/*-------------------------------------------------------------------------
 *
 * freespace.c
 *	  POSTGRES free space map for quickly finding free space in relations
 *
 *
 * Portions Copyright (c) 1996-2021, PostgreSQL Global Development Group
 * Portions Copyright (c) 1994, Regents of the University of California
 *
 * IDENTIFICATION
 *	  src/backend/storage/freespace/freespace.c
 *
 *
 * NOTES:
 *
 *	Free Space Map keeps track of the amount of free space on pages, and
 *	allows quickly searching for a page with enough free space. The FSM is
 *	stored in a dedicated relation fork of all heap relations, and those
 *	index access methods that need it (see also indexfsm.c). See README for
 *	more information.
 *
 *-------------------------------------------------------------------------
 */
#include "postgres.h"

#include "access/htup_details.h"
#include "access/xlogutils.h"
#include "miscadmin.h"
#include "storage/freespace.h"
#include "storage/fsm_internals.h"
#include "storage/lmgr.h"
#include "storage/smgr.h"


/*
 * We use just one byte to store the amount of free space on a page, so we
 * divide the amount of free space a page can have into 256 different
 * categories. The highest category, 255, represents a page with at least
 * MaxFSMRequestSize bytes of free space, and the second highest category
 * represents the range from 254 * FSM_CAT_STEP, inclusive, to
 * MaxFSMRequestSize, exclusive.
 *
 * MaxFSMRequestSize depends on the architecture and BLCKSZ, but assuming
 * default 8k BLCKSZ, and that MaxFSMRequestSize is 8164 bytes, the
 * categories look like this:
 *
 *
 * Range	 Category
 * 0	- 31   0
 * 32	- 63   1
 * ...    ...  ...
 * 8096 - 8127 253
 * 8128 - 8163 254
 * 8164 - 8192 255
 *
 * The reason that MaxFSMRequestSize is special is that if MaxFSMRequestSize
 * isn't equal to a range boundary, a page with exactly MaxFSMRequestSize
 * bytes of free space wouldn't satisfy a request for MaxFSMRequestSize
 * bytes. If there isn't more than MaxFSMRequestSize bytes of free space on a
 * completely empty page, that would mean that we could never satisfy a
 * request of exactly MaxFSMRequestSize bytes.
 */
#define FSM_CATEGORIES	256
#define FSM_CAT_STEP	(BLCKSZ / FSM_CATEGORIES)
#define MaxFSMRequestSize	MaxHeapTupleSize

/*
 * Depth of the on-disk tree. We need to be able to address 2^32-1 blocks,
 * and 1626 is the smallest number that satisfies X^3 >= 2^32-1. Likewise,
 * 216 is the smallest number that satisfies X^4 >= 2^32-1. In practice,
 * this means that 4096 bytes is the smallest BLCKSZ that we can get away
 * with a 3-level tree, and 512 is the smallest we support.
 */
#define FSM_TREE_DEPTH	((SlotsPerFSMPage >= 1626) ? 3 : 4)

#define FSM_ROOT_LEVEL	(FSM_TREE_DEPTH - 1)
#define FSM_BOTTOM_LEVEL 0

/*
 * The internal FSM routines work on a logical addressing scheme. Each
 * level of the tree can be thought of as a separately addressable file.
 */
typedef struct
{
	int			level;			/* level */
	int			logpageno;		/* page number within the level */
} FSMAddress;

/* Address of the root page. */
static const FSMAddress FSM_ROOT_ADDRESS = {FSM_ROOT_LEVEL, 0};

/* functions to navigate the tree */
static FSMAddress fsm_get_child(FSMAddress parent, uint16 slot);
static FSMAddress fsm_get_parent(FSMAddress child, uint16 *slot);
static FSMAddress fsm_get_location(BlockNumber heapblk, uint16 *slot);
static BlockNumber fsm_get_heap_blk(FSMAddress addr, uint16 slot);
static BlockNumber fsm_logical_to_physical(FSMAddress addr);

static Buffer fsm_readbuf(Relation rel, FSMAddress addr, bool extend);
static void fsm_extend(Relation rel, BlockNumber fsm_nblocks);

/* functions to convert amount of free space to a FSM category */
static uint8 fsm_space_avail_to_cat(Size avail);
static uint8 fsm_space_needed_to_cat(Size needed);
static Size fsm_space_cat_to_avail(uint8 cat);

/* workhorse functions for various operations */
static int	fsm_set_and_search(Relation rel, FSMAddress addr, uint16 slot,
							   uint8 newValue, uint8 minValue);
static BlockNumber fsm_search(Relation rel, uint8 min_cat);
static uint8 fsm_vacuum_page(Relation rel, FSMAddress addr,
							 BlockNumber start, BlockNumber end,
							 bool *eof);
static bool fsm_does_block_exist(Relation rel, BlockNumber blknumber);


/******** Public API ********/

/*
 * GetPageWithFreeSpace - try to find a page in the given relation with
 *		at least the specified amount of free space.
 *
 * If successful, return the block number; if not, return InvalidBlockNumber.
 *
 * The caller must be prepared for the possibility that the returned page
 * will turn out to have too little space available by the time the caller
 * gets a lock on it.  In that case, the caller should report the actual
 * amount of free space available on that page and then try again (see
 * RecordAndGetPageWithFreeSpace).  If InvalidBlockNumber is returned,
 * extend the relation.
 *
 * This can trigger FSM updates if any FSM entry is found to point to a block
 * past the end of the relation.
 */
BlockNumber
GetPageWithFreeSpace(Relation rel, Size spaceNeeded)
{
	uint8		min_cat = fsm_space_needed_to_cat(spaceNeeded);

	return fsm_search(rel, min_cat);
}

/*
 * RecordAndGetPageWithFreeSpace - update info about a page and try again.
 *
 * We provide this combo form to save some locking overhead, compared to
 * separate RecordPageWithFreeSpace + GetPageWithFreeSpace calls. There's
 * also some effort to return a page close to the old page; if there's a
 * page with enough free space on the same FSM page where the old one page
 * is located, it is preferred.
 */
BlockNumber
RecordAndGetPageWithFreeSpace(Relation rel, BlockNumber oldPage,
							  Size oldSpaceAvail, Size spaceNeeded)
{
	int			old_cat = fsm_space_avail_to_cat(oldSpaceAvail);
	int			search_cat = fsm_space_needed_to_cat(spaceNeeded);
	FSMAddress	addr;
	uint16		slot;
	int			search_slot;

	/* Get the location of the FSM byte representing the heap block */
	addr = fsm_get_location(oldPage, &slot);

	search_slot = fsm_set_and_search(rel, addr, slot, old_cat, search_cat);

	/*
	 * If fsm_set_and_search found a suitable new block, return that.
	 * Otherwise, search as usual.
	 */
	if (search_slot != -1)
	{
		BlockNumber blknum = fsm_get_heap_blk(addr, search_slot);

		/*
		 * Check that the blknum is actually in the relation. Don't try to
		 * update the FSM in that case, just fall back to the other case
		 */
		if (fsm_does_block_exist(rel, blknum))
			return blknum;
	}
	return fsm_search(rel, search_cat);
}

/*
 * RecordPageWithFreeSpace - update info about a page.
 *
 * Note that if the new spaceAvail value is higher than the old value stored
 * in the FSM, the space might not become visible to searchers until the next
 * FreeSpaceMapVacuum call, which updates the upper level pages.
 */
void
RecordPageWithFreeSpace(Relation rel, BlockNumber heapBlk, Size spaceAvail)
{
	int			new_cat = fsm_space_avail_to_cat(spaceAvail);
	FSMAddress	addr;
	uint16		slot;

	/* Get the location of the FSM byte representing the heap block */
	addr = fsm_get_location(heapBlk, &slot);

	fsm_set_and_search(rel, addr, slot, new_cat, 0);
}

/*
 * XLogRecordPageWithFreeSpace - like RecordPageWithFreeSpace, for use in
 *		WAL replay
 */
void
XLogRecordPageWithFreeSpace(RelFileNode rnode, BlockNumber heapBlk,
							Size spaceAvail)
{
	int			new_cat = fsm_space_avail_to_cat(spaceAvail);
	FSMAddress	addr;
	uint16		slot;
	BlockNumber blkno;
	Buffer		buf;
	Page		page;

	/* Get the location of the FSM byte representing the heap block */
	addr = fsm_get_location(heapBlk, &slot);
	blkno = fsm_logical_to_physical(addr);

	/* If the page doesn't exist already, extend */
	buf = XLogReadBufferExtended(rnode, FSM_FORKNUM, blkno, RBM_ZERO_ON_ERROR);
	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);

	page = BufferGetPage(buf);
	if (PageIsNew(page))
		PageInit(page, BLCKSZ, 0);

	/*
	 * Changes to FSM are usually marked as changed using MarkBufferDirtyHint;
	 * however, during recovery, it does nothing if checksums are enabled. It
	 * is assumed that the page should not be dirtied during recovery while
	 * modifying hints to prevent torn pages, since no new WAL data can be
	 * generated at this point to store FPI. This is not relevant to the FSM
	 * case, as its blocks are zeroed when a checksum mismatch occurs. So, we
	 * need to use regular MarkBufferDirty here to mark the FSM block as
	 * modified during recovery, otherwise changes to the FSM may be lost.
	 */
	if (fsm_set_avail(page, slot, new_cat))
		MarkBufferDirty(buf);
	UnlockReleaseBuffer(buf);
}

/*
 * GetRecordedFreeSpace - return the amount of free space on a particular page,
 *		according to the FSM.
 */
Size
GetRecordedFreeSpace(Relation rel, BlockNumber heapBlk)
{
	FSMAddress	addr;
	uint16		slot;
	Buffer		buf;
	uint8		cat;

	/* Get the location of the FSM byte representing the heap block */
	addr = fsm_get_location(heapBlk, &slot);

	buf = fsm_readbuf(rel, addr, false);
	if (!BufferIsValid(buf))
		return 0;
	cat = fsm_get_avail(BufferGetPage(buf), slot);
	ReleaseBuffer(buf);

	return fsm_space_cat_to_avail(cat);
}

/*
 * FreeSpaceMapPrepareTruncateRel - prepare for truncation of a relation.
 *
 * nblocks is the new size of the heap.
 *
 * Return the number of blocks of new FSM.
 * If it's InvalidBlockNumber, there is nothing to truncate;
 * otherwise the caller is responsible for calling smgrtruncate()
 * to truncate the FSM pages, and FreeSpaceMapVacuumRange()
 * to update upper-level pages in the FSM.
 */
BlockNumber
FreeSpaceMapPrepareTruncateRel(Relation rel, BlockNumber nblocks)
{
	BlockNumber new_nfsmblocks;
	FSMAddress	first_removed_address;
	uint16		first_removed_slot;
	Buffer		buf;

	/*
	 * If no FSM has been created yet for this relation, there's nothing to
	 * truncate.
	 */
	if (!smgrexists(RelationGetSmgr(rel), FSM_FORKNUM))
		return InvalidBlockNumber;

	/* Get the location in the FSM of the first removed heap block */
	first_removed_address = fsm_get_location(nblocks, &first_removed_slot);

	/*
	 * Zero out the tail of the last remaining FSM page. If the slot
	 * representing the first removed heap block is at a page boundary, as the
	 * first slot on the FSM page that first_removed_address points to, we can
	 * just truncate that page altogether.
	 */
	if (first_removed_slot > 0)
	{
		buf = fsm_readbuf(rel, first_removed_address, false);
		if (!BufferIsValid(buf))
			return InvalidBlockNumber;	/* nothing to do; the FSM was already
										 * smaller */
		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);

		/* NO EREPORT(ERROR) from here till changes are logged */
		START_CRIT_SECTION();

		fsm_truncate_avail(BufferGetPage(buf), first_removed_slot);

		/*
		 * This change is non-critical, because fsm_does_block_exist() would
		 * stop us from returning a truncated-away block.  However, since this
		 * may remove up to SlotsPerFSMPage slots, it's nice to avoid the cost
		 * of that many fsm_does_block_exist() rejections.  Use a full
		 * MarkBufferDirty(), not MarkBufferDirtyHint().
		 */
		MarkBufferDirty(buf);

		/*
		 * WAL-log like MarkBufferDirtyHint() might have done, just to avoid
		 * differing from the rest of the file in this respect.  This is
		 * optional; see README mention of full page images.  XXX consider
		 * XLogSaveBufferForHint() for even closer similarity.
		 *
		 * A higher-level operation calls us at WAL replay.  If we crash
		 * before the XLOG_SMGR_TRUNCATE flushes to disk, main fork length has
		 * not changed, and our fork remains valid.  If we crash after that
		 * flush, redo will return here.
		 */
		if (!InRecovery && RelationNeedsWAL(rel) && XLogHintBitIsNeeded())
			log_newpage_buffer(buf, false);

		END_CRIT_SECTION();

		UnlockReleaseBuffer(buf);

		new_nfsmblocks = fsm_logical_to_physical(first_removed_address) + 1;
	}
	else
	{
		new_nfsmblocks = fsm_logical_to_physical(first_removed_address);
		if (smgrnblocks(RelationGetSmgr(rel), FSM_FORKNUM) <= new_nfsmblocks)
			return InvalidBlockNumber;	/* nothing to do; the FSM was already
										 * smaller */
	}

	return new_nfsmblocks;
}

/*
 * FreeSpaceMapVacuum - update upper-level pages in the rel's FSM
 *
 * We assume that the bottom-level pages have already been updated with
 * new free-space information.
 */
void
FreeSpaceMapVacuum(Relation rel)
{
	bool		dummy;

	/* Recursively scan the tree, starting at the root */
	(void) fsm_vacuum_page(rel, FSM_ROOT_ADDRESS,
						   (BlockNumber) 0, InvalidBlockNumber,
						   &dummy);
}

/*
 * FreeSpaceMapVacuumRange - update upper-level pages in the rel's FSM
 *
 * As above, but assume that only heap pages between start and end-1 inclusive
 * have new free-space information, so update only the upper-level slots
 * covering that block range.  end == InvalidBlockNumber is equivalent to
 * "all the rest of the relation".
 */
void
FreeSpaceMapVacuumRange(Relation rel, BlockNumber start, BlockNumber end)
{
	bool		dummy;

	/* Recursively scan the tree, starting at the root */
	if (end > start)
		(void) fsm_vacuum_page(rel, FSM_ROOT_ADDRESS, start, end, &dummy);
}

/******** Internal routines ********/

/*
 * Return category corresponding x bytes of free space
 */
static uint8
fsm_space_avail_to_cat(Size avail)
{
	int			cat;

	Assert(avail < BLCKSZ);

	if (avail >= MaxFSMRequestSize)
		return 255;

	cat = avail / FSM_CAT_STEP;

	/*
	 * The highest category, 255, is reserved for MaxFSMRequestSize bytes or
	 * more.
	 */
	if (cat > 254)
		cat = 254;

	return (uint8) cat;
}

/*
 * Return the lower bound of the range of free space represented by given
 * category.
 */
static Size
fsm_space_cat_to_avail(uint8 cat)
{
	/* The highest category represents exactly MaxFSMRequestSize bytes. */
	if (cat == 255)
		return MaxFSMRequestSize;
	else
		return cat * FSM_CAT_STEP;
}

/*
 * Which category does a page need to have, to accommodate x bytes of data?
 * While fsm_space_avail_to_cat() rounds down, this needs to round up.
 */
static uint8
fsm_space_needed_to_cat(Size needed)
{
	int			cat;

	/* Can't ask for more space than the highest category represents */
	if (needed > MaxFSMRequestSize)
		elog(ERROR, "invalid FSM request size %zu", needed);

	if (needed == 0)
		return 1;

	cat = (needed + FSM_CAT_STEP - 1) / FSM_CAT_STEP;

	if (cat > 255)
		cat = 255;

	return (uint8) cat;
}

/*
 * Returns the physical block number of a FSM page
 */
static BlockNumber
fsm_logical_to_physical(FSMAddress addr)
{
	BlockNumber pages;
	int			leafno;
	int			l;

	/*
	 * Calculate the logical page number of the first leaf page below the
	 * given page.
	 */
	leafno = addr.logpageno;
	for (l = 0; l < addr.level; l++)
		leafno *= SlotsPerFSMPage;

	/* Count upper level nodes required to address the leaf page */
	pages = 0;
	for (l = 0; l < FSM_TREE_DEPTH; l++)
	{
		pages += leafno + 1;
		leafno /= SlotsPerFSMPage;
	}

	/*
	 * If the page we were asked for wasn't at the bottom level, subtract the
	 * additional lower level pages we counted above.
	 */
	pages -= addr.level;

	/* Turn the page count into 0-based block number */
	return pages - 1;
}

/*
 * Return the FSM location corresponding to given heap block.
 */
static FSMAddress
fsm_get_location(BlockNumber heapblk, uint16 *slot)
{
	FSMAddress	addr;

	addr.level = FSM_BOTTOM_LEVEL;
	addr.logpageno = heapblk / SlotsPerFSMPage;
	*slot = heapblk % SlotsPerFSMPage;

	return addr;
}

/*
 * Return the heap block number corresponding to given location in the FSM.
 */
static BlockNumber
fsm_get_heap_blk(FSMAddress addr, uint16 slot)
{
	Assert(addr.level == FSM_BOTTOM_LEVEL);
	return ((unsigned int) addr.logpageno) * SlotsPerFSMPage + slot;
}

/*
 * Given a logical address of a child page, get the logical page number of
 * the parent, and the slot within the parent corresponding to the child.
 */
static FSMAddress
fsm_get_parent(FSMAddress child, uint16 *slot)
{
	FSMAddress	parent;

	Assert(child.level < FSM_ROOT_LEVEL);

	parent.level = child.level + 1;
	parent.logpageno = child.logpageno / SlotsPerFSMPage;
	*slot = child.logpageno % SlotsPerFSMPage;

	return parent;
}

/*
 * Given a logical address of a parent page and a slot number, get the
 * logical address of the corresponding child page.
 */
static FSMAddress
fsm_get_child(FSMAddress parent, uint16 slot)
{
	FSMAddress	child;

	Assert(parent.level > FSM_BOTTOM_LEVEL);

	child.level = parent.level - 1;
	child.logpageno = parent.logpageno * SlotsPerFSMPage + slot;

	return child;
}

/*
 * Read a FSM page.
 *
 * If the page doesn't exist, InvalidBuffer is returned, or if 'extend' is
 * true, the FSM file is extended.
 */
static Buffer
fsm_readbuf(Relation rel, FSMAddress addr, bool extend)
{
	BlockNumber blkno = fsm_logical_to_physical(addr);
	Buffer		buf;
	SMgrRelation reln;

	/*
	 * Caution: re-using this smgr pointer could fail if the relcache entry
	 * gets closed.  It's safe as long as we only do smgr-level operations
	 * between here and the last use of the pointer.
	 */
	reln = RelationGetSmgr(rel);

	/*
	 * If we haven't cached the size of the FSM yet, check it first.  Also
	 * recheck if the requested block seems to be past end, since our cached
	 * value might be stale.  (We send smgr inval messages on truncation, but
	 * not on extension.)
	 */
	if (reln->smgr_cached_nblocks[FSM_FORKNUM] == InvalidBlockNumber ||
		blkno >= reln->smgr_cached_nblocks[FSM_FORKNUM])
	{
		/* Invalidate the cache so smgrnblocks asks the kernel. */
		reln->smgr_cached_nblocks[FSM_FORKNUM] = InvalidBlockNumber;
		if (smgrexists(reln, FSM_FORKNUM))
			smgrnblocks(reln, FSM_FORKNUM);
		else
			reln->smgr_cached_nblocks[FSM_FORKNUM] = 0;
	}

	/* Handle requests beyond EOF */
	if (blkno >= reln->smgr_cached_nblocks[FSM_FORKNUM])
	{
		if (extend)
			fsm_extend(rel, blkno + 1);
		else
			return InvalidBuffer;
	}

	/*
	 * Use ZERO_ON_ERROR mode, and initialize the page if necessary. The FSM
	 * information is not accurate anyway, so it's better to clear corrupt
	 * pages than error out. Since the FSM changes are not WAL-logged, the
	 * so-called torn page problem on crash can lead to pages with corrupt
	 * headers, for example.
	 *
	 * The initialize-the-page part is trickier than it looks, because of the
	 * possibility of multiple backends doing this concurrently, and our
	 * desire to not uselessly take the buffer lock in the normal path where
	 * the page is OK.  We must take the lock to initialize the page, so
	 * recheck page newness after we have the lock, in case someone else
	 * already did it.  Also, because we initially check PageIsNew with no
	 * lock, it's possible to fall through and return the buffer while someone
	 * else is still initializing the page (i.e., we might see pd_upper as set
	 * but other page header fields are still zeroes).  This is harmless for
	 * callers that will take a buffer lock themselves, but some callers
	 * inspect the page without any lock at all.  The latter is OK only so
	 * long as it doesn't depend on the page header having correct contents.
	 * Current usage is safe because PageGetContents() does not require that.
	 */
	buf = ReadBufferExtended(rel, FSM_FORKNUM, blkno, RBM_ZERO_ON_ERROR, NULL);
	if (PageIsNew(BufferGetPage(buf)))
	{
		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
		if (PageIsNew(BufferGetPage(buf)))
			PageInit(BufferGetPage(buf), BLCKSZ, 0);
		LockBuffer(buf, BUFFER_LOCK_UNLOCK);
	}
	return buf;
}

/*
 * Ensure that the FSM fork is at least fsm_nblocks long, extending
 * it if necessary with empty pages. And by empty, I mean pages filled
 * with zeros, meaning there's no free space.
 */
static void
fsm_extend(Relation rel, BlockNumber fsm_nblocks)
{
	BlockNumber fsm_nblocks_now;
	PGAlignedBlock pg;
	SMgrRelation reln;

	PageInit((Page) pg.data, BLCKSZ, 0);

	/*
	 * We use the relation extension lock to lock out other backends trying to
	 * extend the FSM at the same time. It also locks out extension of the
	 * main fork, unnecessarily, but extending the FSM happens seldom enough
	 * that it doesn't seem worthwhile to have a separate lock tag type for
	 * it.
	 *
	 * Note that another backend might have extended or created the relation
	 * by the time we get the lock.
	 */
	LockRelationForExtension(rel, ExclusiveLock);

	/*
	 * Caution: re-using this smgr pointer could fail if the relcache entry
	 * gets closed.  It's safe as long as we only do smgr-level operations
	 * between here and the last use of the pointer.
	 */
	reln = RelationGetSmgr(rel);

	/*
	 * Create the FSM file first if it doesn't exist.  If
	 * smgr_cached_nblocks[FSM_FORKNUM] is positive then it must exist, no
	 * need for an smgrexists call.
	 */
	if ((reln->smgr_cached_nblocks[FSM_FORKNUM] == 0 ||
		 reln->smgr_cached_nblocks[FSM_FORKNUM] == InvalidBlockNumber) &&
		!smgrexists(reln, FSM_FORKNUM))
		smgrcreate(reln, FSM_FORKNUM, false);

	/* Invalidate cache so that smgrnblocks() asks the kernel. */
	reln->smgr_cached_nblocks[FSM_FORKNUM] = InvalidBlockNumber;
	fsm_nblocks_now = smgrnblocks(reln, FSM_FORKNUM);

	/* Extend as needed. */
	while (fsm_nblocks_now < fsm_nblocks)
	{
		PageSetChecksumInplace((Page) pg.data, fsm_nblocks_now);

		smgrextend(reln, FSM_FORKNUM, fsm_nblocks_now,
				   pg.data, false);
		fsm_nblocks_now++;
	}

	UnlockRelationForExtension(rel, ExclusiveLock);
}

/*
 * Set value in given FSM page and slot.
 *
 * If minValue > 0, the updated page is also searched for a page with at
 * least minValue of free space. If one is found, its slot number is
 * returned, -1 otherwise.
 */
static int
fsm_set_and_search(Relation rel, FSMAddress addr, uint16 slot,
				   uint8 newValue, uint8 minValue)
{
	Buffer		buf;
	Page		page;
	int			newslot = -1;

	buf = fsm_readbuf(rel, addr, true);
	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);

	page = BufferGetPage(buf);

	if (fsm_set_avail(page, slot, newValue))
		MarkBufferDirtyHint(buf, false);

	if (minValue != 0)
	{
		/* Search while we still hold the lock */
		newslot = fsm_search_avail(buf, minValue,
								   addr.level == FSM_BOTTOM_LEVEL,
								   true);
	}

	UnlockReleaseBuffer(buf);

	return newslot;
}

/*
 * Search the tree for a heap page with at least min_cat of free space
 */
static BlockNumber
fsm_search(Relation rel, uint8 min_cat)
{
	int			restarts = 0;
	FSMAddress	addr = FSM_ROOT_ADDRESS;

	for (;;)
	{
		int			slot;
		Buffer		buf;
		uint8		max_avail = 0;

		/* Read the FSM page. */
		buf = fsm_readbuf(rel, addr, false);

		/* Search within the page */
		if (BufferIsValid(buf))
		{
			LockBuffer(buf, BUFFER_LOCK_SHARE);
			slot = fsm_search_avail(buf, min_cat,
									(addr.level == FSM_BOTTOM_LEVEL),
									false);
			if (slot == -1)
			{
				max_avail = fsm_get_max_avail(BufferGetPage(buf));
				UnlockReleaseBuffer(buf);
			}
			else
			{
				/* Keep the pin for possible update below */
				LockBuffer(buf, BUFFER_LOCK_UNLOCK);
			}
		}
		else
			slot = -1;

		if (slot != -1)
		{
			/*
			 * Descend the tree, or return the found block if we're at the
			 * bottom.
			 */
			if (addr.level == FSM_BOTTOM_LEVEL)
			{
				BlockNumber blkno = fsm_get_heap_blk(addr, slot);
				Page		page;

				if (fsm_does_block_exist(rel, blkno))
				{
					ReleaseBuffer(buf);
					return blkno;
				}

				/*
				 * Block is past the end of the relation.  Update FSM, and
				 * restart from root.  The usual "advancenext" behavior is
				 * pessimal for this rare scenario, since every later slot is
				 * unusable in the same way.  We could zero all affected slots
				 * on the same FSM page, but don't bet on the benefits of that
				 * optimization justifying its compiled code bulk.
				 */
				page = BufferGetPage(buf);
				LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
				fsm_set_avail(page, slot, 0);
				MarkBufferDirtyHint(buf, false);
				UnlockReleaseBuffer(buf);
				if (restarts++ > 10000) /* same rationale as below */
					return InvalidBlockNumber;
				addr = FSM_ROOT_ADDRESS;
			}
			else
			{
				ReleaseBuffer(buf);
			}
			addr = fsm_get_child(addr, slot);
		}
		else if (addr.level == FSM_ROOT_LEVEL)
		{
			/*
			 * At the root, failure means there's no page with enough free
			 * space in the FSM. Give up.
			 */
			return InvalidBlockNumber;
		}
		else
		{
			uint16		parentslot;
			FSMAddress	parent;

			/*
			 * At lower level, failure can happen if the value in the upper-
			 * level node didn't reflect the value on the lower page. Update
			 * the upper node, to avoid falling into the same trap again, and
			 * start over.
			 *
			 * There's a race condition here, if another backend updates this
			 * page right after we release it, and gets the lock on the parent
			 * page before us. We'll then update the parent page with the now
			 * stale information we had. It's OK, because it should happen
			 * rarely, and will be fixed by the next vacuum.
			 */
			parent = fsm_get_parent(addr, &parentslot);
			fsm_set_and_search(rel, parent, parentslot, max_avail, 0);

			/*
			 * If the upper pages are badly out of date, we might need to loop
			 * quite a few times, updating them as we go. Any inconsistencies
			 * should eventually be corrected and the loop should end. Looping
			 * indefinitely is nevertheless scary, so provide an emergency
			 * valve.
			 */
			if (restarts++ > 10000)
				return InvalidBlockNumber;

			/* Start search all over from the root */
			addr = FSM_ROOT_ADDRESS;
		}
	}
}


/*
 * Recursive guts of FreeSpaceMapVacuum
 *
 * Examine the FSM page indicated by addr, as well as its children, updating
 * upper-level nodes that cover the heap block range from start to end-1.
 * (It's okay if end is beyond the actual end of the map.)
 * Return the maximum freespace value on this page.
 *
 * If addr is past the end of the FSM, set *eof_p to true and return 0.
 *
 * This traverses the tree in depth-first order.  The tree is stored
 * physically in depth-first order, so this should be pretty I/O efficient.
 */
static uint8
fsm_vacuum_page(Relation rel, FSMAddress addr,
				BlockNumber start, BlockNumber end,
				bool *eof_p)
{
	Buffer		buf;
	Page		page;
	uint8		max_avail;

	/* Read the page if it exists, or return EOF */
	buf = fsm_readbuf(rel, addr, false);
	if (!BufferIsValid(buf))
	{
		*eof_p = true;
		return 0;
	}
	else
		*eof_p = false;

	page = BufferGetPage(buf);

	/*
	 * If we're above the bottom level, recurse into children, and fix the
	 * information stored about them at this level.
	 */
	if (addr.level > FSM_BOTTOM_LEVEL)
	{
		FSMAddress	fsm_start,
					fsm_end;
		uint16		fsm_start_slot,
					fsm_end_slot;
		int			slot,
					start_slot,
					end_slot;
		bool		eof = false;

		/*
		 * Compute the range of slots we need to update on this page, given
		 * the requested range of heap blocks to consider.  The first slot to
		 * update is the one covering the "start" block, and the last slot is
		 * the one covering "end - 1".  (Some of this work will be duplicated
		 * in each recursive call, but it's cheap enough to not worry about.)
		 */
		fsm_start = fsm_get_location(start, &fsm_start_slot);
		fsm_end = fsm_get_location(end - 1, &fsm_end_slot);

		while (fsm_start.level < addr.level)
		{
			fsm_start = fsm_get_parent(fsm_start, &fsm_start_slot);
			fsm_end = fsm_get_parent(fsm_end, &fsm_end_slot);
		}
		Assert(fsm_start.level == addr.level);

		if (fsm_start.logpageno == addr.logpageno)
			start_slot = fsm_start_slot;
		else if (fsm_start.logpageno > addr.logpageno)
			start_slot = SlotsPerFSMPage;	/* shouldn't get here... */
		else
			start_slot = 0;

		if (fsm_end.logpageno == addr.logpageno)
			end_slot = fsm_end_slot;
		else if (fsm_end.logpageno > addr.logpageno)
			end_slot = SlotsPerFSMPage - 1;
		else
			end_slot = -1;		/* shouldn't get here... */

		for (slot = start_slot; slot <= end_slot; slot++)
		{
			int			child_avail;

			CHECK_FOR_INTERRUPTS();

			/* After we hit end-of-file, just clear the rest of the slots */
			if (!eof)
				child_avail = fsm_vacuum_page(rel, fsm_get_child(addr, slot),
											  start, end,
											  &eof);
			else
				child_avail = 0;

			/* Update information about the child */
			if (fsm_get_avail(page, slot) != child_avail)
			{
				LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
				fsm_set_avail(page, slot, child_avail);
				MarkBufferDirtyHint(buf, false);
				LockBuffer(buf, BUFFER_LOCK_UNLOCK);
			}
		}
	}

	/* Now get the maximum value on the page, to return to caller */
	max_avail = fsm_get_max_avail(page);

	/*
	 * Reset the next slot pointer. This encourages the use of low-numbered
	 * pages, increasing the chances that a later vacuum can truncate the
	 * relation.  We don't bother with a lock here, nor with marking the page
	 * dirty if it wasn't already, since this is just a hint.
	 */
	((FSMPage) PageGetContents(page))->fp_next_slot = 0;

	ReleaseBuffer(buf);

	return max_avail;
}


/*
 * Check whether a block number is past the end of the relation.  This can
 * happen after WAL replay, if the FSM reached disk but newly-extended pages
 * it refers to did not.
 */
static bool
fsm_does_block_exist(Relation rel, BlockNumber blknumber)
{
	SMgrRelation smgr = RelationGetSmgr(rel);

	/*
	 * If below the cached nblocks, the block surely exists.  Otherwise, we
	 * face a trade-off.  We opt to compare to a fresh nblocks, incurring
	 * lseek() overhead.  The alternative would be to assume the block does
	 * not exist, but that would cause FSM to set zero space available for
	 * blocks that main fork extension just recorded.
	 */
	return ((BlockNumberIsValid(smgr->smgr_cached_nblocks[MAIN_FORKNUM]) &&
			 blknumber < smgr->smgr_cached_nblocks[MAIN_FORKNUM]) ||
			blknumber < RelationGetNumberOfBlocks(rel));
}
