granicus.if.org Git - postgresql/blob - src/backend/commands/analyze.c

   1 /*-------------------------------------------------------------------------
   2  *
   3  * analyze.c
   4  *        the Postgres statistics generator
   5  *
   6  * Portions Copyright (c) 1996-2008, PostgreSQL Global Development Group
   7  * Portions Copyright (c) 1994, Regents of the University of California
   8  *
   9  *
  10  * IDENTIFICATION
  11  *        $PostgreSQL: pgsql/src/backend/commands/analyze.c,v 1.128 2008/11/10 00:49:37 tgl Exp $
  12  *
  13  *-------------------------------------------------------------------------
  14  */
  15 #include "postgres.h"
  16
  17 #include <math.h>
  18
  19 #include "access/heapam.h"
  20 #include "access/transam.h"
  21 #include "access/tuptoaster.h"
  22 #include "access/xact.h"
  23 #include "catalog/index.h"
  24 #include "catalog/indexing.h"
  25 #include "catalog/namespace.h"
  26 #include "catalog/pg_namespace.h"
  27 #include "commands/dbcommands.h"
  28 #include "commands/vacuum.h"
  29 #include "executor/executor.h"
  30 #include "miscadmin.h"
  31 #include "nodes/nodeFuncs.h"
  32 #include "parser/parse_oper.h"
  33 #include "parser/parse_relation.h"
  34 #include "pgstat.h"
  35 #include "postmaster/autovacuum.h"
  36 #include "storage/bufmgr.h"
  37 #include "storage/proc.h"
  38 #include "storage/procarray.h"
  39 #include "utils/acl.h"
  40 #include "utils/datum.h"
  41 #include "utils/lsyscache.h"
  42 #include "utils/memutils.h"
  43 #include "utils/pg_rusage.h"
  44 #include "utils/syscache.h"
  45 #include "utils/tuplesort.h"
  46 #include "utils/tqual.h"
  47
  48
  49 /* Data structure for Algorithm S from Knuth 3.4.2 */
  50 typedef struct
  51 {
  52         BlockNumber N;                          /* number of blocks, known in advance */
  53         int                     n;                              /* desired sample size */
  54         BlockNumber t;                          /* current block number */
  55         int                     m;                              /* blocks selected so far */
  56 } BlockSamplerData;
  57 typedef BlockSamplerData *BlockSampler;
  58
  59 /* Per-index data for ANALYZE */
  60 typedef struct AnlIndexData
  61 {
  62         IndexInfo  *indexInfo;          /* BuildIndexInfo result */
  63         double          tupleFract;             /* fraction of rows for partial index */
  64         VacAttrStats **vacattrstats;    /* index attrs to analyze */
  65         int                     attr_cnt;
  66 } AnlIndexData;
  67
  68
  69 /* Default statistics target (GUC parameter) */
  70 int                     default_statistics_target = 10;
  71
  72 /* A few variables that don't seem worth passing around as parameters */
  73 static int      elevel = -1;
  74
  75 static MemoryContext anl_context = NULL;
  76
  77 static BufferAccessStrategy vac_strategy;
  78
  79
  80 static void BlockSampler_Init(BlockSampler bs, BlockNumber nblocks,
  81                                   int samplesize);
  82 static bool BlockSampler_HasMore(BlockSampler bs);
  83 static BlockNumber BlockSampler_Next(BlockSampler bs);
  84 static void compute_index_stats(Relation onerel, double totalrows,
  85                                         AnlIndexData *indexdata, int nindexes,
  86                                         HeapTuple *rows, int numrows,
  87                                         MemoryContext col_context);
  88 static VacAttrStats *examine_attribute(Relation onerel, int attnum);
  89 static int acquire_sample_rows(Relation onerel, HeapTuple *rows,
  90                                         int targrows, double *totalrows, double *totaldeadrows);
  91 static double random_fract(void);
  92 static double init_selection_state(int n);
  93 static double get_next_S(double t, int n, double *stateptr);
  94 static int      compare_rows(const void *a, const void *b);
  95 static void update_attstats(Oid relid, int natts, VacAttrStats **vacattrstats);
  96 static Datum std_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull);
  97 static Datum ind_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull);
  98
  99 static bool std_typanalyze(VacAttrStats *stats);
 100
 101
 102 /*
 103  *      analyze_rel() -- analyze one relation
 104  */
 105 void
 106 analyze_rel(Oid relid, VacuumStmt *vacstmt,
 107                         BufferAccessStrategy bstrategy)
 108 {
 109         Relation        onerel;
 110         int                     attr_cnt,
 111                                 tcnt,
 112                                 i,
 113                                 ind;
 114         Relation   *Irel;
 115         int                     nindexes;
 116         bool            hasindex;
 117         bool            analyzableindex;
 118         VacAttrStats **vacattrstats;
 119         AnlIndexData *indexdata;
 120         int                     targrows,
 121                                 numrows;
 122         double          totalrows,
 123                                 totaldeadrows;
 124         HeapTuple  *rows;
 125         PGRUsage        ru0;
 126         TimestampTz starttime = 0;
 127         Oid                     save_userid;
 128         bool            save_secdefcxt;
 129
 130         if (vacstmt->verbose)
 131                 elevel = INFO;
 132         else
 133                 elevel = DEBUG2;
 134
 135         vac_strategy = bstrategy;
 136
 137         /*
 138          * Use the current context for storing analysis info.  vacuum.c ensures
 139          * that this context will be cleared when I return, thus releasing the
 140          * memory allocated here.
 141          */
 142         anl_context = CurrentMemoryContext;
 143
 144         /*
 145          * Check for user-requested abort.      Note we want this to be inside a
 146          * transaction, so xact.c doesn't issue useless WARNING.
 147          */
 148         CHECK_FOR_INTERRUPTS();
 149
 150         /*
 151          * Open the relation, getting ShareUpdateExclusiveLock to ensure that two
 152          * ANALYZEs don't run on it concurrently.  (This also locks out a
 153          * concurrent VACUUM, which doesn't matter much at the moment but might
 154          * matter if we ever try to accumulate stats on dead tuples.) If the rel
 155          * has been dropped since we last saw it, we don't need to process it.
 156          */
 157         onerel = try_relation_open(relid, ShareUpdateExclusiveLock);
 158         if (!onerel)
 159                 return;
 160
 161         /*
 162          * Check permissions --- this should match vacuum's check!
 163          */
 164         if (!(pg_class_ownercheck(RelationGetRelid(onerel), GetUserId()) ||
 165                   (pg_database_ownercheck(MyDatabaseId, GetUserId()) && !onerel->rd_rel->relisshared)))
 166         {
 167                 /* No need for a WARNING if we already complained during VACUUM */
 168                 if (!vacstmt->vacuum)
 169                 {
 170                         if (onerel->rd_rel->relisshared)
 171                                 ereport(WARNING,
 172                                                 (errmsg("skipping \"%s\" --- only superuser can analyze it",
 173                                                                 RelationGetRelationName(onerel))));
 174                         else if (onerel->rd_rel->relnamespace == PG_CATALOG_NAMESPACE)
 175                                 ereport(WARNING,
 176                                                 (errmsg("skipping \"%s\" --- only superuser or database owner can analyze it",
 177                                                                 RelationGetRelationName(onerel))));
 178                         else
 179                                 ereport(WARNING,
 180                                                 (errmsg("skipping \"%s\" --- only table or database owner can analyze it",
 181                                                                 RelationGetRelationName(onerel))));
 182                 }
 183                 relation_close(onerel, ShareUpdateExclusiveLock);
 184                 return;
 185         }
 186
 187         /*
 188          * Check that it's a plain table; we used to do this in get_rel_oids() but
 189          * seems safer to check after we've locked the relation.
 190          */
 191         if (onerel->rd_rel->relkind != RELKIND_RELATION)
 192         {
 193                 /* No need for a WARNING if we already complained during VACUUM */
 194                 if (!vacstmt->vacuum)
 195                         ereport(WARNING,
 196                                         (errmsg("skipping \"%s\" --- cannot analyze indexes, views, or special system tables",
 197                                                         RelationGetRelationName(onerel))));
 198                 relation_close(onerel, ShareUpdateExclusiveLock);
 199                 return;
 200         }
 201
 202         /*
 203          * Silently ignore tables that are temp tables of other backends ---
 204          * trying to analyze these is rather pointless, since their contents are
 205          * probably not up-to-date on disk.  (We don't throw a warning here; it
 206          * would just lead to chatter during a database-wide ANALYZE.)
 207          */
 208         if (isOtherTempNamespace(RelationGetNamespace(onerel)))
 209         {
 210                 relation_close(onerel, ShareUpdateExclusiveLock);
 211                 return;
 212         }
 213
 214         /*
 215          * We can ANALYZE any table except pg_statistic. See update_attstats
 216          */
 217         if (RelationGetRelid(onerel) == StatisticRelationId)
 218         {
 219                 relation_close(onerel, ShareUpdateExclusiveLock);
 220                 return;
 221         }
 222
 223         ereport(elevel,
 224                         (errmsg("analyzing \"%s.%s\"",
 225                                         get_namespace_name(RelationGetNamespace(onerel)),
 226                                         RelationGetRelationName(onerel))));
 227
 228         /*
 229          * Switch to the table owner's userid, so that any index functions are
 230          * run as that user.
 231          */
 232         GetUserIdAndContext(&save_userid, &save_secdefcxt);
 233         SetUserIdAndContext(onerel->rd_rel->relowner, true);
 234
 235         /* let others know what I'm doing */
 236         LWLockAcquire(ProcArrayLock, LW_EXCLUSIVE);
 237         MyProc->vacuumFlags |= PROC_IN_ANALYZE;
 238         LWLockRelease(ProcArrayLock);
 239
 240         /* measure elapsed time iff autovacuum logging requires it */
 241         if (IsAutoVacuumWorkerProcess() && Log_autovacuum_min_duration >= 0)
 242         {
 243                 pg_rusage_init(&ru0);
 244                 if (Log_autovacuum_min_duration > 0)
 245                         starttime = GetCurrentTimestamp();
 246         }
 247
 248         /*
 249          * Determine which columns to analyze
 250          *
 251          * Note that system attributes are never analyzed.
 252          */
 253         if (vacstmt->va_cols != NIL)
 254         {
 255                 ListCell   *le;
 256
 257                 vacattrstats = (VacAttrStats **) palloc(list_length(vacstmt->va_cols) *
 258                                                                                                 sizeof(VacAttrStats *));
 259                 tcnt = 0;
 260                 foreach(le, vacstmt->va_cols)
 261                 {
 262                         char       *col = strVal(lfirst(le));
 263
 264                         i = attnameAttNum(onerel, col, false);
 265                         if (i == InvalidAttrNumber)
 266                                 ereport(ERROR,
 267                                                 (errcode(ERRCODE_UNDEFINED_COLUMN),
 268                                         errmsg("column \"%s\" of relation \"%s\" does not exist",
 269                                                    col, RelationGetRelationName(onerel))));
 270                         vacattrstats[tcnt] = examine_attribute(onerel, i);
 271                         if (vacattrstats[tcnt] != NULL)
 272                                 tcnt++;
 273                 }
 274                 attr_cnt = tcnt;
 275         }
 276         else
 277         {
 278                 attr_cnt = onerel->rd_att->natts;
 279                 vacattrstats = (VacAttrStats **)
 280                         palloc(attr_cnt * sizeof(VacAttrStats *));
 281                 tcnt = 0;
 282                 for (i = 1; i <= attr_cnt; i++)
 283                 {
 284                         vacattrstats[tcnt] = examine_attribute(onerel, i);
 285                         if (vacattrstats[tcnt] != NULL)
 286                                 tcnt++;
 287                 }
 288                 attr_cnt = tcnt;
 289         }
 290
 291         /*
 292          * Open all indexes of the relation, and see if there are any analyzable
 293          * columns in the indexes.      We do not analyze index columns if there was
 294          * an explicit column list in the ANALYZE command, however.
 295          */
 296         vac_open_indexes(onerel, AccessShareLock, &nindexes, &Irel);
 297         hasindex = (nindexes > 0);
 298         indexdata = NULL;
 299         analyzableindex = false;
 300         if (hasindex)
 301         {
 302                 indexdata = (AnlIndexData *) palloc0(nindexes * sizeof(AnlIndexData));
 303                 for (ind = 0; ind < nindexes; ind++)
 304                 {
 305                         AnlIndexData *thisdata = &indexdata[ind];
 306                         IndexInfo  *indexInfo;
 307
 308                         thisdata->indexInfo = indexInfo = BuildIndexInfo(Irel[ind]);
 309                         thisdata->tupleFract = 1.0; /* fix later if partial */
 310                         if (indexInfo->ii_Expressions != NIL && vacstmt->va_cols == NIL)
 311                         {
 312                                 ListCell   *indexpr_item = list_head(indexInfo->ii_Expressions);
 313
 314                                 thisdata->vacattrstats = (VacAttrStats **)
 315                                         palloc(indexInfo->ii_NumIndexAttrs * sizeof(VacAttrStats *));
 316                                 tcnt = 0;
 317                                 for (i = 0; i < indexInfo->ii_NumIndexAttrs; i++)
 318                                 {
 319                                         int                     keycol = indexInfo->ii_KeyAttrNumbers[i];
 320
 321                                         if (keycol == 0)
 322                                         {
 323                                                 /* Found an index expression */
 324                                                 Node       *indexkey;
 325
 326                                                 if (indexpr_item == NULL)               /* shouldn't happen */
 327                                                         elog(ERROR, "too few entries in indexprs list");
 328                                                 indexkey = (Node *) lfirst(indexpr_item);
 329                                                 indexpr_item = lnext(indexpr_item);
 330
 331                                                 /*
 332                                                  * Can't analyze if the opclass uses a storage type
 333                                                  * different from the expression result type. We'd get
 334                                                  * confused because the type shown in pg_attribute for
 335                                                  * the index column doesn't match what we are getting
 336                                                  * from the expression. Perhaps this can be fixed
 337                                                  * someday, but for now, punt.
 338                                                  */
 339                                                 if (exprType(indexkey) !=
 340                                                         Irel[ind]->rd_att->attrs[i]->atttypid)
 341                                                         continue;
 342
 343                                                 thisdata->vacattrstats[tcnt] =
 344                                                         examine_attribute(Irel[ind], i + 1);
 345                                                 if (thisdata->vacattrstats[tcnt] != NULL)
 346                                                 {
 347                                                         tcnt++;
 348                                                         analyzableindex = true;
 349                                                 }
 350                                         }
 351                                 }
 352                                 thisdata->attr_cnt = tcnt;
 353                         }
 354                 }
 355         }
 356
 357         /*
 358          * Quit if no analyzable columns
 359          */
 360         if (attr_cnt <= 0 && !analyzableindex)
 361         {
 362                 /*
 363                  * We report that the table is empty; this is just so that the
 364                  * autovacuum code doesn't go nuts trying to get stats about a
 365                  * zero-column table.
 366                  */
 367                 if (!vacstmt->vacuum)
 368                         pgstat_report_analyze(onerel, 0, 0);
 369                 goto cleanup;
 370         }
 371
 372         /*
 373          * Determine how many rows we need to sample, using the worst case from
 374          * all analyzable columns.      We use a lower bound of 100 rows to avoid
 375          * possible overflow in Vitter's algorithm.
 376          */
 377         targrows = 100;
 378         for (i = 0; i < attr_cnt; i++)
 379         {
 380                 if (targrows < vacattrstats[i]->minrows)
 381                         targrows = vacattrstats[i]->minrows;
 382         }
 383         for (ind = 0; ind < nindexes; ind++)
 384         {
 385                 AnlIndexData *thisdata = &indexdata[ind];
 386
 387                 for (i = 0; i < thisdata->attr_cnt; i++)
 388                 {
 389                         if (targrows < thisdata->vacattrstats[i]->minrows)
 390                                 targrows = thisdata->vacattrstats[i]->minrows;
 391                 }
 392         }
 393
 394         /*
 395          * Acquire the sample rows
 396          */
 397         rows = (HeapTuple *) palloc(targrows * sizeof(HeapTuple));
 398         numrows = acquire_sample_rows(onerel, rows, targrows,
 399                                                                   &totalrows, &totaldeadrows);
 400
 401         /*
 402          * Compute the statistics.      Temporary results during the calculations for
 403          * each column are stored in a child context.  The calc routines are
 404          * responsible to make sure that whatever they store into the VacAttrStats
 405          * structure is allocated in anl_context.
 406          */
 407         if (numrows > 0)
 408         {
 409                 MemoryContext col_context,
 410                                         old_context;
 411
 412                 col_context = AllocSetContextCreate(anl_context,
 413                                                                                         "Analyze Column",
 414                                                                                         ALLOCSET_DEFAULT_MINSIZE,
 415                                                                                         ALLOCSET_DEFAULT_INITSIZE,
 416                                                                                         ALLOCSET_DEFAULT_MAXSIZE);
 417                 old_context = MemoryContextSwitchTo(col_context);
 418
 419                 for (i = 0; i < attr_cnt; i++)
 420                 {
 421                         VacAttrStats *stats = vacattrstats[i];
 422
 423                         stats->rows = rows;
 424                         stats->tupDesc = onerel->rd_att;
 425                         (*stats->compute_stats) (stats,
 426                                                                          std_fetch_func,
 427                                                                          numrows,
 428                                                                          totalrows);
 429                         MemoryContextResetAndDeleteChildren(col_context);
 430                 }
 431
 432                 if (hasindex)
 433                         compute_index_stats(onerel, totalrows,
 434                                                                 indexdata, nindexes,
 435                                                                 rows, numrows,
 436                                                                 col_context);
 437
 438                 MemoryContextSwitchTo(old_context);
 439                 MemoryContextDelete(col_context);
 440
 441                 /*
 442                  * Emit the completed stats rows into pg_statistic, replacing any
 443                  * previous statistics for the target columns.  (If there are stats in
 444                  * pg_statistic for columns we didn't process, we leave them alone.)
 445                  */
 446                 update_attstats(relid, attr_cnt, vacattrstats);
 447
 448                 for (ind = 0; ind < nindexes; ind++)
 449                 {
 450                         AnlIndexData *thisdata = &indexdata[ind];
 451
 452                         update_attstats(RelationGetRelid(Irel[ind]),
 453                                                         thisdata->attr_cnt, thisdata->vacattrstats);
 454                 }
 455         }
 456
 457         /*
 458          * If we are running a standalone ANALYZE, update pages/tuples stats in
 459          * pg_class.  We know the accurate page count from the smgr, but only an
 460          * approximate number of tuples; therefore, if we are part of VACUUM
 461          * ANALYZE do *not* overwrite the accurate count already inserted by
 462          * VACUUM.      The same consideration applies to indexes.
 463          */
 464         if (!vacstmt->vacuum)
 465         {
 466                 vac_update_relstats(onerel,
 467                                                         RelationGetNumberOfBlocks(onerel),
 468                                                         totalrows, hasindex, InvalidTransactionId);
 469
 470                 for (ind = 0; ind < nindexes; ind++)
 471                 {
 472                         AnlIndexData *thisdata = &indexdata[ind];
 473                         double          totalindexrows;
 474
 475                         totalindexrows = ceil(thisdata->tupleFract * totalrows);
 476                         vac_update_relstats(Irel[ind],
 477                                                                 RelationGetNumberOfBlocks(Irel[ind]),
 478                                                                 totalindexrows, false, InvalidTransactionId);
 479                 }
 480
 481                 /* report results to the stats collector, too */
 482                 pgstat_report_analyze(onerel, totalrows, totaldeadrows);
 483         }
 484
 485         /* We skip to here if there were no analyzable columns */
 486 cleanup:
 487
 488         /* Done with indexes */
 489         vac_close_indexes(nindexes, Irel, NoLock);
 490
 491         /*
 492          * Close source relation now, but keep lock so that no one deletes it
 493          * before we commit.  (If someone did, they'd fail to clean up the entries
 494          * we made in pg_statistic.  Also, releasing the lock before commit would
 495          * expose us to concurrent-update failures in update_attstats.)
 496          */
 497         relation_close(onerel, NoLock);
 498
 499         /* Log the action if appropriate */
 500         if (IsAutoVacuumWorkerProcess() && Log_autovacuum_min_duration >= 0)
 501         {
 502                 if (Log_autovacuum_min_duration == 0 ||
 503                         TimestampDifferenceExceeds(starttime, GetCurrentTimestamp(),
 504                                                                            Log_autovacuum_min_duration))
 505                         ereport(LOG,
 506                                         (errmsg("automatic analyze of table \"%s.%s.%s\" system usage: %s",
 507                                                         get_database_name(MyDatabaseId),
 508                                                         get_namespace_name(RelationGetNamespace(onerel)),
 509                                                         RelationGetRelationName(onerel),
 510                                                         pg_rusage_show(&ru0))));
 511         }
 512
 513         /*
 514          * Reset my PGPROC flag.  Note: we need this here, and not in vacuum_rel,
 515          * because the vacuum flag is cleared by the end-of-xact code.
 516          */
 517         LWLockAcquire(ProcArrayLock, LW_EXCLUSIVE);
 518         MyProc->vacuumFlags &= ~PROC_IN_ANALYZE;
 519         LWLockRelease(ProcArrayLock);
 520
 521         /* Restore userid */
 522         SetUserIdAndContext(save_userid, save_secdefcxt);
 523 }
 524
 525 /*
 526  * Compute statistics about indexes of a relation
 527  */
 528 static void
 529 compute_index_stats(Relation onerel, double totalrows,
 530                                         AnlIndexData *indexdata, int nindexes,
 531                                         HeapTuple *rows, int numrows,
 532                                         MemoryContext col_context)
 533 {
 534         MemoryContext ind_context,
 535                                 old_context;
 536         Datum           values[INDEX_MAX_KEYS];
 537         bool            isnull[INDEX_MAX_KEYS];
 538         int                     ind,
 539                                 i;
 540
 541         ind_context = AllocSetContextCreate(anl_context,
 542                                                                                 "Analyze Index",
 543                                                                                 ALLOCSET_DEFAULT_MINSIZE,
 544                                                                                 ALLOCSET_DEFAULT_INITSIZE,
 545                                                                                 ALLOCSET_DEFAULT_MAXSIZE);
 546         old_context = MemoryContextSwitchTo(ind_context);
 547
 548         for (ind = 0; ind < nindexes; ind++)
 549         {
 550                 AnlIndexData *thisdata = &indexdata[ind];
 551                 IndexInfo  *indexInfo = thisdata->indexInfo;
 552                 int                     attr_cnt = thisdata->attr_cnt;
 553                 TupleTableSlot *slot;
 554                 EState     *estate;
 555                 ExprContext *econtext;
 556                 List       *predicate;
 557                 Datum      *exprvals;
 558                 bool       *exprnulls;
 559                 int                     numindexrows,
 560                                         tcnt,
 561                                         rowno;
 562                 double          totalindexrows;
 563
 564                 /* Ignore index if no columns to analyze and not partial */
 565                 if (attr_cnt == 0 && indexInfo->ii_Predicate == NIL)
 566                         continue;
 567
 568                 /*
 569                  * Need an EState for evaluation of index expressions and
 570                  * partial-index predicates.  Create it in the per-index context to be
 571                  * sure it gets cleaned up at the bottom of the loop.
 572                  */
 573                 estate = CreateExecutorState();
 574                 econtext = GetPerTupleExprContext(estate);
 575                 /* Need a slot to hold the current heap tuple, too */
 576                 slot = MakeSingleTupleTableSlot(RelationGetDescr(onerel));
 577
 578                 /* Arrange for econtext's scan tuple to be the tuple under test */
 579                 econtext->ecxt_scantuple = slot;
 580
 581                 /* Set up execution state for predicate. */
 582                 predicate = (List *)
 583                         ExecPrepareExpr((Expr *) indexInfo->ii_Predicate,
 584                                                         estate);
 585
 586                 /* Compute and save index expression values */
 587                 exprvals = (Datum *) palloc(numrows * attr_cnt * sizeof(Datum));
 588                 exprnulls = (bool *) palloc(numrows * attr_cnt * sizeof(bool));
 589                 numindexrows = 0;
 590                 tcnt = 0;
 591                 for (rowno = 0; rowno < numrows; rowno++)
 592                 {
 593                         HeapTuple       heapTuple = rows[rowno];
 594
 595                         /* Set up for predicate or expression evaluation */
 596                         ExecStoreTuple(heapTuple, slot, InvalidBuffer, false);
 597
 598                         /* If index is partial, check predicate */
 599                         if (predicate != NIL)
 600                         {
 601                                 if (!ExecQual(predicate, econtext, false))
 602                                         continue;
 603                         }
 604                         numindexrows++;
 605
 606                         if (attr_cnt > 0)
 607                         {
 608                                 /*
 609                                  * Evaluate the index row to compute expression values. We
 610                                  * could do this by hand, but FormIndexDatum is convenient.
 611                                  */
 612                                 FormIndexDatum(indexInfo,
 613                                                            slot,
 614                                                            estate,
 615                                                            values,
 616                                                            isnull);
 617
 618                                 /*
 619                                  * Save just the columns we care about.
 620                                  */
 621                                 for (i = 0; i < attr_cnt; i++)
 622                                 {
 623                                         VacAttrStats *stats = thisdata->vacattrstats[i];
 624                                         int                     attnum = stats->attr->attnum;
 625
 626                                         exprvals[tcnt] = values[attnum - 1];
 627                                         exprnulls[tcnt] = isnull[attnum - 1];
 628                                         tcnt++;
 629                                 }
 630                         }
 631                 }
 632
 633                 /*
 634                  * Having counted the number of rows that pass the predicate in the
 635                  * sample, we can estimate the total number of rows in the index.
 636                  */
 637                 thisdata->tupleFract = (double) numindexrows / (double) numrows;
 638                 totalindexrows = ceil(thisdata->tupleFract * totalrows);
 639
 640                 /*
 641                  * Now we can compute the statistics for the expression columns.
 642                  */
 643                 if (numindexrows > 0)
 644                 {
 645                         MemoryContextSwitchTo(col_context);
 646                         for (i = 0; i < attr_cnt; i++)
 647                         {
 648                                 VacAttrStats *stats = thisdata->vacattrstats[i];
 649
 650                                 stats->exprvals = exprvals + i;
 651                                 stats->exprnulls = exprnulls + i;
 652                                 stats->rowstride = attr_cnt;
 653                                 (*stats->compute_stats) (stats,
 654                                                                                  ind_fetch_func,
 655                                                                                  numindexrows,
 656                                                                                  totalindexrows);
 657                                 MemoryContextResetAndDeleteChildren(col_context);
 658                         }
 659                 }
 660
 661                 /* And clean up */
 662                 MemoryContextSwitchTo(ind_context);
 663
 664                 ExecDropSingleTupleTableSlot(slot);
 665                 FreeExecutorState(estate);
 666                 MemoryContextResetAndDeleteChildren(ind_context);
 667         }
 668
 669         MemoryContextSwitchTo(old_context);
 670         MemoryContextDelete(ind_context);
 671 }
 672
 673 /*
 674  * examine_attribute -- pre-analysis of a single column
 675  *
 676  * Determine whether the column is analyzable; if so, create and initialize
 677  * a VacAttrStats struct for it.  If not, return NULL.
 678  */
 679 static VacAttrStats *
 680 examine_attribute(Relation onerel, int attnum)
 681 {
 682         Form_pg_attribute attr = onerel->rd_att->attrs[attnum - 1];
 683         HeapTuple       typtuple;
 684         VacAttrStats *stats;
 685         int                     i;
 686         bool            ok;
 687
 688         /* Never analyze dropped columns */
 689         if (attr->attisdropped)
 690                 return NULL;
 691
 692         /* Don't analyze column if user has specified not to */
 693         if (attr->attstattarget == 0)
 694                 return NULL;
 695
 696         /*
 697          * Create the VacAttrStats struct.
 698          */
 699         stats = (VacAttrStats *) palloc0(sizeof(VacAttrStats));
 700         stats->attr = (Form_pg_attribute) palloc(ATTRIBUTE_TUPLE_SIZE);
 701         memcpy(stats->attr, attr, ATTRIBUTE_TUPLE_SIZE);
 702         typtuple = SearchSysCache(TYPEOID,
 703                                                           ObjectIdGetDatum(attr->atttypid),
 704                                                           0, 0, 0);
 705         if (!HeapTupleIsValid(typtuple))
 706                 elog(ERROR, "cache lookup failed for type %u", attr->atttypid);
 707         stats->attrtype = (Form_pg_type) palloc(sizeof(FormData_pg_type));
 708         memcpy(stats->attrtype, GETSTRUCT(typtuple), sizeof(FormData_pg_type));
 709         ReleaseSysCache(typtuple);
 710         stats->anl_context = anl_context;
 711         stats->tupattnum = attnum;
 712
 713         /*
 714          * The fields describing the stats->stavalues[n] element types default
 715          * to the type of the field being analyzed, but the type-specific
 716          * typanalyze function can change them if it wants to store something
 717          * else.
 718          */
 719         for (i = 0; i < STATISTIC_NUM_SLOTS; i++)
 720         {
 721                 stats->statypid[i] = stats->attr->atttypid;
 722                 stats->statyplen[i] = stats->attrtype->typlen;
 723                 stats->statypbyval[i] = stats->attrtype->typbyval;
 724                 stats->statypalign[i] = stats->attrtype->typalign;
 725         }
 726
 727         /*
 728          * Call the type-specific typanalyze function.  If none is specified, use
 729          * std_typanalyze().
 730          */
 731         if (OidIsValid(stats->attrtype->typanalyze))
 732                 ok = DatumGetBool(OidFunctionCall1(stats->attrtype->typanalyze,
 733                                                                                    PointerGetDatum(stats)));
 734         else
 735                 ok = std_typanalyze(stats);
 736
 737         if (!ok || stats->compute_stats == NULL || stats->minrows <= 0)
 738         {
 739                 pfree(stats->attrtype);
 740                 pfree(stats->attr);
 741                 pfree(stats);
 742                 return NULL;
 743         }
 744
 745         return stats;
 746 }
 747
 748 /*
 749  * BlockSampler_Init -- prepare for random sampling of blocknumbers
 750  *
 751  * BlockSampler is used for stage one of our new two-stage tuple
 752  * sampling mechanism as discussed on pgsql-hackers 2004-04-02 (subject
 753  * "Large DB").  It selects a random sample of samplesize blocks out of
 754  * the nblocks blocks in the table.  If the table has less than
 755  * samplesize blocks, all blocks are selected.
 756  *
 757  * Since we know the total number of blocks in advance, we can use the
 758  * straightforward Algorithm S from Knuth 3.4.2, rather than Vitter's
 759  * algorithm.
 760  */
 761 static void
 762 BlockSampler_Init(BlockSampler bs, BlockNumber nblocks, int samplesize)
 763 {
 764         bs->N = nblocks;                        /* measured table size */
 765
 766         /*
 767          * If we decide to reduce samplesize for tables that have less or not much
 768          * more than samplesize blocks, here is the place to do it.
 769          */
 770         bs->n = samplesize;
 771         bs->t = 0;                                      /* blocks scanned so far */
 772         bs->m = 0;                                      /* blocks selected so far */
 773 }
 774
 775 static bool
 776 BlockSampler_HasMore(BlockSampler bs)
 777 {
 778         return (bs->t < bs->N) && (bs->m < bs->n);
 779 }
 780
 781 static BlockNumber
 782 BlockSampler_Next(BlockSampler bs)
 783 {
 784         BlockNumber K = bs->N - bs->t;          /* remaining blocks */
 785         int                     k = bs->n - bs->m;              /* blocks still to sample */
 786         double          p;                              /* probability to skip block */
 787         double          V;                              /* random */
 788
 789         Assert(BlockSampler_HasMore(bs));       /* hence K > 0 and k > 0 */
 790
 791         if ((BlockNumber) k >= K)
 792         {
 793                 /* need all the rest */
 794                 bs->m++;
 795                 return bs->t++;
 796         }
 797
 798         /*----------
 799          * It is not obvious that this code matches Knuth's Algorithm S.
 800          * Knuth says to skip the current block with probability 1 - k/K.
 801          * If we are to skip, we should advance t (hence decrease K), and
 802          * repeat the same probabilistic test for the next block.  The naive
 803          * implementation thus requires a random_fract() call for each block
 804          * number.      But we can reduce this to one random_fract() call per
 805          * selected block, by noting that each time the while-test succeeds,
 806          * we can reinterpret V as a uniform random number in the range 0 to p.
 807          * Therefore, instead of choosing a new V, we just adjust p to be
 808          * the appropriate fraction of its former value, and our next loop
 809          * makes the appropriate probabilistic test.
 810          *
 811          * We have initially K > k > 0.  If the loop reduces K to equal k,
 812          * the next while-test must fail since p will become exactly zero
 813          * (we assume there will not be roundoff error in the division).
 814          * (Note: Knuth suggests a "<=" loop condition, but we use "<" just
 815          * to be doubly sure about roundoff error.)  Therefore K cannot become
 816          * less than k, which means that we cannot fail to select enough blocks.
 817          *----------
 818          */
 819         V = random_fract();
 820         p = 1.0 - (double) k / (double) K;
 821         while (V < p)
 822         {
 823                 /* skip */
 824                 bs->t++;
 825                 K--;                                    /* keep K == N - t */
 826
 827                 /* adjust p to be new cutoff point in reduced range */
 828                 p *= 1.0 - (double) k / (double) K;
 829         }
 830
 831         /* select */
 832         bs->m++;
 833         return bs->t++;
 834 }
 835
 836 /*
 837  * acquire_sample_rows -- acquire a random sample of rows from the table
 838  *
 839  * As of May 2004 we use a new two-stage method:  Stage one selects up
 840  * to targrows random blocks (or all blocks, if there aren't so many).
 841  * Stage two scans these blocks and uses the Vitter algorithm to create
 842  * a random sample of targrows rows (or less, if there are less in the
 843  * sample of blocks).  The two stages are executed simultaneously: each
 844  * block is processed as soon as stage one returns its number and while
 845  * the rows are read stage two controls which ones are to be inserted
 846  * into the sample.
 847  *
 848  * Although every row has an equal chance of ending up in the final
 849  * sample, this sampling method is not perfect: not every possible
 850  * sample has an equal chance of being selected.  For large relations
 851  * the number of different blocks represented by the sample tends to be
 852  * too small.  We can live with that for now.  Improvements are welcome.
 853  *
 854  * We also estimate the total numbers of live and dead rows in the table,
 855  * and return them into *totalrows and *totaldeadrows, respectively.
 856  *
 857  * An important property of this sampling method is that because we do
 858  * look at a statistically unbiased set of blocks, we should get
 859  * unbiased estimates of the average numbers of live and dead rows per
 860  * block.  The previous sampling method put too much credence in the row
 861  * density near the start of the table.
 862  *
 863  * The returned list of tuples is in order by physical position in the table.
 864  * (We will rely on this later to derive correlation estimates.)
 865  */
 866 static int
 867 acquire_sample_rows(Relation onerel, HeapTuple *rows, int targrows,
 868                                         double *totalrows, double *totaldeadrows)
 869 {
 870         int                     numrows = 0;    /* # rows now in reservoir */
 871         double          samplerows = 0; /* total # rows collected */
 872         double          liverows = 0;   /* # live rows seen */
 873         double          deadrows = 0;   /* # dead rows seen */
 874         double          rowstoskip = -1;        /* -1 means not set yet */
 875         BlockNumber totalblocks;
 876         TransactionId OldestXmin;
 877         BlockSamplerData bs;
 878         double          rstate;
 879
 880         Assert(targrows > 1);
 881
 882         totalblocks = RelationGetNumberOfBlocks(onerel);
 883
 884         /* Need a cutoff xmin for HeapTupleSatisfiesVacuum */
 885         OldestXmin = GetOldestXmin(onerel->rd_rel->relisshared, true);
 886
 887         /* Prepare for sampling block numbers */
 888         BlockSampler_Init(&bs, totalblocks, targrows);
 889         /* Prepare for sampling rows */
 890         rstate = init_selection_state(targrows);
 891
 892         /* Outer loop over blocks to sample */
 893         while (BlockSampler_HasMore(&bs))
 894         {
 895                 BlockNumber targblock = BlockSampler_Next(&bs);
 896                 Buffer          targbuffer;
 897                 Page            targpage;
 898                 OffsetNumber targoffset,
 899                                         maxoffset;
 900
 901                 vacuum_delay_point();
 902
 903                 /*
 904                  * We must maintain a pin on the target page's buffer to ensure that
 905                  * the maxoffset value stays good (else concurrent VACUUM might delete
 906                  * tuples out from under us).  Hence, pin the page until we are done
 907                  * looking at it.  We also choose to hold sharelock on the buffer
 908                  * throughout --- we could release and re-acquire sharelock for
 909                  * each tuple, but since we aren't doing much work per tuple, the
 910                  * extra lock traffic is probably better avoided.
 911                  */
 912                 targbuffer = ReadBufferExtended(onerel, MAIN_FORKNUM, targblock,
 913                                                                                 RBM_NORMAL, vac_strategy);
 914                 LockBuffer(targbuffer, BUFFER_LOCK_SHARE);
 915                 targpage = BufferGetPage(targbuffer);
 916                 maxoffset = PageGetMaxOffsetNumber(targpage);
 917
 918                 /* Inner loop over all tuples on the selected page */
 919                 for (targoffset = FirstOffsetNumber; targoffset <= maxoffset; targoffset++)
 920                 {
 921                         ItemId          itemid;
 922                         HeapTupleData targtuple;
 923                         bool            sample_it = false;
 924
 925                         itemid = PageGetItemId(targpage, targoffset);
 926
 927                         /*
 928                          * We ignore unused and redirect line pointers.  DEAD line
 929                          * pointers should be counted as dead, because we need vacuum
 930                          * to run to get rid of them.  Note that this rule agrees with
 931                          * the way that heap_page_prune() counts things.
 932                          */
 933                         if (!ItemIdIsNormal(itemid))
 934                         {
 935                                 if (ItemIdIsDead(itemid))
 936                                         deadrows += 1;
 937                                 continue;
 938                         }
 939
 940                         ItemPointerSet(&targtuple.t_self, targblock, targoffset);
 941
 942                         targtuple.t_data = (HeapTupleHeader) PageGetItem(targpage, itemid);
 943                         targtuple.t_len = ItemIdGetLength(itemid);
 944
 945                         switch (HeapTupleSatisfiesVacuum(targtuple.t_data,
 946                                                                                          OldestXmin,
 947                                                                                          targbuffer))
 948                         {
 949                                 case HEAPTUPLE_LIVE:
 950                                         sample_it = true;
 951                                         liverows += 1;
 952                                         break;
 953
 954                                 case HEAPTUPLE_DEAD:
 955                                 case HEAPTUPLE_RECENTLY_DEAD:
 956                                         /* Count dead and recently-dead rows */
 957                                         deadrows += 1;
 958                                         break;
 959
 960                                 case HEAPTUPLE_INSERT_IN_PROGRESS:
 961                                         /*
 962                                          * Insert-in-progress rows are not counted.  We assume
 963                                          * that when the inserting transaction commits or aborts,
 964                                          * it will send a stats message to increment the proper
 965                                          * count.  This works right only if that transaction ends
 966                                          * after we finish analyzing the table; if things happen
 967                                          * in the other order, its stats update will be
 968                                          * overwritten by ours.  However, the error will be
 969                                          * large only if the other transaction runs long enough
 970                                          * to insert many tuples, so assuming it will finish
 971                                          * after us is the safer option.
 972                                          *
 973                                          * A special case is that the inserting transaction might
 974                                          * be our own.  In this case we should count and sample
 975                                          * the row, to accommodate users who load a table and
 976                                          * analyze it in one transaction.  (pgstat_report_analyze
 977                                          * has to adjust the numbers we send to the stats collector
 978                                          * to make this come out right.)
 979                                          */
 980                                         if (TransactionIdIsCurrentTransactionId(HeapTupleHeaderGetXmin(targtuple.t_data)))
 981                                         {
 982                                                 sample_it = true;
 983                                                 liverows += 1;
 984                                         }
 985                                         break;
 986
 987                                 case HEAPTUPLE_DELETE_IN_PROGRESS:
 988                                         /*
 989                                          * We count delete-in-progress rows as still live, using
 990                                          * the same reasoning given above; but we don't bother to
 991                                          * include them in the sample.
 992                                          *
 993                                          * If the delete was done by our own transaction, however,
 994                                          * we must count the row as dead to make
 995                                          * pgstat_report_analyze's stats adjustments come out
 996                                          * right.  (Note: this works out properly when the row
 997                                          * was both inserted and deleted in our xact.)
 998                                          */
 999                                         if (TransactionIdIsCurrentTransactionId(HeapTupleHeaderGetXmax(targtuple.t_data)))
1000                                                 deadrows += 1;
1001                                         else
1002                                                 liverows += 1;
1003                                         break;
1004
1005                                 default:
1006                                         elog(ERROR, "unexpected HeapTupleSatisfiesVacuum result");
1007                                         break;
1008                         }
1009
1010                         if (sample_it)
1011                         {
1012                                 /*
1013                                  * The first targrows sample rows are simply copied into the
1014                                  * reservoir. Then we start replacing tuples in the sample
1015                                  * until we reach the end of the relation.      This algorithm is
1016                                  * from Jeff Vitter's paper (see full citation below). It
1017                                  * works by repeatedly computing the number of tuples to skip
1018                                  * before selecting a tuple, which replaces a randomly chosen
1019                                  * element of the reservoir (current set of tuples).  At all
1020                                  * times the reservoir is a true random sample of the tuples
1021                                  * we've passed over so far, so when we fall off the end of
1022                                  * the relation we're done.
1023                                  */
1024                                 if (numrows < targrows)
1025                                         rows[numrows++] = heap_copytuple(&targtuple);
1026                                 else
1027                                 {
1028                                         /*
1029                                          * t in Vitter's paper is the number of records already
1030                                          * processed.  If we need to compute a new S value, we
1031                                          * must use the not-yet-incremented value of samplerows
1032                                          * as t.
1033                                          */
1034                                         if (rowstoskip < 0)
1035                                                 rowstoskip = get_next_S(samplerows, targrows, &rstate);
1036
1037                                         if (rowstoskip <= 0)
1038                                         {
1039                                                 /*
1040                                                  * Found a suitable tuple, so save it, replacing one
1041                                                  * old tuple at random
1042                                                  */
1043                                                 int                     k = (int) (targrows * random_fract());
1044
1045                                                 Assert(k >= 0 && k < targrows);
1046                                                 heap_freetuple(rows[k]);
1047                                                 rows[k] = heap_copytuple(&targtuple);
1048                                         }
1049
1050                                         rowstoskip -= 1;
1051                                 }
1052
1053                                 samplerows += 1;
1054                         }
1055                 }
1056
1057                 /* Now release the lock and pin on the page */
1058                 UnlockReleaseBuffer(targbuffer);
1059         }
1060
1061         /*
1062          * If we didn't find as many tuples as we wanted then we're done. No sort
1063          * is needed, since they're already in order.
1064          *
1065          * Otherwise we need to sort the collected tuples by position
1066          * (itempointer). It's not worth worrying about corner cases where the
1067          * tuples are already sorted.
1068          */
1069         if (numrows == targrows)
1070                 qsort((void *) rows, numrows, sizeof(HeapTuple), compare_rows);
1071
1072         /*
1073          * Estimate total numbers of rows in relation.
1074          */
1075         if (bs.m > 0)
1076         {
1077                 *totalrows = floor((liverows * totalblocks) / bs.m + 0.5);
1078                 *totaldeadrows = floor((deadrows * totalblocks) / bs.m + 0.5);
1079         }
1080         else
1081         {
1082                 *totalrows = 0.0;
1083                 *totaldeadrows = 0.0;
1084         }
1085
1086         /*
1087          * Emit some interesting relation info
1088          */
1089         ereport(elevel,
1090                         (errmsg("\"%s\": scanned %d of %u pages, "
1091                                         "containing %.0f live rows and %.0f dead rows; "
1092                                         "%d rows in sample, %.0f estimated total rows",
1093                                         RelationGetRelationName(onerel),
1094                                         bs.m, totalblocks,
1095                                         liverows, deadrows,
1096                                         numrows, *totalrows)));
1097
1098         return numrows;
1099 }
1100
1101 /* Select a random value R uniformly distributed in (0 - 1) */
1102 static double
1103 random_fract(void)
1104 {
1105         return ((double) random() + 1) / ((double) MAX_RANDOM_VALUE + 2);
1106 }
1107
1108 /*
1109  * These two routines embody Algorithm Z from "Random sampling with a
1110  * reservoir" by Jeffrey S. Vitter, in ACM Trans. Math. Softw. 11, 1
1111  * (Mar. 1985), Pages 37-57.  Vitter describes his algorithm in terms
1112  * of the count S of records to skip before processing another record.
1113  * It is computed primarily based on t, the number of records already read.
1114  * The only extra state needed between calls is W, a random state variable.
1115  *
1116  * init_selection_state computes the initial W value.
1117  *
1118  * Given that we've already read t records (t >= n), get_next_S
1119  * determines the number of records to skip before the next record is
1120  * processed.
1121  */
1122 static double
1123 init_selection_state(int n)
1124 {
1125         /* Initial value of W (for use when Algorithm Z is first applied) */
1126         return exp(-log(random_fract()) / n);
1127 }
1128
1129 static double
1130 get_next_S(double t, int n, double *stateptr)
1131 {
1132         double          S;
1133
1134         /* The magic constant here is T from Vitter's paper */
1135         if (t <= (22.0 * n))
1136         {
1137                 /* Process records using Algorithm X until t is large enough */
1138                 double          V,
1139                                         quot;
1140
1141                 V = random_fract();             /* Generate V */
1142                 S = 0;
1143                 t += 1;
1144                 /* Note: "num" in Vitter's code is always equal to t - n */
1145                 quot = (t - (double) n) / t;
1146                 /* Find min S satisfying (4.1) */
1147                 while (quot > V)
1148                 {
1149                         S += 1;
1150                         t += 1;
1151                         quot *= (t - (double) n) / t;
1152                 }
1153         }
1154         else
1155         {
1156                 /* Now apply Algorithm Z */
1157                 double          W = *stateptr;
1158                 double          term = t - (double) n + 1;
1159
1160                 for (;;)
1161                 {
1162                         double          numer,
1163                                                 numer_lim,
1164                                                 denom;
1165                         double          U,
1166                                                 X,
1167                                                 lhs,
1168                                                 rhs,
1169                                                 y,
1170                                                 tmp;
1171
1172                         /* Generate U and X */
1173                         U = random_fract();
1174                         X = t * (W - 1.0);
1175                         S = floor(X);           /* S is tentatively set to floor(X) */
1176                         /* Test if U <= h(S)/cg(X) in the manner of (6.3) */
1177                         tmp = (t + 1) / term;
1178                         lhs = exp(log(((U * tmp * tmp) * (term + S)) / (t + X)) / n);
1179                         rhs = (((t + X) / (term + S)) * term) / t;
1180                         if (lhs <= rhs)
1181                         {
1182                                 W = rhs / lhs;
1183                                 break;
1184                         }
1185                         /* Test if U <= f(S)/cg(X) */
1186                         y = (((U * (t + 1)) / term) * (t + S + 1)) / (t + X);
1187                         if ((double) n < S)
1188                         {
1189                                 denom = t;
1190                                 numer_lim = term + S;
1191                         }
1192                         else
1193                         {
1194                                 denom = t - (double) n + S;
1195                                 numer_lim = t + 1;
1196                         }
1197                         for (numer = t + S; numer >= numer_lim; numer -= 1)
1198                         {
1199                                 y *= numer / denom;
1200                                 denom -= 1;
1201                         }
1202                         W = exp(-log(random_fract()) / n);      /* Generate W in advance */
1203                         if (exp(log(y) / n) <= (t + X) / t)
1204                                 break;
1205                 }
1206                 *stateptr = W;
1207         }
1208         return S;
1209 }
1210
1211 /*
1212  * qsort comparator for sorting rows[] array
1213  */
1214 static int
1215 compare_rows(const void *a, const void *b)
1216 {
1217         HeapTuple       ha = *(HeapTuple *) a;
1218         HeapTuple       hb = *(HeapTuple *) b;
1219         BlockNumber ba = ItemPointerGetBlockNumber(&ha->t_self);
1220         OffsetNumber oa = ItemPointerGetOffsetNumber(&ha->t_self);
1221         BlockNumber bb = ItemPointerGetBlockNumber(&hb->t_self);
1222         OffsetNumber ob = ItemPointerGetOffsetNumber(&hb->t_self);
1223
1224         if (ba < bb)
1225                 return -1;
1226         if (ba > bb)
1227                 return 1;
1228         if (oa < ob)
1229                 return -1;
1230         if (oa > ob)
1231                 return 1;
1232         return 0;
1233 }
1234
1235
1236 /*
1237  *      update_attstats() -- update attribute statistics for one relation
1238  *
1239  *              Statistics are stored in several places: the pg_class row for the
1240  *              relation has stats about the whole relation, and there is a
1241  *              pg_statistic row for each (non-system) attribute that has ever
1242  *              been analyzed.  The pg_class values are updated by VACUUM, not here.
1243  *
1244  *              pg_statistic rows are just added or updated normally.  This means
1245  *              that pg_statistic will probably contain some deleted rows at the
1246  *              completion of a vacuum cycle, unless it happens to get vacuumed last.
1247  *
1248  *              To keep things simple, we punt for pg_statistic, and don't try
1249  *              to compute or store rows for pg_statistic itself in pg_statistic.
1250  *              This could possibly be made to work, but it's not worth the trouble.
1251  *              Note analyze_rel() has seen to it that we won't come here when
1252  *              vacuuming pg_statistic itself.
1253  *
1254  *              Note: there would be a race condition here if two backends could
1255  *              ANALYZE the same table concurrently.  Presently, we lock that out
1256  *              by taking a self-exclusive lock on the relation in analyze_rel().
1257  */
1258 static void
1259 update_attstats(Oid relid, int natts, VacAttrStats **vacattrstats)
1260 {
1261         Relation        sd;
1262         int                     attno;
1263
1264         if (natts <= 0)
1265                 return;                                 /* nothing to do */
1266
1267         sd = heap_open(StatisticRelationId, RowExclusiveLock);
1268
1269         for (attno = 0; attno < natts; attno++)
1270         {
1271                 VacAttrStats *stats = vacattrstats[attno];
1272                 HeapTuple       stup,
1273                                         oldtup;
1274                 int                     i,
1275                                         k,
1276                                         n;
1277                 Datum           values[Natts_pg_statistic];
1278                 bool            nulls[Natts_pg_statistic];
1279                 bool            replaces[Natts_pg_statistic];
1280
1281                 /* Ignore attr if we weren't able to collect stats */
1282                 if (!stats->stats_valid)
1283                         continue;
1284
1285                 /*
1286                  * Construct a new pg_statistic tuple
1287                  */
1288                 for (i = 0; i < Natts_pg_statistic; ++i)
1289                 {
1290                         nulls[i] = false;
1291                         replaces[i] = true;
1292                 }
1293
1294                 i = 0;
1295                 values[i++] = ObjectIdGetDatum(relid);  /* starelid */
1296                 values[i++] = Int16GetDatum(stats->attr->attnum);               /* staattnum */
1297                 values[i++] = Float4GetDatum(stats->stanullfrac);               /* stanullfrac */
1298                 values[i++] = Int32GetDatum(stats->stawidth);   /* stawidth */
1299                 values[i++] = Float4GetDatum(stats->stadistinct);               /* stadistinct */
1300                 for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
1301                 {
1302                         values[i++] = Int16GetDatum(stats->stakind[k]);         /* stakindN */
1303                 }
1304                 for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
1305                 {
1306                         values[i++] = ObjectIdGetDatum(stats->staop[k]);        /* staopN */
1307                 }
1308                 for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
1309                 {
1310                         int                     nnum = stats->numnumbers[k];
1311
1312                         if (nnum > 0)
1313                         {
1314                                 Datum      *numdatums = (Datum *) palloc(nnum * sizeof(Datum));
1315                                 ArrayType  *arry;
1316
1317                                 for (n = 0; n < nnum; n++)
1318                                         numdatums[n] = Float4GetDatum(stats->stanumbers[k][n]);
1319                                 /* XXX knows more than it should about type float4: */
1320                                 arry = construct_array(numdatums, nnum,
1321                                                                            FLOAT4OID,
1322                                                                            sizeof(float4), FLOAT4PASSBYVAL, 'i');
1323                                 values[i++] = PointerGetDatum(arry);    /* stanumbersN */
1324                         }
1325                         else
1326                         {
1327                                 nulls[i] = true;
1328                                 values[i++] = (Datum) 0;
1329                         }
1330                 }
1331                 for (k = 0; k < STATISTIC_NUM_SLOTS; k++)
1332                 {
1333                         if (stats->numvalues[k] > 0)
1334                         {
1335                                 ArrayType  *arry;
1336
1337                                 arry = construct_array(stats->stavalues[k],
1338                                                                            stats->numvalues[k],
1339                                                                            stats->statypid[k],
1340                                                                            stats->statyplen[k],
1341                                                                            stats->statypbyval[k],
1342                                                                            stats->statypalign[k]);
1343                                 values[i++] = PointerGetDatum(arry);    /* stavaluesN */
1344                         }
1345                         else
1346                         {
1347                                 nulls[i] = true;
1348                                 values[i++] = (Datum) 0;
1349                         }
1350                 }
1351
1352                 /* Is there already a pg_statistic tuple for this attribute? */
1353                 oldtup = SearchSysCache(STATRELATT,
1354                                                                 ObjectIdGetDatum(relid),
1355                                                                 Int16GetDatum(stats->attr->attnum),
1356                                                                 0, 0);
1357
1358                 if (HeapTupleIsValid(oldtup))
1359                 {
1360                         /* Yes, replace it */
1361                         stup = heap_modify_tuple(oldtup,
1362                                                                         RelationGetDescr(sd),
1363                                                                         values,
1364                                                                         nulls,
1365                                                                         replaces);
1366                         ReleaseSysCache(oldtup);
1367                         simple_heap_update(sd, &stup->t_self, stup);
1368                 }
1369                 else
1370                 {
1371                         /* No, insert new tuple */
1372                         stup = heap_form_tuple(RelationGetDescr(sd), values, nulls);
1373                         simple_heap_insert(sd, stup);
1374                 }
1375
1376                 /* update indexes too */
1377                 CatalogUpdateIndexes(sd, stup);
1378
1379                 heap_freetuple(stup);
1380         }
1381
1382         heap_close(sd, RowExclusiveLock);
1383 }
1384
1385 /*
1386  * Standard fetch function for use by compute_stats subroutines.
1387  *
1388  * This exists to provide some insulation between compute_stats routines
1389  * and the actual storage of the sample data.
1390  */
1391 static Datum
1392 std_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull)
1393 {
1394         int                     attnum = stats->tupattnum;
1395         HeapTuple       tuple = stats->rows[rownum];
1396         TupleDesc       tupDesc = stats->tupDesc;
1397
1398         return heap_getattr(tuple, attnum, tupDesc, isNull);
1399 }
1400
1401 /*
1402  * Fetch function for analyzing index expressions.
1403  *
1404  * We have not bothered to construct index tuples, instead the data is
1405  * just in Datum arrays.
1406  */
1407 static Datum
1408 ind_fetch_func(VacAttrStatsP stats, int rownum, bool *isNull)
1409 {
1410         int                     i;
1411
1412         /* exprvals and exprnulls are already offset for proper column */
1413         i = rownum * stats->rowstride;
1414         *isNull = stats->exprnulls[i];
1415         return stats->exprvals[i];
1416 }
1417
1418
1419 /*==========================================================================
1420  *
1421  * Code below this point represents the "standard" type-specific statistics
1422  * analysis algorithms.  This code can be replaced on a per-data-type basis
1423  * by setting a nonzero value in pg_type.typanalyze.
1424  *
1425  *==========================================================================
1426  */
1427
1428
1429 /*
1430  * To avoid consuming too much memory during analysis and/or too much space
1431  * in the resulting pg_statistic rows, we ignore varlena datums that are wider
1432  * than WIDTH_THRESHOLD (after detoasting!).  This is legitimate for MCV
1433  * and distinct-value calculations since a wide value is unlikely to be
1434  * duplicated at all, much less be a most-common value.  For the same reason,
1435  * ignoring wide values will not affect our estimates of histogram bin
1436  * boundaries very much.
1437  */
1438 #define WIDTH_THRESHOLD  1024
1439
1440 #define swapInt(a,b)    do {int _tmp; _tmp=a; a=b; b=_tmp;} while(0)
1441 #define swapDatum(a,b)  do {Datum _tmp; _tmp=a; a=b; b=_tmp;} while(0)
1442
1443 /*
1444  * Extra information used by the default analysis routines
1445  */
1446 typedef struct
1447 {
1448         Oid                     eqopr;                  /* '=' operator for datatype, if any */
1449         Oid                     eqfunc;                 /* and associated function */
1450         Oid                     ltopr;                  /* '<' operator for datatype, if any */
1451 } StdAnalyzeData;
1452
1453 typedef struct
1454 {
1455         Datum           value;                  /* a data value */
1456         int                     tupno;                  /* position index for tuple it came from */
1457 } ScalarItem;
1458
1459 typedef struct
1460 {
1461         int                     count;                  /* # of duplicates */
1462         int                     first;                  /* values[] index of first occurrence */
1463 } ScalarMCVItem;
1464
1465 typedef struct
1466 {
1467         FmgrInfo   *cmpFn;
1468         int                     cmpFlags;
1469         int                *tupnoLink;
1470 } CompareScalarsContext;
1471
1472
1473 static void compute_minimal_stats(VacAttrStatsP stats,
1474                                           AnalyzeAttrFetchFunc fetchfunc,
1475                                           int samplerows,
1476                                           double totalrows);
1477 static void compute_scalar_stats(VacAttrStatsP stats,
1478                                          AnalyzeAttrFetchFunc fetchfunc,
1479                                          int samplerows,
1480                                          double totalrows);
1481 static int      compare_scalars(const void *a, const void *b, void *arg);
1482 static int      compare_mcvs(const void *a, const void *b);
1483
1484
1485 /*
1486  * std_typanalyze -- the default type-specific typanalyze function
1487  */
1488 static bool
1489 std_typanalyze(VacAttrStats *stats)
1490 {
1491         Form_pg_attribute attr = stats->attr;
1492         Oid                     ltopr;
1493         Oid                     eqopr;
1494         StdAnalyzeData *mystats;
1495
1496         /* If the attstattarget column is negative, use the default value */
1497         /* NB: it is okay to scribble on stats->attr since it's a copy */
1498         if (attr->attstattarget < 0)
1499                 attr->attstattarget = default_statistics_target;
1500
1501         /* Look for default "<" and "=" operators for column's type */
1502         get_sort_group_operators(attr->atttypid,
1503                                                          false, false, false,
1504                                                          &ltopr, &eqopr, NULL);
1505
1506         /* If column has no "=" operator, we can't do much of anything */
1507         if (!OidIsValid(eqopr))
1508                 return false;
1509
1510         /* Save the operator info for compute_stats routines */
1511         mystats = (StdAnalyzeData *) palloc(sizeof(StdAnalyzeData));
1512         mystats->eqopr = eqopr;
1513         mystats->eqfunc = get_opcode(eqopr);
1514         mystats->ltopr = ltopr;
1515         stats->extra_data = mystats;
1516
1517         /*
1518          * Determine which standard statistics algorithm to use
1519          */
1520         if (OidIsValid(ltopr))
1521         {
1522                 /* Seems to be a scalar datatype */
1523                 stats->compute_stats = compute_scalar_stats;
1524                 /*--------------------
1525                  * The following choice of minrows is based on the paper
1526                  * "Random sampling for histogram construction: how much is enough?"
1527                  * by Surajit Chaudhuri, Rajeev Motwani and Vivek Narasayya, in
1528                  * Proceedings of ACM SIGMOD International Conference on Management
1529                  * of Data, 1998, Pages 436-447.  Their Corollary 1 to Theorem 5
1530                  * says that for table size n, histogram size k, maximum relative
1531                  * error in bin size f, and error probability gamma, the minimum
1532                  * random sample size is
1533                  *              r = 4 * k * ln(2*n/gamma) / f^2
1534                  * Taking f = 0.5, gamma = 0.01, n = 1 million rows, we obtain
1535                  *              r = 305.82 * k
1536                  * Note that because of the log function, the dependence on n is
1537                  * quite weak; even at n = 1 billion, a 300*k sample gives <= 0.59
1538                  * bin size error with probability 0.99.  So there's no real need to
1539                  * scale for n, which is a good thing because we don't necessarily
1540                  * know it at this point.
1541                  *--------------------
1542                  */
1543                 stats->minrows = 300 * attr->attstattarget;
1544         }
1545         else
1546         {
1547                 /* Can't do much but the minimal stuff */
1548                 stats->compute_stats = compute_minimal_stats;
1549                 /* Might as well use the same minrows as above */
1550                 stats->minrows = 300 * attr->attstattarget;
1551         }
1552
1553         return true;
1554 }
1555
1556 /*
1557  *      compute_minimal_stats() -- compute minimal column statistics
1558  *
1559  *      We use this when we can find only an "=" operator for the datatype.
1560  *
1561  *      We determine the fraction of non-null rows, the average width, the
1562  *      most common values, and the (estimated) number of distinct values.
1563  *
1564  *      The most common values are determined by brute force: we keep a list
1565  *      of previously seen values, ordered by number of times seen, as we scan
1566  *      the samples.  A newly seen value is inserted just after the last
1567  *      multiply-seen value, causing the bottommost (oldest) singly-seen value
1568  *      to drop off the list.  The accuracy of this method, and also its cost,
1569  *      depend mainly on the length of the list we are willing to keep.
1570  */
1571 static void
1572 compute_minimal_stats(VacAttrStatsP stats,
1573                                           AnalyzeAttrFetchFunc fetchfunc,
1574                                           int samplerows,
1575                                           double totalrows)
1576 {
1577         int                     i;
1578         int                     null_cnt = 0;
1579         int                     nonnull_cnt = 0;
1580         int                     toowide_cnt = 0;
1581         double          total_width = 0;
1582         bool            is_varlena = (!stats->attr->attbyval &&
1583                                                           stats->attr->attlen == -1);
1584         bool            is_varwidth = (!stats->attr->attbyval &&
1585                                                            stats->attr->attlen < 0);
1586         FmgrInfo        f_cmpeq;
1587         typedef struct
1588         {
1589                 Datum           value;
1590                 int                     count;
1591         } TrackItem;
1592         TrackItem  *track;
1593         int                     track_cnt,
1594                                 track_max;
1595         int                     num_mcv = stats->attr->attstattarget;
1596         StdAnalyzeData *mystats = (StdAnalyzeData *) stats->extra_data;
1597
1598         /*
1599          * We track up to 2*n values for an n-element MCV list; but at least 10
1600          */
1601         track_max = 2 * num_mcv;
1602         if (track_max < 10)
1603                 track_max = 10;
1604         track = (TrackItem *) palloc(track_max * sizeof(TrackItem));
1605         track_cnt = 0;
1606
1607         fmgr_info(mystats->eqfunc, &f_cmpeq);
1608
1609         for (i = 0; i < samplerows; i++)
1610         {
1611                 Datum           value;
1612                 bool            isnull;
1613                 bool            match;
1614                 int                     firstcount1,
1615                                         j;
1616
1617                 vacuum_delay_point();
1618
1619                 value = fetchfunc(stats, i, &isnull);
1620
1621                 /* Check for null/nonnull */
1622                 if (isnull)
1623                 {
1624                         null_cnt++;
1625                         continue;
1626                 }
1627                 nonnull_cnt++;
1628
1629                 /*
1630                  * If it's a variable-width field, add up widths for average width
1631                  * calculation.  Note that if the value is toasted, we use the toasted
1632                  * width.  We don't bother with this calculation if it's a fixed-width
1633                  * type.
1634                  */
1635                 if (is_varlena)
1636                 {
1637                         total_width += VARSIZE_ANY(DatumGetPointer(value));
1638
1639                         /*
1640                          * If the value is toasted, we want to detoast it just once to
1641                          * avoid repeated detoastings and resultant excess memory usage
1642                          * during the comparisons.      Also, check to see if the value is
1643                          * excessively wide, and if so don't detoast at all --- just
1644                          * ignore the value.
1645                          */
1646                         if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
1647                         {
1648                                 toowide_cnt++;
1649                                 continue;
1650                         }
1651                         value = PointerGetDatum(PG_DETOAST_DATUM(value));
1652                 }
1653                 else if (is_varwidth)
1654                 {
1655                         /* must be cstring */
1656                         total_width += strlen(DatumGetCString(value)) + 1;
1657                 }
1658
1659                 /*
1660                  * See if the value matches anything we're already tracking.
1661                  */
1662                 match = false;
1663                 firstcount1 = track_cnt;
1664                 for (j = 0; j < track_cnt; j++)
1665                 {
1666                         if (DatumGetBool(FunctionCall2(&f_cmpeq, value, track[j].value)))
1667                         {
1668                                 match = true;
1669                                 break;
1670                         }
1671                         if (j < firstcount1 && track[j].count == 1)
1672                                 firstcount1 = j;
1673                 }
1674
1675                 if (match)
1676                 {
1677                         /* Found a match */
1678                         track[j].count++;
1679                         /* This value may now need to "bubble up" in the track list */
1680                         while (j > 0 && track[j].count > track[j - 1].count)
1681                         {
1682                                 swapDatum(track[j].value, track[j - 1].value);
1683                                 swapInt(track[j].count, track[j - 1].count);
1684                                 j--;
1685                         }
1686                 }
1687                 else
1688                 {
1689                         /* No match.  Insert at head of count-1 list */
1690                         if (track_cnt < track_max)
1691                                 track_cnt++;
1692                         for (j = track_cnt - 1; j > firstcount1; j--)
1693                         {
1694                                 track[j].value = track[j - 1].value;
1695                                 track[j].count = track[j - 1].count;
1696                         }
1697                         if (firstcount1 < track_cnt)
1698                         {
1699                                 track[firstcount1].value = value;
1700                                 track[firstcount1].count = 1;
1701                         }
1702                 }
1703         }
1704
1705         /* We can only compute real stats if we found some non-null values. */
1706         if (nonnull_cnt > 0)
1707         {
1708                 int                     nmultiple,
1709                                         summultiple;
1710
1711                 stats->stats_valid = true;
1712                 /* Do the simple null-frac and width stats */
1713                 stats->stanullfrac = (double) null_cnt / (double) samplerows;
1714                 if (is_varwidth)
1715                         stats->stawidth = total_width / (double) nonnull_cnt;
1716                 else
1717                         stats->stawidth = stats->attrtype->typlen;
1718
1719                 /* Count the number of values we found multiple times */
1720                 summultiple = 0;
1721                 for (nmultiple = 0; nmultiple < track_cnt; nmultiple++)
1722                 {
1723                         if (track[nmultiple].count == 1)
1724                                 break;
1725                         summultiple += track[nmultiple].count;
1726                 }
1727
1728                 if (nmultiple == 0)
1729                 {
1730                         /* If we found no repeated values, assume it's a unique column */
1731                         stats->stadistinct = -1.0;
1732                 }
1733                 else if (track_cnt < track_max && toowide_cnt == 0 &&
1734                                  nmultiple == track_cnt)
1735                 {
1736                         /*
1737                          * Our track list includes every value in the sample, and every
1738                          * value appeared more than once.  Assume the column has just
1739                          * these values.
1740                          */
1741                         stats->stadistinct = track_cnt;
1742                 }
1743                 else
1744                 {
1745                         /*----------
1746                          * Estimate the number of distinct values using the estimator
1747                          * proposed by Haas and Stokes in IBM Research Report RJ 10025:
1748                          *              n*d / (n - f1 + f1*n/N)
1749                          * where f1 is the number of distinct values that occurred
1750                          * exactly once in our sample of n rows (from a total of N),
1751                          * and d is the total number of distinct values in the sample.
1752                          * This is their Duj1 estimator; the other estimators they
1753                          * recommend are considerably more complex, and are numerically
1754                          * very unstable when n is much smaller than N.
1755                          *
1756                          * We assume (not very reliably!) that all the multiply-occurring
1757                          * values are reflected in the final track[] list, and the other
1758                          * nonnull values all appeared but once.  (XXX this usually
1759                          * results in a drastic overestimate of ndistinct.      Can we do
1760                          * any better?)
1761                          *----------
1762                          */
1763                         int                     f1 = nonnull_cnt - summultiple;
1764                         int                     d = f1 + nmultiple;
1765                         double          numer,
1766                                                 denom,
1767                                                 stadistinct;
1768
1769                         numer = (double) samplerows *(double) d;
1770
1771                         denom = (double) (samplerows - f1) +
1772                                 (double) f1 *(double) samplerows / totalrows;
1773
1774                         stadistinct = numer / denom;
1775                         /* Clamp to sane range in case of roundoff error */
1776                         if (stadistinct < (double) d)
1777                                 stadistinct = (double) d;
1778                         if (stadistinct > totalrows)
1779                                 stadistinct = totalrows;
1780                         stats->stadistinct = floor(stadistinct + 0.5);
1781                 }
1782
1783                 /*
1784                  * If we estimated the number of distinct values at more than 10% of
1785                  * the total row count (a very arbitrary limit), then assume that
1786                  * stadistinct should scale with the row count rather than be a fixed
1787                  * value.
1788                  */
1789                 if (stats->stadistinct > 0.1 * totalrows)
1790                         stats->stadistinct = -(stats->stadistinct / totalrows);
1791
1792                 /*
1793                  * Decide how many values are worth storing as most-common values. If
1794                  * we are able to generate a complete MCV list (all the values in the
1795                  * sample will fit, and we think these are all the ones in the table),
1796                  * then do so.  Otherwise, store only those values that are
1797                  * significantly more common than the (estimated) average. We set the
1798                  * threshold rather arbitrarily at 25% more than average, with at
1799                  * least 2 instances in the sample.
1800                  */
1801                 if (track_cnt < track_max && toowide_cnt == 0 &&
1802                         stats->stadistinct > 0 &&
1803                         track_cnt <= num_mcv)
1804                 {
1805                         /* Track list includes all values seen, and all will fit */
1806                         num_mcv = track_cnt;
1807                 }
1808                 else
1809                 {
1810                         double          ndistinct = stats->stadistinct;
1811                         double          avgcount,
1812                                                 mincount;
1813
1814                         if (ndistinct < 0)
1815                                 ndistinct = -ndistinct * totalrows;
1816                         /* estimate # of occurrences in sample of a typical value */
1817                         avgcount = (double) samplerows / ndistinct;
1818                         /* set minimum threshold count to store a value */
1819                         mincount = avgcount * 1.25;
1820                         if (mincount < 2)
1821                                 mincount = 2;
1822                         if (num_mcv > track_cnt)
1823                                 num_mcv = track_cnt;
1824                         for (i = 0; i < num_mcv; i++)
1825                         {
1826                                 if (track[i].count < mincount)
1827                                 {
1828                                         num_mcv = i;
1829                                         break;
1830                                 }
1831                         }
1832                 }
1833
1834                 /* Generate MCV slot entry */
1835                 if (num_mcv > 0)
1836                 {
1837                         MemoryContext old_context;
1838                         Datum      *mcv_values;
1839                         float4     *mcv_freqs;
1840
1841                         /* Must copy the target values into anl_context */
1842                         old_context = MemoryContextSwitchTo(stats->anl_context);
1843                         mcv_values = (Datum *) palloc(num_mcv * sizeof(Datum));
1844                         mcv_freqs = (float4 *) palloc(num_mcv * sizeof(float4));
1845                         for (i = 0; i < num_mcv; i++)
1846                         {
1847                                 mcv_values[i] = datumCopy(track[i].value,
1848                                                                                   stats->attr->attbyval,
1849                                                                                   stats->attr->attlen);
1850                                 mcv_freqs[i] = (double) track[i].count / (double) samplerows;
1851                         }
1852                         MemoryContextSwitchTo(old_context);
1853
1854                         stats->stakind[0] = STATISTIC_KIND_MCV;
1855                         stats->staop[0] = mystats->eqopr;
1856                         stats->stanumbers[0] = mcv_freqs;
1857                         stats->numnumbers[0] = num_mcv;
1858                         stats->stavalues[0] = mcv_values;
1859                         stats->numvalues[0] = num_mcv;
1860                         /*
1861                          * Accept the defaults for stats->statypid and others.
1862                          * They have been set before we were called (see vacuum.h)
1863                          */
1864                 }
1865         }
1866         else if (null_cnt > 0)
1867         {
1868                 /* We found only nulls; assume the column is entirely null */
1869                 stats->stats_valid = true;
1870                 stats->stanullfrac = 1.0;
1871                 if (is_varwidth)
1872                         stats->stawidth = 0;    /* "unknown" */
1873                 else
1874                         stats->stawidth = stats->attrtype->typlen;
1875                 stats->stadistinct = 0.0;               /* "unknown" */
1876         }
1877
1878         /* We don't need to bother cleaning up any of our temporary palloc's */
1879 }
1880
1881
1882 /*
1883  *      compute_scalar_stats() -- compute column statistics
1884  *
1885  *      We use this when we can find "=" and "<" operators for the datatype.
1886  *
1887  *      We determine the fraction of non-null rows, the average width, the
1888  *      most common values, the (estimated) number of distinct values, the
1889  *      distribution histogram, and the correlation of physical to logical order.
1890  *
1891  *      The desired stats can be determined fairly easily after sorting the
1892  *      data values into order.
1893  */
1894 static void
1895 compute_scalar_stats(VacAttrStatsP stats,
1896                                          AnalyzeAttrFetchFunc fetchfunc,
1897                                          int samplerows,
1898                                          double totalrows)
1899 {
1900         int                     i;
1901         int                     null_cnt = 0;
1902         int                     nonnull_cnt = 0;
1903         int                     toowide_cnt = 0;
1904         double          total_width = 0;
1905         bool            is_varlena = (!stats->attr->attbyval &&
1906                                                           stats->attr->attlen == -1);
1907         bool            is_varwidth = (!stats->attr->attbyval &&
1908                                                            stats->attr->attlen < 0);
1909         double          corr_xysum;
1910         Oid                     cmpFn;
1911         int                     cmpFlags;
1912         FmgrInfo        f_cmpfn;
1913         ScalarItem *values;
1914         int                     values_cnt = 0;
1915         int                *tupnoLink;
1916         ScalarMCVItem *track;
1917         int                     track_cnt = 0;
1918         int                     num_mcv = stats->attr->attstattarget;
1919         int                     num_bins = stats->attr->attstattarget;
1920         StdAnalyzeData *mystats = (StdAnalyzeData *) stats->extra_data;
1921
1922         values = (ScalarItem *) palloc(samplerows * sizeof(ScalarItem));
1923         tupnoLink = (int *) palloc(samplerows * sizeof(int));
1924         track = (ScalarMCVItem *) palloc(num_mcv * sizeof(ScalarMCVItem));
1925
1926         SelectSortFunction(mystats->ltopr, false, &cmpFn, &cmpFlags);
1927         fmgr_info(cmpFn, &f_cmpfn);
1928
1929         /* Initial scan to find sortable values */
1930         for (i = 0; i < samplerows; i++)
1931         {
1932                 Datum           value;
1933                 bool            isnull;
1934
1935                 vacuum_delay_point();
1936
1937                 value = fetchfunc(stats, i, &isnull);
1938
1939                 /* Check for null/nonnull */
1940                 if (isnull)
1941                 {
1942                         null_cnt++;
1943                         continue;
1944                 }
1945                 nonnull_cnt++;
1946
1947                 /*
1948                  * If it's a variable-width field, add up widths for average width
1949                  * calculation.  Note that if the value is toasted, we use the toasted
1950                  * width.  We don't bother with this calculation if it's a fixed-width
1951                  * type.
1952                  */
1953                 if (is_varlena)
1954                 {
1955                         total_width += VARSIZE_ANY(DatumGetPointer(value));
1956
1957                         /*
1958                          * If the value is toasted, we want to detoast it just once to
1959                          * avoid repeated detoastings and resultant excess memory usage
1960                          * during the comparisons.      Also, check to see if the value is
1961                          * excessively wide, and if so don't detoast at all --- just
1962                          * ignore the value.
1963                          */
1964                         if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
1965                         {
1966                                 toowide_cnt++;
1967                                 continue;
1968                         }
1969                         value = PointerGetDatum(PG_DETOAST_DATUM(value));
1970                 }
1971                 else if (is_varwidth)
1972                 {
1973                         /* must be cstring */
1974                         total_width += strlen(DatumGetCString(value)) + 1;
1975                 }
1976
1977                 /* Add it to the list to be sorted */
1978                 values[values_cnt].value = value;
1979                 values[values_cnt].tupno = values_cnt;
1980                 tupnoLink[values_cnt] = values_cnt;
1981                 values_cnt++;
1982         }
1983
1984         /* We can only compute real stats if we found some sortable values. */
1985         if (values_cnt > 0)
1986         {
1987                 int                     ndistinct,      /* # distinct values in sample */
1988                                         nmultiple,      /* # that appear multiple times */
1989                                         num_hist,
1990                                         dups_cnt;
1991                 int                     slot_idx = 0;
1992                 CompareScalarsContext cxt;
1993
1994                 /* Sort the collected values */
1995                 cxt.cmpFn = &f_cmpfn;
1996                 cxt.cmpFlags = cmpFlags;
1997                 cxt.tupnoLink = tupnoLink;
1998                 qsort_arg((void *) values, values_cnt, sizeof(ScalarItem),
1999                                   compare_scalars, (void *) &cxt);
2000
2001                 /*
2002                  * Now scan the values in order, find the most common ones, and also
2003                  * accumulate ordering-correlation statistics.
2004                  *
2005                  * To determine which are most common, we first have to count the
2006                  * number of duplicates of each value.  The duplicates are adjacent in
2007                  * the sorted list, so a brute-force approach is to compare successive
2008                  * datum values until we find two that are not equal. However, that
2009                  * requires N-1 invocations of the datum comparison routine, which are
2010                  * completely redundant with work that was done during the sort.  (The
2011                  * sort algorithm must at some point have compared each pair of items
2012                  * that are adjacent in the sorted order; otherwise it could not know
2013                  * that it's ordered the pair correctly.) We exploit this by having
2014                  * compare_scalars remember the highest tupno index that each
2015                  * ScalarItem has been found equal to.  At the end of the sort, a
2016                  * ScalarItem's tupnoLink will still point to itself if and only if it
2017                  * is the last item of its group of duplicates (since the group will
2018                  * be ordered by tupno).
2019                  */
2020                 corr_xysum = 0;
2021                 ndistinct = 0;
2022                 nmultiple = 0;
2023                 dups_cnt = 0;
2024                 for (i = 0; i < values_cnt; i++)
2025                 {
2026                         int                     tupno = values[i].tupno;
2027
2028                         corr_xysum += ((double) i) * ((double) tupno);
2029                         dups_cnt++;
2030                         if (tupnoLink[tupno] == tupno)
2031                         {
2032                                 /* Reached end of duplicates of this value */
2033                                 ndistinct++;
2034                                 if (dups_cnt > 1)
2035                                 {
2036                                         nmultiple++;
2037                                         if (track_cnt < num_mcv ||
2038                                                 dups_cnt > track[track_cnt - 1].count)
2039                                         {
2040                                                 /*
2041                                                  * Found a new item for the mcv list; find its
2042                                                  * position, bubbling down old items if needed. Loop
2043                                                  * invariant is that j points at an empty/ replaceable
2044                                                  * slot.
2045                                                  */
2046                                                 int                     j;
2047
2048                                                 if (track_cnt < num_mcv)
2049                                                         track_cnt++;
2050                                                 for (j = track_cnt - 1; j > 0; j--)
2051                                                 {
2052                                                         if (dups_cnt <= track[j - 1].count)
2053                                                                 break;
2054                                                         track[j].count = track[j - 1].count;
2055                                                         track[j].first = track[j - 1].first;
2056                                                 }
2057                                                 track[j].count = dups_cnt;
2058                                                 track[j].first = i + 1 - dups_cnt;
2059                                         }
2060                                 }
2061                                 dups_cnt = 0;
2062                         }
2063                 }
2064
2065                 stats->stats_valid = true;
2066                 /* Do the simple null-frac and width stats */
2067                 stats->stanullfrac = (double) null_cnt / (double) samplerows;
2068                 if (is_varwidth)
2069                         stats->stawidth = total_width / (double) nonnull_cnt;
2070                 else
2071                         stats->stawidth = stats->attrtype->typlen;
2072
2073                 if (nmultiple == 0)
2074                 {
2075                         /* If we found no repeated values, assume it's a unique column */
2076                         stats->stadistinct = -1.0;
2077                 }
2078                 else if (toowide_cnt == 0 && nmultiple == ndistinct)
2079                 {
2080                         /*
2081                          * Every value in the sample appeared more than once.  Assume the
2082                          * column has just these values.
2083                          */
2084                         stats->stadistinct = ndistinct;
2085                 }
2086                 else
2087                 {
2088                         /*----------
2089                          * Estimate the number of distinct values using the estimator
2090                          * proposed by Haas and Stokes in IBM Research Report RJ 10025:
2091                          *              n*d / (n - f1 + f1*n/N)
2092                          * where f1 is the number of distinct values that occurred
2093                          * exactly once in our sample of n rows (from a total of N),
2094                          * and d is the total number of distinct values in the sample.
2095                          * This is their Duj1 estimator; the other estimators they
2096                          * recommend are considerably more complex, and are numerically
2097                          * very unstable when n is much smaller than N.
2098                          *
2099                          * Overwidth values are assumed to have been distinct.
2100                          *----------
2101                          */
2102                         int                     f1 = ndistinct - nmultiple + toowide_cnt;
2103                         int                     d = f1 + nmultiple;
2104                         double          numer,
2105                                                 denom,
2106                                                 stadistinct;
2107
2108                         numer = (double) samplerows *(double) d;
2109
2110                         denom = (double) (samplerows - f1) +
2111                                 (double) f1 *(double) samplerows / totalrows;
2112
2113                         stadistinct = numer / denom;
2114                         /* Clamp to sane range in case of roundoff error */
2115                         if (stadistinct < (double) d)
2116                                 stadistinct = (double) d;
2117                         if (stadistinct > totalrows)
2118                                 stadistinct = totalrows;
2119                         stats->stadistinct = floor(stadistinct + 0.5);
2120                 }
2121
2122                 /*
2123                  * If we estimated the number of distinct values at more than 10% of
2124                  * the total row count (a very arbitrary limit), then assume that
2125                  * stadistinct should scale with the row count rather than be a fixed
2126                  * value.
2127                  */
2128                 if (stats->stadistinct > 0.1 * totalrows)
2129                         stats->stadistinct = -(stats->stadistinct / totalrows);
2130
2131                 /*
2132                  * Decide how many values are worth storing as most-common values. If
2133                  * we are able to generate a complete MCV list (all the values in the
2134                  * sample will fit, and we think these are all the ones in the table),
2135                  * then do so.  Otherwise, store only those values that are
2136                  * significantly more common than the (estimated) average. We set the
2137                  * threshold rather arbitrarily at 25% more than average, with at
2138                  * least 2 instances in the sample.  Also, we won't suppress values
2139                  * that have a frequency of at least 1/K where K is the intended
2140                  * number of histogram bins; such values might otherwise cause us to
2141                  * emit duplicate histogram bin boundaries.
2142                  */
2143                 if (track_cnt == ndistinct && toowide_cnt == 0 &&
2144                         stats->stadistinct > 0 &&
2145                         track_cnt <= num_mcv)
2146                 {
2147                         /* Track list includes all values seen, and all will fit */
2148                         num_mcv = track_cnt;
2149                 }
2150                 else
2151                 {
2152                         double          ndistinct = stats->stadistinct;
2153                         double          avgcount,
2154                                                 mincount,
2155                                                 maxmincount;
2156
2157                         if (ndistinct < 0)
2158                                 ndistinct = -ndistinct * totalrows;
2159                         /* estimate # of occurrences in sample of a typical value */
2160                         avgcount = (double) samplerows / ndistinct;
2161                         /* set minimum threshold count to store a value */
2162                         mincount = avgcount * 1.25;
2163                         if (mincount < 2)
2164                                 mincount = 2;
2165                         /* don't let threshold exceed 1/K, however */
2166                         maxmincount = (double) samplerows / (double) num_bins;
2167                         if (mincount > maxmincount)
2168                                 mincount = maxmincount;
2169                         if (num_mcv > track_cnt)
2170                                 num_mcv = track_cnt;
2171                         for (i = 0; i < num_mcv; i++)
2172                         {
2173                                 if (track[i].count < mincount)
2174                                 {
2175                                         num_mcv = i;
2176                                         break;
2177                                 }
2178                         }
2179                 }
2180
2181                 /* Generate MCV slot entry */
2182                 if (num_mcv > 0)
2183                 {
2184                         MemoryContext old_context;
2185                         Datum      *mcv_values;
2186                         float4     *mcv_freqs;
2187
2188                         /* Must copy the target values into anl_context */
2189                         old_context = MemoryContextSwitchTo(stats->anl_context);
2190                         mcv_values = (Datum *) palloc(num_mcv * sizeof(Datum));
2191                         mcv_freqs = (float4 *) palloc(num_mcv * sizeof(float4));
2192                         for (i = 0; i < num_mcv; i++)
2193                         {
2194                                 mcv_values[i] = datumCopy(values[track[i].first].value,
2195                                                                                   stats->attr->attbyval,
2196                                                                                   stats->attr->attlen);
2197                                 mcv_freqs[i] = (double) track[i].count / (double) samplerows;
2198                         }
2199                         MemoryContextSwitchTo(old_context);
2200
2201                         stats->stakind[slot_idx] = STATISTIC_KIND_MCV;
2202                         stats->staop[slot_idx] = mystats->eqopr;
2203                         stats->stanumbers[slot_idx] = mcv_freqs;
2204                         stats->numnumbers[slot_idx] = num_mcv;
2205                         stats->stavalues[slot_idx] = mcv_values;
2206                         stats->numvalues[slot_idx] = num_mcv;
2207                         /*
2208                          * Accept the defaults for stats->statypid and others.
2209                          * They have been set before we were called (see vacuum.h)
2210                          */
2211                         slot_idx++;
2212                 }
2213
2214                 /*
2215                  * Generate a histogram slot entry if there are at least two distinct
2216                  * values not accounted for in the MCV list.  (This ensures the
2217                  * histogram won't collapse to empty or a singleton.)
2218                  */
2219                 num_hist = ndistinct - num_mcv;
2220                 if (num_hist > num_bins)
2221                         num_hist = num_bins + 1;
2222                 if (num_hist >= 2)
2223                 {
2224                         MemoryContext old_context;
2225                         Datum      *hist_values;
2226                         int                     nvals;
2227
2228                         /* Sort the MCV items into position order to speed next loop */
2229                         qsort((void *) track, num_mcv,
2230                                   sizeof(ScalarMCVItem), compare_mcvs);
2231
2232                         /*
2233                          * Collapse out the MCV items from the values[] array.
2234                          *
2235                          * Note we destroy the values[] array here... but we don't need it
2236                          * for anything more.  We do, however, still need values_cnt.
2237                          * nvals will be the number of remaining entries in values[].
2238                          */
2239                         if (num_mcv > 0)
2240                         {
2241                                 int                     src,
2242                                                         dest;
2243                                 int                     j;
2244
2245                                 src = dest = 0;
2246                                 j = 0;                  /* index of next interesting MCV item */
2247                                 while (src < values_cnt)
2248                                 {
2249                                         int                     ncopy;
2250
2251                                         if (j < num_mcv)
2252                                         {
2253                                                 int                     first = track[j].first;
2254
2255                                                 if (src >= first)
2256                                                 {
2257                                                         /* advance past this MCV item */
2258                                                         src = first + track[j].count;
2259                                                         j++;
2260                                                         continue;
2261                                                 }
2262                                                 ncopy = first - src;
2263                                         }
2264                                         else
2265                                                 ncopy = values_cnt - src;
2266                                         memmove(&values[dest], &values[src],
2267                                                         ncopy * sizeof(ScalarItem));
2268                                         src += ncopy;
2269                                         dest += ncopy;
2270                                 }
2271                                 nvals = dest;
2272                         }
2273                         else
2274                                 nvals = values_cnt;
2275                         Assert(nvals >= num_hist);
2276
2277                         /* Must copy the target values into anl_context */
2278                         old_context = MemoryContextSwitchTo(stats->anl_context);
2279                         hist_values = (Datum *) palloc(num_hist * sizeof(Datum));
2280                         for (i = 0; i < num_hist; i++)
2281                         {
2282                                 int                     pos;
2283
2284                                 pos = (i * (nvals - 1)) / (num_hist - 1);
2285                                 hist_values[i] = datumCopy(values[pos].value,
2286                                                                                    stats->attr->attbyval,
2287                                                                                    stats->attr->attlen);
2288                         }
2289                         MemoryContextSwitchTo(old_context);
2290
2291                         stats->stakind[slot_idx] = STATISTIC_KIND_HISTOGRAM;
2292                         stats->staop[slot_idx] = mystats->ltopr;
2293                         stats->stavalues[slot_idx] = hist_values;
2294                         stats->numvalues[slot_idx] = num_hist;
2295                         /*
2296                          * Accept the defaults for stats->statypid and others.
2297                          * They have been set before we were called (see vacuum.h)
2298                          */
2299                         slot_idx++;
2300                 }
2301
2302                 /* Generate a correlation entry if there are multiple values */
2303                 if (values_cnt > 1)
2304                 {
2305                         MemoryContext old_context;
2306                         float4     *corrs;
2307                         double          corr_xsum,
2308                                                 corr_x2sum;
2309
2310                         /* Must copy the target values into anl_context */
2311                         old_context = MemoryContextSwitchTo(stats->anl_context);
2312                         corrs = (float4 *) palloc(sizeof(float4));
2313                         MemoryContextSwitchTo(old_context);
2314
2315                         /*----------
2316                          * Since we know the x and y value sets are both
2317                          *              0, 1, ..., values_cnt-1
2318                          * we have sum(x) = sum(y) =
2319                          *              (values_cnt-1)*values_cnt / 2
2320                          * and sum(x^2) = sum(y^2) =
2321                          *              (values_cnt-1)*values_cnt*(2*values_cnt-1) / 6.
2322                          *----------
2323                          */
2324                         corr_xsum = ((double) (values_cnt - 1)) *
2325                                 ((double) values_cnt) / 2.0;
2326                         corr_x2sum = ((double) (values_cnt - 1)) *
2327                                 ((double) values_cnt) * (double) (2 * values_cnt - 1) / 6.0;
2328
2329                         /* And the correlation coefficient reduces to */
2330                         corrs[0] = (values_cnt * corr_xysum - corr_xsum * corr_xsum) /
2331                                 (values_cnt * corr_x2sum - corr_xsum * corr_xsum);
2332
2333                         stats->stakind[slot_idx] = STATISTIC_KIND_CORRELATION;
2334                         stats->staop[slot_idx] = mystats->ltopr;
2335                         stats->stanumbers[slot_idx] = corrs;
2336                         stats->numnumbers[slot_idx] = 1;
2337                         slot_idx++;
2338                 }
2339         }
2340         else if (nonnull_cnt == 0 && null_cnt > 0)
2341         {
2342                 /* We found only nulls; assume the column is entirely null */
2343                 stats->stats_valid = true;
2344                 stats->stanullfrac = 1.0;
2345                 if (is_varwidth)
2346                         stats->stawidth = 0;    /* "unknown" */
2347                 else
2348                         stats->stawidth = stats->attrtype->typlen;
2349                 stats->stadistinct = 0.0;               /* "unknown" */
2350         }
2351
2352         /* We don't need to bother cleaning up any of our temporary palloc's */
2353 }
2354
2355 /*
2356  * qsort_arg comparator for sorting ScalarItems
2357  *
2358  * Aside from sorting the items, we update the tupnoLink[] array
2359  * whenever two ScalarItems are found to contain equal datums.  The array
2360  * is indexed by tupno; for each ScalarItem, it contains the highest
2361  * tupno that that item's datum has been found to be equal to.  This allows
2362  * us to avoid additional comparisons in compute_scalar_stats().
2363  */
2364 static int
2365 compare_scalars(const void *a, const void *b, void *arg)
2366 {
2367         Datum           da = ((ScalarItem *) a)->value;
2368         int                     ta = ((ScalarItem *) a)->tupno;
2369         Datum           db = ((ScalarItem *) b)->value;
2370         int                     tb = ((ScalarItem *) b)->tupno;
2371         CompareScalarsContext *cxt = (CompareScalarsContext *) arg;
2372         int32           compare;
2373
2374         compare = ApplySortFunction(cxt->cmpFn, cxt->cmpFlags,
2375                                                                 da, false, db, false);
2376         if (compare != 0)
2377                 return compare;
2378
2379         /*
2380          * The two datums are equal, so update cxt->tupnoLink[].
2381          */
2382         if (cxt->tupnoLink[ta] < tb)
2383                 cxt->tupnoLink[ta] = tb;
2384         if (cxt->tupnoLink[tb] < ta)
2385                 cxt->tupnoLink[tb] = ta;
2386
2387         /*
2388          * For equal datums, sort by tupno
2389          */
2390         return ta - tb;
2391 }
2392
2393 /*
2394  * qsort comparator for sorting ScalarMCVItems by position
2395  */
2396 static int
2397 compare_mcvs(const void *a, const void *b)
2398 {
2399         int                     da = ((ScalarMCVItem *) a)->first;
2400         int                     db = ((ScalarMCVItem *) b)->first;
2401
2402         return da - db;
2403 }