/src/postgres/src/backend/utils/mmgr/freepage.c

Source
/*-------------------------------------------------------------------------
 *
 * freepage.c
 *    Management of free memory pages.
 *
 * The intention of this code is to provide infrastructure for memory
 * allocators written specifically for PostgreSQL.  At least in the case
 * of dynamic shared memory, we can't simply use malloc() or even
 * relatively thin wrappers like palloc() which sit on top of it, because
 * no allocator built into the operating system will deal with relative
 * pointers.  In the future, we may find other cases in which greater
 * control over our own memory management seems desirable.
 *
 * A FreePageManager keeps track of which 4kB pages of memory are currently
 * unused from the point of view of some higher-level memory allocator.
 * Unlike a user-facing allocator such as palloc(), a FreePageManager can
 * only allocate and free in units of whole pages, and freeing an
 * allocation can only be done given knowledge of its length in pages.
 *
 * Since a free page manager has only a fixed amount of dedicated memory,
 * and since there is no underlying allocator, it uses the free pages
 * it is given to manage to store its bookkeeping data.  It keeps multiple
 * freelists of runs of pages, sorted by the size of the run; the head of
 * each freelist is stored in the FreePageManager itself, and the first
 * page of each run contains a relative pointer to the next run. See
 * FreePageManagerGetInternal for more details on how the freelists are
 * managed.
 *
 * To avoid memory fragmentation, it's important to consolidate adjacent
 * spans of pages whenever possible; otherwise, large allocation requests
 * might not be satisfied even when sufficient contiguous space is
 * available.  Therefore, in addition to the freelists, we maintain an
 * in-memory btree of free page ranges ordered by page number.  If a
 * range being freed precedes or follows a range that is already free,
 * the existing range is extended; if it exactly bridges the gap between
 * free ranges, then the two existing ranges are consolidated with the
 * newly-freed range to form one great big range of free pages.
 *
 * When there is only one range of free pages, the btree is trivial and
 * is stored within the FreePageManager proper; otherwise, pages are
 * allocated from the area under management as needed.  Even in cases
 * where memory fragmentation is very severe, only a tiny fraction of
 * the pages under management are consumed by this btree.
 *
 * Portions Copyright (c) 1996-2026, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *    src/backend/utils/mmgr/freepage.c
 *
 *-------------------------------------------------------------------------
 */

#include "postgres.h"
#include "lib/stringinfo.h"
#include "miscadmin.h"

#include "utils/freepage.h"
#include "utils/relptr.h"


/* Magic numbers to identify various page types */
#define FREE_PAGE_SPAN_LEADER_MAGIC   0xea4020f0
#define FREE_PAGE_LEAF_MAGIC      0x98eae728
#define FREE_PAGE_INTERNAL_MAGIC    0x19aa32c9

/* Doubly linked list of spans of free pages; stored in first page of span. */
struct FreePageSpanLeader
{
  int     magic;      /* always FREE_PAGE_SPAN_LEADER_MAGIC */
  Size    npages;     /* number of pages in span */
  RelptrFreePageSpanLeader prev;
  RelptrFreePageSpanLeader next;
};

/* Common header for btree leaf and internal pages. */
typedef struct FreePageBtreeHeader
{
  int     magic;      /* FREE_PAGE_LEAF_MAGIC or
                 * FREE_PAGE_INTERNAL_MAGIC */
  Size    nused;      /* number of items used */
  RelptrFreePageBtree parent; /* uplink */
} FreePageBtreeHeader;

/* Internal key; points to next level of btree. */
typedef struct FreePageBtreeInternalKey
{
  Size    first_page;   /* low bound for keys on child page */
  RelptrFreePageBtree child;  /* downlink */
} FreePageBtreeInternalKey;

/* Leaf key; no payload data. */
typedef struct FreePageBtreeLeafKey
{
  Size    first_page;   /* first page in span */
  Size    npages;     /* number of pages in span */
} FreePageBtreeLeafKey;

/* Work out how many keys will fit on a page. */
#define FPM_ITEMS_PER_INTERNAL_PAGE \
  ((FPM_PAGE_SIZE - sizeof(FreePageBtreeHeader)) / \
    sizeof(FreePageBtreeInternalKey))
#define FPM_ITEMS_PER_LEAF_PAGE \
  ((FPM_PAGE_SIZE - sizeof(FreePageBtreeHeader)) / \
    sizeof(FreePageBtreeLeafKey))

/* A btree page of either sort */
struct FreePageBtree
{
  FreePageBtreeHeader hdr;
  union
  {
    FreePageBtreeInternalKey internal_key[FPM_ITEMS_PER_INTERNAL_PAGE];
    FreePageBtreeLeafKey leaf_key[FPM_ITEMS_PER_LEAF_PAGE];
  }     u;
};

/* Results of a btree search */
typedef struct FreePageBtreeSearchResult
{
  FreePageBtree *page;
  Size    index;
  bool    found;
  unsigned  split_pages;
} FreePageBtreeSearchResult;

/* Helper functions */
static void FreePageBtreeAdjustAncestorKeys(FreePageManager *fpm,
                      FreePageBtree *btp);
static Size FreePageBtreeCleanup(FreePageManager *fpm);
static FreePageBtree *FreePageBtreeFindLeftSibling(char *base,
                           FreePageBtree *btp);
static FreePageBtree *FreePageBtreeFindRightSibling(char *base,
                          FreePageBtree *btp);
static Size FreePageBtreeFirstKey(FreePageBtree *btp);
static FreePageBtree *FreePageBtreeGetRecycled(FreePageManager *fpm);
static void FreePageBtreeInsertInternal(char *base, FreePageBtree *btp,
                    Size index, Size first_page, FreePageBtree *child);
static void FreePageBtreeInsertLeaf(FreePageBtree *btp, Size index,
                  Size first_page, Size npages);
static void FreePageBtreeRecycle(FreePageManager *fpm, Size pageno);
static void FreePageBtreeRemove(FreePageManager *fpm, FreePageBtree *btp,
                Size index);
static void FreePageBtreeRemovePage(FreePageManager *fpm, FreePageBtree *btp);
static void FreePageBtreeSearch(FreePageManager *fpm, Size first_page,
                FreePageBtreeSearchResult *result);
static Size FreePageBtreeSearchInternal(FreePageBtree *btp, Size first_page);
static Size FreePageBtreeSearchLeaf(FreePageBtree *btp, Size first_page);
static FreePageBtree *FreePageBtreeSplitPage(FreePageManager *fpm,
                       FreePageBtree *btp);
static void FreePageBtreeUpdateParentPointers(char *base, FreePageBtree *btp);
static void FreePageManagerDumpBtree(FreePageManager *fpm, FreePageBtree *btp,
                   FreePageBtree *parent, int level, StringInfo buf);
static void FreePageManagerDumpSpans(FreePageManager *fpm,
                   FreePageSpanLeader *span, Size expected_pages,
                   StringInfo buf);
static bool FreePageManagerGetInternal(FreePageManager *fpm, Size npages,
                     Size *first_page);
static Size FreePageManagerPutInternal(FreePageManager *fpm, Size first_page,
                     Size npages, bool soft);
static void FreePagePopSpanLeader(FreePageManager *fpm, Size pageno);
static void FreePagePushSpanLeader(FreePageManager *fpm, Size first_page,
                   Size npages);
static Size FreePageManagerLargestContiguous(FreePageManager *fpm);
static void FreePageManagerUpdateLargest(FreePageManager *fpm);

#ifdef FPM_EXTRA_ASSERTS
static Size sum_free_pages(FreePageManager *fpm);
#endif

/*
 * Initialize a new, empty free page manager.
 *
 * 'fpm' should reference caller-provided memory large enough to contain a
 * FreePageManager.  We'll initialize it here.
 *
 * 'base' is the address to which all pointers are relative.  When managing
 * a dynamic shared memory segment, it should normally be the base of the
 * segment.  When managing backend-private memory, it can be either NULL or,
 * if managing a single contiguous extent of memory, the start of that extent.
 */
void
FreePageManagerInitialize(FreePageManager *fpm, char *base)
{
  Size    f;

  relptr_store(base, fpm->self, fpm);
  relptr_store(base, fpm->btree_root, (FreePageBtree *) NULL);
  relptr_store(base, fpm->btree_recycle, (FreePageSpanLeader *) NULL);
  fpm->btree_depth = 0;
  fpm->btree_recycle_count = 0;
  fpm->singleton_first_page = 0;
  fpm->singleton_npages = 0;
  fpm->contiguous_pages = 0;
  fpm->contiguous_pages_dirty = true;
#ifdef FPM_EXTRA_ASSERTS
  fpm->free_pages = 0;
#endif

  for (f = 0; f < FPM_NUM_FREELISTS; f++)
    relptr_store(base, fpm->freelist[f], (FreePageSpanLeader *) NULL);
}

/*
 * Allocate a run of pages of the given length from the free page manager.
 * The return value indicates whether we were able to satisfy the request;
 * if true, the first page of the allocation is stored in *first_page.
 */
bool
FreePageManagerGet(FreePageManager *fpm, Size npages, Size *first_page)
{
  bool    result;
  Size    contiguous_pages;

  result = FreePageManagerGetInternal(fpm, npages, first_page);

  /*
   * It's a bit counterintuitive, but allocating pages can actually create
   * opportunities for cleanup that create larger ranges.  We might pull a
   * key out of the btree that enables the item at the head of the btree
   * recycle list to be inserted; and then if there are more items behind it
   * one of those might cause two currently-separated ranges to merge,
   * creating a single range of contiguous pages larger than any that
   * existed previously.  It might be worth trying to improve the cleanup
   * algorithm to avoid such corner cases, but for now we just notice the
   * condition and do the appropriate reporting.
   */
  contiguous_pages = FreePageBtreeCleanup(fpm);
  if (fpm->contiguous_pages < contiguous_pages)
    fpm->contiguous_pages = contiguous_pages;

  /*
   * FreePageManagerGetInternal may have set contiguous_pages_dirty.
   * Recompute contiguous_pages if so.
   */
  FreePageManagerUpdateLargest(fpm);

#ifdef FPM_EXTRA_ASSERTS
  if (result)
  {
    Assert(fpm->free_pages >= npages);
    fpm->free_pages -= npages;
  }
  Assert(fpm->free_pages == sum_free_pages(fpm));
  Assert(fpm->contiguous_pages == FreePageManagerLargestContiguous(fpm));
#endif
  return result;
}

#ifdef FPM_EXTRA_ASSERTS
static void
sum_free_pages_recurse(FreePageManager *fpm, FreePageBtree *btp, Size *sum)
{
  char     *base = fpm_segment_base(fpm);

  Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC ||
       btp->hdr.magic == FREE_PAGE_LEAF_MAGIC);
  ++*sum;
  if (btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC)
  {
    Size    index;


    for (index = 0; index < btp->hdr.nused; ++index)
    {
      FreePageBtree *child;

      child = relptr_access(base, btp->u.internal_key[index].child);
      sum_free_pages_recurse(fpm, child, sum);
    }
  }
}
static Size
sum_free_pages(FreePageManager *fpm)
{
  FreePageSpanLeader *recycle;
  char     *base = fpm_segment_base(fpm);
  Size    sum = 0;
  int     list;

  /* Count the spans by scanning the freelists. */
  for (list = 0; list < FPM_NUM_FREELISTS; ++list)
  {

    if (!relptr_is_null(fpm->freelist[list]))
    {
      FreePageSpanLeader *candidate =
        relptr_access(base, fpm->freelist[list]);

      do
      {
        sum += candidate->npages;
        candidate = relptr_access(base, candidate->next);
      } while (candidate != NULL);
    }
  }

  /* Count btree internal pages. */
  if (fpm->btree_depth > 0)
  {
    FreePageBtree *root = relptr_access(base, fpm->btree_root);

    sum_free_pages_recurse(fpm, root, &sum);
  }

  /* Count the recycle list. */
  for (recycle = relptr_access(base, fpm->btree_recycle);
     recycle != NULL;
     recycle = relptr_access(base, recycle->next))
  {
    Assert(recycle->npages == 1);
    ++sum;
  }

  return sum;
}
#endif

/*
 * Compute the size of the largest run of pages that the user could
 * successfully get.
 */
static Size
FreePageManagerLargestContiguous(FreePageManager *fpm)
{
  char     *base;
  Size    largest;

  base = fpm_segment_base(fpm);
  largest = 0;
  if (!relptr_is_null(fpm->freelist[FPM_NUM_FREELISTS - 1]))
  {
    FreePageSpanLeader *candidate;

    candidate = relptr_access(base, fpm->freelist[FPM_NUM_FREELISTS - 1]);
    do
    {
      if (candidate->npages > largest)
        largest = candidate->npages;
      candidate = relptr_access(base, candidate->next);
    } while (candidate != NULL);
  }
  else
  {
    Size    f = FPM_NUM_FREELISTS - 1;

    do
    {
      --f;
      if (!relptr_is_null(fpm->freelist[f]))
      {
        largest = f + 1;
        break;
      }
    } while (f > 0);
  }

  return largest;
}

/*
 * Recompute the size of the largest run of pages that the user could
 * successfully get, if it has been marked dirty.
 */
static void
FreePageManagerUpdateLargest(FreePageManager *fpm)
{
  if (!fpm->contiguous_pages_dirty)
    return;

  fpm->contiguous_pages = FreePageManagerLargestContiguous(fpm);
  fpm->contiguous_pages_dirty = false;
}

/*
 * Transfer a run of pages to the free page manager.
 */
void
FreePageManagerPut(FreePageManager *fpm, Size first_page, Size npages)
{
  Size    contiguous_pages;

  Assert(npages > 0);

  /* Record the new pages. */
  contiguous_pages =
    FreePageManagerPutInternal(fpm, first_page, npages, false);

  /*
   * If the new range we inserted into the page manager was contiguous with
   * an existing range, it may have opened up cleanup opportunities.
   */
  if (contiguous_pages > npages)
  {
    Size    cleanup_contiguous_pages;

    cleanup_contiguous_pages = FreePageBtreeCleanup(fpm);
    if (cleanup_contiguous_pages > contiguous_pages)
      contiguous_pages = cleanup_contiguous_pages;
  }

  /* See if we now have a new largest chunk. */
  if (fpm->contiguous_pages < contiguous_pages)
    fpm->contiguous_pages = contiguous_pages;

  /*
   * The earlier call to FreePageManagerPutInternal may have set
   * contiguous_pages_dirty if it needed to allocate internal pages, so
   * recompute contiguous_pages if necessary.
   */
  FreePageManagerUpdateLargest(fpm);

#ifdef FPM_EXTRA_ASSERTS
  fpm->free_pages += npages;
  Assert(fpm->free_pages == sum_free_pages(fpm));
  Assert(fpm->contiguous_pages == FreePageManagerLargestContiguous(fpm));
#endif
}

/*
 * Produce a debugging dump of the state of a free page manager.
 */
char *
FreePageManagerDump(FreePageManager *fpm)
{
  char     *base = fpm_segment_base(fpm);
  StringInfoData buf;
  FreePageSpanLeader *recycle;
  bool    dumped_any_freelist = false;
  Size    f;

  /* Initialize output buffer. */
  initStringInfo(&buf);

  /* Dump general stuff. */
  appendStringInfo(&buf, "metadata: self %zu max contiguous pages = %zu\n",
           relptr_offset(fpm->self), fpm->contiguous_pages);

  /* Dump btree. */
  if (fpm->btree_depth > 0)
  {
    FreePageBtree *root;

    appendStringInfo(&buf, "btree depth %u:\n", fpm->btree_depth);
    root = relptr_access(base, fpm->btree_root);
    FreePageManagerDumpBtree(fpm, root, NULL, 0, &buf);
  }
  else if (fpm->singleton_npages > 0)
  {
    appendStringInfo(&buf, "singleton: %zu(%zu)\n",
             fpm->singleton_first_page, fpm->singleton_npages);
  }

  /* Dump btree recycle list. */
  recycle = relptr_access(base, fpm->btree_recycle);
  if (recycle != NULL)
  {
    appendStringInfoString(&buf, "btree recycle:");
    FreePageManagerDumpSpans(fpm, recycle, 1, &buf);
  }

  /* Dump free lists. */
  for (f = 0; f < FPM_NUM_FREELISTS; ++f)
  {
    FreePageSpanLeader *span;

    if (relptr_is_null(fpm->freelist[f]))
      continue;
    if (!dumped_any_freelist)
    {
      appendStringInfoString(&buf, "freelists:\n");
      dumped_any_freelist = true;
    }
    appendStringInfo(&buf, "  %zu:", f + 1);
    span = relptr_access(base, fpm->freelist[f]);
    FreePageManagerDumpSpans(fpm, span, f + 1, &buf);
  }

  /* And return result to caller. */
  return buf.data;
}


/*
 * The first_page value stored at index zero in any non-root page must match
 * the first_page value stored in its parent at the index which points to that
 * page.  So when the value stored at index zero in a btree page changes, we've
 * got to walk up the tree adjusting ancestor keys until we reach an ancestor
 * where that key isn't index zero.  This function should be called after
 * updating the first key on the target page; it will propagate the change
 * upward as far as needed.
 *
 * We assume here that the first key on the page has not changed enough to
 * require changes in the ordering of keys on its ancestor pages.  Thus,
 * if we search the parent page for the first key greater than or equal to
 * the first key on the current page, the downlink to this page will be either
 * the exact index returned by the search (if the first key decreased)
 * or one less (if the first key increased).
 */
static void
FreePageBtreeAdjustAncestorKeys(FreePageManager *fpm, FreePageBtree *btp)
{
  char     *base = fpm_segment_base(fpm);
  Size    first_page;
  FreePageBtree *parent;
  FreePageBtree *child;

  /* This might be either a leaf or an internal page. */
  Assert(btp->hdr.nused > 0);
  if (btp->hdr.magic == FREE_PAGE_LEAF_MAGIC)
  {
    Assert(btp->hdr.nused <= FPM_ITEMS_PER_LEAF_PAGE);
    first_page = btp->u.leaf_key[0].first_page;
  }
  else
  {
    Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
    Assert(btp->hdr.nused <= FPM_ITEMS_PER_INTERNAL_PAGE);
    first_page = btp->u.internal_key[0].first_page;
  }
  child = btp;

  /* Loop until we find an ancestor that does not require adjustment. */
  for (;;)
  {
    Size    s;

    parent = relptr_access(base, child->hdr.parent);
    if (parent == NULL)
      break;
    s = FreePageBtreeSearchInternal(parent, first_page);

    /* Key is either at index s or index s-1; figure out which. */
    if (s >= parent->hdr.nused)
    {
      Assert(s == parent->hdr.nused);
      --s;
    }
    else
    {
      FreePageBtree *check;

      check = relptr_access(base, parent->u.internal_key[s].child);
      if (check != child)
      {
        Assert(s > 0);
        --s;
      }
    }

#ifdef USE_ASSERT_CHECKING
    /* Debugging double-check. */
    {
      FreePageBtree *check;

      check = relptr_access(base, parent->u.internal_key[s].child);
      Assert(s < parent->hdr.nused);
      Assert(child == check);
    }
#endif

    /* Update the parent key. */
    parent->u.internal_key[s].first_page = first_page;

    /*
     * If this is the first key in the parent, go up another level; else
     * done.
     */
    if (s > 0)
      break;
    child = parent;
  }
}

/*
 * Attempt to reclaim space from the free-page btree.  The return value is
 * the largest range of contiguous pages created by the cleanup operation.
 */
static Size
FreePageBtreeCleanup(FreePageManager *fpm)
{
  char     *base = fpm_segment_base(fpm);
  Size    max_contiguous_pages = 0;

  /* Attempt to shrink the depth of the btree. */
  while (!relptr_is_null(fpm->btree_root))
  {
    FreePageBtree *root = relptr_access(base, fpm->btree_root);

    /* If the root contains only one key, reduce depth by one. */
    if (root->hdr.nused == 1)
    {
      /* Shrink depth of tree by one. */
      Assert(fpm->btree_depth > 0);
      --fpm->btree_depth;
      if (root->hdr.magic == FREE_PAGE_LEAF_MAGIC)
      {
        /* If root is a leaf, convert only entry to singleton range. */
        relptr_store(base, fpm->btree_root, (FreePageBtree *) NULL);
        fpm->singleton_first_page = root->u.leaf_key[0].first_page;
        fpm->singleton_npages = root->u.leaf_key[0].npages;
      }
      else
      {
        FreePageBtree *newroot;

        /* If root is an internal page, make only child the root. */
        Assert(root->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
        relptr_copy(fpm->btree_root, root->u.internal_key[0].child);
        newroot = relptr_access(base, fpm->btree_root);
        relptr_store(base, newroot->hdr.parent, (FreePageBtree *) NULL);
      }
      FreePageBtreeRecycle(fpm, fpm_pointer_to_page(base, root));
    }
    else if (root->hdr.nused == 2 &&
         root->hdr.magic == FREE_PAGE_LEAF_MAGIC)
    {
      Size    end_of_first;
      Size    start_of_second;

      end_of_first = root->u.leaf_key[0].first_page +
        root->u.leaf_key[0].npages;
      start_of_second = root->u.leaf_key[1].first_page;

      if (end_of_first + 1 == start_of_second)
      {
        Size    root_page = fpm_pointer_to_page(base, root);

        if (end_of_first == root_page)
        {
          FreePagePopSpanLeader(fpm, root->u.leaf_key[0].first_page);
          FreePagePopSpanLeader(fpm, root->u.leaf_key[1].first_page);
          fpm->singleton_first_page = root->u.leaf_key[0].first_page;
          fpm->singleton_npages = root->u.leaf_key[0].npages +
            root->u.leaf_key[1].npages + 1;
          fpm->btree_depth = 0;
          relptr_store(base, fpm->btree_root,
                 (FreePageBtree *) NULL);
          FreePagePushSpanLeader(fpm, fpm->singleton_first_page,
                       fpm->singleton_npages);
          Assert(max_contiguous_pages == 0);
          max_contiguous_pages = fpm->singleton_npages;
        }
      }

      /* Whether it worked or not, it's time to stop. */
      break;
    }
    else
    {
      /* Nothing more to do.  Stop. */
      break;
    }
  }

  /*
   * Attempt to free recycled btree pages.  We skip this if releasing the
   * recycled page would require a btree page split, because the page we're
   * trying to recycle would be consumed by the split, which would be
   * counterproductive.
   *
   * We also currently only ever attempt to recycle the first page on the
   * list; that could be made more aggressive, but it's not clear that the
   * complexity would be worthwhile.
   */
  while (fpm->btree_recycle_count > 0)
  {
    FreePageBtree *btp;
    Size    first_page;
    Size    contiguous_pages;

    btp = FreePageBtreeGetRecycled(fpm);
    first_page = fpm_pointer_to_page(base, btp);
    contiguous_pages = FreePageManagerPutInternal(fpm, first_page, 1, true);
    if (contiguous_pages == 0)
    {
      FreePageBtreeRecycle(fpm, first_page);
      break;
    }
    else
    {
      if (contiguous_pages > max_contiguous_pages)
        max_contiguous_pages = contiguous_pages;
    }
  }

  return max_contiguous_pages;
}

/*
 * Consider consolidating the given page with its left or right sibling,
 * if it's fairly empty.
 */
static void
FreePageBtreeConsolidate(FreePageManager *fpm, FreePageBtree *btp)
{
  char     *base = fpm_segment_base(fpm);
  FreePageBtree *np;
  Size    max;

  /*
   * We only try to consolidate pages that are less than a third full. We
   * could be more aggressive about this, but that might risk performing
   * consolidation only to end up splitting again shortly thereafter.  Since
   * the btree should be very small compared to the space under management,
   * our goal isn't so much to ensure that it always occupies the absolutely
   * smallest possible number of pages as to reclaim pages before things get
   * too egregiously out of hand.
   */
  if (btp->hdr.magic == FREE_PAGE_LEAF_MAGIC)
    max = FPM_ITEMS_PER_LEAF_PAGE;
  else
  {
    Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
    max = FPM_ITEMS_PER_INTERNAL_PAGE;
  }
  if (btp->hdr.nused >= max / 3)
    return;

  /*
   * If we can fit our right sibling's keys onto this page, consolidate.
   */
  np = FreePageBtreeFindRightSibling(base, btp);
  if (np != NULL && btp->hdr.nused + np->hdr.nused <= max)
  {
    if (btp->hdr.magic == FREE_PAGE_LEAF_MAGIC)
    {
      memcpy(&btp->u.leaf_key[btp->hdr.nused], &np->u.leaf_key[0],
           sizeof(FreePageBtreeLeafKey) * np->hdr.nused);
      btp->hdr.nused += np->hdr.nused;
    }
    else
    {
      memcpy(&btp->u.internal_key[btp->hdr.nused], &np->u.internal_key[0],
           sizeof(FreePageBtreeInternalKey) * np->hdr.nused);
      btp->hdr.nused += np->hdr.nused;
      FreePageBtreeUpdateParentPointers(base, btp);
    }
    FreePageBtreeRemovePage(fpm, np);
    return;
  }

  /*
   * If we can fit our keys onto our left sibling's page, consolidate. In
   * this case, we move our keys onto the other page rather than vice versa,
   * to avoid having to adjust ancestor keys.
   */
  np = FreePageBtreeFindLeftSibling(base, btp);
  if (np != NULL && btp->hdr.nused + np->hdr.nused <= max)
  {
    if (btp->hdr.magic == FREE_PAGE_LEAF_MAGIC)
    {
      memcpy(&np->u.leaf_key[np->hdr.nused], &btp->u.leaf_key[0],
           sizeof(FreePageBtreeLeafKey) * btp->hdr.nused);
      np->hdr.nused += btp->hdr.nused;
    }
    else
    {
      memcpy(&np->u.internal_key[np->hdr.nused], &btp->u.internal_key[0],
           sizeof(FreePageBtreeInternalKey) * btp->hdr.nused);
      np->hdr.nused += btp->hdr.nused;
      FreePageBtreeUpdateParentPointers(base, np);
    }
    FreePageBtreeRemovePage(fpm, btp);
    return;
  }
}

/*
 * Find the passed page's left sibling; that is, the page at the same level
 * of the tree whose keyspace immediately precedes ours.
 */
static FreePageBtree *
FreePageBtreeFindLeftSibling(char *base, FreePageBtree *btp)
{
  FreePageBtree *p = btp;
  int     levels = 0;

  /* Move up until we can move left. */
  for (;;)
  {
    Size    first_page;
    Size    index;

    first_page = FreePageBtreeFirstKey(p);
    p = relptr_access(base, p->hdr.parent);

    if (p == NULL)
      return NULL;   /* we were passed the rightmost page */

    index = FreePageBtreeSearchInternal(p, first_page);
    if (index > 0)
    {
      Assert(p->u.internal_key[index].first_page == first_page);
      p = relptr_access(base, p->u.internal_key[index - 1].child);
      break;
    }
    Assert(index == 0);
    ++levels;
  }

  /* Descend left. */
  while (levels > 0)
  {
    Assert(p->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
    p = relptr_access(base, p->u.internal_key[p->hdr.nused - 1].child);
    --levels;
  }
  Assert(p->hdr.magic == btp->hdr.magic);

  return p;
}

/*
 * Find the passed page's right sibling; that is, the page at the same level
 * of the tree whose keyspace immediately follows ours.
 */
static FreePageBtree *
FreePageBtreeFindRightSibling(char *base, FreePageBtree *btp)
{
  FreePageBtree *p = btp;
  int     levels = 0;

  /* Move up until we can move right. */
  for (;;)
  {
    Size    first_page;
    Size    index;

    first_page = FreePageBtreeFirstKey(p);
    p = relptr_access(base, p->hdr.parent);

    if (p == NULL)
      return NULL;   /* we were passed the rightmost page */

    index = FreePageBtreeSearchInternal(p, first_page);
    if (index < p->hdr.nused - 1)
    {
      Assert(p->u.internal_key[index].first_page == first_page);
      p = relptr_access(base, p->u.internal_key[index + 1].child);
      break;
    }
    Assert(index == p->hdr.nused - 1);
    ++levels;
  }

  /* Descend left. */
  while (levels > 0)
  {
    Assert(p->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
    p = relptr_access(base, p->u.internal_key[0].child);
    --levels;
  }
  Assert(p->hdr.magic == btp->hdr.magic);

  return p;
}

/*
 * Get the first key on a btree page.
 */
static Size
FreePageBtreeFirstKey(FreePageBtree *btp)
{
  Assert(btp->hdr.nused > 0);

  if (btp->hdr.magic == FREE_PAGE_LEAF_MAGIC)
    return btp->u.leaf_key[0].first_page;
  else
  {
    Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
    return btp->u.internal_key[0].first_page;
  }
}

/*
 * Get a page from the btree recycle list for use as a btree page.
 */
static FreePageBtree *
FreePageBtreeGetRecycled(FreePageManager *fpm)
{
  char     *base = fpm_segment_base(fpm);
  FreePageSpanLeader *victim = relptr_access(base, fpm->btree_recycle);
  FreePageSpanLeader *newhead;

  Assert(victim != NULL);
  newhead = relptr_access(base, victim->next);
  if (newhead != NULL)
    relptr_copy(newhead->prev, victim->prev);
  relptr_store(base, fpm->btree_recycle, newhead);
  Assert(fpm_pointer_is_page_aligned(base, victim));
  fpm->btree_recycle_count--;
  return (FreePageBtree *) victim;
}

/*
 * Insert an item into an internal page (there must be room).
 */
static void
FreePageBtreeInsertInternal(char *base, FreePageBtree *btp, Size index,
              Size first_page, FreePageBtree *child)
{
  Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
  Assert(btp->hdr.nused < FPM_ITEMS_PER_INTERNAL_PAGE);
  Assert(index <= btp->hdr.nused);
  memmove(&btp->u.internal_key[index + 1], &btp->u.internal_key[index],
      sizeof(FreePageBtreeInternalKey) * (btp->hdr.nused - index));
  btp->u.internal_key[index].first_page = first_page;
  relptr_store(base, btp->u.internal_key[index].child, child);
  ++btp->hdr.nused;
}

/*
 * Insert an item into a leaf page (there must be room).
 */
static void
FreePageBtreeInsertLeaf(FreePageBtree *btp, Size index, Size first_page,
            Size npages)
{
  Assert(btp->hdr.magic == FREE_PAGE_LEAF_MAGIC);
  Assert(btp->hdr.nused < FPM_ITEMS_PER_LEAF_PAGE);
  Assert(index <= btp->hdr.nused);
  memmove(&btp->u.leaf_key[index + 1], &btp->u.leaf_key[index],
      sizeof(FreePageBtreeLeafKey) * (btp->hdr.nused - index));
  btp->u.leaf_key[index].first_page = first_page;
  btp->u.leaf_key[index].npages = npages;
  ++btp->hdr.nused;
}

/*
 * Put a page on the btree recycle list.
 */
static void
FreePageBtreeRecycle(FreePageManager *fpm, Size pageno)
{
  char     *base = fpm_segment_base(fpm);
  FreePageSpanLeader *head = relptr_access(base, fpm->btree_recycle);
  FreePageSpanLeader *span;

  span = (FreePageSpanLeader *) fpm_page_to_pointer(base, pageno);
  span->magic = FREE_PAGE_SPAN_LEADER_MAGIC;
  span->npages = 1;
  relptr_store(base, span->next, head);
  relptr_store(base, span->prev, (FreePageSpanLeader *) NULL);
  if (head != NULL)
    relptr_store(base, head->prev, span);
  relptr_store(base, fpm->btree_recycle, span);
  fpm->btree_recycle_count++;
}

/*
 * Remove an item from the btree at the given position on the given page.
 */
static void
FreePageBtreeRemove(FreePageManager *fpm, FreePageBtree *btp, Size index)
{
  Assert(btp->hdr.magic == FREE_PAGE_LEAF_MAGIC);
  Assert(index < btp->hdr.nused);

  /* When last item is removed, extirpate entire page from btree. */
  if (btp->hdr.nused == 1)
  {
    FreePageBtreeRemovePage(fpm, btp);
    return;
  }

  /* Physically remove the key from the page. */
  --btp->hdr.nused;
  if (index < btp->hdr.nused)
    memmove(&btp->u.leaf_key[index], &btp->u.leaf_key[index + 1],
        sizeof(FreePageBtreeLeafKey) * (btp->hdr.nused - index));

  /* If we just removed the first key, adjust ancestor keys. */
  if (index == 0)
    FreePageBtreeAdjustAncestorKeys(fpm, btp);

  /* Consider whether to consolidate this page with a sibling. */
  FreePageBtreeConsolidate(fpm, btp);
}

/*
 * Remove a page from the btree.  Caller is responsible for having relocated
 * any keys from this page that are still wanted.  The page is placed on the
 * recycled list.
 */
static void
FreePageBtreeRemovePage(FreePageManager *fpm, FreePageBtree *btp)
{
  char     *base = fpm_segment_base(fpm);
  FreePageBtree *parent;
  Size    index;
  Size    first_page;

  for (;;)
  {
    /* Find parent page. */
    parent = relptr_access(base, btp->hdr.parent);
    if (parent == NULL)
    {
      /* We are removing the root page. */
      relptr_store(base, fpm->btree_root, (FreePageBtree *) NULL);
      fpm->btree_depth = 0;
      Assert(fpm->singleton_first_page == 0);
      Assert(fpm->singleton_npages == 0);
      return;
    }

    /*
     * If the parent contains only one item, we need to remove it as well.
     */
    if (parent->hdr.nused > 1)
      break;
    FreePageBtreeRecycle(fpm, fpm_pointer_to_page(base, btp));
    btp = parent;
  }

  /* Find and remove the downlink. */
  first_page = FreePageBtreeFirstKey(btp);
  if (parent->hdr.magic == FREE_PAGE_LEAF_MAGIC)
  {
    index = FreePageBtreeSearchLeaf(parent, first_page);
    Assert(index < parent->hdr.nused);
    if (index < parent->hdr.nused - 1)
      memmove(&parent->u.leaf_key[index],
          &parent->u.leaf_key[index + 1],
          sizeof(FreePageBtreeLeafKey)
          * (parent->hdr.nused - index - 1));
  }
  else
  {
    index = FreePageBtreeSearchInternal(parent, first_page);
    Assert(index < parent->hdr.nused);
    if (index < parent->hdr.nused - 1)
      memmove(&parent->u.internal_key[index],
          &parent->u.internal_key[index + 1],
          sizeof(FreePageBtreeInternalKey)
          * (parent->hdr.nused - index - 1));
  }
  parent->hdr.nused--;
  Assert(parent->hdr.nused > 0);

  /* Recycle the page. */
  FreePageBtreeRecycle(fpm, fpm_pointer_to_page(base, btp));

  /* Adjust ancestor keys if needed. */
  if (index == 0)
    FreePageBtreeAdjustAncestorKeys(fpm, parent);

  /* Consider whether to consolidate the parent with a sibling. */
  FreePageBtreeConsolidate(fpm, parent);
}

/*
 * Search the btree for an entry for the given first page and initialize
 * *result with the results of the search.  result->page and result->index
 * indicate either the position of an exact match or the position at which
 * the new key should be inserted.  result->found is true for an exact match,
 * otherwise false.  result->split_pages will contain the number of additional
 * btree pages that will be needed when performing a split to insert a key.
 * Except as described above, the contents of fields in the result object are
 * undefined on return.
 */
static void
FreePageBtreeSearch(FreePageManager *fpm, Size first_page,
          FreePageBtreeSearchResult *result)
{
  char     *base = fpm_segment_base(fpm);
  FreePageBtree *btp = relptr_access(base, fpm->btree_root);
  Size    index;

  result->split_pages = 1;

  /* If the btree is empty, there's nothing to find. */
  if (btp == NULL)
  {
    result->page = NULL;
    result->found = false;
    return;
  }

  /* Descend until we hit a leaf. */
  while (btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC)
  {
    FreePageBtree *child;
    bool    found_exact;

    index = FreePageBtreeSearchInternal(btp, first_page);
    found_exact = index < btp->hdr.nused &&
      btp->u.internal_key[index].first_page == first_page;

    /*
     * If we found an exact match we descend directly.  Otherwise, we
     * descend into the child to the left if possible so that we can find
     * the insertion point at that child's high end.
     */
    if (!found_exact && index > 0)
      --index;

    /* Track required split depth for leaf insert. */
    if (btp->hdr.nused >= FPM_ITEMS_PER_INTERNAL_PAGE)
    {
      Assert(btp->hdr.nused == FPM_ITEMS_PER_INTERNAL_PAGE);
      result->split_pages++;
    }
    else
      result->split_pages = 0;

    /* Descend to appropriate child page. */
    Assert(index < btp->hdr.nused);
    child = relptr_access(base, btp->u.internal_key[index].child);
    Assert(relptr_access(base, child->hdr.parent) == btp);
    btp = child;
  }

  /* Track required split depth for leaf insert. */
  if (btp->hdr.nused >= FPM_ITEMS_PER_LEAF_PAGE)
  {
    Assert(btp->hdr.nused == FPM_ITEMS_PER_INTERNAL_PAGE);
    result->split_pages++;
  }
  else
    result->split_pages = 0;

  /* Search leaf page. */
  index = FreePageBtreeSearchLeaf(btp, first_page);

  /* Assemble results. */
  result->page = btp;
  result->index = index;
  result->found = index < btp->hdr.nused &&
    first_page == btp->u.leaf_key[index].first_page;
}

/*
 * Search an internal page for the first key greater than or equal to a given
 * page number.  Returns the index of that key, or one greater than the number
 * of keys on the page if none.
 */
static Size
FreePageBtreeSearchInternal(FreePageBtree *btp, Size first_page)
{
  Size    low = 0;
  Size    high = btp->hdr.nused;

  Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
  Assert(high > 0 && high <= FPM_ITEMS_PER_INTERNAL_PAGE);

  while (low < high)
  {
    Size    mid = (low + high) / 2;
    Size    val = btp->u.internal_key[mid].first_page;

    if (first_page == val)
      return mid;
    else if (first_page < val)
      high = mid;
    else
      low = mid + 1;
  }

  return low;
}

/*
 * Search a leaf page for the first key greater than or equal to a given
 * page number.  Returns the index of that key, or one greater than the number
 * of keys on the page if none.
 */
static Size
FreePageBtreeSearchLeaf(FreePageBtree *btp, Size first_page)
{
  Size    low = 0;
  Size    high = btp->hdr.nused;

  Assert(btp->hdr.magic == FREE_PAGE_LEAF_MAGIC);
  Assert(high > 0 && high <= FPM_ITEMS_PER_LEAF_PAGE);

  while (low < high)
  {
    Size    mid = (low + high) / 2;
    Size    val = btp->u.leaf_key[mid].first_page;

    if (first_page == val)
      return mid;
    else if (first_page < val)
      high = mid;
    else
      low = mid + 1;
  }

  return low;
}

/*
 * Allocate a new btree page and move half the keys from the provided page
 * to the new page.  Caller is responsible for making sure that there's a
 * page available from fpm->btree_recycle.  Returns a pointer to the new page,
 * to which caller must add a downlink.
 */
static FreePageBtree *
FreePageBtreeSplitPage(FreePageManager *fpm, FreePageBtree *btp)
{
  FreePageBtree *newsibling;

  newsibling = FreePageBtreeGetRecycled(fpm);
  newsibling->hdr.magic = btp->hdr.magic;
  newsibling->hdr.nused = btp->hdr.nused / 2;
  relptr_copy(newsibling->hdr.parent, btp->hdr.parent);
  btp->hdr.nused -= newsibling->hdr.nused;

  if (btp->hdr.magic == FREE_PAGE_LEAF_MAGIC)
    memcpy(&newsibling->u.leaf_key,
         &btp->u.leaf_key[btp->hdr.nused],
         sizeof(FreePageBtreeLeafKey) * newsibling->hdr.nused);
  else
  {
    Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
    memcpy(&newsibling->u.internal_key,
         &btp->u.internal_key[btp->hdr.nused],
         sizeof(FreePageBtreeInternalKey) * newsibling->hdr.nused);
    FreePageBtreeUpdateParentPointers(fpm_segment_base(fpm), newsibling);
  }

  return newsibling;
}

/*
 * When internal pages are split or merged, the parent pointers of their
 * children must be updated.
 */
static void
FreePageBtreeUpdateParentPointers(char *base, FreePageBtree *btp)
{
  Size    i;

  Assert(btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC);
  for (i = 0; i < btp->hdr.nused; ++i)
  {
    FreePageBtree *child;

    child = relptr_access(base, btp->u.internal_key[i].child);
    relptr_store(base, child->hdr.parent, btp);
  }
}

/*
 * Debugging dump of btree data.
 */
static void
FreePageManagerDumpBtree(FreePageManager *fpm, FreePageBtree *btp,
             FreePageBtree *parent, int level, StringInfo buf)
{
  char     *base = fpm_segment_base(fpm);
  Size    pageno = fpm_pointer_to_page(base, btp);
  Size    index;
  FreePageBtree *check_parent;

  check_stack_depth();
  check_parent = relptr_access(base, btp->hdr.parent);
  appendStringInfo(buf, "  %zu@%d %c", pageno, level,
           btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC ? 'i' : 'l');
  if (parent != check_parent)
    appendStringInfo(buf, " [actual parent %zu, expected %zu]",
             fpm_pointer_to_page(base, check_parent),
             fpm_pointer_to_page(base, parent));
  appendStringInfoChar(buf, ':');
  for (index = 0; index < btp->hdr.nused; ++index)
  {
    if (btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC)
      appendStringInfo(buf, " %zu->%zu",
               btp->u.internal_key[index].first_page,
               relptr_offset(btp->u.internal_key[index].child) / FPM_PAGE_SIZE);
    else
      appendStringInfo(buf, " %zu(%zu)",
               btp->u.leaf_key[index].first_page,
               btp->u.leaf_key[index].npages);
  }
  appendStringInfoChar(buf, '\n');

  if (btp->hdr.magic == FREE_PAGE_INTERNAL_MAGIC)
  {
    for (index = 0; index < btp->hdr.nused; ++index)
    {
      FreePageBtree *child;

      child = relptr_access(base, btp->u.internal_key[index].child);
      FreePageManagerDumpBtree(fpm, child, btp, level + 1, buf);
    }
  }
}

/*
 * Debugging dump of free-span data.
 */
static void
FreePageManagerDumpSpans(FreePageManager *fpm, FreePageSpanLeader *span,
             Size expected_pages, StringInfo buf)
{
  char     *base = fpm_segment_base(fpm);

  while (span != NULL)
  {
    if (span->npages != expected_pages)
      appendStringInfo(buf, " %zu(%zu)", fpm_pointer_to_page(base, span),
               span->npages);
    else
      appendStringInfo(buf, " %zu", fpm_pointer_to_page(base, span));
    span = relptr_access(base, span->next);
  }

  appendStringInfoChar(buf, '\n');
}

/*
 * This function allocates a run of pages of the given length from the free
 * page manager.
 */
static bool
FreePageManagerGetInternal(FreePageManager *fpm, Size npages, Size *first_page)
{
  char     *base = fpm_segment_base(fpm);
  FreePageSpanLeader *victim = NULL;
  FreePageSpanLeader *prev;
  FreePageSpanLeader *next;
  FreePageBtreeSearchResult result;
  Size    victim_page = 0;  /* placate compiler */
  Size    f;

  /*
   * Search for a free span.
   *
   * Right now, we use a simple best-fit policy here, but it's possible for
   * this to result in memory fragmentation if we're repeatedly asked to
   * allocate chunks just a little smaller than what we have available.
   * Hopefully, this is unlikely, because we expect most requests to be
   * single pages or superblock-sized chunks -- but no policy can be optimal
   * under all circumstances unless it has knowledge of future allocation
   * patterns.
   */
  for (f = Min(npages, FPM_NUM_FREELISTS) - 1; f < FPM_NUM_FREELISTS; ++f)
  {
    /* Skip empty freelists. */
    if (relptr_is_null(fpm->freelist[f]))
      continue;

    /*
     * All of the freelists except the last one contain only items of a
     * single size, so we just take the first one.  But the final free
     * list contains everything too big for any of the other lists, so we
     * need to search the list.
     */
    if (f < FPM_NUM_FREELISTS - 1)
      victim = relptr_access(base, fpm->freelist[f]);
    else
    {
      FreePageSpanLeader *candidate;

      candidate = relptr_access(base, fpm->freelist[f]);
      do
      {
        if (candidate->npages >= npages && (victim == NULL ||
                          victim->npages > candidate->npages))
        {
          victim = candidate;
          if (victim->npages == npages)
            break;
        }
        candidate = relptr_access(base, candidate->next);
      } while (candidate != NULL);
    }
    break;
  }

  /* If we didn't find an allocatable span, return failure. */
  if (victim == NULL)
    return false;

  /* Remove span from free list. */
  Assert(victim->magic == FREE_PAGE_SPAN_LEADER_MAGIC);
  prev = relptr_access(base, victim->prev);
  next = relptr_access(base, victim->next);
  if (prev != NULL)
    relptr_copy(prev->next, victim->next);
  else
    relptr_copy(fpm->freelist[f], victim->next);
  if (next != NULL)
    relptr_copy(next->prev, victim->prev);
  victim_page = fpm_pointer_to_page(base, victim);

  /* Decide whether we might be invalidating contiguous_pages. */
  if (f == FPM_NUM_FREELISTS - 1 &&
    victim->npages == fpm->contiguous_pages)
  {
    /*
     * The victim span came from the oversized freelist, and had the same
     * size as the longest span.  There may or may not be another one of
     * the same size, so contiguous_pages must be recomputed just to be
     * safe.
     */
    fpm->contiguous_pages_dirty = true;
  }
  else if (f + 1 == fpm->contiguous_pages &&
       relptr_is_null(fpm->freelist[f]))
  {
    /*
     * The victim span came from a fixed sized freelist, and it was the
     * list for spans of the same size as the current longest span, and
     * the list is now empty after removing the victim.  So
     * contiguous_pages must be recomputed without a doubt.
     */
    fpm->contiguous_pages_dirty = true;
  }

  /*
   * If we haven't initialized the btree yet, the victim must be the single
   * span stored within the FreePageManager itself.  Otherwise, we need to
   * update the btree.
   */
  if (relptr_is_null(fpm->btree_root))
  {
    Assert(victim_page == fpm->singleton_first_page);
    Assert(victim->npages == fpm->singleton_npages);
    Assert(victim->npages >= npages);
    fpm->singleton_first_page += npages;
    fpm->singleton_npages -= npages;
    if (fpm->singleton_npages > 0)
      FreePagePushSpanLeader(fpm, fpm->singleton_first_page,
                   fpm->singleton_npages);
  }
  else
  {
    /*
     * If the span we found is exactly the right size, remove it from the
     * btree completely.  Otherwise, adjust the btree entry to reflect the
     * still-unallocated portion of the span, and put that portion on the
     * appropriate free list.
     */
    FreePageBtreeSearch(fpm, victim_page, &result);
    Assert(result.found);
    if (victim->npages == npages)
      FreePageBtreeRemove(fpm, result.page, result.index);
    else
    {
      FreePageBtreeLeafKey *key;

      /* Adjust btree to reflect remaining pages. */
      Assert(victim->npages > npages);
      key = &result.page->u.leaf_key[result.index];
      Assert(key->npages == victim->npages);
      key->first_page += npages;
      key->npages -= npages;
      if (result.index == 0)
        FreePageBtreeAdjustAncestorKeys(fpm, result.page);

      /* Put the unallocated pages back on the appropriate free list. */
      FreePagePushSpanLeader(fpm, victim_page + npages,
                   victim->npages - npages);
    }
  }

  /* Return results to caller. */
  *first_page = fpm_pointer_to_page(base, victim);
  return true;
}

/*
 * Put a range of pages into the btree and freelists, consolidating it with
 * existing free spans just before and/or after it.  If 'soft' is true,
 * only perform the insertion if it can be done without allocating new btree
 * pages; if false, do it always.  Returns 0 if the soft flag caused the
 * insertion to be skipped, or otherwise the size of the contiguous span
 * created by the insertion.  This may be larger than npages if we're able
 * to consolidate with an adjacent range.
 */
static Size
FreePageManagerPutInternal(FreePageManager *fpm, Size first_page, Size npages,
               bool soft)
{
  char     *base = fpm_segment_base(fpm);
  FreePageBtreeSearchResult searchresult;
  FreePageBtreeLeafKey *prevkey = NULL;
  FreePageBtreeLeafKey *nextkey = NULL;
  FreePageBtree *np;
  Size    nindex;

  Assert(npages > 0);

  /* We can store a single free span without initializing the btree. */
  if (fpm->btree_depth == 0)
  {
    if (fpm->singleton_npages == 0)
    {
      /* Don't have a span yet; store this one. */
      fpm->singleton_first_page = first_page;
      fpm->singleton_npages = npages;
      FreePagePushSpanLeader(fpm, first_page, npages);
      return fpm->singleton_npages;
    }
    else if (fpm->singleton_first_page + fpm->singleton_npages ==
         first_page)
    {
      /* New span immediately follows sole existing span. */
      fpm->singleton_npages += npages;
      FreePagePopSpanLeader(fpm, fpm->singleton_first_page);
      FreePagePushSpanLeader(fpm, fpm->singleton_first_page,
                   fpm->singleton_npages);
      return fpm->singleton_npages;
    }
    else if (first_page + npages == fpm->singleton_first_page)
    {
      /* New span immediately precedes sole existing span. */
      FreePagePopSpanLeader(fpm, fpm->singleton_first_page);
      fpm->singleton_first_page = first_page;
      fpm->singleton_npages += npages;
      FreePagePushSpanLeader(fpm, fpm->singleton_first_page,
                   fpm->singleton_npages);
      return fpm->singleton_npages;
    }
    else
    {
      /* Not contiguous; we need to initialize the btree. */
      Size    root_page;
      FreePageBtree *root;

      if (!relptr_is_null(fpm->btree_recycle))
        root = FreePageBtreeGetRecycled(fpm);
      else if (soft)
        return 0;   /* Should not allocate if soft. */
      else if (FreePageManagerGetInternal(fpm, 1, &root_page))
        root = (FreePageBtree *) fpm_page_to_pointer(base, root_page);
      else
      {
        /* We'd better be able to get a page from the existing range. */
        elog(FATAL, "free page manager btree is corrupt");
      }

      /* Create the btree and move the preexisting range into it. */
      root->hdr.magic = FREE_PAGE_LEAF_MAGIC;
      root->hdr.nused = 1;
      relptr_store(base, root->hdr.parent, (FreePageBtree *) NULL);
      root->u.leaf_key[0].first_page = fpm->singleton_first_page;
      root->u.leaf_key[0].npages = fpm->singleton_npages;
      relptr_store(base, fpm->btree_root, root);
      fpm->singleton_first_page = 0;
      fpm->singleton_npages = 0;
      fpm->btree_depth = 1;

      /*
       * Corner case: it may be that the btree root took the very last
       * free page.  In that case, the sole btree entry covers a zero
       * page run, which is invalid.  Overwrite it with the entry we're
       * trying to insert and get out.
       */
      if (root->u.leaf_key[0].npages == 0)
      {
        root->u.leaf_key[0].first_page = first_page;
        root->u.leaf_key[0].npages = npages;
        FreePagePushSpanLeader(fpm, first_page, npages);
        return npages;
      }

      /* Fall through to insert the new key. */
    }
  }

  /* Search the btree. */
  FreePageBtreeSearch(fpm, first_page, &searchresult);
  Assert(!searchresult.found);
  if (searchresult.index > 0)
    prevkey = &searchresult.page->u.leaf_key[searchresult.index - 1];
  if (searchresult.index < searchresult.page->hdr.nused)
  {
    np = searchresult.page;
    nindex = searchresult.index;
    nextkey = &searchresult.page->u.leaf_key[searchresult.index];
  }
  else
  {
    np = FreePageBtreeFindRightSibling(base, searchresult.page);
    nindex = 0;
    if (np != NULL)
      nextkey = &np->u.leaf_key[0];
  }

  /* Consolidate with the previous entry if possible. */
  if (prevkey != NULL && prevkey->first_page + prevkey->npages >= first_page)
  {
    bool    remove_next = false;
    Size    result;

    Assert(prevkey->first_page + prevkey->npages == first_page);
    prevkey->npages = (first_page - prevkey->first_page) + npages;

    /* Check whether we can *also* consolidate with the following entry. */
    if (nextkey != NULL &&
      prevkey->first_page + prevkey->npages >= nextkey->first_page)
    {
      Assert(prevkey->first_page + prevkey->npages ==
           nextkey->first_page);
      prevkey->npages = (nextkey->first_page - prevkey->first_page)
        + nextkey->npages;
      FreePagePopSpanLeader(fpm, nextkey->first_page);
      remove_next = true;
    }

    /* Put the span on the correct freelist and save size. */
    FreePagePopSpanLeader(fpm, prevkey->first_page);
    FreePagePushSpanLeader(fpm, prevkey->first_page, prevkey->npages);
    result = prevkey->npages;

    /*
     * If we consolidated with both the preceding and following entries,
     * we must remove the following entry.  We do this last, because
     * removing an element from the btree may invalidate pointers we hold
     * into the current data structure.
     *
     * NB: The btree is technically in an invalid state a this point
     * because we've already updated prevkey to cover the same key space
     * as nextkey.  FreePageBtreeRemove() shouldn't notice that, though.
     */
    if (remove_next)
      FreePageBtreeRemove(fpm, np, nindex);

    return result;
  }

  /* Consolidate with the next entry if possible. */
  if (nextkey != NULL && first_page + npages >= nextkey->first_page)
  {
    Size    newpages;

    /* Compute new size for span. */
    Assert(first_page + npages == nextkey->first_page);
    newpages = (nextkey->first_page - first_page) + nextkey->npages;

    /* Put span on correct free list. */
    FreePagePopSpanLeader(fpm, nextkey->first_page);
    FreePagePushSpanLeader(fpm, first_page, newpages);

    /* Update key in place. */
    nextkey->first_page = first_page;
    nextkey->npages = newpages;

    /* If reducing first key on page, ancestors might need adjustment. */
    if (nindex == 0)
      FreePageBtreeAdjustAncestorKeys(fpm, np);

    return nextkey->npages;
  }

  /* Split leaf page and as many of its ancestors as necessary. */
  if (searchresult.split_pages > 0)
  {
    /*
     * NB: We could consider various coping strategies here to avoid a
     * split; most obviously, if np != result.page, we could target that
     * page instead.   More complicated shuffling strategies could be
     * possible as well; basically, unless every single leaf page is 100%
     * full, we can jam this key in there if we try hard enough.  It's
     * unlikely that trying that hard is worthwhile, but it's possible we
     * might need to make more than no effort.  For now, we just do the
     * easy thing, which is nothing.
     */

    /* If this is a soft insert, it's time to give up. */
    if (soft)
      return 0;

    /* Check whether we need to allocate more btree pages to split. */
    if (searchresult.split_pages > fpm->btree_recycle_count)
    {
      Size    pages_needed;
      Size    recycle_page;
      Size    i;

      /*
       * Allocate the required number of pages and split each one in
       * turn.  This should never fail, because if we've got enough
       * spans of free pages kicking around that we need additional
       * storage space just to remember them all, then we should
       * certainly have enough to expand the btree, which should only
       * ever use a tiny number of pages compared to the number under
       * management.  If it does, something's badly screwed up.
       */
      pages_needed = searchresult.split_pages - fpm->btree_recycle_count;
      for (i = 0; i < pages_needed; ++i)
      {
        if (!FreePageManagerGetInternal(fpm, 1, &recycle_page))
          elog(FATAL, "free page manager btree is corrupt");
        FreePageBtreeRecycle(fpm, recycle_page);
      }

      /*
       * The act of allocating pages to recycle may have invalidated the
       * results of our previous btree research, so repeat it. (We could
       * recheck whether any of our split-avoidance strategies that were
       * not viable before now are, but it hardly seems worthwhile, so
       * we don't bother. Consolidation can't be possible now if it
       * wasn't previously.)
       */
      FreePageBtreeSearch(fpm, first_page, &searchresult);

      /*
       * The act of allocating pages for use in constructing our btree
       * should never cause any page to become more full, so the new
       * split depth should be no greater than the old one, and perhaps
       * less if we fortuitously allocated a chunk that freed up a slot
       * on the page we need to update.
       */
      Assert(searchresult.split_pages <= fpm->btree_recycle_count);
    }

    /* If we still need to perform a split, do it. */
    if (searchresult.split_pages > 0)
    {
      FreePageBtree *split_target = searchresult.page;
      FreePageBtree *child = NULL;
      Size    key = first_page;

      for (;;)
      {
        FreePageBtree *newsibling;
        FreePageBtree *parent;

        /* Identify parent page, which must receive downlink. */
        parent = relptr_access(base, split_target->hdr.parent);

        /* Split the page - downlink not added yet. */
        newsibling = FreePageBtreeSplitPage(fpm, split_target);

        /*
         * At this point in the loop, we're always carrying a pending
         * insertion.  On the first pass, it's the actual key we're
         * trying to insert; on subsequent passes, it's the downlink
         * that needs to be added as a result of the split performed
         * during the previous loop iteration.  Since we've just split
         * the page, there's definitely room on one of the two
         * resulting pages.
         */
        if (child == NULL)
        {
          Size    index;
          FreePageBtree *insert_into;

          insert_into = key < newsibling->u.leaf_key[0].first_page ?
            split_target : newsibling;
          index = FreePageBtreeSearchLeaf(insert_into, key);
          FreePageBtreeInsertLeaf(insert_into, index, key, npages);
          if (index == 0 && insert_into == split_target)
            FreePageBtreeAdjustAncestorKeys(fpm, split_target);
        }
        else
        {
          Size    index;
          FreePageBtree *insert_into;

          insert_into =
            key < newsibling->u.internal_key[0].first_page ?
            split_target : newsibling;
          index = FreePageBtreeSearchInternal(insert_into, key);
          FreePageBtreeInsertInternal(base, insert_into, index,
                        key, child);
          relptr_store(base, child->hdr.parent, insert_into);
          if (index == 0 && insert_into == split_target)
            FreePageBtreeAdjustAncestorKeys(fpm, split_target);
        }

        /* If the page we just split has no parent, split the root. */
        if (parent == NULL)
        {
          FreePageBtree *newroot;

          newroot = FreePageBtreeGetRecycled(fpm);
          newroot->hdr.magic = FREE_PAGE_INTERNAL_MAGIC;
          newroot->hdr.nused = 2;
          relptr_store(base, newroot->hdr.parent,
                 (FreePageBtree *) NULL);
          newroot->u.internal_key[0].first_page =
            FreePageBtreeFirstKey(split_target);
          relptr_store(base, newroot->u.internal_key[0].child,
                 split_target);
          relptr_store(base, split_target->hdr.parent, newroot);
          newroot->u.internal_key[1].first_page =
            FreePageBtreeFirstKey(newsibling);
          relptr_store(base, newroot->u.internal_key[1].child,
                 newsibling);
          relptr_store(base, newsibling->hdr.parent, newroot);
          relptr_store(base, fpm->btree_root, newroot);
          fpm->btree_depth++;

          break;
        }

        /* If the parent page isn't full, insert the downlink. */
        key = newsibling->u.internal_key[0].first_page;
        if (parent->hdr.nused < FPM_ITEMS_PER_INTERNAL_PAGE)
        {
          Size    index;

          index = FreePageBtreeSearchInternal(parent, key);
          FreePageBtreeInsertInternal(base, parent, index,
                        key, newsibling);
          relptr_store(base, newsibling->hdr.parent, parent);
          if (index == 0)
            FreePageBtreeAdjustAncestorKeys(fpm, parent);
          break;
        }

        /* The parent also needs to be split, so loop around. */
        child = newsibling;
        split_target = parent;
      }

      /*
       * The loop above did the insert, so just need to update the free
       * list, and we're done.
       */
      FreePagePushSpanLeader(fpm, first_page, npages);

      return npages;
    }
  }

  /* Physically add the key to the page. */
  Assert(searchresult.page->hdr.nused < FPM_ITEMS_PER_LEAF_PAGE);
  FreePageBtreeInsertLeaf(searchresult.page, searchresult.index, first_page, npages);

  /* If new first key on page, ancestors might need adjustment. */
  if (searchresult.index == 0)
    FreePageBtreeAdjustAncestorKeys(fpm, searchresult.page);

  /* Put it on the free list. */
  FreePagePushSpanLeader(fpm, first_page, npages);

  return npages;
}

/*
 * Remove a FreePageSpanLeader from the linked-list that contains it, either
 * because we're changing the size of the span, or because we're allocating it.
 */
static void
FreePagePopSpanLeader(FreePageManager *fpm, Size pageno)
{
  char     *base = fpm_segment_base(fpm);
  FreePageSpanLeader *span;
  FreePageSpanLeader *next;
  FreePageSpanLeader *prev;

  span = (FreePageSpanLeader *) fpm_page_to_pointer(base, pageno);

  next = relptr_access(base, span->next);
  prev = relptr_access(base, span->prev);
  if (next != NULL)
    relptr_copy(next->prev, span->prev);
  if (prev != NULL)
    relptr_copy(prev->next, span->next);
  else
  {
    Size    f = Min(span->npages, FPM_NUM_FREELISTS) - 1;

    Assert(relptr_offset(fpm->freelist[f]) == pageno * FPM_PAGE_SIZE);
    relptr_copy(fpm->freelist[f], span->next);
  }
}

/*
 * Initialize a new FreePageSpanLeader and put it on the appropriate free list.
 */
static void
FreePagePushSpanLeader(FreePageManager *fpm, Size first_page, Size npages)
{
  char     *base = fpm_segment_base(fpm);
  Size    f = Min(npages, FPM_NUM_FREELISTS) - 1;
  FreePageSpanLeader *head = relptr_access(base, fpm->freelist[f]);
  FreePageSpanLeader *span;

  span = (FreePageSpanLeader *) fpm_page_to_pointer(base, first_page);
  span->magic = FREE_PAGE_SPAN_LEADER_MAGIC;
  span->npages = npages;
  relptr_store(base, span->next, head);
  relptr_store(base, span->prev, (FreePageSpanLeader *) NULL);
  if (head != NULL)
    relptr_store(base, head->prev, span);
  relptr_store(base, fpm->freelist[f], span);
}

Coverage Report

Created: 2026-11-12 07:20