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Diffstat (limited to 'src/backend/access/nbtree/nbtsplitloc.c')
| -rw-r--r-- | src/backend/access/nbtree/nbtsplitloc.c | 1189 |
1 files changed, 1189 insertions, 0 deletions
diff --git a/src/backend/access/nbtree/nbtsplitloc.c b/src/backend/access/nbtree/nbtsplitloc.c new file mode 100644 index 0000000..241e26d --- /dev/null +++ b/src/backend/access/nbtree/nbtsplitloc.c @@ -0,0 +1,1189 @@ +/*------------------------------------------------------------------------- + * + * nbtsplitloc.c + * Choose split point code for Postgres btree implementation. + * + * Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group + * Portions Copyright (c) 1994, Regents of the University of California + * + * + * IDENTIFICATION + * src/backend/access/nbtree/nbtsplitloc.c + * + *------------------------------------------------------------------------- + */ +#include "postgres.h" + +#include "access/nbtree.h" +#include "storage/lmgr.h" + +typedef enum +{ + /* strategy for searching through materialized list of split points */ + SPLIT_DEFAULT, /* give some weight to truncation */ + SPLIT_MANY_DUPLICATES, /* find minimally distinguishing point */ + SPLIT_SINGLE_VALUE /* leave left page almost full */ +} FindSplitStrat; + +typedef struct +{ + /* details of free space left by split */ + int16 curdelta; /* current leftfree/rightfree delta */ + int16 leftfree; /* space left on left page post-split */ + int16 rightfree; /* space left on right page post-split */ + + /* split point identifying fields (returned by _bt_findsplitloc) */ + OffsetNumber firstrightoff; /* first origpage item on rightpage */ + bool newitemonleft; /* new item goes on left, or right? */ +} SplitPoint; + +typedef struct +{ + /* context data for _bt_recsplitloc */ + Relation rel; /* index relation */ + Page origpage; /* page undergoing split */ + IndexTuple newitem; /* new item (cause of page split) */ + Size newitemsz; /* size of newitem (includes line pointer) */ + bool is_leaf; /* T if splitting a leaf page */ + bool is_rightmost; /* T if splitting rightmost page on level */ + OffsetNumber newitemoff; /* where the new item is to be inserted */ + int leftspace; /* space available for items on left page */ + int rightspace; /* space available for items on right page */ + int olddataitemstotal; /* space taken by old items */ + Size minfirstrightsz; /* smallest firstright size */ + + /* candidate split point data */ + int maxsplits; /* maximum number of splits */ + int nsplits; /* current number of splits */ + SplitPoint *splits; /* all candidate split points for page */ + int interval; /* current range of acceptable split points */ +} FindSplitData; + +static void _bt_recsplitloc(FindSplitData *state, + OffsetNumber firstrightoff, bool newitemonleft, + int olddataitemstoleft, + Size firstrightofforigpagetuplesz); +static void _bt_deltasortsplits(FindSplitData *state, double fillfactormult, + bool usemult); +static int _bt_splitcmp(const void *arg1, const void *arg2); +static bool _bt_afternewitemoff(FindSplitData *state, OffsetNumber maxoff, + int leaffillfactor, bool *usemult); +static bool _bt_adjacenthtid(ItemPointer lowhtid, ItemPointer highhtid); +static OffsetNumber _bt_bestsplitloc(FindSplitData *state, int perfectpenalty, + bool *newitemonleft, FindSplitStrat strategy); +static int _bt_defaultinterval(FindSplitData *state); +static int _bt_strategy(FindSplitData *state, SplitPoint *leftpage, + SplitPoint *rightpage, FindSplitStrat *strategy); +static void _bt_interval_edges(FindSplitData *state, + SplitPoint **leftinterval, SplitPoint **rightinterval); +static inline int _bt_split_penalty(FindSplitData *state, SplitPoint *split); +static inline IndexTuple _bt_split_lastleft(FindSplitData *state, + SplitPoint *split); +static inline IndexTuple _bt_split_firstright(FindSplitData *state, + SplitPoint *split); + + +/* + * _bt_findsplitloc() -- find an appropriate place to split a page. + * + * The main goal here is to equalize the free space that will be on each + * split page, *after accounting for the inserted tuple*. (If we fail to + * account for it, we might find ourselves with too little room on the page + * that it needs to go into!) + * + * If the page is the rightmost page on its level, we instead try to arrange + * to leave the left split page fillfactor% full. In this way, when we are + * inserting successively increasing keys (consider sequences, timestamps, + * etc) we will end up with a tree whose pages are about fillfactor% full, + * instead of the 50% full result that we'd get without this special case. + * This is the same as nbtsort.c produces for a newly-created tree. Note + * that leaf and nonleaf pages use different fillfactors. Note also that + * there are a number of further special cases where fillfactor is not + * applied in the standard way. + * + * We are passed the intended insert position of the new tuple, expressed as + * the offsetnumber of the tuple it must go in front of (this could be + * maxoff+1 if the tuple is to go at the end). The new tuple itself is also + * passed, since it's needed to give some weight to how effective suffix + * truncation will be. The implementation picks the split point that + * maximizes the effectiveness of suffix truncation from a small list of + * alternative candidate split points that leave each side of the split with + * about the same share of free space. Suffix truncation is secondary to + * equalizing free space, except in cases with large numbers of duplicates. + * Note that it is always assumed that caller goes on to perform truncation, + * even with pg_upgrade'd indexes where that isn't actually the case + * (!heapkeyspace indexes). See nbtree/README for more information about + * suffix truncation. + * + * We return the index of the first existing tuple that should go on the + * righthand page (which is called firstrightoff), plus a boolean + * indicating whether the new tuple goes on the left or right page. You + * can think of the returned state as a point _between_ two adjacent data + * items (laftleft and firstright data items) on an imaginary version of + * origpage that already includes newitem. The bool is necessary to + * disambiguate the case where firstrightoff == newitemoff (i.e. it is + * sometimes needed to determine if the firstright tuple for the split is + * newitem rather than the tuple from origpage at offset firstrightoff). + */ +OffsetNumber +_bt_findsplitloc(Relation rel, + Page origpage, + OffsetNumber newitemoff, + Size newitemsz, + IndexTuple newitem, + bool *newitemonleft) +{ + BTPageOpaque opaque; + int leftspace, + rightspace, + olddataitemstotal, + olddataitemstoleft, + perfectpenalty, + leaffillfactor; + FindSplitData state; + FindSplitStrat strategy; + ItemId itemid; + OffsetNumber offnum, + maxoff, + firstrightoff; + double fillfactormult; + bool usemult; + SplitPoint leftpage, + rightpage; + + opaque = BTPageGetOpaque(origpage); + maxoff = PageGetMaxOffsetNumber(origpage); + + /* Total free space available on a btree page, after fixed overhead */ + leftspace = rightspace = + PageGetPageSize(origpage) - SizeOfPageHeaderData - + MAXALIGN(sizeof(BTPageOpaqueData)); + + /* The right page will have the same high key as the old page */ + if (!P_RIGHTMOST(opaque)) + { + itemid = PageGetItemId(origpage, P_HIKEY); + rightspace -= (int) (MAXALIGN(ItemIdGetLength(itemid)) + + sizeof(ItemIdData)); + } + + /* Count up total space in data items before actually scanning 'em */ + olddataitemstotal = rightspace - (int) PageGetExactFreeSpace(origpage); + leaffillfactor = BTGetFillFactor(rel); + + /* Passed-in newitemsz is MAXALIGNED but does not include line pointer */ + newitemsz += sizeof(ItemIdData); + state.rel = rel; + state.origpage = origpage; + state.newitem = newitem; + state.newitemsz = newitemsz; + state.is_leaf = P_ISLEAF(opaque); + state.is_rightmost = P_RIGHTMOST(opaque); + state.leftspace = leftspace; + state.rightspace = rightspace; + state.olddataitemstotal = olddataitemstotal; + state.minfirstrightsz = SIZE_MAX; + state.newitemoff = newitemoff; + + /* newitem cannot be a posting list item */ + Assert(!BTreeTupleIsPosting(newitem)); + + /* + * nsplits should never exceed maxoff because there will be at most as + * many candidate split points as there are points _between_ tuples, once + * you imagine that the new item is already on the original page (the + * final number of splits may be slightly lower because not all points + * between tuples will be legal). + */ + state.maxsplits = maxoff; + state.splits = palloc(sizeof(SplitPoint) * state.maxsplits); + state.nsplits = 0; + + /* + * Scan through the data items and calculate space usage for a split at + * each possible position + */ + olddataitemstoleft = 0; + + for (offnum = P_FIRSTDATAKEY(opaque); + offnum <= maxoff; + offnum = OffsetNumberNext(offnum)) + { + Size itemsz; + + itemid = PageGetItemId(origpage, offnum); + itemsz = MAXALIGN(ItemIdGetLength(itemid)) + sizeof(ItemIdData); + + /* + * When item offset number is not newitemoff, neither side of the + * split can be newitem. Record a split after the previous data item + * from original page, but before the current data item from original + * page. (_bt_recsplitloc() will reject the split when there are no + * previous items, which we rely on.) + */ + if (offnum < newitemoff) + _bt_recsplitloc(&state, offnum, false, olddataitemstoleft, itemsz); + else if (offnum > newitemoff) + _bt_recsplitloc(&state, offnum, true, olddataitemstoleft, itemsz); + else + { + /* + * Record a split after all "offnum < newitemoff" original page + * data items, but before newitem + */ + _bt_recsplitloc(&state, offnum, false, olddataitemstoleft, itemsz); + + /* + * Record a split after newitem, but before data item from + * original page at offset newitemoff/current offset + */ + _bt_recsplitloc(&state, offnum, true, olddataitemstoleft, itemsz); + } + + olddataitemstoleft += itemsz; + } + + /* + * Record a split after all original page data items, but before newitem. + * (Though only when it's possible that newitem will end up alone on new + * right page.) + */ + Assert(olddataitemstoleft == olddataitemstotal); + if (newitemoff > maxoff) + _bt_recsplitloc(&state, newitemoff, false, olddataitemstotal, 0); + + /* + * I believe it is not possible to fail to find a feasible split, but just + * in case ... + */ + if (state.nsplits == 0) + elog(ERROR, "could not find a feasible split point for index \"%s\"", + RelationGetRelationName(rel)); + + /* + * Start search for a split point among list of legal split points. Give + * primary consideration to equalizing available free space in each half + * of the split initially (start with default strategy), while applying + * rightmost and split-after-new-item optimizations where appropriate. + * Either of the two other fallback strategies may be required for cases + * with a large number of duplicates around the original/space-optimal + * split point. + * + * Default strategy gives some weight to suffix truncation in deciding a + * split point on leaf pages. It attempts to select a split point where a + * distinguishing attribute appears earlier in the new high key for the + * left side of the split, in order to maximize the number of trailing + * attributes that can be truncated away. Only candidate split points + * that imply an acceptable balance of free space on each side are + * considered. See _bt_defaultinterval(). + */ + if (!state.is_leaf) + { + /* fillfactormult only used on rightmost page */ + usemult = state.is_rightmost; + fillfactormult = BTREE_NONLEAF_FILLFACTOR / 100.0; + } + else if (state.is_rightmost) + { + /* Rightmost leaf page -- fillfactormult always used */ + usemult = true; + fillfactormult = leaffillfactor / 100.0; + } + else if (_bt_afternewitemoff(&state, maxoff, leaffillfactor, &usemult)) + { + /* + * New item inserted at rightmost point among a localized grouping on + * a leaf page -- apply "split after new item" optimization, either by + * applying leaf fillfactor multiplier, or by choosing the exact split + * point that leaves newitem as lastleft. (usemult is set for us.) + */ + if (usemult) + { + /* fillfactormult should be set based on leaf fillfactor */ + fillfactormult = leaffillfactor / 100.0; + } + else + { + /* find precise split point after newitemoff */ + for (int i = 0; i < state.nsplits; i++) + { + SplitPoint *split = state.splits + i; + + if (split->newitemonleft && + newitemoff == split->firstrightoff) + { + pfree(state.splits); + *newitemonleft = true; + return newitemoff; + } + } + + /* + * Cannot legally split after newitemoff; proceed with split + * without using fillfactor multiplier. This is defensive, and + * should never be needed in practice. + */ + fillfactormult = 0.50; + } + } + else + { + /* Other leaf page. 50:50 page split. */ + usemult = false; + /* fillfactormult not used, but be tidy */ + fillfactormult = 0.50; + } + + /* + * Save leftmost and rightmost splits for page before original ordinal + * sort order is lost by delta/fillfactormult sort + */ + leftpage = state.splits[0]; + rightpage = state.splits[state.nsplits - 1]; + + /* Give split points a fillfactormult-wise delta, and sort on deltas */ + _bt_deltasortsplits(&state, fillfactormult, usemult); + + /* Determine split interval for default strategy */ + state.interval = _bt_defaultinterval(&state); + + /* + * Determine if default strategy/split interval will produce a + * sufficiently distinguishing split, or if we should change strategies. + * Alternative strategies change the range of split points that are + * considered acceptable (split interval), and possibly change + * fillfactormult, in order to deal with pages with a large number of + * duplicates gracefully. + * + * Pass low and high splits for the entire page (actually, they're for an + * imaginary version of the page that includes newitem). These are used + * when the initial split interval encloses split points that are full of + * duplicates, and we need to consider if it's even possible to avoid + * appending a heap TID. + */ + perfectpenalty = _bt_strategy(&state, &leftpage, &rightpage, &strategy); + + if (strategy == SPLIT_DEFAULT) + { + /* + * Default strategy worked out (always works out with internal page). + * Original split interval still stands. + */ + } + + /* + * Many duplicates strategy is used when a heap TID would otherwise be + * appended, but the page isn't completely full of logical duplicates. + * + * The split interval is widened to include all legal candidate split + * points. There might be a few as two distinct values in the whole-page + * split interval, though it's also possible that most of the values on + * the page are unique. The final split point will either be to the + * immediate left or to the immediate right of the group of duplicate + * tuples that enclose the first/delta-optimal split point (perfect + * penalty was set so that the lowest delta split point that avoids + * appending a heap TID will be chosen). Maximizing the number of + * attributes that can be truncated away is not a goal of the many + * duplicates strategy. + * + * Single value strategy is used when it is impossible to avoid appending + * a heap TID. It arranges to leave the left page very full. This + * maximizes space utilization in cases where tuples with the same + * attribute values span many pages. Newly inserted duplicates will tend + * to have higher heap TID values, so we'll end up splitting to the right + * consistently. (Single value strategy is harmless though not + * particularly useful with !heapkeyspace indexes.) + */ + else if (strategy == SPLIT_MANY_DUPLICATES) + { + Assert(state.is_leaf); + /* Shouldn't try to truncate away extra user attributes */ + Assert(perfectpenalty == + IndexRelationGetNumberOfKeyAttributes(state.rel)); + /* No need to resort splits -- no change in fillfactormult/deltas */ + state.interval = state.nsplits; + } + else if (strategy == SPLIT_SINGLE_VALUE) + { + Assert(state.is_leaf); + /* Split near the end of the page */ + usemult = true; + fillfactormult = BTREE_SINGLEVAL_FILLFACTOR / 100.0; + /* Resort split points with new delta */ + _bt_deltasortsplits(&state, fillfactormult, usemult); + /* Appending a heap TID is unavoidable, so interval of 1 is fine */ + state.interval = 1; + } + + /* + * Search among acceptable split points (using final split interval) for + * the entry that has the lowest penalty, and is therefore expected to + * maximize fan-out. Sets *newitemonleft for us. + */ + firstrightoff = _bt_bestsplitloc(&state, perfectpenalty, newitemonleft, + strategy); + pfree(state.splits); + + return firstrightoff; +} + +/* + * Subroutine to record a particular point between two tuples (possibly the + * new item) on page (ie, combination of firstrightoff and newitemonleft + * settings) in *state for later analysis. This is also a convenient point to + * check if the split is legal (if it isn't, it won't be recorded). + * + * firstrightoff is the offset of the first item on the original page that + * goes to the right page, and firstrightofforigpagetuplesz is the size of + * that tuple. firstrightoff can be > max offset, which means that all the + * old items go to the left page and only the new item goes to the right page. + * We don't actually use firstrightofforigpagetuplesz in that case (actually, + * we don't use it for _any_ split where the firstright tuple happens to be + * newitem). + * + * olddataitemstoleft is the total size of all old items to the left of the + * split point that is recorded here when legal. Should not include + * newitemsz, since that is handled here. + */ +static void +_bt_recsplitloc(FindSplitData *state, + OffsetNumber firstrightoff, + bool newitemonleft, + int olddataitemstoleft, + Size firstrightofforigpagetuplesz) +{ + int16 leftfree, + rightfree; + Size firstrightsz; + Size postingsz = 0; + bool newitemisfirstright; + + /* Is the new item going to be split point's firstright tuple? */ + newitemisfirstright = (firstrightoff == state->newitemoff && + !newitemonleft); + + if (newitemisfirstright) + firstrightsz = state->newitemsz; + else + { + firstrightsz = firstrightofforigpagetuplesz; + + /* + * Calculate suffix truncation space saving when firstright tuple is a + * posting list tuple, though only when the tuple is over 64 bytes + * including line pointer overhead (arbitrary). This avoids accessing + * the tuple in cases where its posting list must be very small (if + * tuple has one at all). + * + * Note: We don't do this in the case where firstright tuple is + * newitem, since newitem cannot have a posting list. + */ + if (state->is_leaf && firstrightsz > 64) + { + ItemId itemid; + IndexTuple newhighkey; + + itemid = PageGetItemId(state->origpage, firstrightoff); + newhighkey = (IndexTuple) PageGetItem(state->origpage, itemid); + + if (BTreeTupleIsPosting(newhighkey)) + postingsz = IndexTupleSize(newhighkey) - + BTreeTupleGetPostingOffset(newhighkey); + } + } + + /* Account for all the old tuples */ + leftfree = state->leftspace - olddataitemstoleft; + rightfree = state->rightspace - + (state->olddataitemstotal - olddataitemstoleft); + + /* + * The first item on the right page becomes the high key of the left page; + * therefore it counts against left space as well as right space (we + * cannot assume that suffix truncation will make it any smaller). When + * index has included attributes, then those attributes of left page high + * key will be truncated leaving that page with slightly more free space. + * However, that shouldn't affect our ability to find valid split + * location, since we err in the direction of being pessimistic about free + * space on the left half. Besides, even when suffix truncation of + * non-TID attributes occurs, the new high key often won't even be a + * single MAXALIGN() quantum smaller than the firstright tuple it's based + * on. + * + * If we are on the leaf level, assume that suffix truncation cannot avoid + * adding a heap TID to the left half's new high key when splitting at the + * leaf level. In practice the new high key will often be smaller and + * will rarely be larger, but conservatively assume the worst case. We do + * go to the trouble of subtracting away posting list overhead, though + * only when it looks like it will make an appreciable difference. + * (Posting lists are the only case where truncation will typically make + * the final high key far smaller than firstright, so being a bit more + * precise there noticeably improves the balance of free space.) + */ + if (state->is_leaf) + leftfree -= (int16) (firstrightsz + + MAXALIGN(sizeof(ItemPointerData)) - + postingsz); + else + leftfree -= (int16) firstrightsz; + + /* account for the new item */ + if (newitemonleft) + leftfree -= (int16) state->newitemsz; + else + rightfree -= (int16) state->newitemsz; + + /* + * If we are not on the leaf level, we will be able to discard the key + * data from the first item that winds up on the right page. + */ + if (!state->is_leaf) + rightfree += (int16) firstrightsz - + (int16) (MAXALIGN(sizeof(IndexTupleData)) + sizeof(ItemIdData)); + + /* Record split if legal */ + if (leftfree >= 0 && rightfree >= 0) + { + Assert(state->nsplits < state->maxsplits); + + /* Determine smallest firstright tuple size among legal splits */ + state->minfirstrightsz = Min(state->minfirstrightsz, firstrightsz); + + state->splits[state->nsplits].curdelta = 0; + state->splits[state->nsplits].leftfree = leftfree; + state->splits[state->nsplits].rightfree = rightfree; + state->splits[state->nsplits].firstrightoff = firstrightoff; + state->splits[state->nsplits].newitemonleft = newitemonleft; + state->nsplits++; + } +} + +/* + * Subroutine to assign space deltas to materialized array of candidate split + * points based on current fillfactor, and to sort array using that fillfactor + */ +static void +_bt_deltasortsplits(FindSplitData *state, double fillfactormult, + bool usemult) +{ + for (int i = 0; i < state->nsplits; i++) + { + SplitPoint *split = state->splits + i; + int16 delta; + + if (usemult) + delta = fillfactormult * split->leftfree - + (1.0 - fillfactormult) * split->rightfree; + else + delta = split->leftfree - split->rightfree; + + if (delta < 0) + delta = -delta; + + /* Save delta */ + split->curdelta = delta; + } + + qsort(state->splits, state->nsplits, sizeof(SplitPoint), _bt_splitcmp); +} + +/* + * qsort-style comparator used by _bt_deltasortsplits() + */ +static int +_bt_splitcmp(const void *arg1, const void *arg2) +{ + SplitPoint *split1 = (SplitPoint *) arg1; + SplitPoint *split2 = (SplitPoint *) arg2; + + if (split1->curdelta > split2->curdelta) + return 1; + if (split1->curdelta < split2->curdelta) + return -1; + + return 0; +} + +/* + * Subroutine to determine whether or not a non-rightmost leaf page should be + * split immediately after the would-be original page offset for the + * new/incoming tuple (or should have leaf fillfactor applied when new item is + * to the right on original page). This is appropriate when there is a + * pattern of localized monotonically increasing insertions into a composite + * index, where leading attribute values form local groupings, and we + * anticipate further insertions of the same/current grouping (new item's + * grouping) in the near future. This can be thought of as a variation on + * applying leaf fillfactor during rightmost leaf page splits, since cases + * that benefit will converge on packing leaf pages leaffillfactor% full over + * time. + * + * We may leave extra free space remaining on the rightmost page of a "most + * significant column" grouping of tuples if that grouping never ends up + * having future insertions that use the free space. That effect is + * self-limiting; a future grouping that becomes the "nearest on the right" + * grouping of the affected grouping usually puts the extra free space to good + * use. + * + * Caller uses optimization when routine returns true, though the exact action + * taken by caller varies. Caller uses original leaf page fillfactor in + * standard way rather than using the new item offset directly when *usemult + * was also set to true here. Otherwise, caller applies optimization by + * locating the legal split point that makes the new tuple the lastleft tuple + * for the split. + */ +static bool +_bt_afternewitemoff(FindSplitData *state, OffsetNumber maxoff, + int leaffillfactor, bool *usemult) +{ + int16 nkeyatts; + ItemId itemid; + IndexTuple tup; + int keepnatts; + + Assert(state->is_leaf && !state->is_rightmost); + + nkeyatts = IndexRelationGetNumberOfKeyAttributes(state->rel); + + /* Single key indexes not considered here */ + if (nkeyatts == 1) + return false; + + /* Ascending insertion pattern never inferred when new item is first */ + if (state->newitemoff == P_FIRSTKEY) + return false; + + /* + * Only apply optimization on pages with equisized tuples, since ordinal + * keys are likely to be fixed-width. Testing if the new tuple is + * variable width directly might also work, but that fails to apply the + * optimization to indexes with a numeric_ops attribute. + * + * Conclude that page has equisized tuples when the new item is the same + * width as the smallest item observed during pass over page, and other + * non-pivot tuples must be the same width as well. (Note that the + * possibly-truncated existing high key isn't counted in + * olddataitemstotal, and must be subtracted from maxoff.) + */ + if (state->newitemsz != state->minfirstrightsz) + return false; + if (state->newitemsz * (maxoff - 1) != state->olddataitemstotal) + return false; + + /* + * Avoid applying optimization when tuples are wider than a tuple + * consisting of two non-NULL int8/int64 attributes (or four non-NULL + * int4/int32 attributes) + */ + if (state->newitemsz > + MAXALIGN(sizeof(IndexTupleData) + sizeof(int64) * 2) + + sizeof(ItemIdData)) + return false; + + /* + * At least the first attribute's value must be equal to the corresponding + * value in previous tuple to apply optimization. New item cannot be a + * duplicate, either. + * + * Handle case where new item is to the right of all items on the existing + * page. This is suggestive of monotonically increasing insertions in + * itself, so the "heap TID adjacency" test is not applied here. + */ + if (state->newitemoff > maxoff) + { + itemid = PageGetItemId(state->origpage, maxoff); + tup = (IndexTuple) PageGetItem(state->origpage, itemid); + keepnatts = _bt_keep_natts_fast(state->rel, tup, state->newitem); + + if (keepnatts > 1 && keepnatts <= nkeyatts) + { + *usemult = true; + return true; + } + + return false; + } + + /* + * "Low cardinality leading column, high cardinality suffix column" + * indexes with a random insertion pattern (e.g., an index with a boolean + * column, such as an index on '(book_is_in_print, book_isbn)') present us + * with a risk of consistently misapplying the optimization. We're + * willing to accept very occasional misapplication of the optimization, + * provided the cases where we get it wrong are rare and self-limiting. + * + * Heap TID adjacency strongly suggests that the item just to the left was + * inserted very recently, which limits overapplication of the + * optimization. Besides, all inappropriate cases triggered here will + * still split in the middle of the page on average. + */ + itemid = PageGetItemId(state->origpage, OffsetNumberPrev(state->newitemoff)); + tup = (IndexTuple) PageGetItem(state->origpage, itemid); + /* Do cheaper test first */ + if (BTreeTupleIsPosting(tup) || + !_bt_adjacenthtid(&tup->t_tid, &state->newitem->t_tid)) + return false; + /* Check same conditions as rightmost item case, too */ + keepnatts = _bt_keep_natts_fast(state->rel, tup, state->newitem); + + if (keepnatts > 1 && keepnatts <= nkeyatts) + { + double interp = (double) state->newitemoff / ((double) maxoff + 1); + double leaffillfactormult = (double) leaffillfactor / 100.0; + + /* + * Don't allow caller to split after a new item when it will result in + * a split point to the right of the point that a leaf fillfactor + * split would use -- have caller apply leaf fillfactor instead + */ + *usemult = interp > leaffillfactormult; + + return true; + } + + return false; +} + +/* + * Subroutine for determining if two heap TIDS are "adjacent". + * + * Adjacent means that the high TID is very likely to have been inserted into + * heap relation immediately after the low TID, probably during the current + * transaction. + */ +static bool +_bt_adjacenthtid(ItemPointer lowhtid, ItemPointer highhtid) +{ + BlockNumber lowblk, + highblk; + + lowblk = ItemPointerGetBlockNumber(lowhtid); + highblk = ItemPointerGetBlockNumber(highhtid); + + /* Make optimistic assumption of adjacency when heap blocks match */ + if (lowblk == highblk) + return true; + + /* When heap block one up, second offset should be FirstOffsetNumber */ + if (lowblk + 1 == highblk && + ItemPointerGetOffsetNumber(highhtid) == FirstOffsetNumber) + return true; + + return false; +} + +/* + * Subroutine to find the "best" split point among candidate split points. + * The best split point is the split point with the lowest penalty among split + * points that fall within current/final split interval. Penalty is an + * abstract score, with a definition that varies depending on whether we're + * splitting a leaf page or an internal page. See _bt_split_penalty() for + * details. + * + * "perfectpenalty" is assumed to be the lowest possible penalty among + * candidate split points. This allows us to return early without wasting + * cycles on calculating the first differing attribute for all candidate + * splits when that clearly cannot improve our choice (or when we only want a + * minimally distinguishing split point, and don't want to make the split any + * more unbalanced than is necessary). + * + * We return the index of the first existing tuple that should go on the right + * page, plus a boolean indicating if new item is on left of split point. + */ +static OffsetNumber +_bt_bestsplitloc(FindSplitData *state, int perfectpenalty, + bool *newitemonleft, FindSplitStrat strategy) +{ + int bestpenalty, + lowsplit; + int highsplit = Min(state->interval, state->nsplits); + SplitPoint *final; + + bestpenalty = INT_MAX; + lowsplit = 0; + for (int i = lowsplit; i < highsplit; i++) + { + int penalty; + + penalty = _bt_split_penalty(state, state->splits + i); + + if (penalty < bestpenalty) + { + bestpenalty = penalty; + lowsplit = i; + } + + if (penalty <= perfectpenalty) + break; + } + + final = &state->splits[lowsplit]; + + /* + * There is a risk that the "many duplicates" strategy will repeatedly do + * the wrong thing when there are monotonically decreasing insertions to + * the right of a large group of duplicates. Repeated splits could leave + * a succession of right half pages with free space that can never be + * used. This must be avoided. + * + * Consider the example of the leftmost page in a single integer attribute + * NULLS FIRST index which is almost filled with NULLs. Monotonically + * decreasing integer insertions might cause the same leftmost page to + * split repeatedly at the same point. Each split derives its new high + * key from the lowest current value to the immediate right of the large + * group of NULLs, which will always be higher than all future integer + * insertions, directing all future integer insertions to the same + * leftmost page. + */ + if (strategy == SPLIT_MANY_DUPLICATES && !state->is_rightmost && + !final->newitemonleft && final->firstrightoff >= state->newitemoff && + final->firstrightoff < state->newitemoff + 9) + { + /* + * Avoid the problem by performing a 50:50 split when the new item is + * just to the right of the would-be "many duplicates" split point. + * (Note that the test used for an insert that is "just to the right" + * of the split point is conservative.) + */ + final = &state->splits[0]; + } + + *newitemonleft = final->newitemonleft; + return final->firstrightoff; +} + +#define LEAF_SPLIT_DISTANCE 0.050 +#define INTERNAL_SPLIT_DISTANCE 0.075 + +/* + * Return a split interval to use for the default strategy. This is a limit + * on the number of candidate split points to give further consideration to. + * Only a fraction of all candidate splits points (those located at the start + * of the now-sorted splits array) fall within the split interval. Split + * interval is applied within _bt_bestsplitloc(). + * + * Split interval represents an acceptable range of split points -- those that + * have leftfree and rightfree values that are acceptably balanced. The final + * split point chosen is the split point with the lowest "penalty" among split + * points in this split interval (unless we change our entire strategy, in + * which case the interval also changes -- see _bt_strategy()). + * + * The "Prefix B-Trees" paper calls split interval sigma l for leaf splits, + * and sigma b for internal ("branch") splits. It's hard to provide a + * theoretical justification for the size of the split interval, though it's + * clear that a small split interval can make tuples on level L+1 much smaller + * on average, without noticeably affecting space utilization on level L. + * (Note that the way that we calculate split interval might need to change if + * suffix truncation is taught to truncate tuples "within" the last + * attribute/datum for data types like text, which is more or less how it is + * assumed to work in the paper.) + */ +static int +_bt_defaultinterval(FindSplitData *state) +{ + SplitPoint *spaceoptimal; + int16 tolerance, + lowleftfree, + lowrightfree, + highleftfree, + highrightfree; + + /* + * Determine leftfree and rightfree values that are higher and lower than + * we're willing to tolerate. Note that the final split interval will be + * about 10% of nsplits in the common case where all non-pivot tuples + * (data items) from a leaf page are uniformly sized. We're a bit more + * aggressive when splitting internal pages. + */ + if (state->is_leaf) + tolerance = state->olddataitemstotal * LEAF_SPLIT_DISTANCE; + else + tolerance = state->olddataitemstotal * INTERNAL_SPLIT_DISTANCE; + + /* First candidate split point is the most evenly balanced */ + spaceoptimal = state->splits; + lowleftfree = spaceoptimal->leftfree - tolerance; + lowrightfree = spaceoptimal->rightfree - tolerance; + highleftfree = spaceoptimal->leftfree + tolerance; + highrightfree = spaceoptimal->rightfree + tolerance; + + /* + * Iterate through split points, starting from the split immediately after + * 'spaceoptimal'. Find the first split point that divides free space so + * unevenly that including it in the split interval would be unacceptable. + */ + for (int i = 1; i < state->nsplits; i++) + { + SplitPoint *split = state->splits + i; + + /* Cannot use curdelta here, since its value is often weighted */ + if (split->leftfree < lowleftfree || split->rightfree < lowrightfree || + split->leftfree > highleftfree || split->rightfree > highrightfree) + return i; + } + + return state->nsplits; +} + +/* + * Subroutine to decide whether split should use default strategy/initial + * split interval, or whether it should finish splitting the page using + * alternative strategies (this is only possible with leaf pages). + * + * Caller uses alternative strategy (or sticks with default strategy) based + * on how *strategy is set here. Return value is "perfect penalty", which is + * passed to _bt_bestsplitloc() as a final constraint on how far caller is + * willing to go to avoid appending a heap TID when using the many duplicates + * strategy (it also saves _bt_bestsplitloc() useless cycles). + */ +static int +_bt_strategy(FindSplitData *state, SplitPoint *leftpage, + SplitPoint *rightpage, FindSplitStrat *strategy) +{ + IndexTuple leftmost, + rightmost; + SplitPoint *leftinterval, + *rightinterval; + int perfectpenalty; + int indnkeyatts = IndexRelationGetNumberOfKeyAttributes(state->rel); + + /* Assume that alternative strategy won't be used for now */ + *strategy = SPLIT_DEFAULT; + + /* + * Use smallest observed firstright item size for entire page (actually, + * entire imaginary version of page that includes newitem) as perfect + * penalty on internal pages. This can save cycles in the common case + * where most or all splits (not just splits within interval) have + * firstright tuples that are the same size. + */ + if (!state->is_leaf) + return state->minfirstrightsz; + + /* + * Use leftmost and rightmost tuples from leftmost and rightmost splits in + * current split interval + */ + _bt_interval_edges(state, &leftinterval, &rightinterval); + leftmost = _bt_split_lastleft(state, leftinterval); + rightmost = _bt_split_firstright(state, rightinterval); + + /* + * If initial split interval can produce a split point that will at least + * avoid appending a heap TID in new high key, we're done. Finish split + * with default strategy and initial split interval. + */ + perfectpenalty = _bt_keep_natts_fast(state->rel, leftmost, rightmost); + if (perfectpenalty <= indnkeyatts) + return perfectpenalty; + + /* + * Work out how caller should finish split when even their "perfect" + * penalty for initial/default split interval indicates that the interval + * does not contain even a single split that avoids appending a heap TID. + * + * Use the leftmost split's lastleft tuple and the rightmost split's + * firstright tuple to assess every possible split. + */ + leftmost = _bt_split_lastleft(state, leftpage); + rightmost = _bt_split_firstright(state, rightpage); + + /* + * If page (including new item) has many duplicates but is not entirely + * full of duplicates, a many duplicates strategy split will be performed. + * If page is entirely full of duplicates, a single value strategy split + * will be performed. + */ + perfectpenalty = _bt_keep_natts_fast(state->rel, leftmost, rightmost); + if (perfectpenalty <= indnkeyatts) + { + *strategy = SPLIT_MANY_DUPLICATES; + + /* + * Many duplicates strategy should split at either side the group of + * duplicates that enclose the delta-optimal split point. Return + * indnkeyatts rather than the true perfect penalty to make that + * happen. (If perfectpenalty was returned here then low cardinality + * composite indexes could have continual unbalanced splits.) + * + * Note that caller won't go through with a many duplicates split in + * rare cases where it looks like there are ever-decreasing insertions + * to the immediate right of the split point. This must happen just + * before a final decision is made, within _bt_bestsplitloc(). + */ + return indnkeyatts; + } + + /* + * Single value strategy is only appropriate with ever-increasing heap + * TIDs; otherwise, original default strategy split should proceed to + * avoid pathological performance. Use page high key to infer if this is + * the rightmost page among pages that store the same duplicate value. + * This should not prevent insertions of heap TIDs that are slightly out + * of order from using single value strategy, since that's expected with + * concurrent inserters of the same duplicate value. + */ + else if (state->is_rightmost) + *strategy = SPLIT_SINGLE_VALUE; + else + { + ItemId itemid; + IndexTuple hikey; + + itemid = PageGetItemId(state->origpage, P_HIKEY); + hikey = (IndexTuple) PageGetItem(state->origpage, itemid); + perfectpenalty = _bt_keep_natts_fast(state->rel, hikey, + state->newitem); + if (perfectpenalty <= indnkeyatts) + *strategy = SPLIT_SINGLE_VALUE; + else + { + /* + * Have caller finish split using default strategy, since page + * does not appear to be the rightmost page for duplicates of the + * value the page is filled with + */ + } + } + + return perfectpenalty; +} + +/* + * Subroutine to locate leftmost and rightmost splits for current/default + * split interval. Note that it will be the same split iff there is only one + * split in interval. + */ +static void +_bt_interval_edges(FindSplitData *state, SplitPoint **leftinterval, + SplitPoint **rightinterval) +{ + int highsplit = Min(state->interval, state->nsplits); + SplitPoint *deltaoptimal; + + deltaoptimal = state->splits; + *leftinterval = NULL; + *rightinterval = NULL; + + /* + * Delta is an absolute distance to optimal split point, so both the + * leftmost and rightmost split point will usually be at the end of the + * array + */ + for (int i = highsplit - 1; i >= 0; i--) + { + SplitPoint *distant = state->splits + i; + + if (distant->firstrightoff < deltaoptimal->firstrightoff) + { + if (*leftinterval == NULL) + *leftinterval = distant; + } + else if (distant->firstrightoff > deltaoptimal->firstrightoff) + { + if (*rightinterval == NULL) + *rightinterval = distant; + } + else if (!distant->newitemonleft && deltaoptimal->newitemonleft) + { + /* + * "incoming tuple will become firstright" (distant) is to the + * left of "incoming tuple will become lastleft" (delta-optimal) + */ + Assert(distant->firstrightoff == state->newitemoff); + if (*leftinterval == NULL) + *leftinterval = distant; + } + else if (distant->newitemonleft && !deltaoptimal->newitemonleft) + { + /* + * "incoming tuple will become lastleft" (distant) is to the right + * of "incoming tuple will become firstright" (delta-optimal) + */ + Assert(distant->firstrightoff == state->newitemoff); + if (*rightinterval == NULL) + *rightinterval = distant; + } + else + { + /* There was only one or two splits in initial split interval */ + Assert(distant == deltaoptimal); + if (*leftinterval == NULL) + *leftinterval = distant; + if (*rightinterval == NULL) + *rightinterval = distant; + } + + if (*leftinterval && *rightinterval) + return; + } + + Assert(false); +} + +/* + * Subroutine to find penalty for caller's candidate split point. + * + * On leaf pages, penalty is the attribute number that distinguishes each side + * of a split. It's the last attribute that needs to be included in new high + * key for left page. It can be greater than the number of key attributes in + * cases where a heap TID will need to be appended during truncation. + * + * On internal pages, penalty is simply the size of the firstright tuple for + * the split (including line pointer overhead). This tuple will become the + * new high key for the left page. + */ +static inline int +_bt_split_penalty(FindSplitData *state, SplitPoint *split) +{ + IndexTuple lastleft; + IndexTuple firstright; + + if (!state->is_leaf) + { + ItemId itemid; + + if (!split->newitemonleft && + split->firstrightoff == state->newitemoff) + return state->newitemsz; + + itemid = PageGetItemId(state->origpage, split->firstrightoff); + + return MAXALIGN(ItemIdGetLength(itemid)) + sizeof(ItemIdData); + } + + lastleft = _bt_split_lastleft(state, split); + firstright = _bt_split_firstright(state, split); + + return _bt_keep_natts_fast(state->rel, lastleft, firstright); +} + +/* + * Subroutine to get a lastleft IndexTuple for a split point + */ +static inline IndexTuple +_bt_split_lastleft(FindSplitData *state, SplitPoint *split) +{ + ItemId itemid; + + if (split->newitemonleft && split->firstrightoff == state->newitemoff) + return state->newitem; + + itemid = PageGetItemId(state->origpage, + OffsetNumberPrev(split->firstrightoff)); + return (IndexTuple) PageGetItem(state->origpage, itemid); +} + +/* + * Subroutine to get a firstright IndexTuple for a split point + */ +static inline IndexTuple +_bt_split_firstright(FindSplitData *state, SplitPoint *split) +{ + ItemId itemid; + + if (!split->newitemonleft && split->firstrightoff == state->newitemoff) + return state->newitem; + + itemid = PageGetItemId(state->origpage, split->firstrightoff); + return (IndexTuple) PageGetItem(state->origpage, itemid); +} |