Source file src/runtime/mpagealloc.go

     1  // Copyright 2019 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  // Page allocator.
     6  //
     7  // The page allocator manages mapped pages (defined by pageSize, NOT
     8  // physPageSize) for allocation and re-use. It is embedded into mheap.
     9  //
    10  // Pages are managed using a bitmap that is sharded into chunks.
    11  // In the bitmap, 1 means in-use, and 0 means free. The bitmap spans the
    12  // process's address space. Chunks are managed in a sparse-array-style structure
    13  // similar to mheap.arenas, since the bitmap may be large on some systems.
    14  //
    15  // The bitmap is efficiently searched by using a radix tree in combination
    16  // with fast bit-wise intrinsics. Allocation is performed using an address-ordered
    17  // first-fit approach.
    18  //
    19  // Each entry in the radix tree is a summary that describes three properties of
    20  // a particular region of the address space: the number of contiguous free pages
    21  // at the start and end of the region it represents, and the maximum number of
    22  // contiguous free pages found anywhere in that region.
    23  //
    24  // Each level of the radix tree is stored as one contiguous array, which represents
    25  // a different granularity of subdivision of the processes' address space. Thus, this
    26  // radix tree is actually implicit in these large arrays, as opposed to having explicit
    27  // dynamically-allocated pointer-based node structures. Naturally, these arrays may be
    28  // quite large for system with large address spaces, so in these cases they are mapped
    29  // into memory as needed. The leaf summaries of the tree correspond to a bitmap chunk.
    30  //
    31  // The root level (referred to as L0 and index 0 in pageAlloc.summary) has each
    32  // summary represent the largest section of address space (16 GiB on 64-bit systems),
    33  // with each subsequent level representing successively smaller subsections until we
    34  // reach the finest granularity at the leaves, a chunk.
    35  //
    36  // More specifically, each summary in each level (except for leaf summaries)
    37  // represents some number of entries in the following level. For example, each
    38  // summary in the root level may represent a 16 GiB region of address space,
    39  // and in the next level there could be 8 corresponding entries which represent 2
    40  // GiB subsections of that 16 GiB region, each of which could correspond to 8
    41  // entries in the next level which each represent 256 MiB regions, and so on.
    42  //
    43  // Thus, this design only scales to heaps so large, but can always be extended to
    44  // larger heaps by simply adding levels to the radix tree, which mostly costs
    45  // additional virtual address space. The choice of managing large arrays also means
    46  // that a large amount of virtual address space may be reserved by the runtime.
    47  
    48  package runtime
    49  
    50  import (
    51  	"internal/goarch"
    52  	"internal/runtime/atomic"
    53  	"internal/runtime/gc"
    54  	"unsafe"
    55  )
    56  
    57  const (
    58  	// The size of a bitmap chunk, i.e. the amount of bits (that is, pages) to consider
    59  	// in the bitmap at once. It is 4MB on most platforms, except on Wasm it is 512KB.
    60  	// We use a smaller chuck size on Wasm for the same reason as the smaller arena
    61  	// size (see heapArenaBytes).
    62  	pallocChunkPages    = 1 << logPallocChunkPages
    63  	pallocChunkBytes    = pallocChunkPages * pageSize
    64  	logPallocChunkPages = 9*(1-goarch.IsWasm) + 6*goarch.IsWasm
    65  	logPallocChunkBytes = logPallocChunkPages + gc.PageShift
    66  
    67  	// The number of radix bits for each level.
    68  	//
    69  	// The value of 3 is chosen such that the block of summaries we need to scan at
    70  	// each level fits in 64 bytes (2^3 summaries * 8 bytes per summary), which is
    71  	// close to the L1 cache line width on many systems. Also, a value of 3 fits 4 tree
    72  	// levels perfectly into the 21-bit pallocBits summary field at the root level.
    73  	//
    74  	// The following equation explains how each of the constants relate:
    75  	// summaryL0Bits + (summaryLevels-1)*summaryLevelBits + logPallocChunkBytes = heapAddrBits
    76  	//
    77  	// summaryLevels is an architecture-dependent value defined in mpagealloc_*.go.
    78  	summaryLevelBits = 3
    79  	summaryL0Bits    = heapAddrBits - logPallocChunkBytes - (summaryLevels-1)*summaryLevelBits
    80  
    81  	// pallocChunksL2Bits is the number of bits of the chunk index number
    82  	// covered by the second level of the chunks map.
    83  	//
    84  	// See (*pageAlloc).chunks for more details. Update the documentation
    85  	// there should this change.
    86  	pallocChunksL2Bits  = heapAddrBits - logPallocChunkBytes - pallocChunksL1Bits
    87  	pallocChunksL1Shift = pallocChunksL2Bits
    88  
    89  	vmaNamePageAllocIndex = "page alloc index"
    90  )
    91  
    92  // maxSearchAddr returns the maximum searchAddr value, which indicates
    93  // that the heap has no free space.
    94  //
    95  // This function exists just to make it clear that this is the maximum address
    96  // for the page allocator's search space. See maxOffAddr for details.
    97  //
    98  // It's a function (rather than a variable) because it needs to be
    99  // usable before package runtime's dynamic initialization is complete.
   100  // See #51913 for details.
   101  func maxSearchAddr() offAddr { return maxOffAddr }
   102  
   103  // Global chunk index.
   104  //
   105  // Represents an index into the leaf level of the radix tree.
   106  // Similar to arenaIndex, except instead of arenas, it divides the address
   107  // space into chunks.
   108  type chunkIdx uint
   109  
   110  // chunkIndex returns the global index of the palloc chunk containing the
   111  // pointer p.
   112  func chunkIndex(p uintptr) chunkIdx {
   113  	return chunkIdx((p - arenaBaseOffset) / pallocChunkBytes)
   114  }
   115  
   116  // chunkBase returns the base address of the palloc chunk at index ci.
   117  func chunkBase(ci chunkIdx) uintptr {
   118  	return uintptr(ci)*pallocChunkBytes + arenaBaseOffset
   119  }
   120  
   121  // chunkPageIndex computes the index of the page that contains p,
   122  // relative to the chunk which contains p.
   123  func chunkPageIndex(p uintptr) uint {
   124  	return uint(p % pallocChunkBytes / pageSize)
   125  }
   126  
   127  // l1 returns the index into the first level of (*pageAlloc).chunks.
   128  func (i chunkIdx) l1() uint {
   129  	if pallocChunksL1Bits == 0 {
   130  		// Let the compiler optimize this away if there's no
   131  		// L1 map.
   132  		return 0
   133  	} else {
   134  		return uint(i) >> pallocChunksL1Shift
   135  	}
   136  }
   137  
   138  // l2 returns the index into the second level of (*pageAlloc).chunks.
   139  func (i chunkIdx) l2() uint {
   140  	if pallocChunksL1Bits == 0 {
   141  		return uint(i)
   142  	} else {
   143  		return uint(i) & (1<<pallocChunksL2Bits - 1)
   144  	}
   145  }
   146  
   147  // offAddrToLevelIndex converts an address in the offset address space
   148  // to the index into summary[level] containing addr.
   149  func offAddrToLevelIndex(level int, addr offAddr) int {
   150  	return int((addr.a - arenaBaseOffset) >> levelShift[level])
   151  }
   152  
   153  // levelIndexToOffAddr converts an index into summary[level] into
   154  // the corresponding address in the offset address space.
   155  func levelIndexToOffAddr(level, idx int) offAddr {
   156  	return offAddr{(uintptr(idx) << levelShift[level]) + arenaBaseOffset}
   157  }
   158  
   159  // addrsToSummaryRange converts base and limit pointers into a range
   160  // of entries for the given summary level.
   161  //
   162  // The returned range is inclusive on the lower bound and exclusive on
   163  // the upper bound.
   164  func addrsToSummaryRange(level int, base, limit uintptr) (lo int, hi int) {
   165  	// This is slightly more nuanced than just a shift for the exclusive
   166  	// upper-bound. Note that the exclusive upper bound may be within a
   167  	// summary at this level, meaning if we just do the obvious computation
   168  	// hi will end up being an inclusive upper bound. Unfortunately, just
   169  	// adding 1 to that is too broad since we might be on the very edge
   170  	// of a summary's max page count boundary for this level
   171  	// (1 << levelLogPages[level]). So, make limit an inclusive upper bound
   172  	// then shift, then add 1, so we get an exclusive upper bound at the end.
   173  	lo = int((base - arenaBaseOffset) >> levelShift[level])
   174  	hi = int(((limit-1)-arenaBaseOffset)>>levelShift[level]) + 1
   175  	return
   176  }
   177  
   178  // blockAlignSummaryRange aligns indices into the given level to that
   179  // level's block width (1 << levelBits[level]). It assumes lo is inclusive
   180  // and hi is exclusive, and so aligns them down and up respectively.
   181  func blockAlignSummaryRange(level int, lo, hi int) (int, int) {
   182  	e := uintptr(1) << levelBits[level]
   183  	return int(alignDown(uintptr(lo), e)), int(alignUp(uintptr(hi), e))
   184  }
   185  
   186  type pageAlloc struct {
   187  	// Radix tree of summaries.
   188  	//
   189  	// Each slice's cap represents the whole memory reservation.
   190  	// Each slice's len reflects the allocator's maximum known
   191  	// mapped heap address for that level.
   192  	//
   193  	// The backing store of each summary level is reserved in init
   194  	// and may or may not be committed in grow (small address spaces
   195  	// may commit all the memory in init).
   196  	//
   197  	// The purpose of keeping len <= cap is to enforce bounds checks
   198  	// on the top end of the slice so that instead of an unknown
   199  	// runtime segmentation fault, we get a much friendlier out-of-bounds
   200  	// error.
   201  	//
   202  	// To iterate over a summary level, use inUse to determine which ranges
   203  	// are currently available. Otherwise one might try to access
   204  	// memory which is only Reserved which may result in a hard fault.
   205  	//
   206  	// We may still get segmentation faults < len since some of that
   207  	// memory may not be committed yet.
   208  	summary [summaryLevels][]pallocSum
   209  
   210  	// chunks is a slice of bitmap chunks.
   211  	//
   212  	// The total size of chunks is quite large on most 64-bit platforms
   213  	// (O(GiB) or more) if flattened, so rather than making one large mapping
   214  	// (which has problems on some platforms, even when PROT_NONE) we use a
   215  	// two-level sparse array approach similar to the arena index in mheap.
   216  	//
   217  	// To find the chunk containing a memory address `a`, do:
   218  	//   chunkOf(chunkIndex(a))
   219  	//
   220  	// Below is a table describing the configuration for chunks for various
   221  	// heapAddrBits supported by the runtime.
   222  	//
   223  	// heapAddrBits | L1 Bits | L2 Bits | L2 Entry Size
   224  	// ------------------------------------------------
   225  	// 32           | 0       | 10      | 128 KiB
   226  	// 32 (wasm)    | 0       | 13      | 128 KiB
   227  	// 33 (iOS)     | 0       | 11      | 256 KiB
   228  	// 48           | 13      | 13      | 1 MiB
   229  	//
   230  	// There's no reason to use the L1 part of chunks on 32-bit, the
   231  	// address space is small so the L2 is small. For platforms with a
   232  	// 48-bit address space, we pick the L1 such that the L2 is 1 MiB
   233  	// in size, which is a good balance between low granularity without
   234  	// making the impact on BSS too high (note the L1 is stored directly
   235  	// in pageAlloc).
   236  	//
   237  	// To iterate over the bitmap, use inUse to determine which ranges
   238  	// are currently available. Otherwise one might iterate over unused
   239  	// ranges.
   240  	//
   241  	// Protected by mheapLock.
   242  	//
   243  	// TODO(mknyszek): Consider changing the definition of the bitmap
   244  	// such that 1 means free and 0 means in-use so that summaries and
   245  	// the bitmaps align better on zero-values.
   246  	chunks [1 << pallocChunksL1Bits]*[1 << pallocChunksL2Bits]pallocData
   247  
   248  	// The address to start an allocation search with. It must never
   249  	// point to any memory that is not contained in inUse, i.e.
   250  	// inUse.contains(searchAddr.addr()) must always be true. The one
   251  	// exception to this rule is that it may take on the value of
   252  	// maxOffAddr to indicate that the heap is exhausted.
   253  	//
   254  	// We guarantee that all valid heap addresses below this value
   255  	// are allocated and not worth searching.
   256  	searchAddr offAddr
   257  
   258  	// start and end represent the chunk indices
   259  	// which pageAlloc knows about. It assumes
   260  	// chunks in the range [start, end) are
   261  	// currently ready to use.
   262  	start, end chunkIdx
   263  
   264  	// inUse is a slice of ranges of address space which are
   265  	// known by the page allocator to be currently in-use (passed
   266  	// to grow).
   267  	//
   268  	// We care much more about having a contiguous heap in these cases
   269  	// and take additional measures to ensure that, so in nearly all
   270  	// cases this should have just 1 element.
   271  	//
   272  	// All access is protected by the mheapLock.
   273  	inUse addrRanges
   274  
   275  	// scav stores the scavenger state.
   276  	scav struct {
   277  		// index is an efficient index of chunks that have pages available to
   278  		// scavenge.
   279  		index scavengeIndex
   280  
   281  		// releasedBg is the amount of memory released in the background this
   282  		// scavenge cycle.
   283  		releasedBg atomic.Uintptr
   284  
   285  		// releasedEager is the amount of memory released eagerly this scavenge
   286  		// cycle.
   287  		releasedEager atomic.Uintptr
   288  	}
   289  
   290  	// mheap_.lock. This level of indirection makes it possible
   291  	// to test pageAlloc independently of the runtime allocator.
   292  	mheapLock *mutex
   293  
   294  	// sysStat is the runtime memstat to update when new system
   295  	// memory is committed by the pageAlloc for allocation metadata.
   296  	sysStat *sysMemStat
   297  
   298  	// summaryMappedReady is the number of bytes mapped in the Ready state
   299  	// in the summary structure. Used only for testing currently.
   300  	//
   301  	// Protected by mheapLock.
   302  	summaryMappedReady uintptr
   303  
   304  	// chunkHugePages indicates whether page bitmap chunks should be backed
   305  	// by huge pages.
   306  	chunkHugePages bool
   307  
   308  	// Whether or not this struct is being used in tests.
   309  	test bool
   310  }
   311  
   312  func (p *pageAlloc) init(mheapLock *mutex, sysStat *sysMemStat, test bool) {
   313  	if levelLogPages[0] > logMaxPackedValue {
   314  		// We can't represent 1<<levelLogPages[0] pages, the maximum number
   315  		// of pages we need to represent at the root level, in a summary, which
   316  		// is a big problem. Throw.
   317  		print("runtime: root level max pages = ", 1<<levelLogPages[0], "\n")
   318  		print("runtime: summary max pages = ", maxPackedValue, "\n")
   319  		throw("root level max pages doesn't fit in summary")
   320  	}
   321  	p.sysStat = sysStat
   322  
   323  	// Initialize p.inUse.
   324  	p.inUse.init(sysStat)
   325  
   326  	// System-dependent initialization.
   327  	p.sysInit(test)
   328  
   329  	// Start with the searchAddr in a state indicating there's no free memory.
   330  	p.searchAddr = maxSearchAddr()
   331  
   332  	// Set the mheapLock.
   333  	p.mheapLock = mheapLock
   334  
   335  	// Initialize the scavenge index.
   336  	p.summaryMappedReady += p.scav.index.init(test, sysStat)
   337  
   338  	// Set if we're in a test.
   339  	p.test = test
   340  }
   341  
   342  // tryChunkOf returns the bitmap data for the given chunk.
   343  //
   344  // Returns nil if the chunk data has not been mapped.
   345  func (p *pageAlloc) tryChunkOf(ci chunkIdx) *pallocData {
   346  	l2 := p.chunks[ci.l1()]
   347  	if l2 == nil {
   348  		return nil
   349  	}
   350  	return &l2[ci.l2()]
   351  }
   352  
   353  // chunkOf returns the chunk at the given chunk index.
   354  //
   355  // The chunk index must be valid or this method may throw.
   356  func (p *pageAlloc) chunkOf(ci chunkIdx) *pallocData {
   357  	return &p.chunks[ci.l1()][ci.l2()]
   358  }
   359  
   360  // grow sets up the metadata for the address range [base, base+size).
   361  // It may allocate metadata, in which case *p.sysStat will be updated.
   362  //
   363  // p.mheapLock must be held.
   364  func (p *pageAlloc) grow(base, size uintptr) {
   365  	assertLockHeld(p.mheapLock)
   366  
   367  	// Round up to chunks, since we can't deal with increments smaller
   368  	// than chunks. Also, sysGrow expects aligned values.
   369  	limit := alignUp(base+size, pallocChunkBytes)
   370  	base = alignDown(base, pallocChunkBytes)
   371  
   372  	// Grow the summary levels in a system-dependent manner.
   373  	// We just update a bunch of additional metadata here.
   374  	p.sysGrow(base, limit)
   375  
   376  	// Grow the scavenge index.
   377  	p.summaryMappedReady += p.scav.index.grow(base, limit, p.sysStat)
   378  
   379  	// Update p.start and p.end.
   380  	// If no growth happened yet, start == 0. This is generally
   381  	// safe since the zero page is unmapped.
   382  	firstGrowth := p.start == 0
   383  	start, end := chunkIndex(base), chunkIndex(limit)
   384  	if firstGrowth || start < p.start {
   385  		p.start = start
   386  	}
   387  	if end > p.end {
   388  		p.end = end
   389  	}
   390  	// Note that [base, limit) will never overlap with any existing
   391  	// range inUse because grow only ever adds never-used memory
   392  	// regions to the page allocator.
   393  	p.inUse.add(makeAddrRange(base, limit))
   394  
   395  	// A grow operation is a lot like a free operation, so if our
   396  	// chunk ends up below p.searchAddr, update p.searchAddr to the
   397  	// new address, just like in free.
   398  	if b := (offAddr{base}); b.lessThan(p.searchAddr) {
   399  		p.searchAddr = b
   400  	}
   401  
   402  	// Add entries into chunks, which is sparse, if needed. Then,
   403  	// initialize the bitmap.
   404  	//
   405  	// Newly-grown memory is always considered scavenged.
   406  	// Set all the bits in the scavenged bitmaps high.
   407  	for c := chunkIndex(base); c < chunkIndex(limit); c++ {
   408  		if p.chunks[c.l1()] == nil {
   409  			// Create the necessary l2 entry.
   410  			const l2Size = unsafe.Sizeof(*p.chunks[0])
   411  			r := sysAlloc(l2Size, p.sysStat, vmaNamePageAllocIndex)
   412  			if r == nil {
   413  				throw("pageAlloc: out of memory")
   414  			}
   415  			if !p.test {
   416  				// Make the chunk mapping eligible or ineligible
   417  				// for huge pages, depending on what our current
   418  				// state is.
   419  				if p.chunkHugePages {
   420  					sysHugePage(r, l2Size)
   421  				} else {
   422  					sysNoHugePage(r, l2Size)
   423  				}
   424  			}
   425  			// Store the new chunk block but avoid a write barrier.
   426  			// grow is used in call chains that disallow write barriers.
   427  			*(*uintptr)(unsafe.Pointer(&p.chunks[c.l1()])) = uintptr(r)
   428  		}
   429  		p.chunkOf(c).scavenged.setRange(0, pallocChunkPages)
   430  	}
   431  
   432  	// Update summaries accordingly. The grow acts like a free, so
   433  	// we need to ensure this newly-free memory is visible in the
   434  	// summaries.
   435  	p.update(base, size/pageSize, true, false)
   436  }
   437  
   438  // enableChunkHugePages enables huge pages for the chunk bitmap mappings (disabled by default).
   439  //
   440  // This function is idempotent.
   441  //
   442  // A note on latency: for sufficiently small heaps (<10s of GiB) this function will take constant
   443  // time, but may take time proportional to the size of the mapped heap beyond that.
   444  //
   445  // The heap lock must not be held over this operation, since it will briefly acquire
   446  // the heap lock.
   447  //
   448  // Must be called on the system stack because it acquires the heap lock.
   449  //
   450  //go:systemstack
   451  func (p *pageAlloc) enableChunkHugePages() {
   452  	// Grab the heap lock to turn on huge pages for new chunks and clone the current
   453  	// heap address space ranges.
   454  	//
   455  	// After the lock is released, we can be sure that bitmaps for any new chunks may
   456  	// be backed with huge pages, and we have the address space for the rest of the
   457  	// chunks. At the end of this function, all chunk metadata should be backed by huge
   458  	// pages.
   459  	lock(&mheap_.lock)
   460  	if p.chunkHugePages {
   461  		unlock(&mheap_.lock)
   462  		return
   463  	}
   464  	p.chunkHugePages = true
   465  	var inUse addrRanges
   466  	inUse.sysStat = p.sysStat
   467  	p.inUse.cloneInto(&inUse)
   468  	unlock(&mheap_.lock)
   469  
   470  	// This might seem like a lot of work, but all these loops are for generality.
   471  	//
   472  	// For a 1 GiB contiguous heap, a 48-bit address space, 13 L1 bits, a palloc chunk size
   473  	// of 4 MiB, and adherence to the default set of heap address hints, this will result in
   474  	// exactly 1 call to sysHugePage.
   475  	for _, r := range p.inUse.ranges {
   476  		for i := chunkIndex(r.base.addr()).l1(); i < chunkIndex(r.limit.addr()-1).l1(); i++ {
   477  			// N.B. We can assume that p.chunks[i] is non-nil and in a mapped part of p.chunks
   478  			// because it's derived from inUse, which never shrinks.
   479  			sysHugePage(unsafe.Pointer(p.chunks[i]), unsafe.Sizeof(*p.chunks[0]))
   480  		}
   481  	}
   482  }
   483  
   484  // update updates heap metadata. It must be called each time the bitmap
   485  // is updated.
   486  //
   487  // If contig is true, update does some optimizations assuming that there was
   488  // a contiguous allocation or free between addr and addr+npages. alloc indicates
   489  // whether the operation performed was an allocation or a free.
   490  //
   491  // p.mheapLock must be held.
   492  func (p *pageAlloc) update(base, npages uintptr, contig, alloc bool) {
   493  	assertLockHeld(p.mheapLock)
   494  
   495  	// base, limit, start, and end are inclusive.
   496  	limit := base + npages*pageSize - 1
   497  	sc, ec := chunkIndex(base), chunkIndex(limit)
   498  
   499  	// Handle updating the lowest level first.
   500  	if sc == ec {
   501  		// Fast path: the allocation doesn't span more than one chunk,
   502  		// so update this one and if the summary didn't change, return.
   503  		x := p.summary[len(p.summary)-1][sc]
   504  		y := p.chunkOf(sc).summarize()
   505  		if x == y {
   506  			return
   507  		}
   508  		p.summary[len(p.summary)-1][sc] = y
   509  	} else if contig {
   510  		// Slow contiguous path: the allocation spans more than one chunk
   511  		// and at least one summary is guaranteed to change.
   512  		summary := p.summary[len(p.summary)-1]
   513  
   514  		// Update the summary for chunk sc.
   515  		summary[sc] = p.chunkOf(sc).summarize()
   516  
   517  		// Update the summaries for chunks in between, which are
   518  		// either totally allocated or freed.
   519  		whole := p.summary[len(p.summary)-1][sc+1 : ec]
   520  		if alloc {
   521  			clear(whole)
   522  		} else {
   523  			for i := range whole {
   524  				whole[i] = freeChunkSum
   525  			}
   526  		}
   527  
   528  		// Update the summary for chunk ec.
   529  		summary[ec] = p.chunkOf(ec).summarize()
   530  	} else {
   531  		// Slow general path: the allocation spans more than one chunk
   532  		// and at least one summary is guaranteed to change.
   533  		//
   534  		// We can't assume a contiguous allocation happened, so walk over
   535  		// every chunk in the range and manually recompute the summary.
   536  		summary := p.summary[len(p.summary)-1]
   537  		for c := sc; c <= ec; c++ {
   538  			summary[c] = p.chunkOf(c).summarize()
   539  		}
   540  	}
   541  
   542  	// Walk up the radix tree and update the summaries appropriately.
   543  	changed := true
   544  	for l := len(p.summary) - 2; l >= 0 && changed; l-- {
   545  		// Update summaries at level l from summaries at level l+1.
   546  		changed = false
   547  
   548  		// "Constants" for the previous level which we
   549  		// need to compute the summary from that level.
   550  		logEntriesPerBlock := levelBits[l+1]
   551  		logMaxPages := levelLogPages[l+1]
   552  
   553  		// lo and hi describe all the parts of the level we need to look at.
   554  		lo, hi := addrsToSummaryRange(l, base, limit+1)
   555  
   556  		// Iterate over each block, updating the corresponding summary in the less-granular level.
   557  		for i := lo; i < hi; i++ {
   558  			children := p.summary[l+1][i<<logEntriesPerBlock : (i+1)<<logEntriesPerBlock]
   559  			sum := mergeSummaries(children, logMaxPages)
   560  			old := p.summary[l][i]
   561  			if old != sum {
   562  				changed = true
   563  				p.summary[l][i] = sum
   564  			}
   565  		}
   566  	}
   567  }
   568  
   569  // allocRange marks the range of memory [base, base+npages*pageSize) as
   570  // allocated. It also updates the summaries to reflect the newly-updated
   571  // bitmap.
   572  //
   573  // Returns the amount of scavenged memory in bytes present in the
   574  // allocated range.
   575  //
   576  // p.mheapLock must be held.
   577  func (p *pageAlloc) allocRange(base, npages uintptr) uintptr {
   578  	assertLockHeld(p.mheapLock)
   579  
   580  	limit := base + npages*pageSize - 1
   581  	sc, ec := chunkIndex(base), chunkIndex(limit)
   582  	si, ei := chunkPageIndex(base), chunkPageIndex(limit)
   583  
   584  	scav := uint(0)
   585  	if sc == ec {
   586  		// The range doesn't cross any chunk boundaries.
   587  		chunk := p.chunkOf(sc)
   588  		scav += chunk.scavenged.popcntRange(si, ei+1-si)
   589  		chunk.allocRange(si, ei+1-si)
   590  		p.scav.index.alloc(sc, ei+1-si)
   591  	} else {
   592  		// The range crosses at least one chunk boundary.
   593  		chunk := p.chunkOf(sc)
   594  		scav += chunk.scavenged.popcntRange(si, pallocChunkPages-si)
   595  		chunk.allocRange(si, pallocChunkPages-si)
   596  		p.scav.index.alloc(sc, pallocChunkPages-si)
   597  		for c := sc + 1; c < ec; c++ {
   598  			chunk := p.chunkOf(c)
   599  			scav += chunk.scavenged.popcntRange(0, pallocChunkPages)
   600  			chunk.allocAll()
   601  			p.scav.index.alloc(c, pallocChunkPages)
   602  		}
   603  		chunk = p.chunkOf(ec)
   604  		scav += chunk.scavenged.popcntRange(0, ei+1)
   605  		chunk.allocRange(0, ei+1)
   606  		p.scav.index.alloc(ec, ei+1)
   607  	}
   608  	p.update(base, npages, true, true)
   609  	return uintptr(scav) * pageSize
   610  }
   611  
   612  // findMappedAddr returns the smallest mapped offAddr that is
   613  // >= addr. That is, if addr refers to mapped memory, then it is
   614  // returned. If addr is higher than any mapped region, then
   615  // it returns maxOffAddr.
   616  //
   617  // p.mheapLock must be held.
   618  func (p *pageAlloc) findMappedAddr(addr offAddr) offAddr {
   619  	assertLockHeld(p.mheapLock)
   620  
   621  	// If we're not in a test, validate first by checking mheap_.arenas.
   622  	// This is a fast path which is only safe to use outside of testing.
   623  	ai := arenaIndex(addr.addr())
   624  	if p.test || mheap_.arenas[ai.l1()] == nil || mheap_.arenas[ai.l1()][ai.l2()] == nil {
   625  		vAddr, ok := p.inUse.findAddrGreaterEqual(addr.addr())
   626  		if ok {
   627  			return offAddr{vAddr}
   628  		} else {
   629  			// The candidate search address is greater than any
   630  			// known address, which means we definitely have no
   631  			// free memory left.
   632  			return maxOffAddr
   633  		}
   634  	}
   635  	return addr
   636  }
   637  
   638  // find searches for the first (address-ordered) contiguous free region of
   639  // npages in size and returns a base address for that region.
   640  //
   641  // It uses p.searchAddr to prune its search and assumes that no palloc chunks
   642  // below chunkIndex(p.searchAddr) contain any free memory at all.
   643  //
   644  // find also computes and returns a candidate p.searchAddr, which may or
   645  // may not prune more of the address space than p.searchAddr already does.
   646  // This candidate is always a valid p.searchAddr.
   647  //
   648  // find represents the slow path and the full radix tree search.
   649  //
   650  // Returns a base address of 0 on failure, in which case the candidate
   651  // searchAddr returned is invalid and must be ignored.
   652  //
   653  // p.mheapLock must be held.
   654  func (p *pageAlloc) find(npages uintptr) (uintptr, offAddr) {
   655  	assertLockHeld(p.mheapLock)
   656  
   657  	// Search algorithm.
   658  	//
   659  	// This algorithm walks each level l of the radix tree from the root level
   660  	// to the leaf level. It iterates over at most 1 << levelBits[l] of entries
   661  	// in a given level in the radix tree, and uses the summary information to
   662  	// find either:
   663  	//  1) That a given subtree contains a large enough contiguous region, at
   664  	//     which point it continues iterating on the next level, or
   665  	//  2) That there are enough contiguous boundary-crossing bits to satisfy
   666  	//     the allocation, at which point it knows exactly where to start
   667  	//     allocating from.
   668  	//
   669  	// i tracks the index into the current level l's structure for the
   670  	// contiguous 1 << levelBits[l] entries we're actually interested in.
   671  	//
   672  	// NOTE: Technically this search could allocate a region which crosses
   673  	// the arenaBaseOffset boundary, which when arenaBaseOffset != 0, is
   674  	// a discontinuity. However, the only way this could happen is if the
   675  	// page at the zero address is mapped, and this is impossible on
   676  	// every system we support where arenaBaseOffset != 0. So, the
   677  	// discontinuity is already encoded in the fact that the OS will never
   678  	// map the zero page for us, and this function doesn't try to handle
   679  	// this case in any way.
   680  
   681  	// i is the beginning of the block of entries we're searching at the
   682  	// current level.
   683  	i := 0
   684  
   685  	// firstFree is the region of address space that we are certain to
   686  	// find the first free page in the heap. base and bound are the inclusive
   687  	// bounds of this window, and both are addresses in the linearized, contiguous
   688  	// view of the address space (with arenaBaseOffset pre-added). At each level,
   689  	// this window is narrowed as we find the memory region containing the
   690  	// first free page of memory. To begin with, the range reflects the
   691  	// full process address space.
   692  	//
   693  	// firstFree is updated by calling foundFree each time free space in the
   694  	// heap is discovered.
   695  	//
   696  	// At the end of the search, base.addr() is the best new
   697  	// searchAddr we could deduce in this search.
   698  	firstFree := struct {
   699  		base, bound offAddr
   700  	}{
   701  		base:  minOffAddr,
   702  		bound: maxOffAddr,
   703  	}
   704  	// foundFree takes the given address range [addr, addr+size) and
   705  	// updates firstFree if it is a narrower range. The input range must
   706  	// either be fully contained within firstFree or not overlap with it
   707  	// at all.
   708  	//
   709  	// This way, we'll record the first summary we find with any free
   710  	// pages on the root level and narrow that down if we descend into
   711  	// that summary. But as soon as we need to iterate beyond that summary
   712  	// in a level to find a large enough range, we'll stop narrowing.
   713  	foundFree := func(addr offAddr, size uintptr) {
   714  		if firstFree.base.lessEqual(addr) && addr.add(size-1).lessEqual(firstFree.bound) {
   715  			// This range fits within the current firstFree window, so narrow
   716  			// down the firstFree window to the base and bound of this range.
   717  			firstFree.base = addr
   718  			firstFree.bound = addr.add(size - 1)
   719  		} else if !(addr.add(size-1).lessThan(firstFree.base) || firstFree.bound.lessThan(addr)) {
   720  			// This range only partially overlaps with the firstFree range,
   721  			// so throw.
   722  			print("runtime: addr = ", hex(addr.addr()), ", size = ", size, "\n")
   723  			print("runtime: base = ", hex(firstFree.base.addr()), ", bound = ", hex(firstFree.bound.addr()), "\n")
   724  			throw("range partially overlaps")
   725  		}
   726  	}
   727  
   728  	// lastSum is the summary which we saw on the previous level that made us
   729  	// move on to the next level. Used to print additional information in the
   730  	// case of a catastrophic failure.
   731  	// lastSumIdx is that summary's index in the previous level.
   732  	lastSum := packPallocSum(0, 0, 0)
   733  	lastSumIdx := -1
   734  
   735  nextLevel:
   736  	for l := 0; l < len(p.summary); l++ {
   737  		// For the root level, entriesPerBlock is the whole level.
   738  		entriesPerBlock := 1 << levelBits[l]
   739  		logMaxPages := levelLogPages[l]
   740  
   741  		// We've moved into a new level, so let's update i to our new
   742  		// starting index. This is a no-op for level 0.
   743  		i <<= levelBits[l]
   744  
   745  		// Slice out the block of entries we care about.
   746  		entries := p.summary[l][i : i+entriesPerBlock]
   747  
   748  		// Determine j0, the first index we should start iterating from.
   749  		// The searchAddr may help us eliminate iterations if we followed the
   750  		// searchAddr on the previous level or we're on the root level, in which
   751  		// case the searchAddr should be the same as i after levelShift.
   752  		j0 := 0
   753  		if searchIdx := offAddrToLevelIndex(l, p.searchAddr); searchIdx&^(entriesPerBlock-1) == i {
   754  			j0 = searchIdx & (entriesPerBlock - 1)
   755  		}
   756  
   757  		// Run over the level entries looking for
   758  		// a contiguous run of at least npages either
   759  		// within an entry or across entries.
   760  		//
   761  		// base contains the page index (relative to
   762  		// the first entry's first page) of the currently
   763  		// considered run of consecutive pages.
   764  		//
   765  		// size contains the size of the currently considered
   766  		// run of consecutive pages.
   767  		var base, size uint
   768  		for j := j0; j < len(entries); j++ {
   769  			sum := entries[j]
   770  			if sum == 0 {
   771  				// A full entry means we broke any streak and
   772  				// that we should skip it altogether.
   773  				size = 0
   774  				continue
   775  			}
   776  
   777  			// We've encountered a non-zero summary which means
   778  			// free memory, so update firstFree.
   779  			foundFree(levelIndexToOffAddr(l, i+j), (uintptr(1)<<logMaxPages)*pageSize)
   780  
   781  			s := sum.start()
   782  			if size+s >= uint(npages) {
   783  				// If size == 0 we don't have a run yet,
   784  				// which means base isn't valid. So, set
   785  				// base to the first page in this block.
   786  				if size == 0 {
   787  					base = uint(j) << logMaxPages
   788  				}
   789  				// We hit npages; we're done!
   790  				size += s
   791  				break
   792  			}
   793  			if sum.max() >= uint(npages) {
   794  				// The entry itself contains npages contiguous
   795  				// free pages, so continue on the next level
   796  				// to find that run.
   797  				i += j
   798  				lastSumIdx = i
   799  				lastSum = sum
   800  				continue nextLevel
   801  			}
   802  			if size == 0 || s < 1<<logMaxPages {
   803  				// We either don't have a current run started, or this entry
   804  				// isn't totally free (meaning we can't continue the current
   805  				// one), so try to begin a new run by setting size and base
   806  				// based on sum.end.
   807  				size = sum.end()
   808  				base = uint(j+1)<<logMaxPages - size
   809  				continue
   810  			}
   811  			// The entry is completely free, so continue the run.
   812  			size += 1 << logMaxPages
   813  		}
   814  		if size >= uint(npages) {
   815  			// We found a sufficiently large run of free pages straddling
   816  			// some boundary, so compute the address and return it.
   817  			addr := levelIndexToOffAddr(l, i).add(uintptr(base) * pageSize).addr()
   818  			return addr, p.findMappedAddr(firstFree.base)
   819  		}
   820  		if l == 0 {
   821  			// We're at level zero, so that means we've exhausted our search.
   822  			return 0, maxSearchAddr()
   823  		}
   824  
   825  		// We're not at level zero, and we exhausted the level we were looking in.
   826  		// This means that either our calculations were wrong or the level above
   827  		// lied to us. In either case, dump some useful state and throw.
   828  		print("runtime: summary[", l-1, "][", lastSumIdx, "] = ", lastSum.start(), ", ", lastSum.max(), ", ", lastSum.end(), "\n")
   829  		print("runtime: level = ", l, ", npages = ", npages, ", j0 = ", j0, "\n")
   830  		print("runtime: p.searchAddr = ", hex(p.searchAddr.addr()), ", i = ", i, "\n")
   831  		print("runtime: levelShift[level] = ", levelShift[l], ", levelBits[level] = ", levelBits[l], "\n")
   832  		for j := 0; j < len(entries); j++ {
   833  			sum := entries[j]
   834  			print("runtime: summary[", l, "][", i+j, "] = (", sum.start(), ", ", sum.max(), ", ", sum.end(), ")\n")
   835  		}
   836  		throw("bad summary data")
   837  	}
   838  
   839  	// Since we've gotten to this point, that means we haven't found a
   840  	// sufficiently-sized free region straddling some boundary (chunk or larger).
   841  	// This means the last summary we inspected must have had a large enough "max"
   842  	// value, so look inside the chunk to find a suitable run.
   843  	//
   844  	// After iterating over all levels, i must contain a chunk index which
   845  	// is what the final level represents.
   846  	ci := chunkIdx(i)
   847  	j, searchIdx := p.chunkOf(ci).find(npages, 0)
   848  	if j == ^uint(0) {
   849  		// We couldn't find any space in this chunk despite the summaries telling
   850  		// us it should be there. There's likely a bug, so dump some state and throw.
   851  		sum := p.summary[len(p.summary)-1][i]
   852  		print("runtime: summary[", len(p.summary)-1, "][", i, "] = (", sum.start(), ", ", sum.max(), ", ", sum.end(), ")\n")
   853  		print("runtime: npages = ", npages, "\n")
   854  		throw("bad summary data")
   855  	}
   856  
   857  	// Compute the address at which the free space starts.
   858  	addr := chunkBase(ci) + uintptr(j)*pageSize
   859  
   860  	// Since we actually searched the chunk, we may have
   861  	// found an even narrower free window.
   862  	searchAddr := chunkBase(ci) + uintptr(searchIdx)*pageSize
   863  	foundFree(offAddr{searchAddr}, chunkBase(ci+1)-searchAddr)
   864  	return addr, p.findMappedAddr(firstFree.base)
   865  }
   866  
   867  // alloc allocates npages worth of memory from the page heap, returning the base
   868  // address for the allocation and the amount of scavenged memory in bytes
   869  // contained in the region [base address, base address + npages*pageSize).
   870  //
   871  // Returns a 0 base address on failure, in which case other returned values
   872  // should be ignored.
   873  //
   874  // p.mheapLock must be held.
   875  //
   876  // Must run on the system stack because p.mheapLock must be held.
   877  //
   878  //go:systemstack
   879  func (p *pageAlloc) alloc(npages uintptr) (addr uintptr, scav uintptr) {
   880  	assertLockHeld(p.mheapLock)
   881  
   882  	// If the searchAddr refers to a region which has a higher address than
   883  	// any known chunk, then we know we're out of memory.
   884  	if chunkIndex(p.searchAddr.addr()) >= p.end {
   885  		return 0, 0
   886  	}
   887  
   888  	// If npages has a chance of fitting in the chunk where the searchAddr is,
   889  	// search it directly.
   890  	searchAddr := minOffAddr
   891  	if pallocChunkPages-chunkPageIndex(p.searchAddr.addr()) >= uint(npages) {
   892  		// npages is guaranteed to be no greater than pallocChunkPages here.
   893  		i := chunkIndex(p.searchAddr.addr())
   894  		if max := p.summary[len(p.summary)-1][i].max(); max >= uint(npages) {
   895  			j, searchIdx := p.chunkOf(i).find(npages, chunkPageIndex(p.searchAddr.addr()))
   896  			if j == ^uint(0) {
   897  				print("runtime: max = ", max, ", npages = ", npages, "\n")
   898  				print("runtime: searchIdx = ", chunkPageIndex(p.searchAddr.addr()), ", p.searchAddr = ", hex(p.searchAddr.addr()), "\n")
   899  				throw("bad summary data")
   900  			}
   901  			addr = chunkBase(i) + uintptr(j)*pageSize
   902  			searchAddr = offAddr{chunkBase(i) + uintptr(searchIdx)*pageSize}
   903  			goto Found
   904  		}
   905  	}
   906  	// We failed to use a searchAddr for one reason or another, so try
   907  	// the slow path.
   908  	addr, searchAddr = p.find(npages)
   909  	if addr == 0 {
   910  		if npages == 1 {
   911  			// We failed to find a single free page, the smallest unit
   912  			// of allocation. This means we know the heap is completely
   913  			// exhausted. Otherwise, the heap still might have free
   914  			// space in it, just not enough contiguous space to
   915  			// accommodate npages.
   916  			p.searchAddr = maxSearchAddr()
   917  		}
   918  		return 0, 0
   919  	}
   920  Found:
   921  	// Go ahead and actually mark the bits now that we have an address.
   922  	scav = p.allocRange(addr, npages)
   923  
   924  	// If we found a higher searchAddr, we know that all the
   925  	// heap memory before that searchAddr in an offset address space is
   926  	// allocated, so bump p.searchAddr up to the new one.
   927  	if p.searchAddr.lessThan(searchAddr) {
   928  		p.searchAddr = searchAddr
   929  	}
   930  	return addr, scav
   931  }
   932  
   933  // free returns npages worth of memory starting at base back to the page heap.
   934  //
   935  // p.mheapLock must be held.
   936  //
   937  // Must run on the system stack because p.mheapLock must be held.
   938  //
   939  //go:systemstack
   940  func (p *pageAlloc) free(base, npages uintptr) {
   941  	assertLockHeld(p.mheapLock)
   942  
   943  	// If we're freeing pages below the p.searchAddr, update searchAddr.
   944  	if b := (offAddr{base}); b.lessThan(p.searchAddr) {
   945  		p.searchAddr = b
   946  	}
   947  	limit := base + npages*pageSize - 1
   948  	if npages == 1 {
   949  		// Fast path: we're clearing a single bit, and we know exactly
   950  		// where it is, so mark it directly.
   951  		i := chunkIndex(base)
   952  		pi := chunkPageIndex(base)
   953  		p.chunkOf(i).free1(pi)
   954  		p.scav.index.free(i, pi, 1)
   955  	} else {
   956  		// Slow path: we're clearing more bits so we may need to iterate.
   957  		sc, ec := chunkIndex(base), chunkIndex(limit)
   958  		si, ei := chunkPageIndex(base), chunkPageIndex(limit)
   959  
   960  		if sc == ec {
   961  			// The range doesn't cross any chunk boundaries.
   962  			p.chunkOf(sc).free(si, ei+1-si)
   963  			p.scav.index.free(sc, si, ei+1-si)
   964  		} else {
   965  			// The range crosses at least one chunk boundary.
   966  			p.chunkOf(sc).free(si, pallocChunkPages-si)
   967  			p.scav.index.free(sc, si, pallocChunkPages-si)
   968  			for c := sc + 1; c < ec; c++ {
   969  				p.chunkOf(c).freeAll()
   970  				p.scav.index.free(c, 0, pallocChunkPages)
   971  			}
   972  			p.chunkOf(ec).free(0, ei+1)
   973  			p.scav.index.free(ec, 0, ei+1)
   974  		}
   975  	}
   976  	p.update(base, npages, true, false)
   977  }
   978  
   979  // markRandomPaddingPages marks the range of memory [base, base+npages*pageSize]
   980  // as both allocated and scavenged. This is used for randomizing the base heap
   981  // address. Both the alloc and scav bits are set so that the pages are not used
   982  // and so the memory accounting stats are correctly calculated.
   983  //
   984  // Similar to allocRange, it also updates the summaries to reflect the
   985  // newly-updated bitmap.
   986  //
   987  // p.mheapLock must be held.
   988  func (p *pageAlloc) markRandomPaddingPages(base uintptr, npages uintptr) {
   989  	assertLockHeld(p.mheapLock)
   990  
   991  	limit := base + npages*pageSize - 1
   992  	sc, ec := chunkIndex(base), chunkIndex(limit)
   993  	si, ei := chunkPageIndex(base), chunkPageIndex(limit)
   994  	if sc == ec {
   995  		chunk := p.chunkOf(sc)
   996  		chunk.allocRange(si, ei+1-si)
   997  		p.scav.index.alloc(sc, ei+1-si)
   998  		chunk.scavenged.setRange(si, ei+1-si)
   999  	} else {
  1000  		chunk := p.chunkOf(sc)
  1001  		chunk.allocRange(si, pallocChunkPages-si)
  1002  		p.scav.index.alloc(sc, pallocChunkPages-si)
  1003  		chunk.scavenged.setRange(si, pallocChunkPages-si)
  1004  		for c := sc + 1; c < ec; c++ {
  1005  			chunk := p.chunkOf(c)
  1006  			chunk.allocAll()
  1007  			p.scav.index.alloc(c, pallocChunkPages)
  1008  			chunk.scavenged.setAll()
  1009  		}
  1010  		chunk = p.chunkOf(ec)
  1011  		chunk.allocRange(0, ei+1)
  1012  		p.scav.index.alloc(ec, ei+1)
  1013  		chunk.scavenged.setRange(0, ei+1)
  1014  	}
  1015  	p.update(base, npages, true, true)
  1016  }
  1017  
  1018  const (
  1019  	pallocSumBytes = unsafe.Sizeof(pallocSum(0))
  1020  
  1021  	// maxPackedValue is the maximum value that any of the three fields in
  1022  	// the pallocSum may take on.
  1023  	maxPackedValue    = 1 << logMaxPackedValue
  1024  	logMaxPackedValue = logPallocChunkPages + (summaryLevels-1)*summaryLevelBits
  1025  
  1026  	freeChunkSum = pallocSum(uint64(pallocChunkPages) |
  1027  		uint64(pallocChunkPages<<logMaxPackedValue) |
  1028  		uint64(pallocChunkPages<<(2*logMaxPackedValue)))
  1029  )
  1030  
  1031  // pallocSum is a packed summary type which packs three numbers: start, max,
  1032  // and end into a single 8-byte value. Each of these values are a summary of
  1033  // a bitmap and are thus counts, each of which may have a maximum value of
  1034  // 2^21 - 1, or all three may be equal to 2^21. The latter case is represented
  1035  // by just setting the 64th bit.
  1036  type pallocSum uint64
  1037  
  1038  // packPallocSum takes a start, max, and end value and produces a pallocSum.
  1039  func packPallocSum(start, max, end uint) pallocSum {
  1040  	if max == maxPackedValue {
  1041  		return pallocSum(uint64(1 << 63))
  1042  	}
  1043  	return pallocSum((uint64(start) & (maxPackedValue - 1)) |
  1044  		((uint64(max) & (maxPackedValue - 1)) << logMaxPackedValue) |
  1045  		((uint64(end) & (maxPackedValue - 1)) << (2 * logMaxPackedValue)))
  1046  }
  1047  
  1048  // start extracts the start value from a packed sum.
  1049  func (p pallocSum) start() uint {
  1050  	if uint64(p)&uint64(1<<63) != 0 {
  1051  		return maxPackedValue
  1052  	}
  1053  	return uint(uint64(p) & (maxPackedValue - 1))
  1054  }
  1055  
  1056  // max extracts the max value from a packed sum.
  1057  func (p pallocSum) max() uint {
  1058  	if uint64(p)&uint64(1<<63) != 0 {
  1059  		return maxPackedValue
  1060  	}
  1061  	return uint((uint64(p) >> logMaxPackedValue) & (maxPackedValue - 1))
  1062  }
  1063  
  1064  // end extracts the end value from a packed sum.
  1065  func (p pallocSum) end() uint {
  1066  	if uint64(p)&uint64(1<<63) != 0 {
  1067  		return maxPackedValue
  1068  	}
  1069  	return uint((uint64(p) >> (2 * logMaxPackedValue)) & (maxPackedValue - 1))
  1070  }
  1071  
  1072  // unpack unpacks all three values from the summary.
  1073  func (p pallocSum) unpack() (uint, uint, uint) {
  1074  	if uint64(p)&uint64(1<<63) != 0 {
  1075  		return maxPackedValue, maxPackedValue, maxPackedValue
  1076  	}
  1077  	return uint(uint64(p) & (maxPackedValue - 1)),
  1078  		uint((uint64(p) >> logMaxPackedValue) & (maxPackedValue - 1)),
  1079  		uint((uint64(p) >> (2 * logMaxPackedValue)) & (maxPackedValue - 1))
  1080  }
  1081  
  1082  // mergeSummaries merges consecutive summaries which may each represent at
  1083  // most 1 << logMaxPagesPerSum pages each together into one.
  1084  func mergeSummaries(sums []pallocSum, logMaxPagesPerSum uint) pallocSum {
  1085  	// Merge the summaries in sums into one.
  1086  	//
  1087  	// We do this by keeping a running summary representing the merged
  1088  	// summaries of sums[:i] in start, most, and end.
  1089  	start, most, end := sums[0].unpack()
  1090  	for i := 1; i < len(sums); i++ {
  1091  		// Merge in sums[i].
  1092  		si, mi, ei := sums[i].unpack()
  1093  
  1094  		// Merge in sums[i].start only if the running summary is
  1095  		// completely free, otherwise this summary's start
  1096  		// plays no role in the combined sum.
  1097  		if start == uint(i)<<logMaxPagesPerSum {
  1098  			start += si
  1099  		}
  1100  
  1101  		// Recompute the max value of the running sum by looking
  1102  		// across the boundary between the running sum and sums[i]
  1103  		// and at the max sums[i], taking the greatest of those two
  1104  		// and the max of the running sum.
  1105  		most = max(most, end+si, mi)
  1106  
  1107  		// Merge in end by checking if this new summary is totally
  1108  		// free. If it is, then we want to extend the running sum's
  1109  		// end by the new summary. If not, then we have some alloc'd
  1110  		// pages in there and we just want to take the end value in
  1111  		// sums[i].
  1112  		if ei == 1<<logMaxPagesPerSum {
  1113  			end += 1 << logMaxPagesPerSum
  1114  		} else {
  1115  			end = ei
  1116  		}
  1117  	}
  1118  	return packPallocSum(start, most, end)
  1119  }
  1120  

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