the total size of the intersection of segments in the set +// with the given range. +func (s *vmaSet) SpanRange(r __generics_imported0.AddrRange) __generics_imported0.Addr { + switch { + case r.Length() < 0: + panic(fmt.Sprintf("invalid range %v", r)) + case r.Length() == 0: + return 0 + } + var sz __generics_imported0.Addr + for seg := s.LowerBoundSegment(r.Start); seg.Ok() && seg.Start() < r.End; seg = seg.NextSegment() { + sz += seg.Range().Intersect(r).Length() + } + return sz +} + +// FirstSegment returns the first segment in the set. If the set is empty, +// FirstSegment returns a terminal iterator. +func (s *vmaSet) FirstSegment() vmaIterator { + if s.root.nrSegments == 0 { + return vmaIterator{} + } + return s.root.firstSegment() +} + +// LastSegment returns the last segment in the set. If the set is empty, +// LastSegment returns a terminal iterator. +func (s *vmaSet) LastSegment() vmaIterator { + if s.root.nrSegments == 0 { + return vmaIterator{} + } + return s.root.lastSegment() +} + +// FirstGap returns the first gap in the set. +func (s *vmaSet) FirstGap() vmaGapIterator { + n := &s.root + for n.hasChildren { + n = n.children[0] + } + return vmaGapIterator{n, 0} +} + +// LastGap returns the last gap in the set. +func (s *vmaSet) LastGap() vmaGapIterator { + n := &s.root + for n.hasChildren { + n = n.children[n.nrSegments] + } + return vmaGapIterator{n, n.nrSegments} +} + +// Find returns the segment or gap whose range contains the given key. If a +// segment is found, the returned Iterator is non-terminal and the +// returned GapIterator is terminal. Otherwise, the returned Iterator is +// terminal and the returned GapIterator is non-terminal. +func (s *vmaSet) Find(key __generics_imported0.Addr) (vmaIterator, vmaGapIterator) { + n := &s.root + for { + + lower := 0 + upper := n.nrSegments + for lower < upper { + i := lower + (upper-lower)/2 + if r := n.keys[i]; key < r.End { + if key >= r.Start { + return vmaIterator{n, i}, vmaGapIterator{} + } + upper = i + } else { + lower = i + 1 + } + } + i := lower + if !n.hasChildren { + return vmaIterator{}, vmaGapIterator{n, i} + } + n = n.children[i] + } +} + +// FindSegment returns the segment whose range contains the given key. If no +// such segment exists, FindSegment returns a terminal iterator. +func (s *vmaSet) FindSegment(key __generics_imported0.Addr) vmaIterator { + seg, _ := s.Find(key) + return seg +} + +// LowerBoundSegment returns the segment with the lowest range that contains a +// key greater than or equal to min. If no such segment exists, +// LowerBoundSegment returns a terminal iterator. +func (s *vmaSet) LowerBoundSegment(min __generics_imported0.Addr) vmaIterator { + seg, gap := s.Find(min) + if seg.Ok() { + return seg + } + return gap.NextSegment() +} + +// UpperBoundSegment returns the segment with the highest range that contains a +// key less than or equal to max. If no such segment exists, UpperBoundSegment +// returns a terminal iterator. +func (s *vmaSet) UpperBoundSegment(max __generics_imported0.Addr) vmaIterator { + seg, gap := s.Find(max) + if seg.Ok() { + return seg + } + return gap.PrevSegment() +} + +// FindGap returns the gap containing the given key. If no such gap exists +// (i.e. the set contains a segment containing that key), FindGap returns a +// terminal iterator. +func (s *vmaSet) FindGap(key __generics_imported0.Addr) vmaGapIterator { + _, gap := s.Find(key) + return gap +} + +// LowerBoundGap returns the gap with the lowest range that is greater than or +// equal to min. +func (s *vmaSet) LowerBoundGap(min __generics_imported0.Addr) vmaGapIterator { + seg, gap := s.Find(min) + if gap.Ok() { + return gap + } + return seg.NextGap() +} + +// UpperBoundGap returns the gap with the highest range that is less than or +// equal to max. +func (s *vmaSet) UpperBoundGap(max __generics_imported0.Addr) vmaGapIterator { + seg, gap := s.Find(max) + if gap.Ok() { + return gap + } + return seg.PrevGap() +} + +// Add inserts the given segment into the set and returns true. If the new +// segment can be merged with adjacent segments, Add will do so. If the new +// segment would overlap an existing segment, Add returns false. If Add +// succeeds, all existing iterators are invalidated. +func (s *vmaSet) Add(r __generics_imported0.AddrRange, val vma) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.Insert(gap, r, val) + return true +} + +// AddWithoutMerging inserts the given segment into the set and returns true. +// If it would overlap an existing segment, AddWithoutMerging does nothing and +// returns false. If AddWithoutMerging succeeds, all existing iterators are +// invalidated. +func (s *vmaSet) AddWithoutMerging(r __generics_imported0.AddrRange, val vma) bool { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + gap := s.FindGap(r.Start) + if !gap.Ok() { + return false + } + if r.End > gap.End() { + return false + } + s.InsertWithoutMergingUnchecked(gap, r, val) + return true +} + +// Insert inserts the given segment into the given gap. If the new segment can +// be merged with adjacent segments, Insert will do so. Insert returns an +// iterator to the segment containing the inserted value (which may have been +// merged with other values). All existing iterators (including gap, but not +// including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, Insert panics. +// +// Insert is semantically equivalent to a InsertWithoutMerging followed by a +// Merge, but may be more efficient. Note that there is no unchecked variant of +// Insert since Insert must retrieve and inspect gap's predecessor and +// successor segments regardless. +func (s *vmaSet) Insert(gap vmaGapIterator, r __generics_imported0.AddrRange, val vma) vmaIterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + prev, next := gap.PrevSegment(), gap.NextSegment() + if prev.Ok() && prev.End() > r.Start { + panic(fmt.Sprintf("new segment %v overlaps predecessor %v", r, prev.Range())) + } + if next.Ok() && next.Start() < r.End { + panic(fmt.Sprintf("new segment %v overlaps successor %v", r, next.Range())) + } + if prev.Ok() && prev.End() == r.Start { + if mval, ok := (vmaSetFunctions{}).Merge(prev.Range(), prev.Value(), r, val); ok { + shrinkMaxGap := vmatrackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get() + prev.SetEndUnchecked(r.End) + prev.SetValue(mval) + if shrinkMaxGap { + gap.node.updateMaxGapLeaf() + } + if next.Ok() && next.Start() == r.End { + val = mval + if mval, ok := (vmaSetFunctions{}).Merge(prev.Range(), val, next.Range(), next.Value()); ok { + prev.SetEndUnchecked(next.End()) + prev.SetValue(mval) + return s.Remove(next).PrevSegment() + } + } + return prev + } + } + if next.Ok() && next.Start() == r.End { + if mval, ok := (vmaSetFunctions{}).Merge(r, val, next.Range(), next.Value()); ok { + shrinkMaxGap := vmatrackGaps != 0 && gap.Range().Length() == gap.node.maxGap.Get() + next.SetStartUnchecked(r.Start) + next.SetValue(mval) + if shrinkMaxGap { + gap.node.updateMaxGapLeaf() + } + return next + } + } + + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMerging inserts the given segment into the given gap and +// returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// If the gap cannot accommodate the segment, or if r is invalid, +// InsertWithoutMerging panics. +func (s *vmaSet) InsertWithoutMerging(gap vmaGapIterator, r __generics_imported0.AddrRange, val vma) vmaIterator { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if gr := gap.Range(); !gr.IsSupersetOf(r) { + panic(fmt.Sprintf("cannot insert segment range %v into gap range %v", r, gr)) + } + return s.InsertWithoutMergingUnchecked(gap, r, val) +} + +// InsertWithoutMergingUnchecked inserts the given segment into the given gap +// and returns an iterator to the inserted segment. All existing iterators +// (including gap, but not including the returned iterator) are invalidated. +// +// Preconditions: r.Start >= gap.Start(); r.End <= gap.End(). +func (s *vmaSet) InsertWithoutMergingUnchecked(gap vmaGapIterator, r __generics_imported0.AddrRange, val vma) vmaIterator { + gap = gap.node.rebalanceBeforeInsert(gap) + splitMaxGap := vmatrackGaps != 0 && (gap.node.nrSegments == 0 || gap.Range().Length() == gap.node.maxGap.Get()) + copy(gap.node.keys[gap.index+1:], gap.node.keys[gap.index:gap.node.nrSegments]) + copy(gap.node.values[gap.index+1:], gap.node.values[gap.index:gap.node.nrSegments]) + gap.node.keys[gap.index] = r + gap.node.values[gap.index] = val + gap.node.nrSegments++ + if splitMaxGap { + gap.node.updateMaxGapLeaf() + } + return vmaIterator{gap.node, gap.index} +} + +// Remove removes the given segment and returns an iterator to the vacated gap. +// All existing iterators (including seg, but not including the returned +// iterator) are invalidated. +func (s *vmaSet) Remove(seg vmaIterator) vmaGapIterator { + + if seg.node.hasChildren { + + victim := seg.PrevSegment() + + seg.SetRangeUnchecked(victim.Range()) + seg.SetValue(victim.Value()) + + nextAdjacentNode := seg.NextSegment().node + if vmatrackGaps != 0 { + nextAdjacentNode.updateMaxGapLeaf() + } + return s.Remove(victim).NextGap() + } + copy(seg.node.keys[seg.index:], seg.node.keys[seg.index+1:seg.node.nrSegments]) + copy(seg.node.values[seg.index:], seg.node.values[seg.index+1:seg.node.nrSegments]) + vmaSetFunctions{}.ClearValue(&seg.node.values[seg.node.nrSegments-1]) + seg.node.nrSegments-- + if vmatrackGaps != 0 { + seg.node.updateMaxGapLeaf() + } + return seg.node.rebalanceAfterRemove(vmaGapIterator{seg.node, seg.index}) +} + +// RemoveAll removes all segments from the set. All existing iterators are +// invalidated. +func (s *vmaSet) RemoveAll() { + s.root = vmanode{} +} + +// RemoveRange removes all segments in the given range. An iterator to the +// newly formed gap is returned, and all existing iterators are invalidated. +func (s *vmaSet) RemoveRange(r __generics_imported0.AddrRange) vmaGapIterator { + seg, gap := s.Find(r.Start) + if seg.Ok() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + for seg = gap.NextSegment(); seg.Ok() && seg.Start() < r.End; seg = gap.NextSegment() { + seg = s.Isolate(seg, r) + gap = s.Remove(seg) + } + return gap +} + +// Merge attempts to merge two neighboring segments. If successful, Merge +// returns an iterator to the merged segment, and all existing iterators are +// invalidated. Otherwise, Merge returns a terminal iterator. +// +// If first is not the predecessor of second, Merge panics. +func (s *vmaSet) Merge(first, second vmaIterator) vmaIterator { + if first.NextSegment() != second { + panic(fmt.Sprintf("attempt to merge non-neighboring segments %v, %v", first.Range(), second.Range())) + } + return s.MergeUnchecked(first, second) +} + +// MergeUnchecked attempts to merge two neighboring segments. If successful, +// MergeUnchecked returns an iterator to the merged segment, and all existing +// iterators are invalidated. Otherwise, MergeUnchecked returns a terminal +// iterator. +// +// Precondition: first is the predecessor of second: first.NextSegment() == +// second, first == second.PrevSegment(). +func (s *vmaSet) MergeUnchecked(first, second vmaIterator) vmaIterator { + if first.End() == second.Start() { + if mval, ok := (vmaSetFunctions{}).Merge(first.Range(), first.Value(), second.Range(), second.Value()); ok { + + first.SetEndUnchecked(second.End()) + first.SetValue(mval) + + return s.Remove(second).PrevSegment() + } + } + return vmaIterator{} +} + +// MergeAll attempts to merge all adjacent segments in the set. All existing +// iterators are invalidated. +func (s *vmaSet) MergeAll() { + seg := s.FirstSegment() + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeRange attempts to merge all adjacent segments that contain a key in the +// specific range. All existing iterators are invalidated. +func (s *vmaSet) MergeRange(r __generics_imported0.AddrRange) { + seg := s.LowerBoundSegment(r.Start) + if !seg.Ok() { + return + } + next := seg.NextSegment() + for next.Ok() && next.Range().Start < r.End { + if mseg := s.MergeUnchecked(seg, next); mseg.Ok() { + seg, next = mseg, mseg.NextSegment() + } else { + seg, next = next, next.NextSegment() + } + } +} + +// MergeAdjacent attempts to merge the segment containing r.Start with its +// predecessor, and the segment containing r.End-1 with its successor. +func (s *vmaSet) MergeAdjacent(r __generics_imported0.AddrRange) { + first := s.FindSegment(r.Start) + if first.Ok() { + if prev := first.PrevSegment(); prev.Ok() { + s.Merge(prev, first) + } + } + last := s.FindSegment(r.End - 1) + if last.Ok() { + if next := last.NextSegment(); next.Ok() { + s.Merge(last, next) + } + } +} + +// Split splits the given segment at the given key and returns iterators to the +// two resulting segments. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +// +// If the segment cannot be split at split (because split is at the start or +// end of the segment's range, so splitting would produce a segment with zero +// length, or because split falls outside the segment's range altogether), +// Split panics. +func (s *vmaSet) Split(seg vmaIterator, split __generics_imported0.Addr) (vmaIterator, vmaIterator) { + if !seg.Range().CanSplitAt(split) { + panic(fmt.Sprintf("can't split %v at %v", seg.Range(), split)) + } + return s.SplitUnchecked(seg, split) +} + +// SplitUnchecked splits the given segment at the given key and returns +// iterators to the two resulting segments. All existing iterators (including +// seg, but not including the returned iterators) are invalidated. +// +// Preconditions: seg.Start() < key < seg.End(). +func (s *vmaSet) SplitUnchecked(seg vmaIterator, split __generics_imported0.Addr) (vmaIterator, vmaIterator) { + val1, val2 := (vmaSetFunctions{}).Split(seg.Range(), seg.Value(), split) + end2 := seg.End() + seg.SetEndUnchecked(split) + seg.SetValue(val1) + seg2 := s.InsertWithoutMergingUnchecked(seg.NextGap(), __generics_imported0.AddrRange{split, end2}, val2) + + return seg2.PrevSegment(), seg2 +} + +// SplitAt splits the segment straddling split, if one exists. SplitAt returns +// true if a segment was split and false otherwise. If SplitAt splits a +// segment, all existing iterators are invalidated. +func (s *vmaSet) SplitAt(split __generics_imported0.Addr) bool { + if seg := s.FindSegment(split); seg.Ok() && seg.Range().CanSplitAt(split) { + s.SplitUnchecked(seg, split) + return true + } + return false +} + +// Isolate ensures that the given segment's range does not escape r by +// splitting at r.Start and r.End if necessary, and returns an updated iterator +// to the bounded segment. All existing iterators (including seg, but not +// including the returned iterators) are invalidated. +func (s *vmaSet) Isolate(seg vmaIterator, r __generics_imported0.AddrRange) vmaIterator { + if seg.Range().CanSplitAt(r.Start) { + _, seg = s.SplitUnchecked(seg, r.Start) + } + if seg.Range().CanSplitAt(r.End) { + seg, _ = s.SplitUnchecked(seg, r.End) + } + return seg +} + +// ApplyContiguous applies a function to a contiguous range of segments, +// splitting if necessary. The function is applied until the first gap is +// encountered, at which point the gap is returned. If the function is applied +// across the entire range, a terminal gap is returned. All existing iterators +// are invalidated. +// +// N.B. The Iterator must not be invalidated by the function. +func (s *vmaSet) ApplyContiguous(r __generics_imported0.AddrRange, fn func(seg vmaIterator)) vmaGapIterator { + seg, gap := s.Find(r.Start) + if !seg.Ok() { + return gap + } + for { + seg = s.Isolate(seg, r) + fn(seg) + if seg.End() >= r.End { + return vmaGapIterator{} + } + gap = seg.NextGap() + if !gap.IsEmpty() { + return gap + } + seg = gap.NextSegment() + if !seg.Ok() { + + return vmaGapIterator{} + } + } +} + +// +stateify savable +type vmanode struct { + // An internal binary tree node looks like: + // + // K + // / \ + // Cl Cr + // + // where all keys in the subtree rooted by Cl (the left subtree) are less + // than K (the key of the parent node), and all keys in the subtree rooted + // by Cr (the right subtree) are greater than K. + // + // An internal B-tree node's indexes work out to look like: + // + // K0 K1 K2 ... Kn-1 + // / \/ \/ \ ... / \ + // C0 C1 C2 C3 ... Cn-1 Cn + // + // where n is nrSegments. + nrSegments int + + // parent is a pointer to this node's parent. If this node is root, parent + // is nil. + parent *vmanode + + // parentIndex is the index of this node in parent.children. + parentIndex int + + // Flag for internal nodes that is technically redundant with "children[0] + // != nil", but is stored in the first cache line. "hasChildren" rather + // than "isLeaf" because false must be the correct value for an empty root. + hasChildren bool + + // The longest gap within this node. If the node is a leaf, it's simply the + // maximum gap among all the (nrSegments+1) gaps formed by its nrSegments keys + // including the 0th and nrSegments-th gap possibly shared with its upper-level + // nodes; if it's a non-leaf node, it's the max of all children's maxGap. + maxGap vmadynamicGap + + // Nodes store keys and values in separate arrays to maximize locality in + // the common case (scanning keys for lookup). + keys [vmamaxDegree - 1]__generics_imported0.AddrRange + values [vmamaxDegree - 1]vma + children [vmamaxDegree]*vmanode +} + +// firstSegment returns the first segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *vmanode) firstSegment() vmaIterator { + for n.hasChildren { + n = n.children[0] + } + return vmaIterator{n, 0} +} + +// lastSegment returns the last segment in the subtree rooted by n. +// +// Preconditions: n.nrSegments != 0. +func (n *vmanode) lastSegment() vmaIterator { + for n.hasChildren { + n = n.children[n.nrSegments] + } + return vmaIterator{n, n.nrSegments - 1} +} + +func (n *vmanode) prevSibling() *vmanode { + if n.parent == nil || n.parentIndex == 0 { + return nil + } + return n.parent.children[n.parentIndex-1] +} + +func (n *vmanode) nextSibling() *vmanode { + if n.parent == nil || n.parentIndex == n.parent.nrSegments { + return nil + } + return n.parent.children[n.parentIndex+1] +} + +// rebalanceBeforeInsert splits n and its ancestors if they are full, as +// required for insertion, and returns an updated iterator to the position +// represented by gap. +func (n *vmanode) rebalanceBeforeInsert(gap vmaGapIterator) vmaGapIterator { + if n.nrSegments < vmamaxDegree-1 { + return gap + } + if n.parent != nil { + gap = n.parent.rebalanceBeforeInsert(gap) + } + if n.parent == nil { + + left := &vmanode{ + nrSegments: vmaminDegree - 1, + parent: n, + parentIndex: 0, + hasChildren: n.hasChildren, + } + right := &vmanode{ + nrSegments: vmaminDegree - 1, + parent: n, + parentIndex: 1, + hasChildren: n.hasChildren, + } + copy(left.keys[:vmaminDegree-1], n.keys[:vmaminDegree-1]) + copy(left.values[:vmaminDegree-1], n.values[:vmaminDegree-1]) + copy(right.keys[:vmaminDegree-1], n.keys[vmaminDegree:]) + copy(right.values[:vmaminDegree-1], n.values[vmaminDegree:]) + n.keys[0], n.values[0] = n.keys[vmaminDegree-1], n.values[vmaminDegree-1] + vmazeroValueSlice(n.values[1:]) + if n.hasChildren { + copy(left.children[:vmaminDegree], n.children[:vmaminDegree]) + copy(right.children[:vmaminDegree], n.children[vmaminDegree:]) + vmazeroNodeSlice(n.children[2:]) + for i := 0; i < vmaminDegree; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + right.children[i].parent = right + right.children[i].parentIndex = i + } + } + n.nrSegments = 1 + n.hasChildren = true + n.children[0] = left + n.children[1] = right + + if vmatrackGaps != 0 { + left.updateMaxGapLocal() + right.updateMaxGapLocal() + } + if gap.node != n { + return gap + } + if gap.index < vmaminDegree { + return vmaGapIterator{left, gap.index} + } + return vmaGapIterator{right, gap.index - vmaminDegree} + } + + copy(n.parent.keys[n.parentIndex+1:], n.parent.keys[n.parentIndex:n.parent.nrSegments]) + copy(n.parent.values[n.parentIndex+1:], n.parent.values[n.parentIndex:n.parent.nrSegments]) + n.parent.keys[n.parentIndex], n.parent.values[n.parentIndex] = n.keys[vmaminDegree-1], n.values[vmaminDegree-1] + copy(n.parent.children[n.parentIndex+2:], n.parent.children[n.parentIndex+1:n.parent.nrSegments+1]) + for i := n.parentIndex + 2; i < n.parent.nrSegments+2; i++ { + n.parent.children[i].parentIndex = i + } + sibling := &vmanode{ + nrSegments: vmaminDegree - 1, + parent: n.parent, + parentIndex: n.parentIndex + 1, + hasChildren: n.hasChildren, + } + n.parent.children[n.parentIndex+1] = sibling + n.parent.nrSegments++ + copy(sibling.keys[:vmaminDegree-1], n.keys[vmaminDegree:]) + copy(sibling.values[:vmaminDegree-1], n.values[vmaminDegree:]) + vmazeroValueSlice(n.values[vmaminDegree-1:]) + if n.hasChildren { + copy(sibling.children[:vmaminDegree], n.children[vmaminDegree:]) + vmazeroNodeSlice(n.children[vmaminDegree:]) + for i := 0; i < vmaminDegree; i++ { + sibling.children[i].parent = sibling + sibling.children[i].parentIndex = i + } + } + n.nrSegments = vmaminDegree - 1 + + if vmatrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + + if gap.node != n { + return gap + } + if gap.index < vmaminDegree { + return gap + } + return vmaGapIterator{sibling, gap.index - vmaminDegree} +} + +// rebalanceAfterRemove "unsplits" n and its ancestors if they are deficient +// (contain fewer segments than required by B-tree invariants), as required for +// removal, and returns an updated iterator to the position represented by gap. +// +// Precondition: n is the only node in the tree that may currently violate a +// B-tree invariant. +func (n *vmanode) rebalanceAfterRemove(gap vmaGapIterator) vmaGapIterator { + for { + if n.nrSegments >= vmaminDegree-1 { + return gap + } + if n.parent == nil { + + return gap + } + + if sibling := n.prevSibling(); sibling != nil && sibling.nrSegments >= vmaminDegree { + copy(n.keys[1:], n.keys[:n.nrSegments]) + copy(n.values[1:], n.values[:n.nrSegments]) + n.keys[0] = n.parent.keys[n.parentIndex-1] + n.values[0] = n.parent.values[n.parentIndex-1] + n.parent.keys[n.parentIndex-1] = sibling.keys[sibling.nrSegments-1] + n.parent.values[n.parentIndex-1] = sibling.values[sibling.nrSegments-1] + vmaSetFunctions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + copy(n.children[1:], n.children[:n.nrSegments+1]) + n.children[0] = sibling.children[sibling.nrSegments] + sibling.children[sibling.nrSegments] = nil + n.children[0].parent = n + n.children[0].parentIndex = 0 + for i := 1; i < n.nrSegments+2; i++ { + n.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + + if vmatrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + if gap.node == sibling && gap.index == sibling.nrSegments { + return vmaGapIterator{n, 0} + } + if gap.node == n { + return vmaGapIterator{n, gap.index + 1} + } + return gap + } + if sibling := n.nextSibling(); sibling != nil && sibling.nrSegments >= vmaminDegree { + n.keys[n.nrSegments] = n.parent.keys[n.parentIndex] + n.values[n.nrSegments] = n.parent.values[n.parentIndex] + n.parent.keys[n.parentIndex] = sibling.keys[0] + n.parent.values[n.parentIndex] = sibling.values[0] + copy(sibling.keys[:sibling.nrSegments-1], sibling.keys[1:]) + copy(sibling.values[:sibling.nrSegments-1], sibling.values[1:]) + vmaSetFunctions{}.ClearValue(&sibling.values[sibling.nrSegments-1]) + if n.hasChildren { + n.children[n.nrSegments+1] = sibling.children[0] + copy(sibling.children[:sibling.nrSegments], sibling.children[1:]) + sibling.children[sibling.nrSegments] = nil + n.children[n.nrSegments+1].parent = n + n.children[n.nrSegments+1].parentIndex = n.nrSegments + 1 + for i := 0; i < sibling.nrSegments; i++ { + sibling.children[i].parentIndex = i + } + } + n.nrSegments++ + sibling.nrSegments-- + + if vmatrackGaps != 0 { + n.updateMaxGapLocal() + sibling.updateMaxGapLocal() + } + if gap.node == sibling { + if gap.index == 0 { + return vmaGapIterator{n, n.nrSegments} + } + return vmaGapIterator{sibling, gap.index - 1} + } + return gap + } + + p := n.parent + if p.nrSegments == 1 { + + left, right := p.children[0], p.children[1] + p.nrSegments = left.nrSegments + right.nrSegments + 1 + p.hasChildren = left.hasChildren + p.keys[left.nrSegments] = p.keys[0] + p.values[left.nrSegments] = p.values[0] + copy(p.keys[:left.nrSegments], left.keys[:left.nrSegments]) + copy(p.values[:left.nrSegments], left.values[:left.nrSegments]) + copy(p.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(p.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(p.children[:left.nrSegments+1], left.children[:left.nrSegments+1]) + copy(p.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := 0; i < p.nrSegments+1; i++ { + p.children[i].parent = p + p.children[i].parentIndex = i + } + } else { + p.children[0] = nil + p.children[1] = nil + } + + if gap.node == left { + return vmaGapIterator{p, gap.index} + } + if gap.node == right { + return vmaGapIterator{p, gap.index + left.nrSegments + 1} + } + return gap + } + // Merge n and either sibling, along with the segment separating the + // two, into whichever of the two nodes comes first. This is the + // reverse of the non-root splitting case in + // node.rebalanceBeforeInsert. + var left, right *vmanode + if n.parentIndex > 0 { + left = n.prevSibling() + right = n + } else { + left = n + right = n.nextSibling() + } + + if gap.node == right { + gap = vmaGapIterator{left, gap.index + left.nrSegments + 1} + } + left.keys[left.nrSegments] = p.keys[left.parentIndex] + left.values[left.nrSegments] = p.values[left.parentIndex] + copy(left.keys[left.nrSegments+1:], right.keys[:right.nrSegments]) + copy(left.values[left.nrSegments+1:], right.values[:right.nrSegments]) + if left.hasChildren { + copy(left.children[left.nrSegments+1:], right.children[:right.nrSegments+1]) + for i := left.nrSegments + 1; i < left.nrSegments+right.nrSegments+2; i++ { + left.children[i].parent = left + left.children[i].parentIndex = i + } + } + left.nrSegments += right.nrSegments + 1 + copy(p.keys[left.parentIndex:], p.keys[left.parentIndex+1:p.nrSegments]) + copy(p.values[left.parentIndex:], p.values[left.parentIndex+1:p.nrSegments]) + vmaSetFunctions{}.ClearValue(&p.values[p.nrSegments-1]) + copy(p.children[left.parentIndex+1:], p.children[left.parentIndex+2:p.nrSegments+1]) + for i := 0; i < p.nrSegments; i++ { + p.children[i].parentIndex = i + } + p.children[p.nrSegments] = nil + p.nrSegments-- + + if vmatrackGaps != 0 { + left.updateMaxGapLocal() + } + + n = p + } +} + +// updateMaxGapLeaf updates maxGap bottom-up from the calling leaf until no +// necessary update. +// +// Preconditions: n must be a leaf node, trackGaps must be 1. +func (n *vmanode) updateMaxGapLeaf() { + if n.hasChildren { + panic(fmt.Sprintf("updateMaxGapLeaf should always be called on leaf node: %v", n)) + } + max := n.calculateMaxGapLeaf() + if max == n.maxGap.Get() { + + return + } + oldMax := n.maxGap.Get() + n.maxGap.Set(max) + if max > oldMax { + + for p := n.parent; p != nil; p = p.parent { + if p.maxGap.Get() >= max { + + break + } + + p.maxGap.Set(max) + } + return + } + + for p := n.parent; p != nil; p = p.parent { + if p.maxGap.Get() > oldMax { + + break + } + + parentNewMax := p.calculateMaxGapInternal() + if p.maxGap.Get() == parentNewMax { + + break + } + + p.maxGap.Set(parentNewMax) + } +} + +// updateMaxGapLocal updates maxGap of the calling node solely with no +// propagation to ancestor nodes. +// +// Precondition: trackGaps must be 1. +func (n *vmanode) updateMaxGapLocal() { + if !n.hasChildren { + + n.maxGap.Set(n.calculateMaxGapLeaf()) + } else { + + n.maxGap.Set(n.calculateMaxGapInternal()) + } +} + +// calculateMaxGapLeaf iterates the gaps within a leaf node and calculate the +// max. +// +// Preconditions: n must be a leaf node. +func (n *vmanode) calculateMaxGapLeaf() __generics_imported0.Addr { + max := vmaGapIterator{n, 0}.Range().Length() + for i := 1; i <= n.nrSegments; i++ { + if current := (vmaGapIterator{n, i}).Range().Length(); current > max { + max = current + } + } + return max +} + +// calculateMaxGapInternal iterates children's maxGap within an internal node n +// and calculate the max. +// +// Preconditions: n must be a non-leaf node. +func (n *vmanode) calculateMaxGapInternal() __generics_imported0.Addr { + max := n.children[0].maxGap.Get() + for i := 1; i <= n.nrSegments; i++ { + if current := n.children[i].maxGap.Get(); current > max { + max = current + } + } + return max +} + +// searchFirstLargeEnoughGap returns the first gap having at least minSize length +// in the subtree rooted by n. If not found, return a terminal gap iterator. +func (n *vmanode) searchFirstLargeEnoughGap(minSize __generics_imported0.Addr) vmaGapIterator { + if n.maxGap.Get() < minSize { + return vmaGapIterator{} + } + if n.hasChildren { + for i := 0; i <= n.nrSegments; i++ { + if largeEnoughGap := n.children[i].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } + } else { + for i := 0; i <= n.nrSegments; i++ { + currentGap := vmaGapIterator{n, i} + if currentGap.Range().Length() >= minSize { + return currentGap + } + } + } + panic(fmt.Sprintf("invalid maxGap in %v", n)) +} + +// searchLastLargeEnoughGap returns the last gap having at least minSize length +// in the subtree rooted by n. If not found, return a terminal gap iterator. +func (n *vmanode) searchLastLargeEnoughGap(minSize __generics_imported0.Addr) vmaGapIterator { + if n.maxGap.Get() < minSize { + return vmaGapIterator{} + } + if n.hasChildren { + for i := n.nrSegments; i >= 0; i-- { + if largeEnoughGap := n.children[i].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } + } else { + for i := n.nrSegments; i >= 0; i-- { + currentGap := vmaGapIterator{n, i} + if currentGap.Range().Length() >= minSize { + return currentGap + } + } + } + panic(fmt.Sprintf("invalid maxGap in %v", n)) +} + +// A Iterator is conceptually one of: +// +// - A pointer to a segment in a set; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Iterators are copyable values and are meaningfully equality-comparable. The +// zero value of Iterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type vmaIterator struct { + // node is the node containing the iterated segment. If the iterator is + // terminal, node is nil. + node *vmanode + + // index is the index of the segment in node.keys/values. + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (seg vmaIterator) Ok() bool { + return seg.node != nil +} + +// Range returns the iterated segment's range key. +func (seg vmaIterator) Range() __generics_imported0.AddrRange { + return seg.node.keys[seg.index] +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (seg vmaIterator) Start() __generics_imported0.Addr { + return seg.node.keys[seg.index].Start +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (seg vmaIterator) End() __generics_imported0.Addr { + return seg.node.keys[seg.index].End +} + +// SetRangeUnchecked mutates the iterated segment's range key. This operation +// does not invalidate any iterators. +// +// Preconditions: +// +// - r.Length() > 0. +// +// - The new range must not overlap an existing one: If seg.NextSegment().Ok(), +// then r.end <= seg.NextSegment().Start(); if seg.PrevSegment().Ok(), then +// r.start >= seg.PrevSegment().End(). +func (seg vmaIterator) SetRangeUnchecked(r __generics_imported0.AddrRange) { + seg.node.keys[seg.index] = r +} + +// SetRange mutates the iterated segment's range key. If the new range would +// cause the iterated segment to overlap another segment, or if the new range +// is invalid, SetRange panics. This operation does not invalidate any +// iterators. +func (seg vmaIterator) SetRange(r __generics_imported0.AddrRange) { + if r.Length() <= 0 { + panic(fmt.Sprintf("invalid segment range %v", r)) + } + if prev := seg.PrevSegment(); prev.Ok() && r.Start < prev.End() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, prev.Range())) + } + if next := seg.NextSegment(); next.Ok() && r.End > next.Start() { + panic(fmt.Sprintf("new segment range %v overlaps segment range %v", r, next.Range())) + } + seg.SetRangeUnchecked(r) +} + +// SetStartUnchecked mutates the iterated segment's start. This operation does +// not invalidate any iterators. +// +// Preconditions: The new start must be valid: start < seg.End(); if +// seg.PrevSegment().Ok(), then start >= seg.PrevSegment().End(). +func (seg vmaIterator) SetStartUnchecked(start __generics_imported0.Addr) { + seg.node.keys[seg.index].Start = start +} + +// SetStart mutates the iterated segment's start. If the new start value would +// cause the iterated segment to overlap another segment, or would result in an +// invalid range, SetStart panics. This operation does not invalidate any +// iterators. +func (seg vmaIterator) SetStart(start __generics_imported0.Addr) { + if start >= seg.End() { + panic(fmt.Sprintf("new start %v would invalidate segment range %v", start, seg.Range())) + } + if prev := seg.PrevSegment(); prev.Ok() && start < prev.End() { + panic(fmt.Sprintf("new start %v would cause segment range %v to overlap segment range %v", start, seg.Range(), prev.Range())) + } + seg.SetStartUnchecked(start) +} + +// SetEndUnchecked mutates the iterated segment's end. This operation does not +// invalidate any iterators. +// +// Preconditions: The new end must be valid: end > seg.Start(); if +// seg.NextSegment().Ok(), then end <= seg.NextSegment().Start(). +func (seg vmaIterator) SetEndUnchecked(end __generics_imported0.Addr) { + seg.node.keys[seg.index].End = end +} + +// SetEnd mutates the iterated segment's end. If the new end value would cause +// the iterated segment to overlap another segment, or would result in an +// invalid range, SetEnd panics. This operation does not invalidate any +// iterators. +func (seg vmaIterator) SetEnd(end __generics_imported0.Addr) { + if end <= seg.Start() { + panic(fmt.Sprintf("new end %v would invalidate segment range %v", end, seg.Range())) + } + if next := seg.NextSegment(); next.Ok() && end > next.Start() { + panic(fmt.Sprintf("new end %v would cause segment range %v to overlap segment range %v", end, seg.Range(), next.Range())) + } + seg.SetEndUnchecked(end) +} + +// Value returns a copy of the iterated segment's value. +func (seg vmaIterator) Value() vma { + return seg.node.values[seg.index] +} + +// ValuePtr returns a pointer to the iterated segment's value. The pointer is +// invalidated if the iterator is invalidated. This operation does not +// invalidate any iterators. +func (seg vmaIterator) ValuePtr() *vma { + return &seg.node.values[seg.index] +} + +// SetValue mutates the iterated segment's value. This operation does not +// invalidate any iterators. +func (seg vmaIterator) SetValue(val vma) { + seg.node.values[seg.index] = val +} + +// PrevSegment returns the iterated segment's predecessor. If there is no +// preceding segment, PrevSegment returns a terminal iterator. +func (seg vmaIterator) PrevSegment() vmaIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index].lastSegment() + } + if seg.index > 0 { + return vmaIterator{seg.node, seg.index - 1} + } + if seg.node.parent == nil { + return vmaIterator{} + } + return vmasegmentBeforePosition(seg.node.parent, seg.node.parentIndex) +} + +// NextSegment returns the iterated segment's successor. If there is no +// succeeding segment, NextSegment returns a terminal iterator. +func (seg vmaIterator) NextSegment() vmaIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment() + } + if seg.index < seg.node.nrSegments-1 { + return vmaIterator{seg.node, seg.index + 1} + } + if seg.node.parent == nil { + return vmaIterator{} + } + return vmasegmentAfterPosition(seg.node.parent, seg.node.parentIndex) +} + +// PrevGap returns the gap immediately before the iterated segment. +func (seg vmaIterator) PrevGap() vmaGapIterator { + if seg.node.hasChildren { + + return seg.node.children[seg.index].lastSegment().NextGap() + } + return vmaGapIterator{seg.node, seg.index} +} + +// NextGap returns the gap immediately after the iterated segment. +func (seg vmaIterator) NextGap() vmaGapIterator { + if seg.node.hasChildren { + return seg.node.children[seg.index+1].firstSegment().PrevGap() + } + return vmaGapIterator{seg.node, seg.index + 1} +} + +// PrevNonEmpty returns the iterated segment's predecessor if it is adjacent, +// or the gap before the iterated segment otherwise. If seg.Start() == +// Functions.MinKey(), PrevNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by PrevNonEmpty will be +// non-terminal. +func (seg vmaIterator) PrevNonEmpty() (vmaIterator, vmaGapIterator) { + gap := seg.PrevGap() + if gap.Range().Length() != 0 { + return vmaIterator{}, gap + } + return gap.PrevSegment(), vmaGapIterator{} +} + +// NextNonEmpty returns the iterated segment's successor if it is adjacent, or +// the gap after the iterated segment otherwise. If seg.End() == +// Functions.MaxKey(), NextNonEmpty will return two terminal iterators. +// Otherwise, exactly one of the iterators returned by NextNonEmpty will be +// non-terminal. +func (seg vmaIterator) NextNonEmpty() (vmaIterator, vmaGapIterator) { + gap := seg.NextGap() + if gap.Range().Length() != 0 { + return vmaIterator{}, gap + } + return gap.NextSegment(), vmaGapIterator{} +} + +// A GapIterator is conceptually one of: +// +// - A pointer to a position between two segments, before the first segment, or +// after the last segment in a set, called a *gap*; or +// +// - A terminal iterator, which is a sentinel indicating that the end of +// iteration has been reached. +// +// Note that the gap between two adjacent segments exists (iterators to it are +// non-terminal), but has a length of zero. GapIterator.IsEmpty returns true +// for such gaps. An empty set contains a single gap, spanning the entire range +// of the set's keys. +// +// GapIterators are copyable values and are meaningfully equality-comparable. +// The zero value of GapIterator is a terminal iterator. +// +// Unless otherwise specified, any mutation of a set invalidates all existing +// iterators into the set. +type vmaGapIterator struct { + // The representation of a GapIterator is identical to that of an Iterator, + // except that index corresponds to positions between segments in the same + // way as for node.children (see comment for node.nrSegments). + node *vmanode + index int +} + +// Ok returns true if the iterator is not terminal. All other methods are only +// valid for non-terminal iterators. +func (gap vmaGapIterator) Ok() bool { + return gap.node != nil +} + +// Range returns the range spanned by the iterated gap. +func (gap vmaGapIterator) Range() __generics_imported0.AddrRange { + return __generics_imported0.AddrRange{gap.Start(), gap.End()} +} + +// Start is equivalent to Range().Start, but should be preferred if only the +// start of the range is needed. +func (gap vmaGapIterator) Start() __generics_imported0.Addr { + if ps := gap.PrevSegment(); ps.Ok() { + return ps.End() + } + return vmaSetFunctions{}.MinKey() +} + +// End is equivalent to Range().End, but should be preferred if only the end of +// the range is needed. +func (gap vmaGapIterator) End() __generics_imported0.Addr { + if ns := gap.NextSegment(); ns.Ok() { + return ns.Start() + } + return vmaSetFunctions{}.MaxKey() +} + +// IsEmpty returns true if the iterated gap is empty (that is, the "gap" is +// between two adjacent segments.) +func (gap vmaGapIterator) IsEmpty() bool { + return gap.Range().Length() == 0 +} + +// PrevSegment returns the segment immediately before the iterated gap. If no +// such segment exists, PrevSegment returns a terminal iterator. +func (gap vmaGapIterator) PrevSegment() vmaIterator { + return vmasegmentBeforePosition(gap.node, gap.index) +} + +// NextSegment returns the segment immediately after the iterated gap. If no +// such segment exists, NextSegment returns a terminal iterator. +func (gap vmaGapIterator) NextSegment() vmaIterator { + return vmasegmentAfterPosition(gap.node, gap.index) +} + +// PrevGap returns the iterated gap's predecessor. If no such gap exists, +// PrevGap returns a terminal iterator. +func (gap vmaGapIterator) PrevGap() vmaGapIterator { + seg := gap.PrevSegment() + if !seg.Ok() { + return vmaGapIterator{} + } + return seg.PrevGap() +} + +// NextGap returns the iterated gap's successor. If no such gap exists, NextGap +// returns a terminal iterator. +func (gap vmaGapIterator) NextGap() vmaGapIterator { + seg := gap.NextSegment() + if !seg.Ok() { + return vmaGapIterator{} + } + return seg.NextGap() +} + +// NextLargeEnoughGap returns the iterated gap's first next gap with larger +// length than minSize. If not found, return a terminal gap iterator (does NOT +// include this gap itself). +// +// Precondition: trackGaps must be 1. +func (gap vmaGapIterator) NextLargeEnoughGap(minSize __generics_imported0.Addr) vmaGapIterator { + if vmatrackGaps != 1 { + panic("set is not tracking gaps") + } + if gap.node != nil && gap.node.hasChildren && gap.index == gap.node.nrSegments { + + gap.node = gap.NextSegment().node + gap.index = 0 + return gap.nextLargeEnoughGapHelper(minSize) + } + return gap.nextLargeEnoughGapHelper(minSize) +} + +// nextLargeEnoughGapHelper is the helper function used by NextLargeEnoughGap +// to do the real recursions. +// +// Preconditions: gap is NOT the trailing gap of a non-leaf node. +func (gap vmaGapIterator) nextLargeEnoughGapHelper(minSize __generics_imported0.Addr) vmaGapIterator { + + for gap.node != nil && + (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == gap.node.nrSegments)) { + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + + if gap.node == nil { + return vmaGapIterator{} + } + + gap.index++ + for gap.index <= gap.node.nrSegments { + if gap.node.hasChildren { + if largeEnoughGap := gap.node.children[gap.index].searchFirstLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } else { + if gap.Range().Length() >= minSize { + return gap + } + } + gap.index++ + } + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + if gap.node != nil && gap.index == gap.node.nrSegments { + + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + return gap.nextLargeEnoughGapHelper(minSize) +} + +// PrevLargeEnoughGap returns the iterated gap's first prev gap with larger or +// equal length than minSize. If not found, return a terminal gap iterator +// (does NOT include this gap itself). +// +// Precondition: trackGaps must be 1. +func (gap vmaGapIterator) PrevLargeEnoughGap(minSize __generics_imported0.Addr) vmaGapIterator { + if vmatrackGaps != 1 { + panic("set is not tracking gaps") + } + if gap.node != nil && gap.node.hasChildren && gap.index == 0 { + + gap.node = gap.PrevSegment().node + gap.index = gap.node.nrSegments + return gap.prevLargeEnoughGapHelper(minSize) + } + return gap.prevLargeEnoughGapHelper(minSize) +} + +// prevLargeEnoughGapHelper is the helper function used by PrevLargeEnoughGap +// to do the real recursions. +// +// Preconditions: gap is NOT the first gap of a non-leaf node. +func (gap vmaGapIterator) prevLargeEnoughGapHelper(minSize __generics_imported0.Addr) vmaGapIterator { + + for gap.node != nil && + (gap.node.maxGap.Get() < minSize || (!gap.node.hasChildren && gap.index == 0)) { + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + + if gap.node == nil { + return vmaGapIterator{} + } + + gap.index-- + for gap.index >= 0 { + if gap.node.hasChildren { + if largeEnoughGap := gap.node.children[gap.index].searchLastLargeEnoughGap(minSize); largeEnoughGap.Ok() { + return largeEnoughGap + } + } else { + if gap.Range().Length() >= minSize { + return gap + } + } + gap.index-- + } + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + if gap.node != nil && gap.index == 0 { + + gap.node, gap.index = gap.node.parent, gap.node.parentIndex + } + return gap.prevLargeEnoughGapHelper(minSize) +} + +// segmentBeforePosition returns the predecessor segment of the position given +// by n.children[i], which may or may not contain a child. If no such segment +// exists, segmentBeforePosition returns a terminal iterator. +func vmasegmentBeforePosition(n *vmanode, i int) vmaIterator { + for i == 0 { + if n.parent == nil { + return vmaIterator{} + } + n, i = n.parent, n.parentIndex + } + return vmaIterator{n, i - 1} +} + +// segmentAfterPosition returns the successor segment of the position given by +// n.children[i], which may or may not contain a child. If no such segment +// exists, segmentAfterPosition returns a terminal iterator. +func vmasegmentAfterPosition(n *vmanode, i int) vmaIterator { + for i == n.nrSegments { + if n.parent == nil { + return vmaIterator{} + } + n, i = n.parent, n.parentIndex + } + return vmaIterator{n, i} +} + +func vmazeroValueSlice(slice []vma) { + + for i := range slice { + vmaSetFunctions{}.ClearValue(&slice[i]) + } +} + +func vmazeroNodeSlice(slice []*vmanode) { + for i := range slice { + slice[i] = nil + } +} + +// String stringifies a Set for debugging. +func (s *vmaSet) String() string { + return s.root.String() +} + +// String stringifies a node (and all of its children) for debugging. +func (n *vmanode) String() string { + var buf bytes.Buffer + n.writeDebugString(&buf, "") + return buf.String() +} + +func (n *vmanode) writeDebugString(buf *bytes.Buffer, prefix string) { + if n.hasChildren != (n.nrSegments > 0 && n.children[0] != nil) { + buf.WriteString(prefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent value of hasChildren: got %v, want %v\n", n.hasChildren, !n.hasChildren)) + } + for i := 0; i < n.nrSegments; i++ { + if child := n.children[i]; child != nil { + cprefix := fmt.Sprintf("%s- % 3d ", prefix, i) + if child.parent != n || child.parentIndex != i { + buf.WriteString(cprefix) + buf.WriteString(fmt.Sprintf("WARNING: inconsistent linkage to parent: got (%p, %d), want (%p, %d)\n", child.parent, child.parentIndex, n, i)) + } + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, i)) + } + buf.WriteString(prefix) + if n.hasChildren { + if vmatrackGaps != 0 { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v, maxGap: %d\n", i, n.keys[i], n.values[i], n.maxGap.Get())) + } else { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + } else { + buf.WriteString(fmt.Sprintf("- % 3d: %v => %v\n", i, n.keys[i], n.values[i])) + } + } + if child := n.children[n.nrSegments]; child != nil { + child.writeDebugString(buf, fmt.Sprintf("%s- % 3d ", prefix, n.nrSegments)) + } +} + +// SegmentDataSlices represents segments from a set as slices of start, end, and +// values. SegmentDataSlices is primarily used as an intermediate representation +// for save/restore and the layout here is optimized for that. +// +// +stateify savable +type vmaSegmentDataSlices struct { + Start []__generics_imported0.Addr + End []__generics_imported0.Addr + Values []vma +} + +// ExportSortedSlice returns a copy of all segments in the given set, in ascending +// key order. +func (s *vmaSet) ExportSortedSlices() *vmaSegmentDataSlices { + var sds vmaSegmentDataSlices + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + sds.Start = append(sds.Start, seg.Start()) + sds.End = append(sds.End, seg.End()) + sds.Values = append(sds.Values, seg.Value()) + } + sds.Start = sds.Start[:len(sds.Start):len(sds.Start)] + sds.End = sds.End[:len(sds.End):len(sds.End)] + sds.Values = sds.Values[:len(sds.Values):len(sds.Values)] + return &sds +} + +// ImportSortedSlice initializes the given set from the given slice. +// +// Preconditions: s must be empty. sds must represent a valid set (the segments +// in sds must have valid lengths that do not overlap). The segments in sds +// must be sorted in ascending key order. +func (s *vmaSet) ImportSortedSlices(sds *vmaSegmentDataSlices) error { + if !s.IsEmpty() { + return fmt.Errorf("cannot import into non-empty set %v", s) + } + gap := s.FirstGap() + for i := range sds.Start { + r := __generics_imported0.AddrRange{sds.Start[i], sds.End[i]} + if !gap.Range().IsSupersetOf(r) { + return fmt.Errorf("segment overlaps a preceding segment or is incorrectly sorted: [%d, %d) => %v", sds.Start[i], sds.End[i], sds.Values[i]) + } + gap = s.InsertWithoutMerging(gap, r, sds.Values[i]).NextGap() + } + return nil +} + +// segmentTestCheck returns an error if s is incorrectly sorted, does not +// contain exactly expectedSegments segments, or contains a segment which +// fails the passed check. +// +// This should be used only for testing, and has been added to this package for +// templating convenience. +func (s *vmaSet) segmentTestCheck(expectedSegments int, segFunc func(int, __generics_imported0.AddrRange, vma) error) error { + havePrev := false + prev := __generics_imported0.Addr(0) + nrSegments := 0 + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + next := seg.Start() + if havePrev && prev >= next { + return fmt.Errorf("incorrect order: key %d (segment %d) >= key %d (segment %d)", prev, nrSegments-1, next, nrSegments) + } + if segFunc != nil { + if err := segFunc(nrSegments, seg.Range(), seg.Value()); err != nil { + return err + } + } + prev = next + havePrev = true + nrSegments++ + } + if nrSegments != expectedSegments { + return fmt.Errorf("incorrect number of segments: got %d, wanted %d", nrSegments, expectedSegments) + } + return nil +} + +// countSegments counts the number of segments in the set. +// +// Similar to Check, this should only be used for testing. +func (s *vmaSet) countSegments() (segments int) { + for seg := s.FirstSegment(); seg.Ok(); seg = seg.NextSegment() { + segments++ + } + return segments +} +func (s *vmaSet) saveRoot() *vmaSegmentDataSlices { + return s.ExportSortedSlices() +} + +func (s *vmaSet) loadRoot(sds *vmaSegmentDataSlices) { + if err := s.ImportSortedSlices(sds); err != nil { + panic(err) + } +} |