granicus.if.org Git - postgresql/blob - src/backend/utils/adt/selfuncs.c

   1 /*-------------------------------------------------------------------------
   2  *
   3  * selfuncs.c
   4  *        Selectivity functions and index cost estimation functions for
   5  *        standard operators and index access methods.
   6  *
   7  *        Selectivity routines are registered in the pg_operator catalog
   8  *        in the "oprrest" and "oprjoin" attributes.
   9  *
  10  *        Index cost functions are registered in the pg_am catalog
  11  *        in the "amcostestimate" attribute.
  12  *
  13  * Portions Copyright (c) 1996-2011, PostgreSQL Global Development Group
  14  * Portions Copyright (c) 1994, Regents of the University of California
  15  *
  16  *
  17  * IDENTIFICATION
  18  *        src/backend/utils/adt/selfuncs.c
  19  *
  20  *-------------------------------------------------------------------------
  21  */
  22
  23 /*----------
  24  * Operator selectivity estimation functions are called to estimate the
  25  * selectivity of WHERE clauses whose top-level operator is their operator.
  26  * We divide the problem into two cases:
  27  *              Restriction clause estimation: the clause involves vars of just
  28  *                      one relation.
  29  *              Join clause estimation: the clause involves vars of multiple rels.
  30  * Join selectivity estimation is far more difficult and usually less accurate
  31  * than restriction estimation.
  32  *
  33  * When dealing with the inner scan of a nestloop join, we consider the
  34  * join's joinclauses as restriction clauses for the inner relation, and
  35  * treat vars of the outer relation as parameters (a/k/a constants of unknown
  36  * values).  So, restriction estimators need to be able to accept an argument
  37  * telling which relation is to be treated as the variable.
  38  *
  39  * The call convention for a restriction estimator (oprrest function) is
  40  *
  41  *              Selectivity oprrest (PlannerInfo *root,
  42  *                                                       Oid operator,
  43  *                                                       List *args,
  44  *                                                       int varRelid);
  45  *
  46  * root: general information about the query (rtable and RelOptInfo lists
  47  * are particularly important for the estimator).
  48  * operator: OID of the specific operator in question.
  49  * args: argument list from the operator clause.
  50  * varRelid: if not zero, the relid (rtable index) of the relation to
  51  * be treated as the variable relation.  May be zero if the args list
  52  * is known to contain vars of only one relation.
  53  *
  54  * This is represented at the SQL level (in pg_proc) as
  55  *
  56  *              float8 oprrest (internal, oid, internal, int4);
  57  *
  58  * The result is a selectivity, that is, a fraction (0 to 1) of the rows
  59  * of the relation that are expected to produce a TRUE result for the
  60  * given operator.
  61  *
  62  * The call convention for a join estimator (oprjoin function) is similar
  63  * except that varRelid is not needed, and instead join information is
  64  * supplied:
  65  *
  66  *              Selectivity oprjoin (PlannerInfo *root,
  67  *                                                       Oid operator,
  68  *                                                       List *args,
  69  *                                                       JoinType jointype,
  70  *                                                       SpecialJoinInfo *sjinfo);
  71  *
  72  *              float8 oprjoin (internal, oid, internal, int2, internal);
  73  *
  74  * (Before Postgres 8.4, join estimators had only the first four of these
  75  * parameters.  That signature is still allowed, but deprecated.)  The
  76  * relationship between jointype and sjinfo is explained in the comments for
  77  * clause_selectivity() --- the short version is that jointype is usually
  78  * best ignored in favor of examining sjinfo.
  79  *
  80  * Join selectivity for regular inner and outer joins is defined as the
  81  * fraction (0 to 1) of the cross product of the relations that is expected
  82  * to produce a TRUE result for the given operator.  For both semi and anti
  83  * joins, however, the selectivity is defined as the fraction of the left-hand
  84  * side relation's rows that are expected to have a match (ie, at least one
  85  * row with a TRUE result) in the right-hand side.
  86  *----------
  87  */
  88
  89 #include "postgres.h"
  90
  91 #include <ctype.h>
  92 #include <math.h>
  93
  94 #include "access/gin.h"
  95 #include "access/sysattr.h"
  96 #include "catalog/index.h"
  97 #include "catalog/pg_collation.h"
  98 #include "catalog/pg_opfamily.h"
  99 #include "catalog/pg_statistic.h"
 100 #include "catalog/pg_type.h"
 101 #include "executor/executor.h"
 102 #include "mb/pg_wchar.h"
 103 #include "nodes/makefuncs.h"
 104 #include "nodes/nodeFuncs.h"
 105 #include "optimizer/clauses.h"
 106 #include "optimizer/cost.h"
 107 #include "optimizer/pathnode.h"
 108 #include "optimizer/paths.h"
 109 #include "optimizer/plancat.h"
 110 #include "optimizer/predtest.h"
 111 #include "optimizer/restrictinfo.h"
 112 #include "optimizer/var.h"
 113 #include "parser/parse_coerce.h"
 114 #include "parser/parsetree.h"
 115 #include "utils/builtins.h"
 116 #include "utils/bytea.h"
 117 #include "utils/date.h"
 118 #include "utils/datum.h"
 119 #include "utils/fmgroids.h"
 120 #include "utils/lsyscache.h"
 121 #include "utils/nabstime.h"
 122 #include "utils/pg_locale.h"
 123 #include "utils/selfuncs.h"
 124 #include "utils/spccache.h"
 125 #include "utils/syscache.h"
 126 #include "utils/tqual.h"
 127
 128
 129 /* Hooks for plugins to get control when we ask for stats */
 130 get_relation_stats_hook_type get_relation_stats_hook = NULL;
 131 get_index_stats_hook_type get_index_stats_hook = NULL;
 132
 133 static double var_eq_const(VariableStatData *vardata, Oid operator,
 134                          Datum constval, bool constisnull,
 135                          bool varonleft);
 136 static double var_eq_non_const(VariableStatData *vardata, Oid operator,
 137                                  Node *other,
 138                                  bool varonleft);
 139 static double ineq_histogram_selectivity(PlannerInfo *root,
 140                                                    VariableStatData *vardata,
 141                                                    FmgrInfo *opproc, bool isgt,
 142                                                    Datum constval, Oid consttype);
 143 static double eqjoinsel_inner(Oid operator,
 144                                 VariableStatData *vardata1, VariableStatData *vardata2);
 145 static double eqjoinsel_semi(Oid operator,
 146                            VariableStatData *vardata1, VariableStatData *vardata2);
 147 static bool convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
 148                                   Datum lobound, Datum hibound, Oid boundstypid,
 149                                   double *scaledlobound, double *scaledhibound);
 150 static double convert_numeric_to_scalar(Datum value, Oid typid);
 151 static void convert_string_to_scalar(char *value,
 152                                                  double *scaledvalue,
 153                                                  char *lobound,
 154                                                  double *scaledlobound,
 155                                                  char *hibound,
 156                                                  double *scaledhibound);
 157 static void convert_bytea_to_scalar(Datum value,
 158                                                 double *scaledvalue,
 159                                                 Datum lobound,
 160                                                 double *scaledlobound,
 161                                                 Datum hibound,
 162                                                 double *scaledhibound);
 163 static double convert_one_string_to_scalar(char *value,
 164                                                          int rangelo, int rangehi);
 165 static double convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
 166                                                         int rangelo, int rangehi);
 167 static char *convert_string_datum(Datum value, Oid typid);
 168 static double convert_timevalue_to_scalar(Datum value, Oid typid);
 169 static bool get_variable_range(PlannerInfo *root, VariableStatData *vardata,
 170                                    Oid sortop, Datum *min, Datum *max);
 171 static bool get_actual_variable_range(PlannerInfo *root,
 172                                                   VariableStatData *vardata,
 173                                                   Oid sortop,
 174                                                   Datum *min, Datum *max);
 175 static Selectivity prefix_selectivity(PlannerInfo *root,
 176                                    VariableStatData *vardata,
 177                                    Oid vartype, Oid opfamily, Const *prefixcon);
 178 static Selectivity pattern_selectivity(Const *patt, Pattern_Type ptype);
 179 static Datum string_to_datum(const char *str, Oid datatype);
 180 static Const *string_to_const(const char *str, Oid datatype);
 181 static Const *string_to_bytea_const(const char *str, size_t str_len);
 182
 183
 184 /*
 185  *              eqsel                   - Selectivity of "=" for any data types.
 186  *
 187  * Note: this routine is also used to estimate selectivity for some
 188  * operators that are not "=" but have comparable selectivity behavior,
 189  * such as "~=" (geometric approximate-match).  Even for "=", we must
 190  * keep in mind that the left and right datatypes may differ.
 191  */
 192 Datum
 193 eqsel(PG_FUNCTION_ARGS)
 194 {
 195         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
 196         Oid                     operator = PG_GETARG_OID(1);
 197         List       *args = (List *) PG_GETARG_POINTER(2);
 198         int                     varRelid = PG_GETARG_INT32(3);
 199         VariableStatData vardata;
 200         Node       *other;
 201         bool            varonleft;
 202         double          selec;
 203
 204         /*
 205          * If expression is not variable = something or something = variable, then
 206          * punt and return a default estimate.
 207          */
 208         if (!get_restriction_variable(root, args, varRelid,
 209                                                                   &vardata, &other, &varonleft))
 210                 PG_RETURN_FLOAT8(DEFAULT_EQ_SEL);
 211
 212         /*
 213          * We can do a lot better if the something is a constant.  (Note: the
 214          * Const might result from estimation rather than being a simple constant
 215          * in the query.)
 216          */
 217         if (IsA(other, Const))
 218                 selec = var_eq_const(&vardata, operator,
 219                                                          ((Const *) other)->constvalue,
 220                                                          ((Const *) other)->constisnull,
 221                                                          varonleft);
 222         else
 223                 selec = var_eq_non_const(&vardata, operator, other,
 224                                                                  varonleft);
 225
 226         ReleaseVariableStats(vardata);
 227
 228         PG_RETURN_FLOAT8((float8) selec);
 229 }
 230
 231 /*
 232  * var_eq_const --- eqsel for var = const case
 233  *
 234  * This is split out so that some other estimation functions can use it.
 235  */
 236 static double
 237 var_eq_const(VariableStatData *vardata, Oid operator,
 238                          Datum constval, bool constisnull,
 239                          bool varonleft)
 240 {
 241         double          selec;
 242
 243         /*
 244          * If the constant is NULL, assume operator is strict and return zero, ie,
 245          * operator will never return TRUE.
 246          */
 247         if (constisnull)
 248                 return 0.0;
 249
 250         /*
 251          * If we matched the var to a unique index, assume there is exactly one
 252          * match regardless of anything else.  (This is slightly bogus, since the
 253          * index's equality operator might be different from ours, but it's more
 254          * likely to be right than ignoring the information.)
 255          */
 256         if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
 257                 return 1.0 / vardata->rel->tuples;
 258
 259         if (HeapTupleIsValid(vardata->statsTuple))
 260         {
 261                 Form_pg_statistic stats;
 262                 Datum      *values;
 263                 int                     nvalues;
 264                 float4     *numbers;
 265                 int                     nnumbers;
 266                 bool            match = false;
 267                 int                     i;
 268
 269                 stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
 270
 271                 /*
 272                  * Is the constant "=" to any of the column's most common values?
 273                  * (Although the given operator may not really be "=", we will assume
 274                  * that seeing whether it returns TRUE is an appropriate test.  If you
 275                  * don't like this, maybe you shouldn't be using eqsel for your
 276                  * operator...)
 277                  */
 278                 if (get_attstatsslot(vardata->statsTuple,
 279                                                          vardata->atttype, vardata->atttypmod,
 280                                                          STATISTIC_KIND_MCV, InvalidOid,
 281                                                          NULL,
 282                                                          &values, &nvalues,
 283                                                          &numbers, &nnumbers))
 284                 {
 285                         FmgrInfo        eqproc;
 286
 287                         fmgr_info(get_opcode(operator), &eqproc);
 288                         fmgr_info_set_collation(DEFAULT_COLLATION_OID, &eqproc);
 289
 290                         for (i = 0; i < nvalues; i++)
 291                         {
 292                                 /* be careful to apply operator right way 'round */
 293                                 if (varonleft)
 294                                         match = DatumGetBool(FunctionCall2(&eqproc,
 295                                                                                                            values[i],
 296                                                                                                            constval));
 297                                 else
 298                                         match = DatumGetBool(FunctionCall2(&eqproc,
 299                                                                                                            constval,
 300                                                                                                            values[i]));
 301                                 if (match)
 302                                         break;
 303                         }
 304                 }
 305                 else
 306                 {
 307                         /* no most-common-value info available */
 308                         values = NULL;
 309                         numbers = NULL;
 310                         i = nvalues = nnumbers = 0;
 311                 }
 312
 313                 if (match)
 314                 {
 315                         /*
 316                          * Constant is "=" to this common value.  We know selectivity
 317                          * exactly (or as exactly as ANALYZE could calculate it, anyway).
 318                          */
 319                         selec = numbers[i];
 320                 }
 321                 else
 322                 {
 323                         /*
 324                          * Comparison is against a constant that is neither NULL nor any
 325                          * of the common values.  Its selectivity cannot be more than
 326                          * this:
 327                          */
 328                         double          sumcommon = 0.0;
 329                         double          otherdistinct;
 330
 331                         for (i = 0; i < nnumbers; i++)
 332                                 sumcommon += numbers[i];
 333                         selec = 1.0 - sumcommon - stats->stanullfrac;
 334                         CLAMP_PROBABILITY(selec);
 335
 336                         /*
 337                          * and in fact it's probably a good deal less. We approximate that
 338                          * all the not-common values share this remaining fraction
 339                          * equally, so we divide by the number of other distinct values.
 340                          */
 341                         otherdistinct = get_variable_numdistinct(vardata) - nnumbers;
 342                         if (otherdistinct > 1)
 343                                 selec /= otherdistinct;
 344
 345                         /*
 346                          * Another cross-check: selectivity shouldn't be estimated as more
 347                          * than the least common "most common value".
 348                          */
 349                         if (nnumbers > 0 && selec > numbers[nnumbers - 1])
 350                                 selec = numbers[nnumbers - 1];
 351                 }
 352
 353                 free_attstatsslot(vardata->atttype, values, nvalues,
 354                                                   numbers, nnumbers);
 355         }
 356         else
 357         {
 358                 /*
 359                  * No ANALYZE stats available, so make a guess using estimated number
 360                  * of distinct values and assuming they are equally common. (The guess
 361                  * is unlikely to be very good, but we do know a few special cases.)
 362                  */
 363                 selec = 1.0 / get_variable_numdistinct(vardata);
 364         }
 365
 366         /* result should be in range, but make sure... */
 367         CLAMP_PROBABILITY(selec);
 368
 369         return selec;
 370 }
 371
 372 /*
 373  * var_eq_non_const --- eqsel for var = something-other-than-const case
 374  */
 375 static double
 376 var_eq_non_const(VariableStatData *vardata, Oid operator,
 377                                  Node *other,
 378                                  bool varonleft)
 379 {
 380         double          selec;
 381
 382         /*
 383          * If we matched the var to a unique index, assume there is exactly one
 384          * match regardless of anything else.  (This is slightly bogus, since the
 385          * index's equality operator might be different from ours, but it's more
 386          * likely to be right than ignoring the information.)
 387          */
 388         if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
 389                 return 1.0 / vardata->rel->tuples;
 390
 391         if (HeapTupleIsValid(vardata->statsTuple))
 392         {
 393                 Form_pg_statistic stats;
 394                 double          ndistinct;
 395                 float4     *numbers;
 396                 int                     nnumbers;
 397
 398                 stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
 399
 400                 /*
 401                  * Search is for a value that we do not know a priori, but we will
 402                  * assume it is not NULL.  Estimate the selectivity as non-null
 403                  * fraction divided by number of distinct values, so that we get a
 404                  * result averaged over all possible values whether common or
 405                  * uncommon.  (Essentially, we are assuming that the not-yet-known
 406                  * comparison value is equally likely to be any of the possible
 407                  * values, regardless of their frequency in the table.  Is that a good
 408                  * idea?)
 409                  */
 410                 selec = 1.0 - stats->stanullfrac;
 411                 ndistinct = get_variable_numdistinct(vardata);
 412                 if (ndistinct > 1)
 413                         selec /= ndistinct;
 414
 415                 /*
 416                  * Cross-check: selectivity should never be estimated as more than the
 417                  * most common value's.
 418                  */
 419                 if (get_attstatsslot(vardata->statsTuple,
 420                                                          vardata->atttype, vardata->atttypmod,
 421                                                          STATISTIC_KIND_MCV, InvalidOid,
 422                                                          NULL,
 423                                                          NULL, NULL,
 424                                                          &numbers, &nnumbers))
 425                 {
 426                         if (nnumbers > 0 && selec > numbers[0])
 427                                 selec = numbers[0];
 428                         free_attstatsslot(vardata->atttype, NULL, 0, numbers, nnumbers);
 429                 }
 430         }
 431         else
 432         {
 433                 /*
 434                  * No ANALYZE stats available, so make a guess using estimated number
 435                  * of distinct values and assuming they are equally common. (The guess
 436                  * is unlikely to be very good, but we do know a few special cases.)
 437                  */
 438                 selec = 1.0 / get_variable_numdistinct(vardata);
 439         }
 440
 441         /* result should be in range, but make sure... */
 442         CLAMP_PROBABILITY(selec);
 443
 444         return selec;
 445 }
 446
 447 /*
 448  *              neqsel                  - Selectivity of "!=" for any data types.
 449  *
 450  * This routine is also used for some operators that are not "!="
 451  * but have comparable selectivity behavior.  See above comments
 452  * for eqsel().
 453  */
 454 Datum
 455 neqsel(PG_FUNCTION_ARGS)
 456 {
 457         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
 458         Oid                     operator = PG_GETARG_OID(1);
 459         List       *args = (List *) PG_GETARG_POINTER(2);
 460         int                     varRelid = PG_GETARG_INT32(3);
 461         Oid                     eqop;
 462         float8          result;
 463
 464         /*
 465          * We want 1 - eqsel() where the equality operator is the one associated
 466          * with this != operator, that is, its negator.
 467          */
 468         eqop = get_negator(operator);
 469         if (eqop)
 470         {
 471                 result = DatumGetFloat8(DirectFunctionCall4(eqsel,
 472                                                                                                         PointerGetDatum(root),
 473                                                                                                         ObjectIdGetDatum(eqop),
 474                                                                                                         PointerGetDatum(args),
 475                                                                                                         Int32GetDatum(varRelid)));
 476         }
 477         else
 478         {
 479                 /* Use default selectivity (should we raise an error instead?) */
 480                 result = DEFAULT_EQ_SEL;
 481         }
 482         result = 1.0 - result;
 483         PG_RETURN_FLOAT8(result);
 484 }
 485
 486 /*
 487  *      scalarineqsel           - Selectivity of "<", "<=", ">", ">=" for scalars.
 488  *
 489  * This is the guts of both scalarltsel and scalargtsel.  The caller has
 490  * commuted the clause, if necessary, so that we can treat the variable as
 491  * being on the left.  The caller must also make sure that the other side
 492  * of the clause is a non-null Const, and dissect same into a value and
 493  * datatype.
 494  *
 495  * This routine works for any datatype (or pair of datatypes) known to
 496  * convert_to_scalar().  If it is applied to some other datatype,
 497  * it will return a default estimate.
 498  */
 499 static double
 500 scalarineqsel(PlannerInfo *root, Oid operator, bool isgt,
 501                           VariableStatData *vardata, Datum constval, Oid consttype)
 502 {
 503         Form_pg_statistic stats;
 504         FmgrInfo        opproc;
 505         double          mcv_selec,
 506                                 hist_selec,
 507                                 sumcommon;
 508         double          selec;
 509
 510         if (!HeapTupleIsValid(vardata->statsTuple))
 511         {
 512                 /* no stats available, so default result */
 513                 return DEFAULT_INEQ_SEL;
 514         }
 515         stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
 516
 517         fmgr_info(get_opcode(operator), &opproc);
 518         fmgr_info_set_collation(DEFAULT_COLLATION_OID, &opproc);
 519
 520         /*
 521          * If we have most-common-values info, add up the fractions of the MCV
 522          * entries that satisfy MCV OP CONST.  These fractions contribute directly
 523          * to the result selectivity.  Also add up the total fraction represented
 524          * by MCV entries.
 525          */
 526         mcv_selec = mcv_selectivity(vardata, &opproc, constval, true,
 527                                                                 &sumcommon);
 528
 529         /*
 530          * If there is a histogram, determine which bin the constant falls in, and
 531          * compute the resulting contribution to selectivity.
 532          */
 533         hist_selec = ineq_histogram_selectivity(root, vardata, &opproc, isgt,
 534                                                                                         constval, consttype);
 535
 536         /*
 537          * Now merge the results from the MCV and histogram calculations,
 538          * realizing that the histogram covers only the non-null values that are
 539          * not listed in MCV.
 540          */
 541         selec = 1.0 - stats->stanullfrac - sumcommon;
 542
 543         if (hist_selec >= 0.0)
 544                 selec *= hist_selec;
 545         else
 546         {
 547                 /*
 548                  * If no histogram but there are values not accounted for by MCV,
 549                  * arbitrarily assume half of them will match.
 550                  */
 551                 selec *= 0.5;
 552         }
 553
 554         selec += mcv_selec;
 555
 556         /* result should be in range, but make sure... */
 557         CLAMP_PROBABILITY(selec);
 558
 559         return selec;
 560 }
 561
 562 /*
 563  *      mcv_selectivity                 - Examine the MCV list for selectivity estimates
 564  *
 565  * Determine the fraction of the variable's MCV population that satisfies
 566  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft.  Also
 567  * compute the fraction of the total column population represented by the MCV
 568  * list.  This code will work for any boolean-returning predicate operator.
 569  *
 570  * The function result is the MCV selectivity, and the fraction of the
 571  * total population is returned into *sumcommonp.  Zeroes are returned
 572  * if there is no MCV list.
 573  */
 574 double
 575 mcv_selectivity(VariableStatData *vardata, FmgrInfo *opproc,
 576                                 Datum constval, bool varonleft,
 577                                 double *sumcommonp)
 578 {
 579         double          mcv_selec,
 580                                 sumcommon;
 581         Datum      *values;
 582         int                     nvalues;
 583         float4     *numbers;
 584         int                     nnumbers;
 585         int                     i;
 586
 587         mcv_selec = 0.0;
 588         sumcommon = 0.0;
 589
 590         if (HeapTupleIsValid(vardata->statsTuple) &&
 591                 get_attstatsslot(vardata->statsTuple,
 592                                                  vardata->atttype, vardata->atttypmod,
 593                                                  STATISTIC_KIND_MCV, InvalidOid,
 594                                                  NULL,
 595                                                  &values, &nvalues,
 596                                                  &numbers, &nnumbers))
 597         {
 598                 for (i = 0; i < nvalues; i++)
 599                 {
 600                         if (varonleft ?
 601                                 DatumGetBool(FunctionCall2(opproc,
 602                                                                                    values[i],
 603                                                                                    constval)) :
 604                                 DatumGetBool(FunctionCall2(opproc,
 605                                                                                    constval,
 606                                                                                    values[i])))
 607                                 mcv_selec += numbers[i];
 608                         sumcommon += numbers[i];
 609                 }
 610                 free_attstatsslot(vardata->atttype, values, nvalues,
 611                                                   numbers, nnumbers);
 612         }
 613
 614         *sumcommonp = sumcommon;
 615         return mcv_selec;
 616 }
 617
 618 /*
 619  *      histogram_selectivity   - Examine the histogram for selectivity estimates
 620  *
 621  * Determine the fraction of the variable's histogram entries that satisfy
 622  * the predicate (VAR OP CONST), or (CONST OP VAR) if !varonleft.
 623  *
 624  * This code will work for any boolean-returning predicate operator, whether
 625  * or not it has anything to do with the histogram sort operator.  We are
 626  * essentially using the histogram just as a representative sample.  However,
 627  * small histograms are unlikely to be all that representative, so the caller
 628  * should be prepared to fall back on some other estimation approach when the
 629  * histogram is missing or very small.  It may also be prudent to combine this
 630  * approach with another one when the histogram is small.
 631  *
 632  * If the actual histogram size is not at least min_hist_size, we won't bother
 633  * to do the calculation at all.  Also, if the n_skip parameter is > 0, we
 634  * ignore the first and last n_skip histogram elements, on the grounds that
 635  * they are outliers and hence not very representative.  Typical values for
 636  * these parameters are 10 and 1.
 637  *
 638  * The function result is the selectivity, or -1 if there is no histogram
 639  * or it's smaller than min_hist_size.
 640  *
 641  * The output parameter *hist_size receives the actual histogram size,
 642  * or zero if no histogram.  Callers may use this number to decide how
 643  * much faith to put in the function result.
 644  *
 645  * Note that the result disregards both the most-common-values (if any) and
 646  * null entries.  The caller is expected to combine this result with
 647  * statistics for those portions of the column population.      It may also be
 648  * prudent to clamp the result range, ie, disbelieve exact 0 or 1 outputs.
 649  */
 650 double
 651 histogram_selectivity(VariableStatData *vardata, FmgrInfo *opproc,
 652                                           Datum constval, bool varonleft,
 653                                           int min_hist_size, int n_skip,
 654                                           int *hist_size)
 655 {
 656         double          result;
 657         Datum      *values;
 658         int                     nvalues;
 659
 660         /* check sanity of parameters */
 661         Assert(n_skip >= 0);
 662         Assert(min_hist_size > 2 * n_skip);
 663
 664         if (HeapTupleIsValid(vardata->statsTuple) &&
 665                 get_attstatsslot(vardata->statsTuple,
 666                                                  vardata->atttype, vardata->atttypmod,
 667                                                  STATISTIC_KIND_HISTOGRAM, InvalidOid,
 668                                                  NULL,
 669                                                  &values, &nvalues,
 670                                                  NULL, NULL))
 671         {
 672                 *hist_size = nvalues;
 673                 if (nvalues >= min_hist_size)
 674                 {
 675                         int                     nmatch = 0;
 676                         int                     i;
 677
 678                         for (i = n_skip; i < nvalues - n_skip; i++)
 679                         {
 680                                 if (varonleft ?
 681                                         DatumGetBool(FunctionCall2(opproc,
 682                                                                                            values[i],
 683                                                                                            constval)) :
 684                                         DatumGetBool(FunctionCall2(opproc,
 685                                                                                            constval,
 686                                                                                            values[i])))
 687                                         nmatch++;
 688                         }
 689                         result = ((double) nmatch) / ((double) (nvalues - 2 * n_skip));
 690                 }
 691                 else
 692                         result = -1;
 693                 free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
 694         }
 695         else
 696         {
 697                 *hist_size = 0;
 698                 result = -1;
 699         }
 700
 701         return result;
 702 }
 703
 704 /*
 705  *      ineq_histogram_selectivity      - Examine the histogram for scalarineqsel
 706  *
 707  * Determine the fraction of the variable's histogram population that
 708  * satisfies the inequality condition, ie, VAR < CONST or VAR > CONST.
 709  *
 710  * Returns -1 if there is no histogram (valid results will always be >= 0).
 711  *
 712  * Note that the result disregards both the most-common-values (if any) and
 713  * null entries.  The caller is expected to combine this result with
 714  * statistics for those portions of the column population.
 715  */
 716 static double
 717 ineq_histogram_selectivity(PlannerInfo *root,
 718                                                    VariableStatData *vardata,
 719                                                    FmgrInfo *opproc, bool isgt,
 720                                                    Datum constval, Oid consttype)
 721 {
 722         double          hist_selec;
 723         Oid                     hist_op;
 724         Datum      *values;
 725         int                     nvalues;
 726
 727         hist_selec = -1.0;
 728
 729         /*
 730          * Someday, ANALYZE might store more than one histogram per rel/att,
 731          * corresponding to more than one possible sort ordering defined for the
 732          * column type.  However, to make that work we will need to figure out
 733          * which staop to search for --- it's not necessarily the one we have at
 734          * hand!  (For example, we might have a '<=' operator rather than the '<'
 735          * operator that will appear in staop.)  For now, assume that whatever
 736          * appears in pg_statistic is sorted the same way our operator sorts, or
 737          * the reverse way if isgt is TRUE.
 738          */
 739         if (HeapTupleIsValid(vardata->statsTuple) &&
 740                 get_attstatsslot(vardata->statsTuple,
 741                                                  vardata->atttype, vardata->atttypmod,
 742                                                  STATISTIC_KIND_HISTOGRAM, InvalidOid,
 743                                                  &hist_op,
 744                                                  &values, &nvalues,
 745                                                  NULL, NULL))
 746         {
 747                 if (nvalues > 1)
 748                 {
 749                         /*
 750                          * Use binary search to find proper location, ie, the first slot
 751                          * at which the comparison fails.  (If the given operator isn't
 752                          * actually sort-compatible with the histogram, you'll get garbage
 753                          * results ... but probably not any more garbage-y than you would
 754                          * from the old linear search.)
 755                          *
 756                          * If the binary search accesses the first or last histogram
 757                          * entry, we try to replace that endpoint with the true column min
 758                          * or max as found by get_actual_variable_range().      This
 759                          * ameliorates misestimates when the min or max is moving as a
 760                          * result of changes since the last ANALYZE.  Note that this could
 761                          * result in effectively including MCVs into the histogram that
 762                          * weren't there before, but we don't try to correct for that.
 763                          */
 764                         double          histfrac;
 765                         int                     lobound = 0;    /* first possible slot to search */
 766                         int                     hibound = nvalues;              /* last+1 slot to search */
 767                         bool            have_end = false;
 768
 769                         /*
 770                          * If there are only two histogram entries, we'll want up-to-date
 771                          * values for both.  (If there are more than two, we need at most
 772                          * one of them to be updated, so we deal with that within the
 773                          * loop.)
 774                          */
 775                         if (nvalues == 2)
 776                                 have_end = get_actual_variable_range(root,
 777                                                                                                          vardata,
 778                                                                                                          hist_op,
 779                                                                                                          &values[0],
 780                                                                                                          &values[1]);
 781
 782                         while (lobound < hibound)
 783                         {
 784                                 int                     probe = (lobound + hibound) / 2;
 785                                 bool            ltcmp;
 786
 787                                 /*
 788                                  * If we find ourselves about to compare to the first or last
 789                                  * histogram entry, first try to replace it with the actual
 790                                  * current min or max (unless we already did so above).
 791                                  */
 792                                 if (probe == 0 && nvalues > 2)
 793                                         have_end = get_actual_variable_range(root,
 794                                                                                                                  vardata,
 795                                                                                                                  hist_op,
 796                                                                                                                  &values[0],
 797                                                                                                                  NULL);
 798                                 else if (probe == nvalues - 1 && nvalues > 2)
 799                                         have_end = get_actual_variable_range(root,
 800                                                                                                                  vardata,
 801                                                                                                                  hist_op,
 802                                                                                                                  NULL,
 803                                                                                                                  &values[probe]);
 804
 805                                 ltcmp = DatumGetBool(FunctionCall2(opproc,
 806                                                                                                    values[probe],
 807                                                                                                    constval));
 808                                 if (isgt)
 809                                         ltcmp = !ltcmp;
 810                                 if (ltcmp)
 811                                         lobound = probe + 1;
 812                                 else
 813                                         hibound = probe;
 814                         }
 815
 816                         if (lobound <= 0)
 817                         {
 818                                 /* Constant is below lower histogram boundary. */
 819                                 histfrac = 0.0;
 820                         }
 821                         else if (lobound >= nvalues)
 822                         {
 823                                 /* Constant is above upper histogram boundary. */
 824                                 histfrac = 1.0;
 825                         }
 826                         else
 827                         {
 828                                 int                     i = lobound;
 829                                 double          val,
 830                                                         high,
 831                                                         low;
 832                                 double          binfrac;
 833
 834                                 /*
 835                                  * We have values[i-1] <= constant <= values[i].
 836                                  *
 837                                  * Convert the constant and the two nearest bin boundary
 838                                  * values to a uniform comparison scale, and do a linear
 839                                  * interpolation within this bin.
 840                                  */
 841                                 if (convert_to_scalar(constval, consttype, &val,
 842                                                                           values[i - 1], values[i],
 843                                                                           vardata->vartype,
 844                                                                           &low, &high))
 845                                 {
 846                                         if (high <= low)
 847                                         {
 848                                                 /* cope if bin boundaries appear identical */
 849                                                 binfrac = 0.5;
 850                                         }
 851                                         else if (val <= low)
 852                                                 binfrac = 0.0;
 853                                         else if (val >= high)
 854                                                 binfrac = 1.0;
 855                                         else
 856                                         {
 857                                                 binfrac = (val - low) / (high - low);
 858
 859                                                 /*
 860                                                  * Watch out for the possibility that we got a NaN or
 861                                                  * Infinity from the division.  This can happen
 862                                                  * despite the previous checks, if for example "low"
 863                                                  * is -Infinity.
 864                                                  */
 865                                                 if (isnan(binfrac) ||
 866                                                         binfrac < 0.0 || binfrac > 1.0)
 867                                                         binfrac = 0.5;
 868                                         }
 869                                 }
 870                                 else
 871                                 {
 872                                         /*
 873                                          * Ideally we'd produce an error here, on the grounds that
 874                                          * the given operator shouldn't have scalarXXsel
 875                                          * registered as its selectivity func unless we can deal
 876                                          * with its operand types.      But currently, all manner of
 877                                          * stuff is invoking scalarXXsel, so give a default
 878                                          * estimate until that can be fixed.
 879                                          */
 880                                         binfrac = 0.5;
 881                                 }
 882
 883                                 /*
 884                                  * Now, compute the overall selectivity across the values
 885                                  * represented by the histogram.  We have i-1 full bins and
 886                                  * binfrac partial bin below the constant.
 887                                  */
 888                                 histfrac = (double) (i - 1) + binfrac;
 889                                 histfrac /= (double) (nvalues - 1);
 890                         }
 891
 892                         /*
 893                          * Now histfrac = fraction of histogram entries below the
 894                          * constant.
 895                          *
 896                          * Account for "<" vs ">"
 897                          */
 898                         hist_selec = isgt ? (1.0 - histfrac) : histfrac;
 899
 900                         /*
 901                          * The histogram boundaries are only approximate to begin with,
 902                          * and may well be out of date anyway.  Therefore, don't believe
 903                          * extremely small or large selectivity estimates --- unless we
 904                          * got actual current endpoint values from the table.
 905                          */
 906                         if (have_end)
 907                                 CLAMP_PROBABILITY(hist_selec);
 908                         else
 909                         {
 910                                 if (hist_selec < 0.0001)
 911                                         hist_selec = 0.0001;
 912                                 else if (hist_selec > 0.9999)
 913                                         hist_selec = 0.9999;
 914                         }
 915                 }
 916
 917                 free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
 918         }
 919
 920         return hist_selec;
 921 }
 922
 923 /*
 924  *              scalarltsel             - Selectivity of "<" (also "<=") for scalars.
 925  */
 926 Datum
 927 scalarltsel(PG_FUNCTION_ARGS)
 928 {
 929         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
 930         Oid                     operator = PG_GETARG_OID(1);
 931         List       *args = (List *) PG_GETARG_POINTER(2);
 932         int                     varRelid = PG_GETARG_INT32(3);
 933         VariableStatData vardata;
 934         Node       *other;
 935         bool            varonleft;
 936         Datum           constval;
 937         Oid                     consttype;
 938         bool            isgt;
 939         double          selec;
 940
 941         /*
 942          * If expression is not variable op something or something op variable,
 943          * then punt and return a default estimate.
 944          */
 945         if (!get_restriction_variable(root, args, varRelid,
 946                                                                   &vardata, &other, &varonleft))
 947                 PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
 948
 949         /*
 950          * Can't do anything useful if the something is not a constant, either.
 951          */
 952         if (!IsA(other, Const))
 953         {
 954                 ReleaseVariableStats(vardata);
 955                 PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
 956         }
 957
 958         /*
 959          * If the constant is NULL, assume operator is strict and return zero, ie,
 960          * operator will never return TRUE.
 961          */
 962         if (((Const *) other)->constisnull)
 963         {
 964                 ReleaseVariableStats(vardata);
 965                 PG_RETURN_FLOAT8(0.0);
 966         }
 967         constval = ((Const *) other)->constvalue;
 968         consttype = ((Const *) other)->consttype;
 969
 970         /*
 971          * Force the var to be on the left to simplify logic in scalarineqsel.
 972          */
 973         if (varonleft)
 974         {
 975                 /* we have var < other */
 976                 isgt = false;
 977         }
 978         else
 979         {
 980                 /* we have other < var, commute to make var > other */
 981                 operator = get_commutator(operator);
 982                 if (!operator)
 983                 {
 984                         /* Use default selectivity (should we raise an error instead?) */
 985                         ReleaseVariableStats(vardata);
 986                         PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
 987                 }
 988                 isgt = true;
 989         }
 990
 991         selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
 992
 993         ReleaseVariableStats(vardata);
 994
 995         PG_RETURN_FLOAT8((float8) selec);
 996 }
 997
 998 /*
 999  *              scalargtsel             - Selectivity of ">" (also ">=") for integers.
1000  */
1001 Datum
1002 scalargtsel(PG_FUNCTION_ARGS)
1003 {
1004         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1005         Oid                     operator = PG_GETARG_OID(1);
1006         List       *args = (List *) PG_GETARG_POINTER(2);
1007         int                     varRelid = PG_GETARG_INT32(3);
1008         VariableStatData vardata;
1009         Node       *other;
1010         bool            varonleft;
1011         Datum           constval;
1012         Oid                     consttype;
1013         bool            isgt;
1014         double          selec;
1015
1016         /*
1017          * If expression is not variable op something or something op variable,
1018          * then punt and return a default estimate.
1019          */
1020         if (!get_restriction_variable(root, args, varRelid,
1021                                                                   &vardata, &other, &varonleft))
1022                 PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
1023
1024         /*
1025          * Can't do anything useful if the something is not a constant, either.
1026          */
1027         if (!IsA(other, Const))
1028         {
1029                 ReleaseVariableStats(vardata);
1030                 PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
1031         }
1032
1033         /*
1034          * If the constant is NULL, assume operator is strict and return zero, ie,
1035          * operator will never return TRUE.
1036          */
1037         if (((Const *) other)->constisnull)
1038         {
1039                 ReleaseVariableStats(vardata);
1040                 PG_RETURN_FLOAT8(0.0);
1041         }
1042         constval = ((Const *) other)->constvalue;
1043         consttype = ((Const *) other)->consttype;
1044
1045         /*
1046          * Force the var to be on the left to simplify logic in scalarineqsel.
1047          */
1048         if (varonleft)
1049         {
1050                 /* we have var > other */
1051                 isgt = true;
1052         }
1053         else
1054         {
1055                 /* we have other > var, commute to make var < other */
1056                 operator = get_commutator(operator);
1057                 if (!operator)
1058                 {
1059                         /* Use default selectivity (should we raise an error instead?) */
1060                         ReleaseVariableStats(vardata);
1061                         PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
1062                 }
1063                 isgt = false;
1064         }
1065
1066         selec = scalarineqsel(root, operator, isgt, &vardata, constval, consttype);
1067
1068         ReleaseVariableStats(vardata);
1069
1070         PG_RETURN_FLOAT8((float8) selec);
1071 }
1072
1073 /*
1074  * patternsel                   - Generic code for pattern-match selectivity.
1075  */
1076 static double
1077 patternsel(PG_FUNCTION_ARGS, Pattern_Type ptype, bool negate)
1078 {
1079         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1080         Oid                     operator = PG_GETARG_OID(1);
1081         List       *args = (List *) PG_GETARG_POINTER(2);
1082         int                     varRelid = PG_GETARG_INT32(3);
1083         VariableStatData vardata;
1084         Node       *variable;
1085         Node       *other;
1086         bool            varonleft;
1087         Datum           constval;
1088         Oid                     consttype;
1089         Oid                     vartype;
1090         Oid                     opfamily;
1091         Pattern_Prefix_Status pstatus;
1092         Const      *patt = NULL;
1093         Const      *prefix = NULL;
1094         Const      *rest = NULL;
1095         double          result;
1096
1097         /*
1098          * If this is for a NOT LIKE or similar operator, get the corresponding
1099          * positive-match operator and work with that.  Set result to the correct
1100          * default estimate, too.
1101          */
1102         if (negate)
1103         {
1104                 operator = get_negator(operator);
1105                 if (!OidIsValid(operator))
1106                         elog(ERROR, "patternsel called for operator without a negator");
1107                 result = 1.0 - DEFAULT_MATCH_SEL;
1108         }
1109         else
1110         {
1111                 result = DEFAULT_MATCH_SEL;
1112         }
1113
1114         /*
1115          * If expression is not variable op constant, then punt and return a
1116          * default estimate.
1117          */
1118         if (!get_restriction_variable(root, args, varRelid,
1119                                                                   &vardata, &other, &varonleft))
1120                 return result;
1121         if (!varonleft || !IsA(other, Const))
1122         {
1123                 ReleaseVariableStats(vardata);
1124                 return result;
1125         }
1126         variable = (Node *) linitial(args);
1127
1128         /*
1129          * If the constant is NULL, assume operator is strict and return zero, ie,
1130          * operator will never return TRUE.  (It's zero even for a negator op.)
1131          */
1132         if (((Const *) other)->constisnull)
1133         {
1134                 ReleaseVariableStats(vardata);
1135                 return 0.0;
1136         }
1137         constval = ((Const *) other)->constvalue;
1138         consttype = ((Const *) other)->consttype;
1139
1140         /*
1141          * The right-hand const is type text or bytea for all supported operators.
1142          * We do not expect to see binary-compatible types here, since
1143          * const-folding should have relabeled the const to exactly match the
1144          * operator's declared type.
1145          */
1146         if (consttype != TEXTOID && consttype != BYTEAOID)
1147         {
1148                 ReleaseVariableStats(vardata);
1149                 return result;
1150         }
1151
1152         /*
1153          * Similarly, the exposed type of the left-hand side should be one of
1154          * those we know.  (Do not look at vardata.atttype, which might be
1155          * something binary-compatible but different.)  We can use it to choose
1156          * the index opfamily from which we must draw the comparison operators.
1157          *
1158          * NOTE: It would be more correct to use the PATTERN opfamilies than the
1159          * simple ones, but at the moment ANALYZE will not generate statistics for
1160          * the PATTERN operators.  But our results are so approximate anyway that
1161          * it probably hardly matters.
1162          */
1163         vartype = vardata.vartype;
1164
1165         switch (vartype)
1166         {
1167                 case TEXTOID:
1168                         opfamily = TEXT_BTREE_FAM_OID;
1169                         break;
1170                 case BPCHAROID:
1171                         opfamily = BPCHAR_BTREE_FAM_OID;
1172                         break;
1173                 case NAMEOID:
1174                         opfamily = NAME_BTREE_FAM_OID;
1175                         break;
1176                 case BYTEAOID:
1177                         opfamily = BYTEA_BTREE_FAM_OID;
1178                         break;
1179                 default:
1180                         ReleaseVariableStats(vardata);
1181                         return result;
1182         }
1183
1184         /* divide pattern into fixed prefix and remainder */
1185         patt = (Const *) other;
1186         pstatus = pattern_fixed_prefix(patt, ptype, &prefix, &rest);
1187
1188         /*
1189          * If necessary, coerce the prefix constant to the right type. (The "rest"
1190          * constant need not be changed.)
1191          */
1192         if (prefix && prefix->consttype != vartype)
1193         {
1194                 char       *prefixstr;
1195
1196                 switch (prefix->consttype)
1197                 {
1198                         case TEXTOID:
1199                                 prefixstr = TextDatumGetCString(prefix->constvalue);
1200                                 break;
1201                         case BYTEAOID:
1202                                 prefixstr = DatumGetCString(DirectFunctionCall1(byteaout,
1203                                                                                                                 prefix->constvalue));
1204                                 break;
1205                         default:
1206                                 elog(ERROR, "unrecognized consttype: %u",
1207                                          prefix->consttype);
1208                                 ReleaseVariableStats(vardata);
1209                                 return result;
1210                 }
1211                 prefix = string_to_const(prefixstr, vartype);
1212                 pfree(prefixstr);
1213         }
1214
1215         if (pstatus == Pattern_Prefix_Exact)
1216         {
1217                 /*
1218                  * Pattern specifies an exact match, so pretend operator is '='
1219                  */
1220                 Oid                     eqopr = get_opfamily_member(opfamily, vartype, vartype,
1221                                                                                                 BTEqualStrategyNumber);
1222
1223                 if (eqopr == InvalidOid)
1224                         elog(ERROR, "no = operator for opfamily %u", opfamily);
1225                 result = var_eq_const(&vardata, eqopr, prefix->constvalue,
1226                                                           false, true);
1227         }
1228         else
1229         {
1230                 /*
1231                  * Not exact-match pattern.  If we have a sufficiently large
1232                  * histogram, estimate selectivity for the histogram part of the
1233                  * population by counting matches in the histogram.  If not, estimate
1234                  * selectivity of the fixed prefix and remainder of pattern
1235                  * separately, then combine the two to get an estimate of the
1236                  * selectivity for the part of the column population represented by
1237                  * the histogram.  (For small histograms, we combine these
1238                  * approaches.)
1239                  *
1240                  * We then add up data for any most-common-values values; these are
1241                  * not in the histogram population, and we can get exact answers for
1242                  * them by applying the pattern operator, so there's no reason to
1243                  * approximate.  (If the MCVs cover a significant part of the total
1244                  * population, this gives us a big leg up in accuracy.)
1245                  */
1246                 Selectivity selec;
1247                 int                     hist_size;
1248                 FmgrInfo        opproc;
1249                 double          nullfrac,
1250                                         mcv_selec,
1251                                         sumcommon;
1252
1253                 /* Try to use the histogram entries to get selectivity */
1254                 fmgr_info(get_opcode(operator), &opproc);
1255                 fmgr_info_set_collation(DEFAULT_COLLATION_OID, &opproc);
1256
1257                 selec = histogram_selectivity(&vardata, &opproc, constval, true,
1258                                                                           10, 1, &hist_size);
1259
1260                 /* If not at least 100 entries, use the heuristic method */
1261                 if (hist_size < 100)
1262                 {
1263                         Selectivity heursel;
1264                         Selectivity prefixsel;
1265                         Selectivity restsel;
1266
1267                         if (pstatus == Pattern_Prefix_Partial)
1268                                 prefixsel = prefix_selectivity(root, &vardata, vartype,
1269                                                                                            opfamily, prefix);
1270                         else
1271                                 prefixsel = 1.0;
1272                         restsel = pattern_selectivity(rest, ptype);
1273                         heursel = prefixsel * restsel;
1274
1275                         if (selec < 0)          /* fewer than 10 histogram entries? */
1276                                 selec = heursel;
1277                         else
1278                         {
1279                                 /*
1280                                  * For histogram sizes from 10 to 100, we combine the
1281                                  * histogram and heuristic selectivities, putting increasingly
1282                                  * more trust in the histogram for larger sizes.
1283                                  */
1284                                 double          hist_weight = hist_size / 100.0;
1285
1286                                 selec = selec * hist_weight + heursel * (1.0 - hist_weight);
1287                         }
1288                 }
1289
1290                 /* In any case, don't believe extremely small or large estimates. */
1291                 if (selec < 0.0001)
1292                         selec = 0.0001;
1293                 else if (selec > 0.9999)
1294                         selec = 0.9999;
1295
1296                 /*
1297                  * If we have most-common-values info, add up the fractions of the MCV
1298                  * entries that satisfy MCV OP PATTERN.  These fractions contribute
1299                  * directly to the result selectivity.  Also add up the total fraction
1300                  * represented by MCV entries.
1301                  */
1302                 mcv_selec = mcv_selectivity(&vardata, &opproc, constval, true,
1303                                                                         &sumcommon);
1304
1305                 if (HeapTupleIsValid(vardata.statsTuple))
1306                         nullfrac = ((Form_pg_statistic) GETSTRUCT(vardata.statsTuple))->stanullfrac;
1307                 else
1308                         nullfrac = 0.0;
1309
1310                 /*
1311                  * Now merge the results from the MCV and histogram calculations,
1312                  * realizing that the histogram covers only the non-null values that
1313                  * are not listed in MCV.
1314                  */
1315                 selec *= 1.0 - nullfrac - sumcommon;
1316                 selec += mcv_selec;
1317
1318                 /* result should be in range, but make sure... */
1319                 CLAMP_PROBABILITY(selec);
1320                 result = selec;
1321         }
1322
1323         if (prefix)
1324         {
1325                 pfree(DatumGetPointer(prefix->constvalue));
1326                 pfree(prefix);
1327         }
1328
1329         ReleaseVariableStats(vardata);
1330
1331         return negate ? (1.0 - result) : result;
1332 }
1333
1334 /*
1335  *              regexeqsel              - Selectivity of regular-expression pattern match.
1336  */
1337 Datum
1338 regexeqsel(PG_FUNCTION_ARGS)
1339 {
1340         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex, false));
1341 }
1342
1343 /*
1344  *              icregexeqsel    - Selectivity of case-insensitive regex match.
1345  */
1346 Datum
1347 icregexeqsel(PG_FUNCTION_ARGS)
1348 {
1349         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex_IC, false));
1350 }
1351
1352 /*
1353  *              likesel                 - Selectivity of LIKE pattern match.
1354  */
1355 Datum
1356 likesel(PG_FUNCTION_ARGS)
1357 {
1358         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like, false));
1359 }
1360
1361 /*
1362  *              iclikesel                       - Selectivity of ILIKE pattern match.
1363  */
1364 Datum
1365 iclikesel(PG_FUNCTION_ARGS)
1366 {
1367         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like_IC, false));
1368 }
1369
1370 /*
1371  *              regexnesel              - Selectivity of regular-expression pattern non-match.
1372  */
1373 Datum
1374 regexnesel(PG_FUNCTION_ARGS)
1375 {
1376         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex, true));
1377 }
1378
1379 /*
1380  *              icregexnesel    - Selectivity of case-insensitive regex non-match.
1381  */
1382 Datum
1383 icregexnesel(PG_FUNCTION_ARGS)
1384 {
1385         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Regex_IC, true));
1386 }
1387
1388 /*
1389  *              nlikesel                - Selectivity of LIKE pattern non-match.
1390  */
1391 Datum
1392 nlikesel(PG_FUNCTION_ARGS)
1393 {
1394         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like, true));
1395 }
1396
1397 /*
1398  *              icnlikesel              - Selectivity of ILIKE pattern non-match.
1399  */
1400 Datum
1401 icnlikesel(PG_FUNCTION_ARGS)
1402 {
1403         PG_RETURN_FLOAT8(patternsel(fcinfo, Pattern_Type_Like_IC, true));
1404 }
1405
1406 /*
1407  *              booltestsel             - Selectivity of BooleanTest Node.
1408  */
1409 Selectivity
1410 booltestsel(PlannerInfo *root, BoolTestType booltesttype, Node *arg,
1411                         int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1412 {
1413         VariableStatData vardata;
1414         double          selec;
1415
1416         examine_variable(root, arg, varRelid, &vardata);
1417
1418         if (HeapTupleIsValid(vardata.statsTuple))
1419         {
1420                 Form_pg_statistic stats;
1421                 double          freq_null;
1422                 Datum      *values;
1423                 int                     nvalues;
1424                 float4     *numbers;
1425                 int                     nnumbers;
1426
1427                 stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
1428                 freq_null = stats->stanullfrac;
1429
1430                 if (get_attstatsslot(vardata.statsTuple,
1431                                                          vardata.atttype, vardata.atttypmod,
1432                                                          STATISTIC_KIND_MCV, InvalidOid,
1433                                                          NULL,
1434                                                          &values, &nvalues,
1435                                                          &numbers, &nnumbers)
1436                         && nnumbers > 0)
1437                 {
1438                         double          freq_true;
1439                         double          freq_false;
1440
1441                         /*
1442                          * Get first MCV frequency and derive frequency for true.
1443                          */
1444                         if (DatumGetBool(values[0]))
1445                                 freq_true = numbers[0];
1446                         else
1447                                 freq_true = 1.0 - numbers[0] - freq_null;
1448
1449                         /*
1450                          * Next derive frequency for false. Then use these as appropriate
1451                          * to derive frequency for each case.
1452                          */
1453                         freq_false = 1.0 - freq_true - freq_null;
1454
1455                         switch (booltesttype)
1456                         {
1457                                 case IS_UNKNOWN:
1458                                         /* select only NULL values */
1459                                         selec = freq_null;
1460                                         break;
1461                                 case IS_NOT_UNKNOWN:
1462                                         /* select non-NULL values */
1463                                         selec = 1.0 - freq_null;
1464                                         break;
1465                                 case IS_TRUE:
1466                                         /* select only TRUE values */
1467                                         selec = freq_true;
1468                                         break;
1469                                 case IS_NOT_TRUE:
1470                                         /* select non-TRUE values */
1471                                         selec = 1.0 - freq_true;
1472                                         break;
1473                                 case IS_FALSE:
1474                                         /* select only FALSE values */
1475                                         selec = freq_false;
1476                                         break;
1477                                 case IS_NOT_FALSE:
1478                                         /* select non-FALSE values */
1479                                         selec = 1.0 - freq_false;
1480                                         break;
1481                                 default:
1482                                         elog(ERROR, "unrecognized booltesttype: %d",
1483                                                  (int) booltesttype);
1484                                         selec = 0.0;    /* Keep compiler quiet */
1485                                         break;
1486                         }
1487
1488                         free_attstatsslot(vardata.atttype, values, nvalues,
1489                                                           numbers, nnumbers);
1490                 }
1491                 else
1492                 {
1493                         /*
1494                          * No most-common-value info available. Still have null fraction
1495                          * information, so use it for IS [NOT] UNKNOWN. Otherwise adjust
1496                          * for null fraction and assume an even split for boolean tests.
1497                          */
1498                         switch (booltesttype)
1499                         {
1500                                 case IS_UNKNOWN:
1501
1502                                         /*
1503                                          * Use freq_null directly.
1504                                          */
1505                                         selec = freq_null;
1506                                         break;
1507                                 case IS_NOT_UNKNOWN:
1508
1509                                         /*
1510                                          * Select not unknown (not null) values. Calculate from
1511                                          * freq_null.
1512                                          */
1513                                         selec = 1.0 - freq_null;
1514                                         break;
1515                                 case IS_TRUE:
1516                                 case IS_NOT_TRUE:
1517                                 case IS_FALSE:
1518                                 case IS_NOT_FALSE:
1519                                         selec = (1.0 - freq_null) / 2.0;
1520                                         break;
1521                                 default:
1522                                         elog(ERROR, "unrecognized booltesttype: %d",
1523                                                  (int) booltesttype);
1524                                         selec = 0.0;    /* Keep compiler quiet */
1525                                         break;
1526                         }
1527                 }
1528         }
1529         else
1530         {
1531                 /*
1532                  * If we can't get variable statistics for the argument, perhaps
1533                  * clause_selectivity can do something with it.  We ignore the
1534                  * possibility of a NULL value when using clause_selectivity, and just
1535                  * assume the value is either TRUE or FALSE.
1536                  */
1537                 switch (booltesttype)
1538                 {
1539                         case IS_UNKNOWN:
1540                                 selec = DEFAULT_UNK_SEL;
1541                                 break;
1542                         case IS_NOT_UNKNOWN:
1543                                 selec = DEFAULT_NOT_UNK_SEL;
1544                                 break;
1545                         case IS_TRUE:
1546                         case IS_NOT_FALSE:
1547                                 selec = (double) clause_selectivity(root, arg,
1548                                                                                                         varRelid,
1549                                                                                                         jointype, sjinfo);
1550                                 break;
1551                         case IS_FALSE:
1552                         case IS_NOT_TRUE:
1553                                 selec = 1.0 - (double) clause_selectivity(root, arg,
1554                                                                                                                   varRelid,
1555                                                                                                                   jointype, sjinfo);
1556                                 break;
1557                         default:
1558                                 elog(ERROR, "unrecognized booltesttype: %d",
1559                                          (int) booltesttype);
1560                                 selec = 0.0;    /* Keep compiler quiet */
1561                                 break;
1562                 }
1563         }
1564
1565         ReleaseVariableStats(vardata);
1566
1567         /* result should be in range, but make sure... */
1568         CLAMP_PROBABILITY(selec);
1569
1570         return (Selectivity) selec;
1571 }
1572
1573 /*
1574  *              nulltestsel             - Selectivity of NullTest Node.
1575  */
1576 Selectivity
1577 nulltestsel(PlannerInfo *root, NullTestType nulltesttype, Node *arg,
1578                         int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1579 {
1580         VariableStatData vardata;
1581         double          selec;
1582
1583         examine_variable(root, arg, varRelid, &vardata);
1584
1585         if (HeapTupleIsValid(vardata.statsTuple))
1586         {
1587                 Form_pg_statistic stats;
1588                 double          freq_null;
1589
1590                 stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
1591                 freq_null = stats->stanullfrac;
1592
1593                 switch (nulltesttype)
1594                 {
1595                         case IS_NULL:
1596
1597                                 /*
1598                                  * Use freq_null directly.
1599                                  */
1600                                 selec = freq_null;
1601                                 break;
1602                         case IS_NOT_NULL:
1603
1604                                 /*
1605                                  * Select not unknown (not null) values. Calculate from
1606                                  * freq_null.
1607                                  */
1608                                 selec = 1.0 - freq_null;
1609                                 break;
1610                         default:
1611                                 elog(ERROR, "unrecognized nulltesttype: %d",
1612                                          (int) nulltesttype);
1613                                 return (Selectivity) 0; /* keep compiler quiet */
1614                 }
1615         }
1616         else
1617         {
1618                 /*
1619                  * No ANALYZE stats available, so make a guess
1620                  */
1621                 switch (nulltesttype)
1622                 {
1623                         case IS_NULL:
1624                                 selec = DEFAULT_UNK_SEL;
1625                                 break;
1626                         case IS_NOT_NULL:
1627                                 selec = DEFAULT_NOT_UNK_SEL;
1628                                 break;
1629                         default:
1630                                 elog(ERROR, "unrecognized nulltesttype: %d",
1631                                          (int) nulltesttype);
1632                                 return (Selectivity) 0; /* keep compiler quiet */
1633                 }
1634         }
1635
1636         ReleaseVariableStats(vardata);
1637
1638         /* result should be in range, but make sure... */
1639         CLAMP_PROBABILITY(selec);
1640
1641         return (Selectivity) selec;
1642 }
1643
1644 /*
1645  * strip_array_coercion - strip binary-compatible relabeling from an array expr
1646  *
1647  * For array values, the parser normally generates ArrayCoerceExpr conversions,
1648  * but it seems possible that RelabelType might show up.  Also, the planner
1649  * is not currently tense about collapsing stacked ArrayCoerceExpr nodes,
1650  * so we need to be ready to deal with more than one level.
1651  */
1652 static Node *
1653 strip_array_coercion(Node *node)
1654 {
1655         for (;;)
1656         {
1657                 if (node && IsA(node, ArrayCoerceExpr) &&
1658                         ((ArrayCoerceExpr *) node)->elemfuncid == InvalidOid)
1659                 {
1660                         node = (Node *) ((ArrayCoerceExpr *) node)->arg;
1661                 }
1662                 else if (node && IsA(node, RelabelType))
1663                 {
1664                         /* We don't really expect this case, but may as well cope */
1665                         node = (Node *) ((RelabelType *) node)->arg;
1666                 }
1667                 else
1668                         break;
1669         }
1670         return node;
1671 }
1672
1673 /*
1674  *              scalararraysel          - Selectivity of ScalarArrayOpExpr Node.
1675  */
1676 Selectivity
1677 scalararraysel(PlannerInfo *root,
1678                            ScalarArrayOpExpr *clause,
1679                            bool is_join_clause,
1680                            int varRelid,
1681                            JoinType jointype,
1682                            SpecialJoinInfo *sjinfo)
1683 {
1684         Oid                     operator = clause->opno;
1685         bool            useOr = clause->useOr;
1686         Node       *leftop;
1687         Node       *rightop;
1688         Oid                     nominal_element_type;
1689         Oid                     nominal_element_collation;
1690         RegProcedure oprsel;
1691         FmgrInfo        oprselproc;
1692         Selectivity s1;
1693
1694         /*
1695          * First, look up the underlying operator's selectivity estimator. Punt if
1696          * it hasn't got one.
1697          */
1698         if (is_join_clause)
1699                 oprsel = get_oprjoin(operator);
1700         else
1701                 oprsel = get_oprrest(operator);
1702         if (!oprsel)
1703                 return (Selectivity) 0.5;
1704         fmgr_info(oprsel, &oprselproc);
1705         fmgr_info_set_collation(DEFAULT_COLLATION_OID, &oprselproc);
1706
1707         /* deconstruct the expression */
1708         Assert(list_length(clause->args) == 2);
1709         leftop = (Node *) linitial(clause->args);
1710         rightop = (Node *) lsecond(clause->args);
1711
1712         /* get nominal (after relabeling) element type of rightop */
1713         nominal_element_type = get_base_element_type(exprType(rightop));
1714         if (!OidIsValid(nominal_element_type))
1715                 return (Selectivity) 0.5;               /* probably shouldn't happen */
1716         /* get nominal collation, too, for generating constants */
1717         nominal_element_collation = exprCollation(rightop);
1718
1719         /* look through any binary-compatible relabeling of rightop */
1720         rightop = strip_array_coercion(rightop);
1721
1722         /*
1723          * We consider three cases:
1724          *
1725          * 1. rightop is an Array constant: deconstruct the array, apply the
1726          * operator's selectivity function for each array element, and merge the
1727          * results in the same way that clausesel.c does for AND/OR combinations.
1728          *
1729          * 2. rightop is an ARRAY[] construct: apply the operator's selectivity
1730          * function for each element of the ARRAY[] construct, and merge.
1731          *
1732          * 3. otherwise, make a guess ...
1733          */
1734         if (rightop && IsA(rightop, Const))
1735         {
1736                 Datum           arraydatum = ((Const *) rightop)->constvalue;
1737                 bool            arrayisnull = ((Const *) rightop)->constisnull;
1738                 ArrayType  *arrayval;
1739                 int16           elmlen;
1740                 bool            elmbyval;
1741                 char            elmalign;
1742                 int                     num_elems;
1743                 Datum      *elem_values;
1744                 bool       *elem_nulls;
1745                 int                     i;
1746
1747                 if (arrayisnull)                /* qual can't succeed if null array */
1748                         return (Selectivity) 0.0;
1749                 arrayval = DatumGetArrayTypeP(arraydatum);
1750                 get_typlenbyvalalign(ARR_ELEMTYPE(arrayval),
1751                                                          &elmlen, &elmbyval, &elmalign);
1752                 deconstruct_array(arrayval,
1753                                                   ARR_ELEMTYPE(arrayval),
1754                                                   elmlen, elmbyval, elmalign,
1755                                                   &elem_values, &elem_nulls, &num_elems);
1756                 s1 = useOr ? 0.0 : 1.0;
1757                 for (i = 0; i < num_elems; i++)
1758                 {
1759                         List       *args;
1760                         Selectivity s2;
1761
1762                         args = list_make2(leftop,
1763                                                           makeConst(nominal_element_type,
1764                                                                                 -1,
1765                                                                                 nominal_element_collation,
1766                                                                                 elmlen,
1767                                                                                 elem_values[i],
1768                                                                                 elem_nulls[i],
1769                                                                                 elmbyval));
1770                         if (is_join_clause)
1771                                 s2 = DatumGetFloat8(FunctionCall5(&oprselproc,
1772                                                                                                   PointerGetDatum(root),
1773                                                                                                   ObjectIdGetDatum(operator),
1774                                                                                                   PointerGetDatum(args),
1775                                                                                                   Int16GetDatum(jointype),
1776                                                                                                   PointerGetDatum(sjinfo)));
1777                         else
1778                                 s2 = DatumGetFloat8(FunctionCall4(&oprselproc,
1779                                                                                                   PointerGetDatum(root),
1780                                                                                                   ObjectIdGetDatum(operator),
1781                                                                                                   PointerGetDatum(args),
1782                                                                                                   Int32GetDatum(varRelid)));
1783                         if (useOr)
1784                                 s1 = s1 + s2 - s1 * s2;
1785                         else
1786                                 s1 = s1 * s2;
1787                 }
1788         }
1789         else if (rightop && IsA(rightop, ArrayExpr) &&
1790                          !((ArrayExpr *) rightop)->multidims)
1791         {
1792                 ArrayExpr  *arrayexpr = (ArrayExpr *) rightop;
1793                 int16           elmlen;
1794                 bool            elmbyval;
1795                 ListCell   *l;
1796
1797                 get_typlenbyval(arrayexpr->element_typeid,
1798                                                 &elmlen, &elmbyval);
1799                 s1 = useOr ? 0.0 : 1.0;
1800                 foreach(l, arrayexpr->elements)
1801                 {
1802                         Node       *elem = (Node *) lfirst(l);
1803                         List       *args;
1804                         Selectivity s2;
1805
1806                         /*
1807                          * Theoretically, if elem isn't of nominal_element_type we should
1808                          * insert a RelabelType, but it seems unlikely that any operator
1809                          * estimation function would really care ...
1810                          */
1811                         args = list_make2(leftop, elem);
1812                         if (is_join_clause)
1813                                 s2 = DatumGetFloat8(FunctionCall5(&oprselproc,
1814                                                                                                   PointerGetDatum(root),
1815                                                                                                   ObjectIdGetDatum(operator),
1816                                                                                                   PointerGetDatum(args),
1817                                                                                                   Int16GetDatum(jointype),
1818                                                                                                   PointerGetDatum(sjinfo)));
1819                         else
1820                                 s2 = DatumGetFloat8(FunctionCall4(&oprselproc,
1821                                                                                                   PointerGetDatum(root),
1822                                                                                                   ObjectIdGetDatum(operator),
1823                                                                                                   PointerGetDatum(args),
1824                                                                                                   Int32GetDatum(varRelid)));
1825                         if (useOr)
1826                                 s1 = s1 + s2 - s1 * s2;
1827                         else
1828                                 s1 = s1 * s2;
1829                 }
1830         }
1831         else
1832         {
1833                 CaseTestExpr *dummyexpr;
1834                 List       *args;
1835                 Selectivity s2;
1836                 int                     i;
1837
1838                 /*
1839                  * We need a dummy rightop to pass to the operator selectivity
1840                  * routine.  It can be pretty much anything that doesn't look like a
1841                  * constant; CaseTestExpr is a convenient choice.
1842                  */
1843                 dummyexpr = makeNode(CaseTestExpr);
1844                 dummyexpr->typeId = nominal_element_type;
1845                 dummyexpr->typeMod = -1;
1846                 dummyexpr->collation = clause->inputcollid;
1847                 args = list_make2(leftop, dummyexpr);
1848                 if (is_join_clause)
1849                         s2 = DatumGetFloat8(FunctionCall5(&oprselproc,
1850                                                                                           PointerGetDatum(root),
1851                                                                                           ObjectIdGetDatum(operator),
1852                                                                                           PointerGetDatum(args),
1853                                                                                           Int16GetDatum(jointype),
1854                                                                                           PointerGetDatum(sjinfo)));
1855                 else
1856                         s2 = DatumGetFloat8(FunctionCall4(&oprselproc,
1857                                                                                           PointerGetDatum(root),
1858                                                                                           ObjectIdGetDatum(operator),
1859                                                                                           PointerGetDatum(args),
1860                                                                                           Int32GetDatum(varRelid)));
1861                 s1 = useOr ? 0.0 : 1.0;
1862
1863                 /*
1864                  * Arbitrarily assume 10 elements in the eventual array value (see
1865                  * also estimate_array_length)
1866                  */
1867                 for (i = 0; i < 10; i++)
1868                 {
1869                         if (useOr)
1870                                 s1 = s1 + s2 - s1 * s2;
1871                         else
1872                                 s1 = s1 * s2;
1873                 }
1874         }
1875
1876         /* result should be in range, but make sure... */
1877         CLAMP_PROBABILITY(s1);
1878
1879         return s1;
1880 }
1881
1882 /*
1883  * Estimate number of elements in the array yielded by an expression.
1884  *
1885  * It's important that this agree with scalararraysel.
1886  */
1887 int
1888 estimate_array_length(Node *arrayexpr)
1889 {
1890         /* look through any binary-compatible relabeling of arrayexpr */
1891         arrayexpr = strip_array_coercion(arrayexpr);
1892
1893         if (arrayexpr && IsA(arrayexpr, Const))
1894         {
1895                 Datum           arraydatum = ((Const *) arrayexpr)->constvalue;
1896                 bool            arrayisnull = ((Const *) arrayexpr)->constisnull;
1897                 ArrayType  *arrayval;
1898
1899                 if (arrayisnull)
1900                         return 0;
1901                 arrayval = DatumGetArrayTypeP(arraydatum);
1902                 return ArrayGetNItems(ARR_NDIM(arrayval), ARR_DIMS(arrayval));
1903         }
1904         else if (arrayexpr && IsA(arrayexpr, ArrayExpr) &&
1905                          !((ArrayExpr *) arrayexpr)->multidims)
1906         {
1907                 return list_length(((ArrayExpr *) arrayexpr)->elements);
1908         }
1909         else
1910         {
1911                 /* default guess --- see also scalararraysel */
1912                 return 10;
1913         }
1914 }
1915
1916 /*
1917  *              rowcomparesel           - Selectivity of RowCompareExpr Node.
1918  *
1919  * We estimate RowCompare selectivity by considering just the first (high
1920  * order) columns, which makes it equivalent to an ordinary OpExpr.  While
1921  * this estimate could be refined by considering additional columns, it
1922  * seems unlikely that we could do a lot better without multi-column
1923  * statistics.
1924  */
1925 Selectivity
1926 rowcomparesel(PlannerInfo *root,
1927                           RowCompareExpr *clause,
1928                           int varRelid, JoinType jointype, SpecialJoinInfo *sjinfo)
1929 {
1930         Selectivity s1;
1931         Oid                     opno = linitial_oid(clause->opnos);
1932         List       *opargs;
1933         bool            is_join_clause;
1934
1935         /* Build equivalent arg list for single operator */
1936         opargs = list_make2(linitial(clause->largs), linitial(clause->rargs));
1937
1938         /*
1939          * Decide if it's a join clause.  This should match clausesel.c's
1940          * treat_as_join_clause(), except that we intentionally consider only the
1941          * leading columns and not the rest of the clause.
1942          */
1943         if (varRelid != 0)
1944         {
1945                 /*
1946                  * Caller is forcing restriction mode (eg, because we are examining an
1947                  * inner indexscan qual).
1948                  */
1949                 is_join_clause = false;
1950         }
1951         else if (sjinfo == NULL)
1952         {
1953                 /*
1954                  * It must be a restriction clause, since it's being evaluated at a
1955                  * scan node.
1956                  */
1957                 is_join_clause = false;
1958         }
1959         else
1960         {
1961                 /*
1962                  * Otherwise, it's a join if there's more than one relation used.
1963                  */
1964                 is_join_clause = (NumRelids((Node *) opargs) > 1);
1965         }
1966
1967         if (is_join_clause)
1968         {
1969                 /* Estimate selectivity for a join clause. */
1970                 s1 = join_selectivity(root, opno,
1971                                                           opargs,
1972                                                           jointype,
1973                                                           sjinfo);
1974         }
1975         else
1976         {
1977                 /* Estimate selectivity for a restriction clause. */
1978                 s1 = restriction_selectivity(root, opno,
1979                                                                          opargs,
1980                                                                          varRelid);
1981         }
1982
1983         return s1;
1984 }
1985
1986 /*
1987  *              eqjoinsel               - Join selectivity of "="
1988  */
1989 Datum
1990 eqjoinsel(PG_FUNCTION_ARGS)
1991 {
1992         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
1993         Oid                     operator = PG_GETARG_OID(1);
1994         List       *args = (List *) PG_GETARG_POINTER(2);
1995
1996 #ifdef NOT_USED
1997         JoinType        jointype = (JoinType) PG_GETARG_INT16(3);
1998 #endif
1999         SpecialJoinInfo *sjinfo = (SpecialJoinInfo *) PG_GETARG_POINTER(4);
2000         double          selec;
2001         VariableStatData vardata1;
2002         VariableStatData vardata2;
2003         bool            join_is_reversed;
2004
2005         get_join_variables(root, args, sjinfo,
2006                                            &vardata1, &vardata2, &join_is_reversed);
2007
2008         switch (sjinfo->jointype)
2009         {
2010                 case JOIN_INNER:
2011                 case JOIN_LEFT:
2012                 case JOIN_FULL:
2013                         selec = eqjoinsel_inner(operator, &vardata1, &vardata2);
2014                         break;
2015                 case JOIN_SEMI:
2016                 case JOIN_ANTI:
2017                         if (!join_is_reversed)
2018                                 selec = eqjoinsel_semi(operator, &vardata1, &vardata2);
2019                         else
2020                                 selec = eqjoinsel_semi(get_commutator(operator),
2021                                                                            &vardata2, &vardata1);
2022                         break;
2023                 default:
2024                         /* other values not expected here */
2025                         elog(ERROR, "unrecognized join type: %d",
2026                                  (int) sjinfo->jointype);
2027                         selec = 0;                      /* keep compiler quiet */
2028                         break;
2029         }
2030
2031         ReleaseVariableStats(vardata1);
2032         ReleaseVariableStats(vardata2);
2033
2034         CLAMP_PROBABILITY(selec);
2035
2036         PG_RETURN_FLOAT8((float8) selec);
2037 }
2038
2039 /*
2040  * eqjoinsel_inner --- eqjoinsel for normal inner join
2041  *
2042  * We also use this for LEFT/FULL outer joins; it's not presently clear
2043  * that it's worth trying to distinguish them here.
2044  */
2045 static double
2046 eqjoinsel_inner(Oid operator,
2047                                 VariableStatData *vardata1, VariableStatData *vardata2)
2048 {
2049         double          selec;
2050         double          nd1;
2051         double          nd2;
2052         Form_pg_statistic stats1 = NULL;
2053         Form_pg_statistic stats2 = NULL;
2054         bool            have_mcvs1 = false;
2055         Datum      *values1 = NULL;
2056         int                     nvalues1 = 0;
2057         float4     *numbers1 = NULL;
2058         int                     nnumbers1 = 0;
2059         bool            have_mcvs2 = false;
2060         Datum      *values2 = NULL;
2061         int                     nvalues2 = 0;
2062         float4     *numbers2 = NULL;
2063         int                     nnumbers2 = 0;
2064
2065         nd1 = get_variable_numdistinct(vardata1);
2066         nd2 = get_variable_numdistinct(vardata2);
2067
2068         if (HeapTupleIsValid(vardata1->statsTuple))
2069         {
2070                 stats1 = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
2071                 have_mcvs1 = get_attstatsslot(vardata1->statsTuple,
2072                                                                           vardata1->atttype,
2073                                                                           vardata1->atttypmod,
2074                                                                           STATISTIC_KIND_MCV,
2075                                                                           InvalidOid,
2076                                                                           NULL,
2077                                                                           &values1, &nvalues1,
2078                                                                           &numbers1, &nnumbers1);
2079         }
2080
2081         if (HeapTupleIsValid(vardata2->statsTuple))
2082         {
2083                 stats2 = (Form_pg_statistic) GETSTRUCT(vardata2->statsTuple);
2084                 have_mcvs2 = get_attstatsslot(vardata2->statsTuple,
2085                                                                           vardata2->atttype,
2086                                                                           vardata2->atttypmod,
2087                                                                           STATISTIC_KIND_MCV,
2088                                                                           InvalidOid,
2089                                                                           NULL,
2090                                                                           &values2, &nvalues2,
2091                                                                           &numbers2, &nnumbers2);
2092         }
2093
2094         if (have_mcvs1 && have_mcvs2)
2095         {
2096                 /*
2097                  * We have most-common-value lists for both relations.  Run through
2098                  * the lists to see which MCVs actually join to each other with the
2099                  * given operator.      This allows us to determine the exact join
2100                  * selectivity for the portion of the relations represented by the MCV
2101                  * lists.  We still have to estimate for the remaining population, but
2102                  * in a skewed distribution this gives us a big leg up in accuracy.
2103                  * For motivation see the analysis in Y. Ioannidis and S.
2104                  * Christodoulakis, "On the propagation of errors in the size of join
2105                  * results", Technical Report 1018, Computer Science Dept., University
2106                  * of Wisconsin, Madison, March 1991 (available from ftp.cs.wisc.edu).
2107                  */
2108                 FmgrInfo        eqproc;
2109                 bool       *hasmatch1;
2110                 bool       *hasmatch2;
2111                 double          nullfrac1 = stats1->stanullfrac;
2112                 double          nullfrac2 = stats2->stanullfrac;
2113                 double          matchprodfreq,
2114                                         matchfreq1,
2115                                         matchfreq2,
2116                                         unmatchfreq1,
2117                                         unmatchfreq2,
2118                                         otherfreq1,
2119                                         otherfreq2,
2120                                         totalsel1,
2121                                         totalsel2;
2122                 int                     i,
2123                                         nmatches;
2124
2125                 fmgr_info(get_opcode(operator), &eqproc);
2126                 fmgr_info_set_collation(DEFAULT_COLLATION_OID, &eqproc);
2127                 hasmatch1 = (bool *) palloc0(nvalues1 * sizeof(bool));
2128                 hasmatch2 = (bool *) palloc0(nvalues2 * sizeof(bool));
2129
2130                 /*
2131                  * Note we assume that each MCV will match at most one member of the
2132                  * other MCV list.      If the operator isn't really equality, there could
2133                  * be multiple matches --- but we don't look for them, both for speed
2134                  * and because the math wouldn't add up...
2135                  */
2136                 matchprodfreq = 0.0;
2137                 nmatches = 0;
2138                 for (i = 0; i < nvalues1; i++)
2139                 {
2140                         int                     j;
2141
2142                         for (j = 0; j < nvalues2; j++)
2143                         {
2144                                 if (hasmatch2[j])
2145                                         continue;
2146                                 if (DatumGetBool(FunctionCall2(&eqproc,
2147                                                                                            values1[i],
2148                                                                                            values2[j])))
2149                                 {
2150                                         hasmatch1[i] = hasmatch2[j] = true;
2151                                         matchprodfreq += numbers1[i] * numbers2[j];
2152                                         nmatches++;
2153                                         break;
2154                                 }
2155                         }
2156                 }
2157                 CLAMP_PROBABILITY(matchprodfreq);
2158                 /* Sum up frequencies of matched and unmatched MCVs */
2159                 matchfreq1 = unmatchfreq1 = 0.0;
2160                 for (i = 0; i < nvalues1; i++)
2161                 {
2162                         if (hasmatch1[i])
2163                                 matchfreq1 += numbers1[i];
2164                         else
2165                                 unmatchfreq1 += numbers1[i];
2166                 }
2167                 CLAMP_PROBABILITY(matchfreq1);
2168                 CLAMP_PROBABILITY(unmatchfreq1);
2169                 matchfreq2 = unmatchfreq2 = 0.0;
2170                 for (i = 0; i < nvalues2; i++)
2171                 {
2172                         if (hasmatch2[i])
2173                                 matchfreq2 += numbers2[i];
2174                         else
2175                                 unmatchfreq2 += numbers2[i];
2176                 }
2177                 CLAMP_PROBABILITY(matchfreq2);
2178                 CLAMP_PROBABILITY(unmatchfreq2);
2179                 pfree(hasmatch1);
2180                 pfree(hasmatch2);
2181
2182                 /*
2183                  * Compute total frequency of non-null values that are not in the MCV
2184                  * lists.
2185                  */
2186                 otherfreq1 = 1.0 - nullfrac1 - matchfreq1 - unmatchfreq1;
2187                 otherfreq2 = 1.0 - nullfrac2 - matchfreq2 - unmatchfreq2;
2188                 CLAMP_PROBABILITY(otherfreq1);
2189                 CLAMP_PROBABILITY(otherfreq2);
2190
2191                 /*
2192                  * We can estimate the total selectivity from the point of view of
2193                  * relation 1 as: the known selectivity for matched MCVs, plus
2194                  * unmatched MCVs that are assumed to match against random members of
2195                  * relation 2's non-MCV population, plus non-MCV values that are
2196                  * assumed to match against random members of relation 2's unmatched
2197                  * MCVs plus non-MCV values.
2198                  */
2199                 totalsel1 = matchprodfreq;
2200                 if (nd2 > nvalues2)
2201                         totalsel1 += unmatchfreq1 * otherfreq2 / (nd2 - nvalues2);
2202                 if (nd2 > nmatches)
2203                         totalsel1 += otherfreq1 * (otherfreq2 + unmatchfreq2) /
2204                                 (nd2 - nmatches);
2205                 /* Same estimate from the point of view of relation 2. */
2206                 totalsel2 = matchprodfreq;
2207                 if (nd1 > nvalues1)
2208                         totalsel2 += unmatchfreq2 * otherfreq1 / (nd1 - nvalues1);
2209                 if (nd1 > nmatches)
2210                         totalsel2 += otherfreq2 * (otherfreq1 + unmatchfreq1) /
2211                                 (nd1 - nmatches);
2212
2213                 /*
2214                  * Use the smaller of the two estimates.  This can be justified in
2215                  * essentially the same terms as given below for the no-stats case: to
2216                  * a first approximation, we are estimating from the point of view of
2217                  * the relation with smaller nd.
2218                  */
2219                 selec = (totalsel1 < totalsel2) ? totalsel1 : totalsel2;
2220         }
2221         else
2222         {
2223                 /*
2224                  * We do not have MCV lists for both sides.  Estimate the join
2225                  * selectivity as MIN(1/nd1,1/nd2)*(1-nullfrac1)*(1-nullfrac2). This
2226                  * is plausible if we assume that the join operator is strict and the
2227                  * non-null values are about equally distributed: a given non-null
2228                  * tuple of rel1 will join to either zero or N2*(1-nullfrac2)/nd2 rows
2229                  * of rel2, so total join rows are at most
2230                  * N1*(1-nullfrac1)*N2*(1-nullfrac2)/nd2 giving a join selectivity of
2231                  * not more than (1-nullfrac1)*(1-nullfrac2)/nd2. By the same logic it
2232                  * is not more than (1-nullfrac1)*(1-nullfrac2)/nd1, so the expression
2233                  * with MIN() is an upper bound.  Using the MIN() means we estimate
2234                  * from the point of view of the relation with smaller nd (since the
2235                  * larger nd is determining the MIN).  It is reasonable to assume that
2236                  * most tuples in this rel will have join partners, so the bound is
2237                  * probably reasonably tight and should be taken as-is.
2238                  *
2239                  * XXX Can we be smarter if we have an MCV list for just one side? It
2240                  * seems that if we assume equal distribution for the other side, we
2241                  * end up with the same answer anyway.
2242                  *
2243                  * An additional hack we use here is to clamp the nd1 and nd2 values
2244                  * to not more than what we are estimating the input relation sizes to
2245                  * be, providing a crude correction for the selectivity of restriction
2246                  * clauses on those relations.  (We don't do that in the other path
2247                  * since there we are comparing the nd values to stats for the whole
2248                  * relations.)
2249                  */
2250                 double          nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
2251                 double          nullfrac2 = stats2 ? stats2->stanullfrac : 0.0;
2252
2253                 if (vardata1->rel)
2254                         nd1 = Min(nd1, vardata1->rel->rows);
2255                 if (vardata2->rel)
2256                         nd2 = Min(nd2, vardata2->rel->rows);
2257
2258                 selec = (1.0 - nullfrac1) * (1.0 - nullfrac2);
2259                 if (nd1 > nd2)
2260                         selec /= nd1;
2261                 else
2262                         selec /= nd2;
2263         }
2264
2265         if (have_mcvs1)
2266                 free_attstatsslot(vardata1->atttype, values1, nvalues1,
2267                                                   numbers1, nnumbers1);
2268         if (have_mcvs2)
2269                 free_attstatsslot(vardata2->atttype, values2, nvalues2,
2270                                                   numbers2, nnumbers2);
2271
2272         return selec;
2273 }
2274
2275 /*
2276  * eqjoinsel_semi --- eqjoinsel for semi join
2277  *
2278  * (Also used for anti join, which we are supposed to estimate the same way.)
2279  * Caller has ensured that vardata1 is the LHS variable.
2280  */
2281 static double
2282 eqjoinsel_semi(Oid operator,
2283                            VariableStatData *vardata1, VariableStatData *vardata2)
2284 {
2285         double          selec;
2286         double          nd1;
2287         double          nd2;
2288         Form_pg_statistic stats1 = NULL;
2289         Form_pg_statistic stats2 = NULL;
2290         bool            have_mcvs1 = false;
2291         Datum      *values1 = NULL;
2292         int                     nvalues1 = 0;
2293         float4     *numbers1 = NULL;
2294         int                     nnumbers1 = 0;
2295         bool            have_mcvs2 = false;
2296         Datum      *values2 = NULL;
2297         int                     nvalues2 = 0;
2298         float4     *numbers2 = NULL;
2299         int                     nnumbers2 = 0;
2300
2301         nd1 = get_variable_numdistinct(vardata1);
2302         nd2 = get_variable_numdistinct(vardata2);
2303
2304         if (HeapTupleIsValid(vardata1->statsTuple))
2305         {
2306                 stats1 = (Form_pg_statistic) GETSTRUCT(vardata1->statsTuple);
2307                 have_mcvs1 = get_attstatsslot(vardata1->statsTuple,
2308                                                                           vardata1->atttype,
2309                                                                           vardata1->atttypmod,
2310                                                                           STATISTIC_KIND_MCV,
2311                                                                           InvalidOid,
2312                                                                           NULL,
2313                                                                           &values1, &nvalues1,
2314                                                                           &numbers1, &nnumbers1);
2315         }
2316
2317         if (HeapTupleIsValid(vardata2->statsTuple))
2318         {
2319                 stats2 = (Form_pg_statistic) GETSTRUCT(vardata2->statsTuple);
2320                 have_mcvs2 = get_attstatsslot(vardata2->statsTuple,
2321                                                                           vardata2->atttype,
2322                                                                           vardata2->atttypmod,
2323                                                                           STATISTIC_KIND_MCV,
2324                                                                           InvalidOid,
2325                                                                           NULL,
2326                                                                           &values2, &nvalues2,
2327                                                                           &numbers2, &nnumbers2);
2328         }
2329
2330         if (have_mcvs1 && have_mcvs2 && OidIsValid(operator))
2331         {
2332                 /*
2333                  * We have most-common-value lists for both relations.  Run through
2334                  * the lists to see which MCVs actually join to each other with the
2335                  * given operator.      This allows us to determine the exact join
2336                  * selectivity for the portion of the relations represented by the MCV
2337                  * lists.  We still have to estimate for the remaining population, but
2338                  * in a skewed distribution this gives us a big leg up in accuracy.
2339                  */
2340                 FmgrInfo        eqproc;
2341                 bool       *hasmatch1;
2342                 bool       *hasmatch2;
2343                 double          nullfrac1 = stats1->stanullfrac;
2344                 double          matchfreq1;
2345                 int                     i,
2346                                         nmatches;
2347
2348                 fmgr_info(get_opcode(operator), &eqproc);
2349                 fmgr_info_set_collation(DEFAULT_COLLATION_OID, &eqproc);
2350                 hasmatch1 = (bool *) palloc0(nvalues1 * sizeof(bool));
2351                 hasmatch2 = (bool *) palloc0(nvalues2 * sizeof(bool));
2352
2353                 /*
2354                  * Note we assume that each MCV will match at most one member of the
2355                  * other MCV list.      If the operator isn't really equality, there could
2356                  * be multiple matches --- but we don't look for them, both for speed
2357                  * and because the math wouldn't add up...
2358                  */
2359                 nmatches = 0;
2360                 for (i = 0; i < nvalues1; i++)
2361                 {
2362                         int                     j;
2363
2364                         for (j = 0; j < nvalues2; j++)
2365                         {
2366                                 if (hasmatch2[j])
2367                                         continue;
2368                                 if (DatumGetBool(FunctionCall2(&eqproc,
2369                                                                                            values1[i],
2370                                                                                            values2[j])))
2371                                 {
2372                                         hasmatch1[i] = hasmatch2[j] = true;
2373                                         nmatches++;
2374                                         break;
2375                                 }
2376                         }
2377                 }
2378                 /* Sum up frequencies of matched MCVs */
2379                 matchfreq1 = 0.0;
2380                 for (i = 0; i < nvalues1; i++)
2381                 {
2382                         if (hasmatch1[i])
2383                                 matchfreq1 += numbers1[i];
2384                 }
2385                 CLAMP_PROBABILITY(matchfreq1);
2386                 pfree(hasmatch1);
2387                 pfree(hasmatch2);
2388
2389                 /*
2390                  * Now we need to estimate the fraction of relation 1 that has at
2391                  * least one join partner.      We know for certain that the matched MCVs
2392                  * do, so that gives us a lower bound, but we're really in the dark
2393                  * about everything else.  Our crude approach is: if nd1 <= nd2 then
2394                  * assume all non-null rel1 rows have join partners, else assume for
2395                  * the uncertain rows that a fraction nd2/nd1 have join partners. We
2396                  * can discount the known-matched MCVs from the distinct-values counts
2397                  * before doing the division.
2398                  */
2399                 nd1 -= nmatches;
2400                 nd2 -= nmatches;
2401                 if (nd1 <= nd2 || nd2 <= 0)
2402                         selec = Max(matchfreq1, 1.0 - nullfrac1);
2403                 else
2404                 {
2405                         double          uncertain = 1.0 - matchfreq1 - nullfrac1;
2406
2407                         CLAMP_PROBABILITY(uncertain);
2408                         selec = matchfreq1 + (nd2 / nd1) * uncertain;
2409                 }
2410         }
2411         else
2412         {
2413                 /*
2414                  * Without MCV lists for both sides, we can only use the heuristic
2415                  * about nd1 vs nd2.
2416                  */
2417                 double          nullfrac1 = stats1 ? stats1->stanullfrac : 0.0;
2418
2419                 if (vardata1->rel)
2420                         nd1 = Min(nd1, vardata1->rel->rows);
2421                 if (vardata2->rel)
2422                         nd2 = Min(nd2, vardata2->rel->rows);
2423
2424                 if (nd1 <= nd2 || nd2 <= 0)
2425                         selec = 1.0 - nullfrac1;
2426                 else
2427                         selec = (nd2 / nd1) * (1.0 - nullfrac1);
2428         }
2429
2430         if (have_mcvs1)
2431                 free_attstatsslot(vardata1->atttype, values1, nvalues1,
2432                                                   numbers1, nnumbers1);
2433         if (have_mcvs2)
2434                 free_attstatsslot(vardata2->atttype, values2, nvalues2,
2435                                                   numbers2, nnumbers2);
2436
2437         return selec;
2438 }
2439
2440 /*
2441  *              neqjoinsel              - Join selectivity of "!="
2442  */
2443 Datum
2444 neqjoinsel(PG_FUNCTION_ARGS)
2445 {
2446         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
2447         Oid                     operator = PG_GETARG_OID(1);
2448         List       *args = (List *) PG_GETARG_POINTER(2);
2449         JoinType        jointype = (JoinType) PG_GETARG_INT16(3);
2450         SpecialJoinInfo *sjinfo = (SpecialJoinInfo *) PG_GETARG_POINTER(4);
2451         Oid                     eqop;
2452         float8          result;
2453
2454         /*
2455          * We want 1 - eqjoinsel() where the equality operator is the one
2456          * associated with this != operator, that is, its negator.
2457          */
2458         eqop = get_negator(operator);
2459         if (eqop)
2460         {
2461                 result = DatumGetFloat8(DirectFunctionCall5(eqjoinsel,
2462                                                                                                         PointerGetDatum(root),
2463                                                                                                         ObjectIdGetDatum(eqop),
2464                                                                                                         PointerGetDatum(args),
2465                                                                                                         Int16GetDatum(jointype),
2466                                                                                                         PointerGetDatum(sjinfo)));
2467         }
2468         else
2469         {
2470                 /* Use default selectivity (should we raise an error instead?) */
2471                 result = DEFAULT_EQ_SEL;
2472         }
2473         result = 1.0 - result;
2474         PG_RETURN_FLOAT8(result);
2475 }
2476
2477 /*
2478  *              scalarltjoinsel - Join selectivity of "<" and "<=" for scalars
2479  */
2480 Datum
2481 scalarltjoinsel(PG_FUNCTION_ARGS)
2482 {
2483         PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
2484 }
2485
2486 /*
2487  *              scalargtjoinsel - Join selectivity of ">" and ">=" for scalars
2488  */
2489 Datum
2490 scalargtjoinsel(PG_FUNCTION_ARGS)
2491 {
2492         PG_RETURN_FLOAT8(DEFAULT_INEQ_SEL);
2493 }
2494
2495 /*
2496  * patternjoinsel               - Generic code for pattern-match join selectivity.
2497  */
2498 static double
2499 patternjoinsel(PG_FUNCTION_ARGS, Pattern_Type ptype, bool negate)
2500 {
2501         /* For the moment we just punt. */
2502         return negate ? (1.0 - DEFAULT_MATCH_SEL) : DEFAULT_MATCH_SEL;
2503 }
2504
2505 /*
2506  *              regexeqjoinsel  - Join selectivity of regular-expression pattern match.
2507  */
2508 Datum
2509 regexeqjoinsel(PG_FUNCTION_ARGS)
2510 {
2511         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex, false));
2512 }
2513
2514 /*
2515  *              icregexeqjoinsel        - Join selectivity of case-insensitive regex match.
2516  */
2517 Datum
2518 icregexeqjoinsel(PG_FUNCTION_ARGS)
2519 {
2520         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex_IC, false));
2521 }
2522
2523 /*
2524  *              likejoinsel                     - Join selectivity of LIKE pattern match.
2525  */
2526 Datum
2527 likejoinsel(PG_FUNCTION_ARGS)
2528 {
2529         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like, false));
2530 }
2531
2532 /*
2533  *              iclikejoinsel                   - Join selectivity of ILIKE pattern match.
2534  */
2535 Datum
2536 iclikejoinsel(PG_FUNCTION_ARGS)
2537 {
2538         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like_IC, false));
2539 }
2540
2541 /*
2542  *              regexnejoinsel  - Join selectivity of regex non-match.
2543  */
2544 Datum
2545 regexnejoinsel(PG_FUNCTION_ARGS)
2546 {
2547         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex, true));
2548 }
2549
2550 /*
2551  *              icregexnejoinsel        - Join selectivity of case-insensitive regex non-match.
2552  */
2553 Datum
2554 icregexnejoinsel(PG_FUNCTION_ARGS)
2555 {
2556         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Regex_IC, true));
2557 }
2558
2559 /*
2560  *              nlikejoinsel            - Join selectivity of LIKE pattern non-match.
2561  */
2562 Datum
2563 nlikejoinsel(PG_FUNCTION_ARGS)
2564 {
2565         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like, true));
2566 }
2567
2568 /*
2569  *              icnlikejoinsel          - Join selectivity of ILIKE pattern non-match.
2570  */
2571 Datum
2572 icnlikejoinsel(PG_FUNCTION_ARGS)
2573 {
2574         PG_RETURN_FLOAT8(patternjoinsel(fcinfo, Pattern_Type_Like_IC, true));
2575 }
2576
2577 /*
2578  * mergejoinscansel                     - Scan selectivity of merge join.
2579  *
2580  * A merge join will stop as soon as it exhausts either input stream.
2581  * Therefore, if we can estimate the ranges of both input variables,
2582  * we can estimate how much of the input will actually be read.  This
2583  * can have a considerable impact on the cost when using indexscans.
2584  *
2585  * Also, we can estimate how much of each input has to be read before the
2586  * first join pair is found, which will affect the join's startup time.
2587  *
2588  * clause should be a clause already known to be mergejoinable.  opfamily,
2589  * strategy, and nulls_first specify the sort ordering being used.
2590  *
2591  * The outputs are:
2592  *              *leftstart is set to the fraction of the left-hand variable expected
2593  *               to be scanned before the first join pair is found (0 to 1).
2594  *              *leftend is set to the fraction of the left-hand variable expected
2595  *               to be scanned before the join terminates (0 to 1).
2596  *              *rightstart, *rightend similarly for the right-hand variable.
2597  */
2598 void
2599 mergejoinscansel(PlannerInfo *root, Node *clause,
2600                                  Oid opfamily, int strategy, bool nulls_first,
2601                                  Selectivity *leftstart, Selectivity *leftend,
2602                                  Selectivity *rightstart, Selectivity *rightend)
2603 {
2604         Node       *left,
2605                            *right;
2606         VariableStatData leftvar,
2607                                 rightvar;
2608         int                     op_strategy;
2609         Oid                     op_lefttype;
2610         Oid                     op_righttype;
2611         Oid                     opno,
2612                                 lsortop,
2613                                 rsortop,
2614                                 lstatop,
2615                                 rstatop,
2616                                 ltop,
2617                                 leop,
2618                                 revltop,
2619                                 revleop;
2620         bool            isgt;
2621         Datum           leftmin,
2622                                 leftmax,
2623                                 rightmin,
2624                                 rightmax;
2625         double          selec;
2626
2627         /* Set default results if we can't figure anything out. */
2628         /* XXX should default "start" fraction be a bit more than 0? */
2629         *leftstart = *rightstart = 0.0;
2630         *leftend = *rightend = 1.0;
2631
2632         /* Deconstruct the merge clause */
2633         if (!is_opclause(clause))
2634                 return;                                 /* shouldn't happen */
2635         opno = ((OpExpr *) clause)->opno;
2636         left = get_leftop((Expr *) clause);
2637         right = get_rightop((Expr *) clause);
2638         if (!right)
2639                 return;                                 /* shouldn't happen */
2640
2641         /* Look for stats for the inputs */
2642         examine_variable(root, left, 0, &leftvar);
2643         examine_variable(root, right, 0, &rightvar);
2644
2645         /* Extract the operator's declared left/right datatypes */
2646         get_op_opfamily_properties(opno, opfamily, false,
2647                                                            &op_strategy,
2648                                                            &op_lefttype,
2649                                                            &op_righttype);
2650         Assert(op_strategy == BTEqualStrategyNumber);
2651
2652         /*
2653          * Look up the various operators we need.  If we don't find them all, it
2654          * probably means the opfamily is broken, but we just fail silently.
2655          *
2656          * Note: we expect that pg_statistic histograms will be sorted by the '<'
2657          * operator, regardless of which sort direction we are considering.
2658          */
2659         switch (strategy)
2660         {
2661                 case BTLessStrategyNumber:
2662                         isgt = false;
2663                         if (op_lefttype == op_righttype)
2664                         {
2665                                 /* easy case */
2666                                 ltop = get_opfamily_member(opfamily,
2667                                                                                    op_lefttype, op_righttype,
2668                                                                                    BTLessStrategyNumber);
2669                                 leop = get_opfamily_member(opfamily,
2670                                                                                    op_lefttype, op_righttype,
2671                                                                                    BTLessEqualStrategyNumber);
2672                                 lsortop = ltop;
2673                                 rsortop = ltop;
2674                                 lstatop = lsortop;
2675                                 rstatop = rsortop;
2676                                 revltop = ltop;
2677                                 revleop = leop;
2678                         }
2679                         else
2680                         {
2681                                 ltop = get_opfamily_member(opfamily,
2682                                                                                    op_lefttype, op_righttype,
2683                                                                                    BTLessStrategyNumber);
2684                                 leop = get_opfamily_member(opfamily,
2685                                                                                    op_lefttype, op_righttype,
2686                                                                                    BTLessEqualStrategyNumber);
2687                                 lsortop = get_opfamily_member(opfamily,
2688                                                                                           op_lefttype, op_lefttype,
2689                                                                                           BTLessStrategyNumber);
2690                                 rsortop = get_opfamily_member(opfamily,
2691                                                                                           op_righttype, op_righttype,
2692                                                                                           BTLessStrategyNumber);
2693                                 lstatop = lsortop;
2694                                 rstatop = rsortop;
2695                                 revltop = get_opfamily_member(opfamily,
2696                                                                                           op_righttype, op_lefttype,
2697                                                                                           BTLessStrategyNumber);
2698                                 revleop = get_opfamily_member(opfamily,
2699                                                                                           op_righttype, op_lefttype,
2700                                                                                           BTLessEqualStrategyNumber);
2701                         }
2702                         break;
2703                 case BTGreaterStrategyNumber:
2704                         /* descending-order case */
2705                         isgt = true;
2706                         if (op_lefttype == op_righttype)
2707                         {
2708                                 /* easy case */
2709                                 ltop = get_opfamily_member(opfamily,
2710                                                                                    op_lefttype, op_righttype,
2711                                                                                    BTGreaterStrategyNumber);
2712                                 leop = get_opfamily_member(opfamily,
2713                                                                                    op_lefttype, op_righttype,
2714                                                                                    BTGreaterEqualStrategyNumber);
2715                                 lsortop = ltop;
2716                                 rsortop = ltop;
2717                                 lstatop = get_opfamily_member(opfamily,
2718                                                                                           op_lefttype, op_lefttype,
2719                                                                                           BTLessStrategyNumber);
2720                                 rstatop = lstatop;
2721                                 revltop = ltop;
2722                                 revleop = leop;
2723                         }
2724                         else
2725                         {
2726                                 ltop = get_opfamily_member(opfamily,
2727                                                                                    op_lefttype, op_righttype,
2728                                                                                    BTGreaterStrategyNumber);
2729                                 leop = get_opfamily_member(opfamily,
2730                                                                                    op_lefttype, op_righttype,
2731                                                                                    BTGreaterEqualStrategyNumber);
2732                                 lsortop = get_opfamily_member(opfamily,
2733                                                                                           op_lefttype, op_lefttype,
2734                                                                                           BTGreaterStrategyNumber);
2735                                 rsortop = get_opfamily_member(opfamily,
2736                                                                                           op_righttype, op_righttype,
2737                                                                                           BTGreaterStrategyNumber);
2738                                 lstatop = get_opfamily_member(opfamily,
2739                                                                                           op_lefttype, op_lefttype,
2740                                                                                           BTLessStrategyNumber);
2741                                 rstatop = get_opfamily_member(opfamily,
2742                                                                                           op_righttype, op_righttype,
2743                                                                                           BTLessStrategyNumber);
2744                                 revltop = get_opfamily_member(opfamily,
2745                                                                                           op_righttype, op_lefttype,
2746                                                                                           BTGreaterStrategyNumber);
2747                                 revleop = get_opfamily_member(opfamily,
2748                                                                                           op_righttype, op_lefttype,
2749                                                                                           BTGreaterEqualStrategyNumber);
2750                         }
2751                         break;
2752                 default:
2753                         goto fail;                      /* shouldn't get here */
2754         }
2755
2756         if (!OidIsValid(lsortop) ||
2757                 !OidIsValid(rsortop) ||
2758                 !OidIsValid(lstatop) ||
2759                 !OidIsValid(rstatop) ||
2760                 !OidIsValid(ltop) ||
2761                 !OidIsValid(leop) ||
2762                 !OidIsValid(revltop) ||
2763                 !OidIsValid(revleop))
2764                 goto fail;                              /* insufficient info in catalogs */
2765
2766         /* Try to get ranges of both inputs */
2767         if (!isgt)
2768         {
2769                 if (!get_variable_range(root, &leftvar, lstatop,
2770                                                                 &leftmin, &leftmax))
2771                         goto fail;                      /* no range available from stats */
2772                 if (!get_variable_range(root, &rightvar, rstatop,
2773                                                                 &rightmin, &rightmax))
2774                         goto fail;                      /* no range available from stats */
2775         }
2776         else
2777         {
2778                 /* need to swap the max and min */
2779                 if (!get_variable_range(root, &leftvar, lstatop,
2780                                                                 &leftmax, &leftmin))
2781                         goto fail;                      /* no range available from stats */
2782                 if (!get_variable_range(root, &rightvar, rstatop,
2783                                                                 &rightmax, &rightmin))
2784                         goto fail;                      /* no range available from stats */
2785         }
2786
2787         /*
2788          * Now, the fraction of the left variable that will be scanned is the
2789          * fraction that's <= the right-side maximum value.  But only believe
2790          * non-default estimates, else stick with our 1.0.
2791          */
2792         selec = scalarineqsel(root, leop, isgt, &leftvar,
2793                                                   rightmax, op_righttype);
2794         if (selec != DEFAULT_INEQ_SEL)
2795                 *leftend = selec;
2796
2797         /* And similarly for the right variable. */
2798         selec = scalarineqsel(root, revleop, isgt, &rightvar,
2799                                                   leftmax, op_lefttype);
2800         if (selec != DEFAULT_INEQ_SEL)
2801                 *rightend = selec;
2802
2803         /*
2804          * Only one of the two "end" fractions can really be less than 1.0;
2805          * believe the smaller estimate and reset the other one to exactly 1.0. If
2806          * we get exactly equal estimates (as can easily happen with self-joins),
2807          * believe neither.
2808          */
2809         if (*leftend > *rightend)
2810                 *leftend = 1.0;
2811         else if (*leftend < *rightend)
2812                 *rightend = 1.0;
2813         else
2814                 *leftend = *rightend = 1.0;
2815
2816         /*
2817          * Also, the fraction of the left variable that will be scanned before the
2818          * first join pair is found is the fraction that's < the right-side
2819          * minimum value.  But only believe non-default estimates, else stick with
2820          * our own default.
2821          */
2822         selec = scalarineqsel(root, ltop, isgt, &leftvar,
2823                                                   rightmin, op_righttype);
2824         if (selec != DEFAULT_INEQ_SEL)
2825                 *leftstart = selec;
2826
2827         /* And similarly for the right variable. */
2828         selec = scalarineqsel(root, revltop, isgt, &rightvar,
2829                                                   leftmin, op_lefttype);
2830         if (selec != DEFAULT_INEQ_SEL)
2831                 *rightstart = selec;
2832
2833         /*
2834          * Only one of the two "start" fractions can really be more than zero;
2835          * believe the larger estimate and reset the other one to exactly 0.0. If
2836          * we get exactly equal estimates (as can easily happen with self-joins),
2837          * believe neither.
2838          */
2839         if (*leftstart < *rightstart)
2840                 *leftstart = 0.0;
2841         else if (*leftstart > *rightstart)
2842                 *rightstart = 0.0;
2843         else
2844                 *leftstart = *rightstart = 0.0;
2845
2846         /*
2847          * If the sort order is nulls-first, we're going to have to skip over any
2848          * nulls too.  These would not have been counted by scalarineqsel, and we
2849          * can safely add in this fraction regardless of whether we believe
2850          * scalarineqsel's results or not.  But be sure to clamp the sum to 1.0!
2851          */
2852         if (nulls_first)
2853         {
2854                 Form_pg_statistic stats;
2855
2856                 if (HeapTupleIsValid(leftvar.statsTuple))
2857                 {
2858                         stats = (Form_pg_statistic) GETSTRUCT(leftvar.statsTuple);
2859                         *leftstart += stats->stanullfrac;
2860                         CLAMP_PROBABILITY(*leftstart);
2861                         *leftend += stats->stanullfrac;
2862                         CLAMP_PROBABILITY(*leftend);
2863                 }
2864                 if (HeapTupleIsValid(rightvar.statsTuple))
2865                 {
2866                         stats = (Form_pg_statistic) GETSTRUCT(rightvar.statsTuple);
2867                         *rightstart += stats->stanullfrac;
2868                         CLAMP_PROBABILITY(*rightstart);
2869                         *rightend += stats->stanullfrac;
2870                         CLAMP_PROBABILITY(*rightend);
2871                 }
2872         }
2873
2874         /* Disbelieve start >= end, just in case that can happen */
2875         if (*leftstart >= *leftend)
2876         {
2877                 *leftstart = 0.0;
2878                 *leftend = 1.0;
2879         }
2880         if (*rightstart >= *rightend)
2881         {
2882                 *rightstart = 0.0;
2883                 *rightend = 1.0;
2884         }
2885
2886 fail:
2887         ReleaseVariableStats(leftvar);
2888         ReleaseVariableStats(rightvar);
2889 }
2890
2891
2892 /*
2893  * Helper routine for estimate_num_groups: add an item to a list of
2894  * GroupVarInfos, but only if it's not known equal to any of the existing
2895  * entries.
2896  */
2897 typedef struct
2898 {
2899         Node       *var;                        /* might be an expression, not just a Var */
2900         RelOptInfo *rel;                        /* relation it belongs to */
2901         double          ndistinct;              /* # distinct values */
2902 } GroupVarInfo;
2903
2904 static List *
2905 add_unique_group_var(PlannerInfo *root, List *varinfos,
2906                                          Node *var, VariableStatData *vardata)
2907 {
2908         GroupVarInfo *varinfo;
2909         double          ndistinct;
2910         ListCell   *lc;
2911
2912         ndistinct = get_variable_numdistinct(vardata);
2913
2914         /* cannot use foreach here because of possible list_delete */
2915         lc = list_head(varinfos);
2916         while (lc)
2917         {
2918                 varinfo = (GroupVarInfo *) lfirst(lc);
2919
2920                 /* must advance lc before list_delete possibly pfree's it */
2921                 lc = lnext(lc);
2922
2923                 /* Drop exact duplicates */
2924                 if (equal(var, varinfo->var))
2925                         return varinfos;
2926
2927                 /*
2928                  * Drop known-equal vars, but only if they belong to different
2929                  * relations (see comments for estimate_num_groups)
2930                  */
2931                 if (vardata->rel != varinfo->rel &&
2932                         exprs_known_equal(root, var, varinfo->var))
2933                 {
2934                         if (varinfo->ndistinct <= ndistinct)
2935                         {
2936                                 /* Keep older item, forget new one */
2937                                 return varinfos;
2938                         }
2939                         else
2940                         {
2941                                 /* Delete the older item */
2942                                 varinfos = list_delete_ptr(varinfos, varinfo);
2943                         }
2944                 }
2945         }
2946
2947         varinfo = (GroupVarInfo *) palloc(sizeof(GroupVarInfo));
2948
2949         varinfo->var = var;
2950         varinfo->rel = vardata->rel;
2951         varinfo->ndistinct = ndistinct;
2952         varinfos = lappend(varinfos, varinfo);
2953         return varinfos;
2954 }
2955
2956 /*
2957  * estimate_num_groups          - Estimate number of groups in a grouped query
2958  *
2959  * Given a query having a GROUP BY clause, estimate how many groups there
2960  * will be --- ie, the number of distinct combinations of the GROUP BY
2961  * expressions.
2962  *
2963  * This routine is also used to estimate the number of rows emitted by
2964  * a DISTINCT filtering step; that is an isomorphic problem.  (Note:
2965  * actually, we only use it for DISTINCT when there's no grouping or
2966  * aggregation ahead of the DISTINCT.)
2967  *
2968  * Inputs:
2969  *      root - the query
2970  *      groupExprs - list of expressions being grouped by
2971  *      input_rows - number of rows estimated to arrive at the group/unique
2972  *              filter step
2973  *
2974  * Given the lack of any cross-correlation statistics in the system, it's
2975  * impossible to do anything really trustworthy with GROUP BY conditions
2976  * involving multiple Vars.  We should however avoid assuming the worst
2977  * case (all possible cross-product terms actually appear as groups) since
2978  * very often the grouped-by Vars are highly correlated.  Our current approach
2979  * is as follows:
2980  *      1.      Expressions yielding boolean are assumed to contribute two groups,
2981  *              independently of their content, and are ignored in the subsequent
2982  *              steps.  This is mainly because tests like "col IS NULL" break the
2983  *              heuristic used in step 2 especially badly.
2984  *      2.      Reduce the given expressions to a list of unique Vars used.  For
2985  *              example, GROUP BY a, a + b is treated the same as GROUP BY a, b.
2986  *              It is clearly correct not to count the same Var more than once.
2987  *              It is also reasonable to treat f(x) the same as x: f() cannot
2988  *              increase the number of distinct values (unless it is volatile,
2989  *              which we consider unlikely for grouping), but it probably won't
2990  *              reduce the number of distinct values much either.
2991  *              As a special case, if a GROUP BY expression can be matched to an
2992  *              expressional index for which we have statistics, then we treat the
2993  *              whole expression as though it were just a Var.
2994  *      3.      If the list contains Vars of different relations that are known equal
2995  *              due to equivalence classes, then drop all but one of the Vars from each
2996  *              known-equal set, keeping the one with smallest estimated # of values
2997  *              (since the extra values of the others can't appear in joined rows).
2998  *              Note the reason we only consider Vars of different relations is that
2999  *              if we considered ones of the same rel, we'd be double-counting the
3000  *              restriction selectivity of the equality in the next step.
3001  *      4.      For Vars within a single source rel, we multiply together the numbers
3002  *              of values, clamp to the number of rows in the rel (divided by 10 if
3003  *              more than one Var), and then multiply by the selectivity of the
3004  *              restriction clauses for that rel.  When there's more than one Var,
3005  *              the initial product is probably too high (it's the worst case) but
3006  *              clamping to a fraction of the rel's rows seems to be a helpful
3007  *              heuristic for not letting the estimate get out of hand.  (The factor
3008  *              of 10 is derived from pre-Postgres-7.4 practice.)  Multiplying
3009  *              by the restriction selectivity is effectively assuming that the
3010  *              restriction clauses are independent of the grouping, which is a crummy
3011  *              assumption, but it's hard to do better.
3012  *      5.      If there are Vars from multiple rels, we repeat step 4 for each such
3013  *              rel, and multiply the results together.
3014  * Note that rels not containing grouped Vars are ignored completely, as are
3015  * join clauses.  Such rels cannot increase the number of groups, and we
3016  * assume such clauses do not reduce the number either (somewhat bogus,
3017  * but we don't have the info to do better).
3018  */
3019 double
3020 estimate_num_groups(PlannerInfo *root, List *groupExprs, double input_rows)
3021 {
3022         List       *varinfos = NIL;
3023         double          numdistinct;
3024         ListCell   *l;
3025
3026         /* We should not be called unless query has GROUP BY (or DISTINCT) */
3027         Assert(groupExprs != NIL);
3028
3029         /*
3030          * Count groups derived from boolean grouping expressions.      For other
3031          * expressions, find the unique Vars used, treating an expression as a Var
3032          * if we can find stats for it.  For each one, record the statistical
3033          * estimate of number of distinct values (total in its table, without
3034          * regard for filtering).
3035          */
3036         numdistinct = 1.0;
3037
3038         foreach(l, groupExprs)
3039         {
3040                 Node       *groupexpr = (Node *) lfirst(l);
3041                 VariableStatData vardata;
3042                 List       *varshere;
3043                 ListCell   *l2;
3044
3045                 /* Short-circuit for expressions returning boolean */
3046                 if (exprType(groupexpr) == BOOLOID)
3047                 {
3048                         numdistinct *= 2.0;
3049                         continue;
3050                 }
3051
3052                 /*
3053                  * If examine_variable is able to deduce anything about the GROUP BY
3054                  * expression, treat it as a single variable even if it's really more
3055                  * complicated.
3056                  */
3057                 examine_variable(root, groupexpr, 0, &vardata);
3058                 if (HeapTupleIsValid(vardata.statsTuple) || vardata.isunique)
3059                 {
3060                         varinfos = add_unique_group_var(root, varinfos,
3061                                                                                         groupexpr, &vardata);
3062                         ReleaseVariableStats(vardata);
3063                         continue;
3064                 }
3065                 ReleaseVariableStats(vardata);
3066
3067                 /*
3068                  * Else pull out the component Vars.  Handle PlaceHolderVars by
3069                  * recursing into their arguments (effectively assuming that the
3070                  * PlaceHolderVar doesn't change the number of groups, which boils
3071                  * down to ignoring the possible addition of nulls to the result set).
3072                  */
3073                 varshere = pull_var_clause(groupexpr, PVC_RECURSE_PLACEHOLDERS);
3074
3075                 /*
3076                  * If we find any variable-free GROUP BY item, then either it is a
3077                  * constant (and we can ignore it) or it contains a volatile function;
3078                  * in the latter case we punt and assume that each input row will
3079                  * yield a distinct group.
3080                  */
3081                 if (varshere == NIL)
3082                 {
3083                         if (contain_volatile_functions(groupexpr))
3084                                 return input_rows;
3085                         continue;
3086                 }
3087
3088                 /*
3089                  * Else add variables to varinfos list
3090                  */
3091                 foreach(l2, varshere)
3092                 {
3093                         Node       *var = (Node *) lfirst(l2);
3094
3095                         examine_variable(root, var, 0, &vardata);
3096                         varinfos = add_unique_group_var(root, varinfos, var, &vardata);
3097                         ReleaseVariableStats(vardata);
3098                 }
3099         }
3100
3101         /*
3102          * If now no Vars, we must have an all-constant or all-boolean GROUP BY
3103          * list.
3104          */
3105         if (varinfos == NIL)
3106         {
3107                 /* Guard against out-of-range answers */
3108                 if (numdistinct > input_rows)
3109                         numdistinct = input_rows;
3110                 return numdistinct;
3111         }
3112
3113         /*
3114          * Group Vars by relation and estimate total numdistinct.
3115          *
3116          * For each iteration of the outer loop, we process the frontmost Var in
3117          * varinfos, plus all other Vars in the same relation.  We remove these
3118          * Vars from the newvarinfos list for the next iteration. This is the
3119          * easiest way to group Vars of same rel together.
3120          */
3121         do
3122         {
3123                 GroupVarInfo *varinfo1 = (GroupVarInfo *) linitial(varinfos);
3124                 RelOptInfo *rel = varinfo1->rel;
3125                 double          reldistinct = varinfo1->ndistinct;
3126                 double          relmaxndistinct = reldistinct;
3127                 int                     relvarcount = 1;
3128                 List       *newvarinfos = NIL;
3129
3130                 /*
3131                  * Get the product of numdistinct estimates of the Vars for this rel.
3132                  * Also, construct new varinfos list of remaining Vars.
3133                  */
3134                 for_each_cell(l, lnext(list_head(varinfos)))
3135                 {
3136                         GroupVarInfo *varinfo2 = (GroupVarInfo *) lfirst(l);
3137
3138                         if (varinfo2->rel == varinfo1->rel)
3139                         {
3140                                 reldistinct *= varinfo2->ndistinct;
3141                                 if (relmaxndistinct < varinfo2->ndistinct)
3142                                         relmaxndistinct = varinfo2->ndistinct;
3143                                 relvarcount++;
3144                         }
3145                         else
3146                         {
3147                                 /* not time to process varinfo2 yet */
3148                                 newvarinfos = lcons(varinfo2, newvarinfos);
3149                         }
3150                 }
3151
3152                 /*
3153                  * Sanity check --- don't divide by zero if empty relation.
3154                  */
3155                 Assert(rel->reloptkind == RELOPT_BASEREL);
3156                 if (rel->tuples > 0)
3157                 {
3158                         /*
3159                          * Clamp to size of rel, or size of rel / 10 if multiple Vars. The
3160                          * fudge factor is because the Vars are probably correlated but we
3161                          * don't know by how much.  We should never clamp to less than the
3162                          * largest ndistinct value for any of the Vars, though, since
3163                          * there will surely be at least that many groups.
3164                          */
3165                         double          clamp = rel->tuples;
3166
3167                         if (relvarcount > 1)
3168                         {
3169                                 clamp *= 0.1;
3170                                 if (clamp < relmaxndistinct)
3171                                 {
3172                                         clamp = relmaxndistinct;
3173                                         /* for sanity in case some ndistinct is too large: */
3174                                         if (clamp > rel->tuples)
3175                                                 clamp = rel->tuples;
3176                                 }
3177                         }
3178                         if (reldistinct > clamp)
3179                                 reldistinct = clamp;
3180
3181                         /*
3182                          * Multiply by restriction selectivity.
3183                          */
3184                         reldistinct *= rel->rows / rel->tuples;
3185
3186                         /*
3187                          * Update estimate of total distinct groups.
3188                          */
3189                         numdistinct *= reldistinct;
3190                 }
3191
3192                 varinfos = newvarinfos;
3193         } while (varinfos != NIL);
3194
3195         numdistinct = ceil(numdistinct);
3196
3197         /* Guard against out-of-range answers */
3198         if (numdistinct > input_rows)
3199                 numdistinct = input_rows;
3200         if (numdistinct < 1.0)
3201                 numdistinct = 1.0;
3202
3203         return numdistinct;
3204 }
3205
3206 /*
3207  * Estimate hash bucketsize fraction (ie, number of entries in a bucket
3208  * divided by total tuples in relation) if the specified expression is used
3209  * as a hash key.
3210  *
3211  * XXX This is really pretty bogus since we're effectively assuming that the
3212  * distribution of hash keys will be the same after applying restriction
3213  * clauses as it was in the underlying relation.  However, we are not nearly
3214  * smart enough to figure out how the restrict clauses might change the
3215  * distribution, so this will have to do for now.
3216  *
3217  * We are passed the number of buckets the executor will use for the given
3218  * input relation.      If the data were perfectly distributed, with the same
3219  * number of tuples going into each available bucket, then the bucketsize
3220  * fraction would be 1/nbuckets.  But this happy state of affairs will occur
3221  * only if (a) there are at least nbuckets distinct data values, and (b)
3222  * we have a not-too-skewed data distribution.  Otherwise the buckets will
3223  * be nonuniformly occupied.  If the other relation in the join has a key
3224  * distribution similar to this one's, then the most-loaded buckets are
3225  * exactly those that will be probed most often.  Therefore, the "average"
3226  * bucket size for costing purposes should really be taken as something close
3227  * to the "worst case" bucket size.  We try to estimate this by adjusting the
3228  * fraction if there are too few distinct data values, and then scaling up
3229  * by the ratio of the most common value's frequency to the average frequency.
3230  *
3231  * If no statistics are available, use a default estimate of 0.1.  This will
3232  * discourage use of a hash rather strongly if the inner relation is large,
3233  * which is what we want.  We do not want to hash unless we know that the
3234  * inner rel is well-dispersed (or the alternatives seem much worse).
3235  */
3236 Selectivity
3237 estimate_hash_bucketsize(PlannerInfo *root, Node *hashkey, double nbuckets)
3238 {
3239         VariableStatData vardata;
3240         double          estfract,
3241                                 ndistinct,
3242                                 stanullfrac,
3243                                 mcvfreq,
3244                                 avgfreq;
3245         float4     *numbers;
3246         int                     nnumbers;
3247
3248         examine_variable(root, hashkey, 0, &vardata);
3249
3250         /* Get number of distinct values and fraction that are null */
3251         ndistinct = get_variable_numdistinct(&vardata);
3252
3253         if (HeapTupleIsValid(vardata.statsTuple))
3254         {
3255                 Form_pg_statistic stats;
3256
3257                 stats = (Form_pg_statistic) GETSTRUCT(vardata.statsTuple);
3258                 stanullfrac = stats->stanullfrac;
3259         }
3260         else
3261         {
3262                 /*
3263                  * Believe a default ndistinct only if it came from stats. Otherwise
3264                  * punt and return 0.1, per comments above.
3265                  */
3266                 if (ndistinct == DEFAULT_NUM_DISTINCT)
3267                 {
3268                         ReleaseVariableStats(vardata);
3269                         return (Selectivity) 0.1;
3270                 }
3271
3272                 stanullfrac = 0.0;
3273         }
3274
3275         /* Compute avg freq of all distinct data values in raw relation */
3276         avgfreq = (1.0 - stanullfrac) / ndistinct;
3277
3278         /*
3279          * Adjust ndistinct to account for restriction clauses.  Observe we are
3280          * assuming that the data distribution is affected uniformly by the
3281          * restriction clauses!
3282          *
3283          * XXX Possibly better way, but much more expensive: multiply by
3284          * selectivity of rel's restriction clauses that mention the target Var.
3285          */
3286         if (vardata.rel)
3287                 ndistinct *= vardata.rel->rows / vardata.rel->tuples;
3288
3289         /*
3290          * Initial estimate of bucketsize fraction is 1/nbuckets as long as the
3291          * number of buckets is less than the expected number of distinct values;
3292          * otherwise it is 1/ndistinct.
3293          */
3294         if (ndistinct > nbuckets)
3295                 estfract = 1.0 / nbuckets;
3296         else
3297                 estfract = 1.0 / ndistinct;
3298
3299         /*
3300          * Look up the frequency of the most common value, if available.
3301          */
3302         mcvfreq = 0.0;
3303
3304         if (HeapTupleIsValid(vardata.statsTuple))
3305         {
3306                 if (get_attstatsslot(vardata.statsTuple,
3307                                                          vardata.atttype, vardata.atttypmod,
3308                                                          STATISTIC_KIND_MCV, InvalidOid,
3309                                                          NULL,
3310                                                          NULL, NULL,
3311                                                          &numbers, &nnumbers))
3312                 {
3313                         /*
3314                          * The first MCV stat is for the most common value.
3315                          */
3316                         if (nnumbers > 0)
3317                                 mcvfreq = numbers[0];
3318                         free_attstatsslot(vardata.atttype, NULL, 0,
3319                                                           numbers, nnumbers);
3320                 }
3321         }
3322
3323         /*
3324          * Adjust estimated bucketsize upward to account for skewed distribution.
3325          */
3326         if (avgfreq > 0.0 && mcvfreq > avgfreq)
3327                 estfract *= mcvfreq / avgfreq;
3328
3329         /*
3330          * Clamp bucketsize to sane range (the above adjustment could easily
3331          * produce an out-of-range result).  We set the lower bound a little above
3332          * zero, since zero isn't a very sane result.
3333          */
3334         if (estfract < 1.0e-6)
3335                 estfract = 1.0e-6;
3336         else if (estfract > 1.0)
3337                 estfract = 1.0;
3338
3339         ReleaseVariableStats(vardata);
3340
3341         return (Selectivity) estfract;
3342 }
3343
3344
3345 /*-------------------------------------------------------------------------
3346  *
3347  * Support routines
3348  *
3349  *-------------------------------------------------------------------------
3350  */
3351
3352 /*
3353  * convert_to_scalar
3354  *        Convert non-NULL values of the indicated types to the comparison
3355  *        scale needed by scalarineqsel().
3356  *        Returns "true" if successful.
3357  *
3358  * XXX this routine is a hack: ideally we should look up the conversion
3359  * subroutines in pg_type.
3360  *
3361  * All numeric datatypes are simply converted to their equivalent
3362  * "double" values.  (NUMERIC values that are outside the range of "double"
3363  * are clamped to +/- HUGE_VAL.)
3364  *
3365  * String datatypes are converted by convert_string_to_scalar(),
3366  * which is explained below.  The reason why this routine deals with
3367  * three values at a time, not just one, is that we need it for strings.
3368  *
3369  * The bytea datatype is just enough different from strings that it has
3370  * to be treated separately.
3371  *
3372  * The several datatypes representing absolute times are all converted
3373  * to Timestamp, which is actually a double, and then we just use that
3374  * double value.  Note this will give correct results even for the "special"
3375  * values of Timestamp, since those are chosen to compare correctly;
3376  * see timestamp_cmp.
3377  *
3378  * The several datatypes representing relative times (intervals) are all
3379  * converted to measurements expressed in seconds.
3380  */
3381 static bool
3382 convert_to_scalar(Datum value, Oid valuetypid, double *scaledvalue,
3383                                   Datum lobound, Datum hibound, Oid boundstypid,
3384                                   double *scaledlobound, double *scaledhibound)
3385 {
3386         /*
3387          * Both the valuetypid and the boundstypid should exactly match the
3388          * declared input type(s) of the operator we are invoked for, so we just
3389          * error out if either is not recognized.
3390          *
3391          * XXX The histogram we are interpolating between points of could belong
3392          * to a column that's only binary-compatible with the declared type. In
3393          * essence we are assuming that the semantics of binary-compatible types
3394          * are enough alike that we can use a histogram generated with one type's
3395          * operators to estimate selectivity for the other's.  This is outright
3396          * wrong in some cases --- in particular signed versus unsigned
3397          * interpretation could trip us up.  But it's useful enough in the
3398          * majority of cases that we do it anyway.      Should think about more
3399          * rigorous ways to do it.
3400          */
3401         switch (valuetypid)
3402         {
3403                         /*
3404                          * Built-in numeric types
3405                          */
3406                 case BOOLOID:
3407                 case INT2OID:
3408                 case INT4OID:
3409                 case INT8OID:
3410                 case FLOAT4OID:
3411                 case FLOAT8OID:
3412                 case NUMERICOID:
3413                 case OIDOID:
3414                 case REGPROCOID:
3415                 case REGPROCEDUREOID:
3416                 case REGOPEROID:
3417                 case REGOPERATOROID:
3418                 case REGCLASSOID:
3419                 case REGTYPEOID:
3420                 case REGCONFIGOID:
3421                 case REGDICTIONARYOID:
3422                         *scaledvalue = convert_numeric_to_scalar(value, valuetypid);
3423                         *scaledlobound = convert_numeric_to_scalar(lobound, boundstypid);
3424                         *scaledhibound = convert_numeric_to_scalar(hibound, boundstypid);
3425                         return true;
3426
3427                         /*
3428                          * Built-in string types
3429                          */
3430                 case CHAROID:
3431                 case BPCHAROID:
3432                 case VARCHAROID:
3433                 case TEXTOID:
3434                 case NAMEOID:
3435                         {
3436                                 char       *valstr = convert_string_datum(value, valuetypid);
3437                                 char       *lostr = convert_string_datum(lobound, boundstypid);
3438                                 char       *histr = convert_string_datum(hibound, boundstypid);
3439
3440                                 convert_string_to_scalar(valstr, scaledvalue,
3441                                                                                  lostr, scaledlobound,
3442                                                                                  histr, scaledhibound);
3443                                 pfree(valstr);
3444                                 pfree(lostr);
3445                                 pfree(histr);
3446                                 return true;
3447                         }
3448
3449                         /*
3450                          * Built-in bytea type
3451                          */
3452                 case BYTEAOID:
3453                         {
3454                                 convert_bytea_to_scalar(value, scaledvalue,
3455                                                                                 lobound, scaledlobound,
3456                                                                                 hibound, scaledhibound);
3457                                 return true;
3458                         }
3459
3460                         /*
3461                          * Built-in time types
3462                          */
3463                 case TIMESTAMPOID:
3464                 case TIMESTAMPTZOID:
3465                 case ABSTIMEOID:
3466                 case DATEOID:
3467                 case INTERVALOID:
3468                 case RELTIMEOID:
3469                 case TINTERVALOID:
3470                 case TIMEOID:
3471                 case TIMETZOID:
3472                         *scaledvalue = convert_timevalue_to_scalar(value, valuetypid);
3473                         *scaledlobound = convert_timevalue_to_scalar(lobound, boundstypid);
3474                         *scaledhibound = convert_timevalue_to_scalar(hibound, boundstypid);
3475                         return true;
3476
3477                         /*
3478                          * Built-in network types
3479                          */
3480                 case INETOID:
3481                 case CIDROID:
3482                 case MACADDROID:
3483                         *scaledvalue = convert_network_to_scalar(value, valuetypid);
3484                         *scaledlobound = convert_network_to_scalar(lobound, boundstypid);
3485                         *scaledhibound = convert_network_to_scalar(hibound, boundstypid);
3486                         return true;
3487         }
3488         /* Don't know how to convert */
3489         *scaledvalue = *scaledlobound = *scaledhibound = 0;
3490         return false;
3491 }
3492
3493 /*
3494  * Do convert_to_scalar()'s work for any numeric data type.
3495  */
3496 static double
3497 convert_numeric_to_scalar(Datum value, Oid typid)
3498 {
3499         switch (typid)
3500         {
3501                 case BOOLOID:
3502                         return (double) DatumGetBool(value);
3503                 case INT2OID:
3504                         return (double) DatumGetInt16(value);
3505                 case INT4OID:
3506                         return (double) DatumGetInt32(value);
3507                 case INT8OID:
3508                         return (double) DatumGetInt64(value);
3509                 case FLOAT4OID:
3510                         return (double) DatumGetFloat4(value);
3511                 case FLOAT8OID:
3512                         return (double) DatumGetFloat8(value);
3513                 case NUMERICOID:
3514                         /* Note: out-of-range values will be clamped to +-HUGE_VAL */
3515                         return (double)
3516                                 DatumGetFloat8(DirectFunctionCall1(numeric_float8_no_overflow,
3517                                                                                                    value));
3518                 case OIDOID:
3519                 case REGPROCOID:
3520                 case REGPROCEDUREOID:
3521                 case REGOPEROID:
3522                 case REGOPERATOROID:
3523                 case REGCLASSOID:
3524                 case REGTYPEOID:
3525                 case REGCONFIGOID:
3526                 case REGDICTIONARYOID:
3527                         /* we can treat OIDs as integers... */
3528                         return (double) DatumGetObjectId(value);
3529         }
3530
3531         /*
3532          * Can't get here unless someone tries to use scalarltsel/scalargtsel on
3533          * an operator with one numeric and one non-numeric operand.
3534          */
3535         elog(ERROR, "unsupported type: %u", typid);
3536         return 0;
3537 }
3538
3539 /*
3540  * Do convert_to_scalar()'s work for any character-string data type.
3541  *
3542  * String datatypes are converted to a scale that ranges from 0 to 1,
3543  * where we visualize the bytes of the string as fractional digits.
3544  *
3545  * We do not want the base to be 256, however, since that tends to
3546  * generate inflated selectivity estimates; few databases will have
3547  * occurrences of all 256 possible byte values at each position.
3548  * Instead, use the smallest and largest byte values seen in the bounds
3549  * as the estimated range for each byte, after some fudging to deal with
3550  * the fact that we probably aren't going to see the full range that way.
3551  *
3552  * An additional refinement is that we discard any common prefix of the
3553  * three strings before computing the scaled values.  This allows us to
3554  * "zoom in" when we encounter a narrow data range.  An example is a phone
3555  * number database where all the values begin with the same area code.
3556  * (Actually, the bounds will be adjacent histogram-bin-boundary values,
3557  * so this is more likely to happen than you might think.)
3558  */
3559 static void
3560 convert_string_to_scalar(char *value,
3561                                                  double *scaledvalue,
3562                                                  char *lobound,
3563                                                  double *scaledlobound,
3564                                                  char *hibound,
3565                                                  double *scaledhibound)
3566 {
3567         int                     rangelo,
3568                                 rangehi;
3569         char       *sptr;
3570
3571         rangelo = rangehi = (unsigned char) hibound[0];
3572         for (sptr = lobound; *sptr; sptr++)
3573         {
3574                 if (rangelo > (unsigned char) *sptr)
3575                         rangelo = (unsigned char) *sptr;
3576                 if (rangehi < (unsigned char) *sptr)
3577                         rangehi = (unsigned char) *sptr;
3578         }
3579         for (sptr = hibound; *sptr; sptr++)
3580         {
3581                 if (rangelo > (unsigned char) *sptr)
3582                         rangelo = (unsigned char) *sptr;
3583                 if (rangehi < (unsigned char) *sptr)
3584                         rangehi = (unsigned char) *sptr;
3585         }
3586         /* If range includes any upper-case ASCII chars, make it include all */
3587         if (rangelo <= 'Z' && rangehi >= 'A')
3588         {
3589                 if (rangelo > 'A')
3590                         rangelo = 'A';
3591                 if (rangehi < 'Z')
3592                         rangehi = 'Z';
3593         }
3594         /* Ditto lower-case */
3595         if (rangelo <= 'z' && rangehi >= 'a')
3596         {
3597                 if (rangelo > 'a')
3598                         rangelo = 'a';
3599                 if (rangehi < 'z')
3600                         rangehi = 'z';
3601         }
3602         /* Ditto digits */
3603         if (rangelo <= '9' && rangehi >= '0')
3604         {
3605                 if (rangelo > '0')
3606                         rangelo = '0';
3607                 if (rangehi < '9')
3608                         rangehi = '9';
3609         }
3610
3611         /*
3612          * If range includes less than 10 chars, assume we have not got enough
3613          * data, and make it include regular ASCII set.
3614          */
3615         if (rangehi - rangelo < 9)
3616         {
3617                 rangelo = ' ';
3618                 rangehi = 127;
3619         }
3620
3621         /*
3622          * Now strip any common prefix of the three strings.
3623          */
3624         while (*lobound)
3625         {
3626                 if (*lobound != *hibound || *lobound != *value)
3627                         break;
3628                 lobound++, hibound++, value++;
3629         }
3630
3631         /*
3632          * Now we can do the conversions.
3633          */
3634         *scaledvalue = convert_one_string_to_scalar(value, rangelo, rangehi);
3635         *scaledlobound = convert_one_string_to_scalar(lobound, rangelo, rangehi);
3636         *scaledhibound = convert_one_string_to_scalar(hibound, rangelo, rangehi);
3637 }
3638
3639 static double
3640 convert_one_string_to_scalar(char *value, int rangelo, int rangehi)
3641 {
3642         int                     slen = strlen(value);
3643         double          num,
3644                                 denom,
3645                                 base;
3646
3647         if (slen <= 0)
3648                 return 0.0;                             /* empty string has scalar value 0 */
3649
3650         /*
3651          * Since base is at least 10, need not consider more than about 20 chars
3652          */
3653         if (slen > 20)
3654                 slen = 20;
3655
3656         /* Convert initial characters to fraction */
3657         base = rangehi - rangelo + 1;
3658         num = 0.0;
3659         denom = base;
3660         while (slen-- > 0)
3661         {
3662                 int                     ch = (unsigned char) *value++;
3663
3664                 if (ch < rangelo)
3665                         ch = rangelo - 1;
3666                 else if (ch > rangehi)
3667                         ch = rangehi + 1;
3668                 num += ((double) (ch - rangelo)) / denom;
3669                 denom *= base;
3670         }
3671
3672         return num;
3673 }
3674
3675 /*
3676  * Convert a string-type Datum into a palloc'd, null-terminated string.
3677  *
3678  * When using a non-C locale, we must pass the string through strxfrm()
3679  * before continuing, so as to generate correct locale-specific results.
3680  */
3681 static char *
3682 convert_string_datum(Datum value, Oid typid)
3683 {
3684         char       *val;
3685
3686         switch (typid)
3687         {
3688                 case CHAROID:
3689                         val = (char *) palloc(2);
3690                         val[0] = DatumGetChar(value);
3691                         val[1] = '\0';
3692                         break;
3693                 case BPCHAROID:
3694                 case VARCHAROID:
3695                 case TEXTOID:
3696                         val = TextDatumGetCString(value);
3697                         break;
3698                 case NAMEOID:
3699                         {
3700                                 NameData   *nm = (NameData *) DatumGetPointer(value);
3701
3702                                 val = pstrdup(NameStr(*nm));
3703                                 break;
3704                         }
3705                 default:
3706
3707                         /*
3708                          * Can't get here unless someone tries to use scalarltsel on an
3709                          * operator with one string and one non-string operand.
3710                          */
3711                         elog(ERROR, "unsupported type: %u", typid);
3712                         return NULL;
3713         }
3714
3715         if (!lc_collate_is_c(DEFAULT_COLLATION_OID))
3716         {
3717                 char       *xfrmstr;
3718                 size_t          xfrmlen;
3719                 size_t          xfrmlen2;
3720
3721                 /*
3722                  * Note: originally we guessed at a suitable output buffer size, and
3723                  * only needed to call strxfrm twice if our guess was too small.
3724                  * However, it seems that some versions of Solaris have buggy strxfrm
3725                  * that can write past the specified buffer length in that scenario.
3726                  * So, do it the dumb way for portability.
3727                  *
3728                  * Yet other systems (e.g., glibc) sometimes return a smaller value
3729                  * from the second call than the first; thus the Assert must be <= not
3730                  * == as you'd expect.  Can't any of these people program their way
3731                  * out of a paper bag?
3732                  *
3733                  * XXX: strxfrm doesn't support UTF-8 encoding on Win32, it can return
3734                  * bogus data or set an error. This is not really a problem unless it
3735                  * crashes since it will only give an estimation error and nothing
3736                  * fatal.
3737                  */
3738 #if _MSC_VER == 1400                    /* VS.Net 2005 */
3739
3740                 /*
3741                  *
3742                  * http://connect.microsoft.com/VisualStudio/feedback/ViewFeedback.aspx?
3743                  * FeedbackID=99694 */
3744                 {
3745                         char            x[1];
3746
3747                         xfrmlen = strxfrm(x, val, 0);
3748                 }
3749 #else
3750                 xfrmlen = strxfrm(NULL, val, 0);
3751 #endif
3752 #ifdef WIN32
3753
3754                 /*
3755                  * On Windows, strxfrm returns INT_MAX when an error occurs. Instead
3756                  * of trying to allocate this much memory (and fail), just return the
3757                  * original string unmodified as if we were in the C locale.
3758                  */
3759                 if (xfrmlen == INT_MAX)
3760                         return val;
3761 #endif
3762                 xfrmstr = (char *) palloc(xfrmlen + 1);
3763                 xfrmlen2 = strxfrm(xfrmstr, val, xfrmlen + 1);
3764                 Assert(xfrmlen2 <= xfrmlen);
3765                 pfree(val);
3766                 val = xfrmstr;
3767         }
3768
3769         return val;
3770 }
3771
3772 /*
3773  * Do convert_to_scalar()'s work for any bytea data type.
3774  *
3775  * Very similar to convert_string_to_scalar except we can't assume
3776  * null-termination and therefore pass explicit lengths around.
3777  *
3778  * Also, assumptions about likely "normal" ranges of characters have been
3779  * removed - a data range of 0..255 is always used, for now.  (Perhaps
3780  * someday we will add information about actual byte data range to
3781  * pg_statistic.)
3782  */
3783 static void
3784 convert_bytea_to_scalar(Datum value,
3785                                                 double *scaledvalue,
3786                                                 Datum lobound,
3787                                                 double *scaledlobound,
3788                                                 Datum hibound,
3789                                                 double *scaledhibound)
3790 {
3791         int                     rangelo,
3792                                 rangehi,
3793                                 valuelen = VARSIZE(DatumGetPointer(value)) - VARHDRSZ,
3794                                 loboundlen = VARSIZE(DatumGetPointer(lobound)) - VARHDRSZ,
3795                                 hiboundlen = VARSIZE(DatumGetPointer(hibound)) - VARHDRSZ,
3796                                 i,
3797                                 minlen;
3798         unsigned char *valstr = (unsigned char *) VARDATA(DatumGetPointer(value)),
3799                            *lostr = (unsigned char *) VARDATA(DatumGetPointer(lobound)),
3800                            *histr = (unsigned char *) VARDATA(DatumGetPointer(hibound));
3801
3802         /*
3803          * Assume bytea data is uniformly distributed across all byte values.
3804          */
3805         rangelo = 0;
3806         rangehi = 255;
3807
3808         /*
3809          * Now strip any common prefix of the three strings.
3810          */
3811         minlen = Min(Min(valuelen, loboundlen), hiboundlen);
3812         for (i = 0; i < minlen; i++)
3813         {
3814                 if (*lostr != *histr || *lostr != *valstr)
3815                         break;
3816                 lostr++, histr++, valstr++;
3817                 loboundlen--, hiboundlen--, valuelen--;
3818         }
3819
3820         /*
3821          * Now we can do the conversions.
3822          */
3823         *scaledvalue = convert_one_bytea_to_scalar(valstr, valuelen, rangelo, rangehi);
3824         *scaledlobound = convert_one_bytea_to_scalar(lostr, loboundlen, rangelo, rangehi);
3825         *scaledhibound = convert_one_bytea_to_scalar(histr, hiboundlen, rangelo, rangehi);
3826 }
3827
3828 static double
3829 convert_one_bytea_to_scalar(unsigned char *value, int valuelen,
3830                                                         int rangelo, int rangehi)
3831 {
3832         double          num,
3833                                 denom,
3834                                 base;
3835
3836         if (valuelen <= 0)
3837                 return 0.0;                             /* empty string has scalar value 0 */
3838
3839         /*
3840          * Since base is 256, need not consider more than about 10 chars (even
3841          * this many seems like overkill)
3842          */
3843         if (valuelen > 10)
3844                 valuelen = 10;
3845
3846         /* Convert initial characters to fraction */
3847         base = rangehi - rangelo + 1;
3848         num = 0.0;
3849         denom = base;
3850         while (valuelen-- > 0)
3851         {
3852                 int                     ch = *value++;
3853
3854                 if (ch < rangelo)
3855                         ch = rangelo - 1;
3856                 else if (ch > rangehi)
3857                         ch = rangehi + 1;
3858                 num += ((double) (ch - rangelo)) / denom;
3859                 denom *= base;
3860         }
3861
3862         return num;
3863 }
3864
3865 /*
3866  * Do convert_to_scalar()'s work for any timevalue data type.
3867  */
3868 static double
3869 convert_timevalue_to_scalar(Datum value, Oid typid)
3870 {
3871         switch (typid)
3872         {
3873                 case TIMESTAMPOID:
3874                         return DatumGetTimestamp(value);
3875                 case TIMESTAMPTZOID:
3876                         return DatumGetTimestampTz(value);
3877                 case ABSTIMEOID:
3878                         return DatumGetTimestamp(DirectFunctionCall1(abstime_timestamp,
3879                                                                                                                  value));
3880                 case DATEOID:
3881                         return date2timestamp_no_overflow(DatumGetDateADT(value));
3882                 case INTERVALOID:
3883                         {
3884                                 Interval   *interval = DatumGetIntervalP(value);
3885
3886                                 /*
3887                                  * Convert the month part of Interval to days using assumed
3888                                  * average month length of 365.25/12.0 days.  Not too
3889                                  * accurate, but plenty good enough for our purposes.
3890                                  */
3891 #ifdef HAVE_INT64_TIMESTAMP
3892                                 return interval->time + interval->day * (double) USECS_PER_DAY +
3893                                         interval->month * ((DAYS_PER_YEAR / (double) MONTHS_PER_YEAR) * USECS_PER_DAY);
3894 #else
3895                                 return interval->time + interval->day * SECS_PER_DAY +
3896                                         interval->month * ((DAYS_PER_YEAR / (double) MONTHS_PER_YEAR) * (double) SECS_PER_DAY);
3897 #endif
3898                         }
3899                 case RELTIMEOID:
3900 #ifdef HAVE_INT64_TIMESTAMP
3901                         return (DatumGetRelativeTime(value) * 1000000.0);
3902 #else
3903                         return DatumGetRelativeTime(value);
3904 #endif
3905                 case TINTERVALOID:
3906                         {
3907                                 TimeInterval tinterval = DatumGetTimeInterval(value);
3908
3909 #ifdef HAVE_INT64_TIMESTAMP
3910                                 if (tinterval->status != 0)
3911                                         return ((tinterval->data[1] - tinterval->data[0]) * 1000000.0);
3912 #else
3913                                 if (tinterval->status != 0)
3914                                         return tinterval->data[1] - tinterval->data[0];
3915 #endif
3916                                 return 0;               /* for lack of a better idea */
3917                         }
3918                 case TIMEOID:
3919                         return DatumGetTimeADT(value);
3920                 case TIMETZOID:
3921                         {
3922                                 TimeTzADT  *timetz = DatumGetTimeTzADTP(value);
3923
3924                                 /* use GMT-equivalent time */
3925 #ifdef HAVE_INT64_TIMESTAMP
3926                                 return (double) (timetz->time + (timetz->zone * 1000000.0));
3927 #else
3928                                 return (double) (timetz->time + timetz->zone);
3929 #endif
3930                         }
3931         }
3932
3933         /*
3934          * Can't get here unless someone tries to use scalarltsel/scalargtsel on
3935          * an operator with one timevalue and one non-timevalue operand.
3936          */
3937         elog(ERROR, "unsupported type: %u", typid);
3938         return 0;
3939 }
3940
3941
3942 /*
3943  * get_restriction_variable
3944  *              Examine the args of a restriction clause to see if it's of the
3945  *              form (variable op pseudoconstant) or (pseudoconstant op variable),
3946  *              where "variable" could be either a Var or an expression in vars of a
3947  *              single relation.  If so, extract information about the variable,
3948  *              and also indicate which side it was on and the other argument.
3949  *
3950  * Inputs:
3951  *      root: the planner info
3952  *      args: clause argument list
3953  *      varRelid: see specs for restriction selectivity functions
3954  *
3955  * Outputs: (these are valid only if TRUE is returned)
3956  *      *vardata: gets information about variable (see examine_variable)
3957  *      *other: gets other clause argument, aggressively reduced to a constant
3958  *      *varonleft: set TRUE if variable is on the left, FALSE if on the right
3959  *
3960  * Returns TRUE if a variable is identified, otherwise FALSE.
3961  *
3962  * Note: if there are Vars on both sides of the clause, we must fail, because
3963  * callers are expecting that the other side will act like a pseudoconstant.
3964  */
3965 bool
3966 get_restriction_variable(PlannerInfo *root, List *args, int varRelid,
3967                                                  VariableStatData *vardata, Node **other,
3968                                                  bool *varonleft)
3969 {
3970         Node       *left,
3971                            *right;
3972         VariableStatData rdata;
3973
3974         /* Fail if not a binary opclause (probably shouldn't happen) */
3975         if (list_length(args) != 2)
3976                 return false;
3977
3978         left = (Node *) linitial(args);
3979         right = (Node *) lsecond(args);
3980
3981         /*
3982          * Examine both sides.  Note that when varRelid is nonzero, Vars of other
3983          * relations will be treated as pseudoconstants.
3984          */
3985         examine_variable(root, left, varRelid, vardata);
3986         examine_variable(root, right, varRelid, &rdata);
3987
3988         /*
3989          * If one side is a variable and the other not, we win.
3990          */
3991         if (vardata->rel && rdata.rel == NULL)
3992         {
3993                 *varonleft = true;
3994                 *other = estimate_expression_value(root, rdata.var);
3995                 /* Assume we need no ReleaseVariableStats(rdata) here */
3996                 return true;
3997         }
3998
3999         if (vardata->rel == NULL && rdata.rel)
4000         {
4001                 *varonleft = false;
4002                 *other = estimate_expression_value(root, vardata->var);
4003                 /* Assume we need no ReleaseVariableStats(*vardata) here */
4004                 *vardata = rdata;
4005                 return true;
4006         }
4007
4008         /* Ooops, clause has wrong structure (probably var op var) */
4009         ReleaseVariableStats(*vardata);
4010         ReleaseVariableStats(rdata);
4011
4012         return false;
4013 }
4014
4015 /*
4016  * get_join_variables
4017  *              Apply examine_variable() to each side of a join clause.
4018  *              Also, attempt to identify whether the join clause has the same
4019  *              or reversed sense compared to the SpecialJoinInfo.
4020  *
4021  * We consider the join clause "normal" if it is "lhs_var OP rhs_var",
4022  * or "reversed" if it is "rhs_var OP lhs_var".  In complicated cases
4023  * where we can't tell for sure, we default to assuming it's normal.
4024  */
4025 void
4026 get_join_variables(PlannerInfo *root, List *args, SpecialJoinInfo *sjinfo,
4027                                    VariableStatData *vardata1, VariableStatData *vardata2,
4028                                    bool *join_is_reversed)
4029 {
4030         Node       *left,
4031                            *right;
4032
4033         if (list_length(args) != 2)
4034                 elog(ERROR, "join operator should take two arguments");
4035
4036         left = (Node *) linitial(args);
4037         right = (Node *) lsecond(args);
4038
4039         examine_variable(root, left, 0, vardata1);
4040         examine_variable(root, right, 0, vardata2);
4041
4042         if (vardata1->rel &&
4043                 bms_is_subset(vardata1->rel->relids, sjinfo->syn_righthand))
4044                 *join_is_reversed = true;               /* var1 is on RHS */
4045         else if (vardata2->rel &&
4046                          bms_is_subset(vardata2->rel->relids, sjinfo->syn_lefthand))
4047                 *join_is_reversed = true;               /* var2 is on LHS */
4048         else
4049                 *join_is_reversed = false;
4050 }
4051
4052 /*
4053  * examine_variable
4054  *              Try to look up statistical data about an expression.
4055  *              Fill in a VariableStatData struct to describe the expression.
4056  *
4057  * Inputs:
4058  *      root: the planner info
4059  *      node: the expression tree to examine
4060  *      varRelid: see specs for restriction selectivity functions
4061  *
4062  * Outputs: *vardata is filled as follows:
4063  *      var: the input expression (with any binary relabeling stripped, if
4064  *              it is or contains a variable; but otherwise the type is preserved)
4065  *      rel: RelOptInfo for relation containing variable; NULL if expression
4066  *              contains no Vars (NOTE this could point to a RelOptInfo of a
4067  *              subquery, not one in the current query).
4068  *      statsTuple: the pg_statistic entry for the variable, if one exists;
4069  *              otherwise NULL.
4070  *      freefunc: pointer to a function to release statsTuple with.
4071  *      vartype: exposed type of the expression; this should always match
4072  *              the declared input type of the operator we are estimating for.
4073  *      atttype, atttypmod: type data to pass to get_attstatsslot().  This is
4074  *              commonly the same as the exposed type of the variable argument,
4075  *              but can be different in binary-compatible-type cases.
4076  *      isunique: TRUE if we were able to match the var to a unique index,
4077  *              implying its values are unique for this query.
4078  *
4079  * Caller is responsible for doing ReleaseVariableStats() before exiting.
4080  */
4081 void
4082 examine_variable(PlannerInfo *root, Node *node, int varRelid,
4083                                  VariableStatData *vardata)
4084 {
4085         Node       *basenode;
4086         Relids          varnos;
4087         RelOptInfo *onerel;
4088
4089         /* Make sure we don't return dangling pointers in vardata */
4090         MemSet(vardata, 0, sizeof(VariableStatData));
4091
4092         /* Save the exposed type of the expression */
4093         vardata->vartype = exprType(node);
4094
4095         /* Look inside any binary-compatible relabeling */
4096
4097         if (IsA(node, RelabelType))
4098                 basenode = (Node *) ((RelabelType *) node)->arg;
4099         else
4100                 basenode = node;
4101
4102         /* Fast path for a simple Var */
4103
4104         if (IsA(basenode, Var) &&
4105                 (varRelid == 0 || varRelid == ((Var *) basenode)->varno))
4106         {
4107                 Var                *var = (Var *) basenode;
4108                 RangeTblEntry *rte;
4109
4110                 vardata->var = basenode;        /* return Var without relabeling */
4111                 vardata->rel = find_base_rel(root, var->varno);
4112                 vardata->atttype = var->vartype;
4113                 vardata->atttypmod = var->vartypmod;
4114                 vardata->isunique = has_unique_index(vardata->rel, var->varattno);
4115
4116                 rte = root->simple_rte_array[var->varno];
4117
4118                 if (get_relation_stats_hook &&
4119                         (*get_relation_stats_hook) (root, rte, var->varattno, vardata))
4120                 {
4121                         /*
4122                          * The hook took control of acquiring a stats tuple.  If it did
4123                          * supply a tuple, it'd better have supplied a freefunc.
4124                          */
4125                         if (HeapTupleIsValid(vardata->statsTuple) &&
4126                                 !vardata->freefunc)
4127                                 elog(ERROR, "no function provided to release variable stats with");
4128                 }
4129                 else if (rte->rtekind == RTE_RELATION)
4130                 {
4131                         vardata->statsTuple = SearchSysCache3(STATRELATTINH,
4132                                                                                                 ObjectIdGetDatum(rte->relid),
4133                                                                                                 Int16GetDatum(var->varattno),
4134                                                                                                   BoolGetDatum(rte->inh));
4135                         vardata->freefunc = ReleaseSysCache;
4136                 }
4137                 else
4138                 {
4139                         /*
4140                          * XXX This means the Var comes from a JOIN or sub-SELECT. Later
4141                          * add code to dig down into the join etc and see if we can trace
4142                          * the variable to something with stats.  (But beware of
4143                          * sub-SELECTs with DISTINCT/GROUP BY/etc.      Perhaps there are no
4144                          * cases where this would really be useful, because we'd have
4145                          * flattened the subselect if it is??)
4146                          */
4147                 }
4148
4149                 return;
4150         }
4151
4152         /*
4153          * Okay, it's a more complicated expression.  Determine variable
4154          * membership.  Note that when varRelid isn't zero, only vars of that
4155          * relation are considered "real" vars.
4156          */
4157         varnos = pull_varnos(basenode);
4158
4159         onerel = NULL;
4160
4161         switch (bms_membership(varnos))
4162         {
4163                 case BMS_EMPTY_SET:
4164                         /* No Vars at all ... must be pseudo-constant clause */
4165                         break;
4166                 case BMS_SINGLETON:
4167                         if (varRelid == 0 || bms_is_member(varRelid, varnos))
4168                         {
4169                                 onerel = find_base_rel(root,
4170                                            (varRelid ? varRelid : bms_singleton_member(varnos)));
4171                                 vardata->rel = onerel;
4172                                 node = basenode;        /* strip any relabeling */
4173                         }
4174                         /* else treat it as a constant */
4175                         break;
4176                 case BMS_MULTIPLE:
4177                         if (varRelid == 0)
4178                         {
4179                                 /* treat it as a variable of a join relation */
4180                                 vardata->rel = find_join_rel(root, varnos);
4181                                 node = basenode;        /* strip any relabeling */
4182                         }
4183                         else if (bms_is_member(varRelid, varnos))
4184                         {
4185                                 /* ignore the vars belonging to other relations */
4186                                 vardata->rel = find_base_rel(root, varRelid);
4187                                 node = basenode;        /* strip any relabeling */
4188                                 /* note: no point in expressional-index search here */
4189                         }
4190                         /* else treat it as a constant */
4191                         break;
4192         }
4193
4194         bms_free(varnos);
4195
4196         vardata->var = node;
4197         vardata->atttype = exprType(node);
4198         vardata->atttypmod = exprTypmod(node);
4199
4200         if (onerel)
4201         {
4202                 /*
4203                  * We have an expression in vars of a single relation.  Try to match
4204                  * it to expressional index columns, in hopes of finding some
4205                  * statistics.
4206                  *
4207                  * XXX it's conceivable that there are multiple matches with different
4208                  * index opfamilies; if so, we need to pick one that matches the
4209                  * operator we are estimating for.      FIXME later.
4210                  */
4211                 ListCell   *ilist;
4212
4213                 foreach(ilist, onerel->indexlist)
4214                 {
4215                         IndexOptInfo *index = (IndexOptInfo *) lfirst(ilist);
4216                         ListCell   *indexpr_item;
4217                         int                     pos;
4218
4219                         indexpr_item = list_head(index->indexprs);
4220                         if (indexpr_item == NULL)
4221                                 continue;               /* no expressions here... */
4222
4223                         for (pos = 0; pos < index->ncolumns; pos++)
4224                         {
4225                                 if (index->indexkeys[pos] == 0)
4226                                 {
4227                                         Node       *indexkey;
4228
4229                                         if (indexpr_item == NULL)
4230                                                 elog(ERROR, "too few entries in indexprs list");
4231                                         indexkey = (Node *) lfirst(indexpr_item);
4232                                         if (indexkey && IsA(indexkey, RelabelType))
4233                                                 indexkey = (Node *) ((RelabelType *) indexkey)->arg;
4234                                         if (equal(node, indexkey))
4235                                         {
4236                                                 /*
4237                                                  * Found a match ... is it a unique index? Tests here
4238                                                  * should match has_unique_index().
4239                                                  */
4240                                                 if (index->unique &&
4241                                                         index->ncolumns == 1 &&
4242                                                         (index->indpred == NIL || index->predOK))
4243                                                         vardata->isunique = true;
4244
4245                                                 /*
4246                                                  * Has it got stats?  We only consider stats for
4247                                                  * non-partial indexes, since partial indexes probably
4248                                                  * don't reflect whole-relation statistics; the above
4249                                                  * check for uniqueness is the only info we take from
4250                                                  * a partial index.
4251                                                  *
4252                                                  * An index stats hook, however, must make its own
4253                                                  * decisions about what to do with partial indexes.
4254                                                  */
4255                                                 if (get_index_stats_hook &&
4256                                                         (*get_index_stats_hook) (root, index->indexoid,
4257                                                                                                          pos + 1, vardata))
4258                                                 {
4259                                                         /*
4260                                                          * The hook took control of acquiring a stats
4261                                                          * tuple.  If it did supply a tuple, it'd better
4262                                                          * have supplied a freefunc.
4263                                                          */
4264                                                         if (HeapTupleIsValid(vardata->statsTuple) &&
4265                                                                 !vardata->freefunc)
4266                                                                 elog(ERROR, "no function provided to release variable stats with");
4267                                                 }
4268                                                 else if (index->indpred == NIL)
4269                                                 {
4270                                                         vardata->statsTuple =
4271                                                                 SearchSysCache3(STATRELATTINH,
4272                                                                                    ObjectIdGetDatum(index->indexoid),
4273                                                                                                 Int16GetDatum(pos + 1),
4274                                                                                                 BoolGetDatum(false));
4275                                                         vardata->freefunc = ReleaseSysCache;
4276                                                 }
4277                                                 if (vardata->statsTuple)
4278                                                         break;
4279                                         }
4280                                         indexpr_item = lnext(indexpr_item);
4281                                 }
4282                         }
4283                         if (vardata->statsTuple)
4284                                 break;
4285                 }
4286         }
4287 }
4288
4289 /*
4290  * get_variable_numdistinct
4291  *        Estimate the number of distinct values of a variable.
4292  *
4293  * vardata: results of examine_variable
4294  *
4295  * NB: be careful to produce an integral result, since callers may compare
4296  * the result to exact integer counts.
4297  */
4298 double
4299 get_variable_numdistinct(VariableStatData *vardata)
4300 {
4301         double          stadistinct;
4302         double          ntuples;
4303
4304         /*
4305          * Determine the stadistinct value to use.      There are cases where we can
4306          * get an estimate even without a pg_statistic entry, or can get a better
4307          * value than is in pg_statistic.
4308          */
4309         if (HeapTupleIsValid(vardata->statsTuple))
4310         {
4311                 /* Use the pg_statistic entry */
4312                 Form_pg_statistic stats;
4313
4314                 stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
4315                 stadistinct = stats->stadistinct;
4316         }
4317         else if (vardata->vartype == BOOLOID)
4318         {
4319                 /*
4320                  * Special-case boolean columns: presumably, two distinct values.
4321                  *
4322                  * Are there any other datatypes we should wire in special estimates
4323                  * for?
4324                  */
4325                 stadistinct = 2.0;
4326         }
4327         else
4328         {
4329                 /*
4330                  * We don't keep statistics for system columns, but in some cases we
4331                  * can infer distinctness anyway.
4332                  */
4333                 if (vardata->var && IsA(vardata->var, Var))
4334                 {
4335                         switch (((Var *) vardata->var)->varattno)
4336                         {
4337                                 case ObjectIdAttributeNumber:
4338                                 case SelfItemPointerAttributeNumber:
4339                                         stadistinct = -1.0; /* unique */
4340                                         break;
4341                                 case TableOidAttributeNumber:
4342                                         stadistinct = 1.0;      /* only 1 value */
4343                                         break;
4344                                 default:
4345                                         stadistinct = 0.0;      /* means "unknown" */
4346                                         break;
4347                         }
4348                 }
4349                 else
4350                         stadistinct = 0.0;      /* means "unknown" */
4351
4352                 /*
4353                  * XXX consider using estimate_num_groups on expressions?
4354                  */
4355         }
4356
4357         /*
4358          * If there is a unique index for the variable, assume it is unique no
4359          * matter what pg_statistic says; the statistics could be out of date, or
4360          * we might have found a partial unique index that proves the var is
4361          * unique for this query.
4362          */
4363         if (vardata->isunique)
4364                 stadistinct = -1.0;
4365
4366         /*
4367          * If we had an absolute estimate, use that.
4368          */
4369         if (stadistinct > 0.0)
4370                 return stadistinct;
4371
4372         /*
4373          * Otherwise we need to get the relation size; punt if not available.
4374          */
4375         if (vardata->rel == NULL)
4376                 return DEFAULT_NUM_DISTINCT;
4377         ntuples = vardata->rel->tuples;
4378         if (ntuples <= 0.0)
4379                 return DEFAULT_NUM_DISTINCT;
4380
4381         /*
4382          * If we had a relative estimate, use that.
4383          */
4384         if (stadistinct < 0.0)
4385                 return floor((-stadistinct * ntuples) + 0.5);
4386
4387         /*
4388          * With no data, estimate ndistinct = ntuples if the table is small, else
4389          * use default.
4390          */
4391         if (ntuples < DEFAULT_NUM_DISTINCT)
4392                 return ntuples;
4393
4394         return DEFAULT_NUM_DISTINCT;
4395 }
4396
4397 /*
4398  * get_variable_range
4399  *              Estimate the minimum and maximum value of the specified variable.
4400  *              If successful, store values in *min and *max, and return TRUE.
4401  *              If no data available, return FALSE.
4402  *
4403  * sortop is the "<" comparison operator to use.  This should generally
4404  * be "<" not ">", as only the former is likely to be found in pg_statistic.
4405  */
4406 static bool
4407 get_variable_range(PlannerInfo *root, VariableStatData *vardata, Oid sortop,
4408                                    Datum *min, Datum *max)
4409 {
4410         Datum           tmin = 0;
4411         Datum           tmax = 0;
4412         bool            have_data = false;
4413         Form_pg_statistic stats;
4414         int16           typLen;
4415         bool            typByVal;
4416         Datum      *values;
4417         int                     nvalues;
4418         int                     i;
4419
4420         /*
4421          * XXX It's very tempting to try to use the actual column min and max, if
4422          * we can get them relatively-cheaply with an index probe.      However, since
4423          * this function is called many times during join planning, that could
4424          * have unpleasant effects on planning speed.  Need more investigation
4425          * before enabling this.
4426          */
4427 #ifdef NOT_USED
4428         if (get_actual_variable_range(root, vardata, sortop, min, max))
4429                 return true;
4430 #endif
4431
4432         if (!HeapTupleIsValid(vardata->statsTuple))
4433         {
4434                 /* no stats available, so default result */
4435                 return false;
4436         }
4437         stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
4438
4439         get_typlenbyval(vardata->atttype, &typLen, &typByVal);
4440
4441         /*
4442          * If there is a histogram, grab the first and last values.
4443          *
4444          * If there is a histogram that is sorted with some other operator than
4445          * the one we want, fail --- this suggests that there is data we can't
4446          * use.
4447          */
4448         if (get_attstatsslot(vardata->statsTuple,
4449                                                  vardata->atttype, vardata->atttypmod,
4450                                                  STATISTIC_KIND_HISTOGRAM, sortop,
4451                                                  NULL,
4452                                                  &values, &nvalues,
4453                                                  NULL, NULL))
4454         {
4455                 if (nvalues > 0)
4456                 {
4457                         tmin = datumCopy(values[0], typByVal, typLen);
4458                         tmax = datumCopy(values[nvalues - 1], typByVal, typLen);
4459                         have_data = true;
4460                 }
4461                 free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
4462         }
4463         else if (get_attstatsslot(vardata->statsTuple,
4464                                                           vardata->atttype, vardata->atttypmod,
4465                                                           STATISTIC_KIND_HISTOGRAM, InvalidOid,
4466                                                           NULL,
4467                                                           &values, &nvalues,
4468                                                           NULL, NULL))
4469         {
4470                 free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
4471                 return false;
4472         }
4473
4474         /*
4475          * If we have most-common-values info, look for extreme MCVs.  This is
4476          * needed even if we also have a histogram, since the histogram excludes
4477          * the MCVs.  However, usually the MCVs will not be the extreme values, so
4478          * avoid unnecessary data copying.
4479          */
4480         if (get_attstatsslot(vardata->statsTuple,
4481                                                  vardata->atttype, vardata->atttypmod,
4482                                                  STATISTIC_KIND_MCV, InvalidOid,
4483                                                  NULL,
4484                                                  &values, &nvalues,
4485                                                  NULL, NULL))
4486         {
4487                 bool            tmin_is_mcv = false;
4488                 bool            tmax_is_mcv = false;
4489                 FmgrInfo        opproc;
4490
4491                 fmgr_info(get_opcode(sortop), &opproc);
4492                 fmgr_info_set_collation(DEFAULT_COLLATION_OID, &opproc);
4493
4494                 for (i = 0; i < nvalues; i++)
4495                 {
4496                         if (!have_data)
4497                         {
4498                                 tmin = tmax = values[i];
4499                                 tmin_is_mcv = tmax_is_mcv = have_data = true;
4500                                 continue;
4501                         }
4502                         if (DatumGetBool(FunctionCall2(&opproc, values[i], tmin)))
4503                         {
4504                                 tmin = values[i];
4505                                 tmin_is_mcv = true;
4506                         }
4507                         if (DatumGetBool(FunctionCall2(&opproc, tmax, values[i])))
4508                         {
4509                                 tmax = values[i];
4510                                 tmax_is_mcv = true;
4511                         }
4512                 }
4513                 if (tmin_is_mcv)
4514                         tmin = datumCopy(tmin, typByVal, typLen);
4515                 if (tmax_is_mcv)
4516                         tmax = datumCopy(tmax, typByVal, typLen);
4517                 free_attstatsslot(vardata->atttype, values, nvalues, NULL, 0);
4518         }
4519
4520         *min = tmin;
4521         *max = tmax;
4522         return have_data;
4523 }
4524
4525
4526 /*
4527  * get_actual_variable_range
4528  *              Attempt to identify the current *actual* minimum and/or maximum
4529  *              of the specified variable, by looking for a suitable btree index
4530  *              and fetching its low and/or high values.
4531  *              If successful, store values in *min and *max, and return TRUE.
4532  *              (Either pointer can be NULL if that endpoint isn't needed.)
4533  *              If no data available, return FALSE.
4534  *
4535  * sortop is the "<" comparison operator to use.
4536  */
4537 static bool
4538 get_actual_variable_range(PlannerInfo *root, VariableStatData *vardata,
4539                                                   Oid sortop,
4540                                                   Datum *min, Datum *max)
4541 {
4542         bool            have_data = false;
4543         RelOptInfo *rel = vardata->rel;
4544         RangeTblEntry *rte;
4545         ListCell   *lc;
4546
4547         /* No hope if no relation or it doesn't have indexes */
4548         if (rel == NULL || rel->indexlist == NIL)
4549                 return false;
4550         /* If it has indexes it must be a plain relation */
4551         rte = root->simple_rte_array[rel->relid];
4552         Assert(rte->rtekind == RTE_RELATION);
4553
4554         /* Search through the indexes to see if any match our problem */
4555         foreach(lc, rel->indexlist)
4556         {
4557                 IndexOptInfo *index = (IndexOptInfo *) lfirst(lc);
4558                 ScanDirection indexscandir;
4559
4560                 /* Ignore non-btree indexes */
4561                 if (index->relam != BTREE_AM_OID)
4562                         continue;
4563
4564                 /*
4565                  * Ignore partial indexes --- we only want stats that cover the entire
4566                  * relation.
4567                  */
4568                 if (index->indpred != NIL)
4569                         continue;
4570
4571                 /*
4572                  * The index list might include hypothetical indexes inserted by a
4573                  * get_relation_info hook --- don't try to access them.
4574                  */
4575                 if (index->hypothetical)
4576                         continue;
4577
4578                 /*
4579                  * The first index column must match the desired variable and sort
4580                  * operator --- but we can use a descending-order index.
4581                  */
4582                 if (!match_index_to_operand(vardata->var, 0, index))
4583                         continue;
4584                 switch (get_op_opfamily_strategy(sortop, index->sortopfamily[0]))
4585                 {
4586                         case BTLessStrategyNumber:
4587                                 if (index->reverse_sort[0])
4588                                         indexscandir = BackwardScanDirection;
4589                                 else
4590                                         indexscandir = ForwardScanDirection;
4591                                 break;
4592                         case BTGreaterStrategyNumber:
4593                                 if (index->reverse_sort[0])
4594                                         indexscandir = ForwardScanDirection;
4595                                 else
4596                                         indexscandir = BackwardScanDirection;
4597                                 break;
4598                         default:
4599                                 /* index doesn't match the sortop */
4600                                 continue;
4601                 }
4602
4603                 /*
4604                  * Found a suitable index to extract data from.  We'll need an EState
4605                  * and a bunch of other infrastructure.
4606                  */
4607                 {
4608                         EState     *estate;
4609                         ExprContext *econtext;
4610                         MemoryContext tmpcontext;
4611                         MemoryContext oldcontext;
4612                         Relation        heapRel;
4613                         Relation        indexRel;
4614                         IndexInfo  *indexInfo;
4615                         TupleTableSlot *slot;
4616                         int16           typLen;
4617                         bool            typByVal;
4618                         ScanKeyData scankeys[1];
4619                         IndexScanDesc index_scan;
4620                         HeapTuple       tup;
4621                         Datum           values[INDEX_MAX_KEYS];
4622                         bool            isnull[INDEX_MAX_KEYS];
4623
4624                         estate = CreateExecutorState();
4625                         econtext = GetPerTupleExprContext(estate);
4626                         /* Make sure any cruft is generated in the econtext's memory */
4627                         tmpcontext = econtext->ecxt_per_tuple_memory;
4628                         oldcontext = MemoryContextSwitchTo(tmpcontext);
4629
4630                         /*
4631                          * Open the table and index so we can read from them.  We should
4632                          * already have at least AccessShareLock on the table, but not
4633                          * necessarily on the index.
4634                          */
4635                         heapRel = heap_open(rte->relid, NoLock);
4636                         indexRel = index_open(index->indexoid, AccessShareLock);
4637
4638                         /* extract index key information from the index's pg_index info */
4639                         indexInfo = BuildIndexInfo(indexRel);
4640
4641                         /* some other stuff */
4642                         slot = MakeSingleTupleTableSlot(RelationGetDescr(heapRel));
4643                         econtext->ecxt_scantuple = slot;
4644                         get_typlenbyval(vardata->atttype, &typLen, &typByVal);
4645
4646                         /* set up an IS NOT NULL scan key so that we ignore nulls */
4647                         ScanKeyEntryInitialize(&scankeys[0],
4648                                                                    SK_ISNULL | SK_SEARCHNOTNULL,
4649                                                                    1,   /* index col to scan */
4650                                                                    InvalidStrategy,             /* no strategy */
4651                                                                    InvalidOid,  /* no strategy subtype */
4652                                                                    InvalidOid,  /* no collation */
4653                                                                    InvalidOid,  /* no reg proc for this */
4654                                                                    (Datum) 0);  /* constant */
4655
4656                         have_data = true;
4657
4658                         /* If min is requested ... */
4659                         if (min)
4660                         {
4661                                 index_scan = index_beginscan(heapRel, indexRel, SnapshotNow,
4662                                                                                          1, 0);
4663                                 index_rescan(index_scan, scankeys, 1, NULL, 0);
4664
4665                                 /* Fetch first tuple in sortop's direction */
4666                                 if ((tup = index_getnext(index_scan,
4667                                                                                  indexscandir)) != NULL)
4668                                 {
4669                                         /* Extract the index column values from the heap tuple */
4670                                         ExecStoreTuple(tup, slot, InvalidBuffer, false);
4671                                         FormIndexDatum(indexInfo, slot, estate,
4672                                                                    values, isnull);
4673
4674                                         /* Shouldn't have got a null, but be careful */
4675                                         if (isnull[0])
4676                                                 elog(ERROR, "found unexpected null value in index \"%s\"",
4677                                                          RelationGetRelationName(indexRel));
4678
4679                                         /* Copy the index column value out to caller's context */
4680                                         MemoryContextSwitchTo(oldcontext);
4681                                         *min = datumCopy(values[0], typByVal, typLen);
4682                                         MemoryContextSwitchTo(tmpcontext);
4683                                 }
4684                                 else
4685                                         have_data = false;
4686
4687                                 index_endscan(index_scan);
4688                         }
4689
4690                         /* If max is requested, and we didn't find the index is empty */
4691                         if (max && have_data)
4692                         {
4693                                 index_scan = index_beginscan(heapRel, indexRel, SnapshotNow,
4694                                                                                          1, 0);
4695                                 index_rescan(index_scan, scankeys, 1, NULL, 0);
4696
4697                                 /* Fetch first tuple in reverse direction */
4698                                 if ((tup = index_getnext(index_scan,
4699                                                                                  -indexscandir)) != NULL)
4700                                 {
4701                                         /* Extract the index column values from the heap tuple */
4702                                         ExecStoreTuple(tup, slot, InvalidBuffer, false);
4703                                         FormIndexDatum(indexInfo, slot, estate,
4704                                                                    values, isnull);
4705
4706                                         /* Shouldn't have got a null, but be careful */
4707                                         if (isnull[0])
4708                                                 elog(ERROR, "found unexpected null value in index \"%s\"",
4709                                                          RelationGetRelationName(indexRel));
4710
4711                                         /* Copy the index column value out to caller's context */
4712                                         MemoryContextSwitchTo(oldcontext);
4713                                         *max = datumCopy(values[0], typByVal, typLen);
4714                                         MemoryContextSwitchTo(tmpcontext);
4715                                 }
4716                                 else
4717                                         have_data = false;
4718
4719                                 index_endscan(index_scan);
4720                         }
4721
4722                         /* Clean everything up */
4723                         ExecDropSingleTupleTableSlot(slot);
4724
4725                         index_close(indexRel, AccessShareLock);
4726                         heap_close(heapRel, NoLock);
4727
4728                         MemoryContextSwitchTo(oldcontext);
4729                         FreeExecutorState(estate);
4730
4731                         /* And we're done */
4732                         break;
4733                 }
4734         }
4735
4736         return have_data;
4737 }
4738
4739
4740 /*-------------------------------------------------------------------------
4741  *
4742  * Pattern analysis functions
4743  *
4744  * These routines support analysis of LIKE and regular-expression patterns
4745  * by the planner/optimizer.  It's important that they agree with the
4746  * regular-expression code in backend/regex/ and the LIKE code in
4747  * backend/utils/adt/like.c.  Also, the computation of the fixed prefix
4748  * must be conservative: if we report a string longer than the true fixed
4749  * prefix, the query may produce actually wrong answers, rather than just
4750  * getting a bad selectivity estimate!
4751  *
4752  * Note that the prefix-analysis functions are called from
4753  * backend/optimizer/path/indxpath.c as well as from routines in this file.
4754  *
4755  *-------------------------------------------------------------------------
4756  */
4757
4758 /*
4759  * Extract the fixed prefix, if any, for a pattern.
4760  *
4761  * *prefix is set to a palloc'd prefix string (in the form of a Const node),
4762  *      or to NULL if no fixed prefix exists for the pattern.
4763  * *rest is set to a palloc'd Const representing the remainder of the pattern
4764  *      after the portion describing the fixed prefix.
4765  * Each of these has the same type (TEXT or BYTEA) as the given pattern Const.
4766  *
4767  * The return value distinguishes no fixed prefix, a partial prefix,
4768  * or an exact-match-only pattern.
4769  */
4770
4771 static Pattern_Prefix_Status
4772 like_fixed_prefix(Const *patt_const, bool case_insensitive,
4773                                   Const **prefix_const, Const **rest_const)
4774 {
4775         char       *match;
4776         char       *patt;
4777         int                     pattlen;
4778         char       *rest;
4779         Oid                     typeid = patt_const->consttype;
4780         int                     pos,
4781                                 match_pos;
4782         bool            is_multibyte = (pg_database_encoding_max_length() > 1);
4783
4784         /* the right-hand const is type text or bytea */
4785         Assert(typeid == BYTEAOID || typeid == TEXTOID);
4786
4787         if (typeid == BYTEAOID && case_insensitive)
4788                 ereport(ERROR,
4789                                 (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
4790                    errmsg("case insensitive matching not supported on type bytea")));
4791
4792         if (typeid != BYTEAOID)
4793         {
4794                 patt = TextDatumGetCString(patt_const->constvalue);
4795                 pattlen = strlen(patt);
4796         }
4797         else
4798         {
4799                 bytea      *bstr = DatumGetByteaP(patt_const->constvalue);
4800
4801                 pattlen = VARSIZE(bstr) - VARHDRSZ;
4802                 patt = (char *) palloc(pattlen);
4803                 memcpy(patt, VARDATA(bstr), pattlen);
4804                 if ((Pointer) bstr != DatumGetPointer(patt_const->constvalue))
4805                         pfree(bstr);
4806         }
4807
4808         match = palloc(pattlen + 1);
4809         match_pos = 0;
4810         for (pos = 0; pos < pattlen; pos++)
4811         {
4812                 /* % and _ are wildcard characters in LIKE */
4813                 if (patt[pos] == '%' ||
4814                         patt[pos] == '_')
4815                         break;
4816
4817                 /* Backslash escapes the next character */
4818                 if (patt[pos] == '\\')
4819                 {
4820                         pos++;
4821                         if (pos >= pattlen)
4822                                 break;
4823                 }
4824
4825                 /*
4826                  * XXX In multibyte character sets, we can't trust isalpha, so assume
4827                  * any multibyte char is potentially case-varying.
4828                  */
4829                 if (case_insensitive)
4830                 {
4831                         if (is_multibyte && (unsigned char) patt[pos] >= 0x80)
4832                                 break;
4833                         if (isalpha((unsigned char) patt[pos]))
4834                                 break;
4835                 }
4836
4837                 /*
4838                  * NOTE: this code used to think that %% meant a literal %, but
4839                  * textlike() itself does not think that, and the SQL92 spec doesn't
4840                  * say any such thing either.
4841                  */
4842                 match[match_pos++] = patt[pos];
4843         }
4844
4845         match[match_pos] = '\0';
4846         rest = &patt[pos];
4847
4848         if (typeid != BYTEAOID)
4849         {
4850                 *prefix_const = string_to_const(match, typeid);
4851                 *rest_const = string_to_const(rest, typeid);
4852         }
4853         else
4854         {
4855                 *prefix_const = string_to_bytea_const(match, match_pos);
4856                 *rest_const = string_to_bytea_const(rest, pattlen - pos);
4857         }
4858
4859         pfree(patt);
4860         pfree(match);
4861
4862         /* in LIKE, an empty pattern is an exact match! */
4863         if (pos == pattlen)
4864                 return Pattern_Prefix_Exact;    /* reached end of pattern, so exact */
4865
4866         if (match_pos > 0)
4867                 return Pattern_Prefix_Partial;
4868
4869         return Pattern_Prefix_None;
4870 }
4871
4872 static Pattern_Prefix_Status
4873 regex_fixed_prefix(Const *patt_const, bool case_insensitive,
4874                                    Const **prefix_const, Const **rest_const)
4875 {
4876         char       *match;
4877         int                     pos,
4878                                 match_pos,
4879                                 prev_pos,
4880                                 prev_match_pos;
4881         bool            have_leading_paren;
4882         char       *patt;
4883         char       *rest;
4884         Oid                     typeid = patt_const->consttype;
4885         bool            is_multibyte = (pg_database_encoding_max_length() > 1);
4886
4887         /*
4888          * Should be unnecessary, there are no bytea regex operators defined. As
4889          * such, it should be noted that the rest of this function has *not* been
4890          * made safe for binary (possibly NULL containing) strings.
4891          */
4892         if (typeid == BYTEAOID)
4893                 ereport(ERROR,
4894                                 (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
4895                  errmsg("regular-expression matching not supported on type bytea")));
4896
4897         /* the right-hand const is type text for all of these */
4898         patt = TextDatumGetCString(patt_const->constvalue);
4899
4900         /*
4901          * Check for ARE director prefix.  It's worth our trouble to recognize
4902          * this because similar_escape() used to use it, and some other code might
4903          * still use it, to force ARE mode.
4904          */
4905         pos = 0;
4906         if (strncmp(patt, "***:", 4) == 0)
4907                 pos = 4;
4908
4909         /* Pattern must be anchored left */
4910         if (patt[pos] != '^')
4911         {
4912                 rest = patt;
4913
4914                 *prefix_const = NULL;
4915                 *rest_const = string_to_const(rest, typeid);
4916
4917                 return Pattern_Prefix_None;
4918         }
4919         pos++;
4920
4921         /*
4922          * If '|' is present in pattern, then there may be multiple alternatives
4923          * for the start of the string.  (There are cases where this isn't so, for
4924          * instance if the '|' is inside parens, but detecting that reliably is
4925          * too hard.)
4926          */
4927         if (strchr(patt + pos, '|') != NULL)
4928         {
4929                 rest = patt;
4930
4931                 *prefix_const = NULL;
4932                 *rest_const = string_to_const(rest, typeid);
4933
4934                 return Pattern_Prefix_None;
4935         }
4936
4937         /* OK, allocate space for pattern */
4938         match = palloc(strlen(patt) + 1);
4939         prev_match_pos = match_pos = 0;
4940
4941         /*
4942          * We special-case the syntax '^(...)$' because psql uses it.  But beware:
4943          * sequences beginning "(?" are not what they seem, unless they're "(?:".
4944          * (We must recognize that because of similar_escape().)
4945          */
4946         have_leading_paren = false;
4947         if (patt[pos] == '(' &&
4948                 (patt[pos + 1] != '?' || patt[pos + 2] == ':'))
4949         {
4950                 have_leading_paren = true;
4951                 pos += (patt[pos + 1] != '?' ? 1 : 3);
4952         }
4953
4954         /* Scan remainder of pattern */
4955         prev_pos = pos;
4956         while (patt[pos])
4957         {
4958                 int                     len;
4959
4960                 /*
4961                  * Check for characters that indicate multiple possible matches here.
4962                  * Also, drop out at ')' or '$' so the termination test works right.
4963                  */
4964                 if (patt[pos] == '.' ||
4965                         patt[pos] == '(' ||
4966                         patt[pos] == ')' ||
4967                         patt[pos] == '[' ||
4968                         patt[pos] == '^' ||
4969                         patt[pos] == '$')
4970                         break;
4971
4972                 /*
4973                  * XXX In multibyte character sets, we can't trust isalpha, so assume
4974                  * any multibyte char is potentially case-varying.
4975                  */
4976                 if (case_insensitive)
4977                 {
4978                         if (is_multibyte && (unsigned char) patt[pos] >= 0x80)
4979                                 break;
4980                         if (isalpha((unsigned char) patt[pos]))
4981                                 break;
4982                 }
4983
4984                 /*
4985                  * Check for quantifiers.  Except for +, this means the preceding
4986                  * character is optional, so we must remove it from the prefix too!
4987                  */
4988                 if (patt[pos] == '*' ||
4989                         patt[pos] == '?' ||
4990                         patt[pos] == '{')
4991                 {
4992                         match_pos = prev_match_pos;
4993                         pos = prev_pos;
4994                         break;
4995                 }
4996                 if (patt[pos] == '+')
4997                 {
4998                         pos = prev_pos;
4999                         break;
5000                 }
5001
5002                 /*
5003                  * Normally, backslash quotes the next character.  But in AREs,
5004                  * backslash followed by alphanumeric is an escape, not a quoted
5005                  * character.  Must treat it as having multiple possible matches.
5006                  * Note: since only ASCII alphanumerics are escapes, we don't have to
5007                  * be paranoid about multibyte here.
5008                  */
5009                 if (patt[pos] == '\\')
5010                 {
5011                         if (isalnum((unsigned char) patt[pos + 1]))
5012                                 break;
5013                         pos++;
5014                         if (patt[pos] == '\0')
5015                                 break;
5016                 }
5017                 /* save position in case we need to back up on next loop cycle */
5018                 prev_match_pos = match_pos;
5019                 prev_pos = pos;
5020                 /* must use encoding-aware processing here */
5021                 len = pg_mblen(&patt[pos]);
5022                 memcpy(&match[match_pos], &patt[pos], len);
5023                 match_pos += len;
5024                 pos += len;
5025         }
5026
5027         match[match_pos] = '\0';
5028         rest = &patt[pos];
5029
5030         if (have_leading_paren && patt[pos] == ')')
5031                 pos++;
5032
5033         if (patt[pos] == '$' && patt[pos + 1] == '\0')
5034         {
5035                 rest = &patt[pos + 1];
5036
5037                 *prefix_const = string_to_const(match, typeid);
5038                 *rest_const = string_to_const(rest, typeid);
5039
5040                 pfree(patt);
5041                 pfree(match);
5042
5043                 return Pattern_Prefix_Exact;    /* pattern specifies exact match */
5044         }
5045
5046         *prefix_const = string_to_const(match, typeid);
5047         *rest_const = string_to_const(rest, typeid);
5048
5049         pfree(patt);
5050         pfree(match);
5051
5052         if (match_pos > 0)
5053                 return Pattern_Prefix_Partial;
5054
5055         return Pattern_Prefix_None;
5056 }
5057
5058 Pattern_Prefix_Status
5059 pattern_fixed_prefix(Const *patt, Pattern_Type ptype,
5060                                          Const **prefix, Const **rest)
5061 {
5062         Pattern_Prefix_Status result;
5063
5064         switch (ptype)
5065         {
5066                 case Pattern_Type_Like:
5067                         result = like_fixed_prefix(patt, false, prefix, rest);
5068                         break;
5069                 case Pattern_Type_Like_IC:
5070                         result = like_fixed_prefix(patt, true, prefix, rest);
5071                         break;
5072                 case Pattern_Type_Regex:
5073                         result = regex_fixed_prefix(patt, false, prefix, rest);
5074                         break;
5075                 case Pattern_Type_Regex_IC:
5076                         result = regex_fixed_prefix(patt, true, prefix, rest);
5077                         break;
5078                 default:
5079                         elog(ERROR, "unrecognized ptype: %d", (int) ptype);
5080                         result = Pattern_Prefix_None;           /* keep compiler quiet */
5081                         break;
5082         }
5083         return result;
5084 }
5085
5086 /*
5087  * Estimate the selectivity of a fixed prefix for a pattern match.
5088  *
5089  * A fixed prefix "foo" is estimated as the selectivity of the expression
5090  * "variable >= 'foo' AND variable < 'fop'" (see also indxpath.c).
5091  *
5092  * The selectivity estimate is with respect to the portion of the column
5093  * population represented by the histogram --- the caller must fold this
5094  * together with info about MCVs and NULLs.
5095  *
5096  * We use the >= and < operators from the specified btree opfamily to do the
5097  * estimation.  The given variable and Const must be of the associated
5098  * datatype.
5099  *
5100  * XXX Note: we make use of the upper bound to estimate operator selectivity
5101  * even if the locale is such that we cannot rely on the upper-bound string.
5102  * The selectivity only needs to be approximately right anyway, so it seems
5103  * more useful to use the upper-bound code than not.
5104  */
5105 static Selectivity
5106 prefix_selectivity(PlannerInfo *root, VariableStatData *vardata,
5107                                    Oid vartype, Oid opfamily, Const *prefixcon)
5108 {
5109         Selectivity prefixsel;
5110         Oid                     cmpopr;
5111         FmgrInfo        opproc;
5112         Const      *greaterstrcon;
5113         Selectivity eq_sel;
5114
5115         cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5116                                                                  BTGreaterEqualStrategyNumber);
5117         if (cmpopr == InvalidOid)
5118                 elog(ERROR, "no >= operator for opfamily %u", opfamily);
5119         fmgr_info(get_opcode(cmpopr), &opproc);
5120         fmgr_info_set_collation(DEFAULT_COLLATION_OID, &opproc);
5121
5122         prefixsel = ineq_histogram_selectivity(root, vardata, &opproc, true,
5123                                                                                    prefixcon->constvalue,
5124                                                                                    prefixcon->consttype);
5125
5126         if (prefixsel < 0.0)
5127         {
5128                 /* No histogram is present ... return a suitable default estimate */
5129                 return DEFAULT_MATCH_SEL;
5130         }
5131
5132         /*-------
5133          * If we can create a string larger than the prefix, say
5134          *      "x < greaterstr".
5135          *-------
5136          */
5137         cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5138                                                                  BTLessStrategyNumber);
5139         if (cmpopr == InvalidOid)
5140                 elog(ERROR, "no < operator for opfamily %u", opfamily);
5141         fmgr_info(get_opcode(cmpopr), &opproc);
5142         fmgr_info_set_collation(DEFAULT_COLLATION_OID, &opproc);
5143
5144         greaterstrcon = make_greater_string(prefixcon, &opproc);
5145         if (greaterstrcon)
5146         {
5147                 Selectivity topsel;
5148
5149                 topsel = ineq_histogram_selectivity(root, vardata, &opproc, false,
5150                                                                                         greaterstrcon->constvalue,
5151                                                                                         greaterstrcon->consttype);
5152
5153                 /* ineq_histogram_selectivity worked before, it shouldn't fail now */
5154                 Assert(topsel >= 0.0);
5155
5156                 /*
5157                  * Merge the two selectivities in the same way as for a range query
5158                  * (see clauselist_selectivity()).      Note that we don't need to worry
5159                  * about double-exclusion of nulls, since ineq_histogram_selectivity
5160                  * doesn't count those anyway.
5161                  */
5162                 prefixsel = topsel + prefixsel - 1.0;
5163         }
5164
5165         /*
5166          * If the prefix is long then the two bounding values might be too close
5167          * together for the histogram to distinguish them usefully, resulting in a
5168          * zero estimate (plus or minus roundoff error). To avoid returning a
5169          * ridiculously small estimate, compute the estimated selectivity for
5170          * "variable = 'foo'", and clamp to that. (Obviously, the resultant
5171          * estimate should be at least that.)
5172          *
5173          * We apply this even if we couldn't make a greater string.  That case
5174          * suggests that the prefix is near the maximum possible, and thus
5175          * probably off the end of the histogram, and thus we probably got a very
5176          * small estimate from the >= condition; so we still need to clamp.
5177          */
5178         cmpopr = get_opfamily_member(opfamily, vartype, vartype,
5179                                                                  BTEqualStrategyNumber);
5180         if (cmpopr == InvalidOid)
5181                 elog(ERROR, "no = operator for opfamily %u", opfamily);
5182         eq_sel = var_eq_const(vardata, cmpopr, prefixcon->constvalue,
5183                                                   false, true);
5184
5185         prefixsel = Max(prefixsel, eq_sel);
5186
5187         return prefixsel;
5188 }
5189
5190
5191 /*
5192  * Estimate the selectivity of a pattern of the specified type.
5193  * Note that any fixed prefix of the pattern will have been removed already.
5194  *
5195  * For now, we use a very simplistic approach: fixed characters reduce the
5196  * selectivity a good deal, character ranges reduce it a little,
5197  * wildcards (such as % for LIKE or .* for regex) increase it.
5198  */
5199
5200 #define FIXED_CHAR_SEL  0.20    /* about 1/5 */
5201 #define CHAR_RANGE_SEL  0.25
5202 #define ANY_CHAR_SEL    0.9             /* not 1, since it won't match end-of-string */
5203 #define FULL_WILDCARD_SEL 5.0
5204 #define PARTIAL_WILDCARD_SEL 2.0
5205
5206 static Selectivity
5207 like_selectivity(Const *patt_const, bool case_insensitive)
5208 {
5209         Selectivity sel = 1.0;
5210         int                     pos;
5211         Oid                     typeid = patt_const->consttype;
5212         char       *patt;
5213         int                     pattlen;
5214
5215         /* the right-hand const is type text or bytea */
5216         Assert(typeid == BYTEAOID || typeid == TEXTOID);
5217
5218         if (typeid == BYTEAOID && case_insensitive)
5219                 ereport(ERROR,
5220                                 (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5221                    errmsg("case insensitive matching not supported on type bytea")));
5222
5223         if (typeid != BYTEAOID)
5224         {
5225                 patt = TextDatumGetCString(patt_const->constvalue);
5226                 pattlen = strlen(patt);
5227         }
5228         else
5229         {
5230                 bytea      *bstr = DatumGetByteaP(patt_const->constvalue);
5231
5232                 pattlen = VARSIZE(bstr) - VARHDRSZ;
5233                 patt = (char *) palloc(pattlen);
5234                 memcpy(patt, VARDATA(bstr), pattlen);
5235                 if ((Pointer) bstr != DatumGetPointer(patt_const->constvalue))
5236                         pfree(bstr);
5237         }
5238
5239         /* Skip any leading wildcard; it's already factored into initial sel */
5240         for (pos = 0; pos < pattlen; pos++)
5241         {
5242                 if (patt[pos] != '%' && patt[pos] != '_')
5243                         break;
5244         }
5245
5246         for (; pos < pattlen; pos++)
5247         {
5248                 /* % and _ are wildcard characters in LIKE */
5249                 if (patt[pos] == '%')
5250                         sel *= FULL_WILDCARD_SEL;
5251                 else if (patt[pos] == '_')
5252                         sel *= ANY_CHAR_SEL;
5253                 else if (patt[pos] == '\\')
5254                 {
5255                         /* Backslash quotes the next character */
5256                         pos++;
5257                         if (pos >= pattlen)
5258                                 break;
5259                         sel *= FIXED_CHAR_SEL;
5260                 }
5261                 else
5262                         sel *= FIXED_CHAR_SEL;
5263         }
5264         /* Could get sel > 1 if multiple wildcards */
5265         if (sel > 1.0)
5266                 sel = 1.0;
5267
5268         pfree(patt);
5269         return sel;
5270 }
5271
5272 static Selectivity
5273 regex_selectivity_sub(char *patt, int pattlen, bool case_insensitive)
5274 {
5275         Selectivity sel = 1.0;
5276         int                     paren_depth = 0;
5277         int                     paren_pos = 0;  /* dummy init to keep compiler quiet */
5278         int                     pos;
5279
5280         for (pos = 0; pos < pattlen; pos++)
5281         {
5282                 if (patt[pos] == '(')
5283                 {
5284                         if (paren_depth == 0)
5285                                 paren_pos = pos;        /* remember start of parenthesized item */
5286                         paren_depth++;
5287                 }
5288                 else if (patt[pos] == ')' && paren_depth > 0)
5289                 {
5290                         paren_depth--;
5291                         if (paren_depth == 0)
5292                                 sel *= regex_selectivity_sub(patt + (paren_pos + 1),
5293                                                                                          pos - (paren_pos + 1),
5294                                                                                          case_insensitive);
5295                 }
5296                 else if (patt[pos] == '|' && paren_depth == 0)
5297                 {
5298                         /*
5299                          * If unquoted | is present at paren level 0 in pattern, we have
5300                          * multiple alternatives; sum their probabilities.
5301                          */
5302                         sel += regex_selectivity_sub(patt + (pos + 1),
5303                                                                                  pattlen - (pos + 1),
5304                                                                                  case_insensitive);
5305                         break;                          /* rest of pattern is now processed */
5306                 }
5307                 else if (patt[pos] == '[')
5308                 {
5309                         bool            negclass = false;
5310
5311                         if (patt[++pos] == '^')
5312                         {
5313                                 negclass = true;
5314                                 pos++;
5315                         }
5316                         if (patt[pos] == ']')           /* ']' at start of class is not
5317                                                                                  * special */
5318                                 pos++;
5319                         while (pos < pattlen && patt[pos] != ']')
5320                                 pos++;
5321                         if (paren_depth == 0)
5322                                 sel *= (negclass ? (1.0 - CHAR_RANGE_SEL) : CHAR_RANGE_SEL);
5323                 }
5324                 else if (patt[pos] == '.')
5325                 {
5326                         if (paren_depth == 0)
5327                                 sel *= ANY_CHAR_SEL;
5328                 }
5329                 else if (patt[pos] == '*' ||
5330                                  patt[pos] == '?' ||
5331                                  patt[pos] == '+')
5332                 {
5333                         /* Ought to be smarter about quantifiers... */
5334                         if (paren_depth == 0)
5335                                 sel *= PARTIAL_WILDCARD_SEL;
5336                 }
5337                 else if (patt[pos] == '{')
5338                 {
5339                         while (pos < pattlen && patt[pos] != '}')
5340                                 pos++;
5341                         if (paren_depth == 0)
5342                                 sel *= PARTIAL_WILDCARD_SEL;
5343                 }
5344                 else if (patt[pos] == '\\')
5345                 {
5346                         /* backslash quotes the next character */
5347                         pos++;
5348                         if (pos >= pattlen)
5349                                 break;
5350                         if (paren_depth == 0)
5351                                 sel *= FIXED_CHAR_SEL;
5352                 }
5353                 else
5354                 {
5355                         if (paren_depth == 0)
5356                                 sel *= FIXED_CHAR_SEL;
5357                 }
5358         }
5359         /* Could get sel > 1 if multiple wildcards */
5360         if (sel > 1.0)
5361                 sel = 1.0;
5362         return sel;
5363 }
5364
5365 static Selectivity
5366 regex_selectivity(Const *patt_const, bool case_insensitive)
5367 {
5368         Selectivity sel;
5369         char       *patt;
5370         int                     pattlen;
5371         Oid                     typeid = patt_const->consttype;
5372
5373         /*
5374          * Should be unnecessary, there are no bytea regex operators defined. As
5375          * such, it should be noted that the rest of this function has *not* been
5376          * made safe for binary (possibly NULL containing) strings.
5377          */
5378         if (typeid == BYTEAOID)
5379                 ereport(ERROR,
5380                                 (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
5381                  errmsg("regular-expression matching not supported on type bytea")));
5382
5383         /* the right-hand const is type text for all of these */
5384         patt = TextDatumGetCString(patt_const->constvalue);
5385         pattlen = strlen(patt);
5386
5387         /* If patt doesn't end with $, consider it to have a trailing wildcard */
5388         if (pattlen > 0 && patt[pattlen - 1] == '$' &&
5389                 (pattlen == 1 || patt[pattlen - 2] != '\\'))
5390         {
5391                 /* has trailing $ */
5392                 sel = regex_selectivity_sub(patt, pattlen - 1, case_insensitive);
5393         }
5394         else
5395         {
5396                 /* no trailing $ */
5397                 sel = regex_selectivity_sub(patt, pattlen, case_insensitive);
5398                 sel *= FULL_WILDCARD_SEL;
5399                 if (sel > 1.0)
5400                         sel = 1.0;
5401         }
5402         return sel;
5403 }
5404
5405 static Selectivity
5406 pattern_selectivity(Const *patt, Pattern_Type ptype)
5407 {
5408         Selectivity result;
5409
5410         switch (ptype)
5411         {
5412                 case Pattern_Type_Like:
5413                         result = like_selectivity(patt, false);
5414                         break;
5415                 case Pattern_Type_Like_IC:
5416                         result = like_selectivity(patt, true);
5417                         break;
5418                 case Pattern_Type_Regex:
5419                         result = regex_selectivity(patt, false);
5420                         break;
5421                 case Pattern_Type_Regex_IC:
5422                         result = regex_selectivity(patt, true);
5423                         break;
5424                 default:
5425                         elog(ERROR, "unrecognized ptype: %d", (int) ptype);
5426                         result = 1.0;           /* keep compiler quiet */
5427                         break;
5428         }
5429         return result;
5430 }
5431
5432
5433 /*
5434  * Try to generate a string greater than the given string or any
5435  * string it is a prefix of.  If successful, return a palloc'd string
5436  * in the form of a Const node; else return NULL.
5437  *
5438  * The caller must provide the appropriate "less than" comparison function
5439  * for testing the strings.  In particular, ltproc->fn_collation specifies
5440  * the locale for comparisons.
5441  *
5442  * The key requirement here is that given a prefix string, say "foo",
5443  * we must be able to generate another string "fop" that is greater than
5444  * all strings "foobar" starting with "foo".  We can test that we have
5445  * generated a string greater than the prefix string, but in non-C locales
5446  * that is not a bulletproof guarantee that an extension of the string might
5447  * not sort after it; an example is that "foo " is less than "foo!", but it
5448  * is not clear that a "dictionary" sort ordering will consider "foo!" less
5449  * than "foo bar".      CAUTION: Therefore, this function should be used only for
5450  * estimation purposes when working in a non-C locale.
5451  *
5452  * To try to catch most cases where an extended string might otherwise sort
5453  * before the result value, we determine which of the strings "Z", "z", "y",
5454  * and "9" is seen as largest by the locale, and append that to the given
5455  * prefix before trying to find a string that compares as larger.
5456  *
5457  * If we max out the righthand byte, truncate off the last character
5458  * and start incrementing the next.  For example, if "z" were the last
5459  * character in the sort order, then we could produce "foo" as a
5460  * string greater than "fonz".
5461  *
5462  * This could be rather slow in the worst case, but in most cases we
5463  * won't have to try more than one or two strings before succeeding.
5464  */
5465 Const *
5466 make_greater_string(const Const *str_const, FmgrInfo *ltproc)
5467 {
5468         Oid                     datatype = str_const->consttype;
5469         char       *workstr;
5470         int                     len;
5471         Datum           cmpstr;
5472         text       *cmptxt = NULL;
5473
5474         /*
5475          * Get a modifiable copy of the prefix string in C-string format, and set
5476          * up the string we will compare to as a Datum.  In C locale this can just
5477          * be the given prefix string, otherwise we need to add a suffix.  Types
5478          * NAME and BYTEA sort bytewise so they don't need a suffix either.
5479          */
5480         if (datatype == NAMEOID)
5481         {
5482                 workstr = DatumGetCString(DirectFunctionCall1(nameout,
5483                                                                                                           str_const->constvalue));
5484                 len = strlen(workstr);
5485                 cmpstr = str_const->constvalue;
5486         }
5487         else if (datatype == BYTEAOID)
5488         {
5489                 bytea      *bstr = DatumGetByteaP(str_const->constvalue);
5490
5491                 len = VARSIZE(bstr) - VARHDRSZ;
5492                 workstr = (char *) palloc(len);
5493                 memcpy(workstr, VARDATA(bstr), len);
5494                 if ((Pointer) bstr != DatumGetPointer(str_const->constvalue))
5495                         pfree(bstr);
5496                 cmpstr = str_const->constvalue;
5497         }
5498         else
5499         {
5500                 workstr = TextDatumGetCString(str_const->constvalue);
5501                 len = strlen(workstr);
5502                 if (lc_collate_is_c(ltproc->fn_collation) || len == 0)
5503                         cmpstr = str_const->constvalue;
5504                 else
5505                 {
5506                         /* If first time through, determine the suffix to use */
5507                         static char suffixchar = 0;
5508                         static Oid      suffixcollation = 0;
5509
5510                         if (!suffixchar || suffixcollation != ltproc->fn_collation)
5511                         {
5512                                 char       *best;
5513
5514                                 best = "Z";
5515                                 if (varstr_cmp(best, 1, "z", 1, ltproc->fn_collation) < 0)
5516                                         best = "z";
5517                                 if (varstr_cmp(best, 1, "y", 1, ltproc->fn_collation) < 0)
5518                                         best = "y";
5519                                 if (varstr_cmp(best, 1, "9", 1, ltproc->fn_collation) < 0)
5520                                         best = "9";
5521                                 suffixchar = *best;
5522                                 suffixcollation = ltproc->fn_collation;
5523                         }
5524
5525                         /* And build the string to compare to */
5526                         cmptxt = (text *) palloc(VARHDRSZ + len + 1);
5527                         SET_VARSIZE(cmptxt, VARHDRSZ + len + 1);
5528                         memcpy(VARDATA(cmptxt), workstr, len);
5529                         *(VARDATA(cmptxt) + len) = suffixchar;
5530                         cmpstr = PointerGetDatum(cmptxt);
5531                 }
5532         }
5533
5534         while (len > 0)
5535         {
5536                 unsigned char *lastchar = (unsigned char *) (workstr + len - 1);
5537                 unsigned char savelastchar = *lastchar;
5538
5539                 /*
5540                  * Try to generate a larger string by incrementing the last byte.
5541                  */
5542                 while (*lastchar < (unsigned char) 255)
5543                 {
5544                         Const      *workstr_const;
5545
5546                         (*lastchar)++;
5547
5548                         if (datatype != BYTEAOID)
5549                         {
5550                                 /* do not generate invalid encoding sequences */
5551                                 if (!pg_verifymbstr(workstr, len, true))
5552                                         continue;
5553                                 workstr_const = string_to_const(workstr, datatype);
5554                         }
5555                         else
5556                                 workstr_const = string_to_bytea_const(workstr, len);
5557
5558                         if (DatumGetBool(FunctionCall2(ltproc,
5559                                                                                    cmpstr,
5560                                                                                    workstr_const->constvalue)))
5561                         {
5562                                 /* Successfully made a string larger than cmpstr */
5563                                 if (cmptxt)
5564                                         pfree(cmptxt);
5565                                 pfree(workstr);
5566                                 return workstr_const;
5567                         }
5568
5569                         /* No good, release unusable value and try again */
5570                         pfree(DatumGetPointer(workstr_const->constvalue));
5571                         pfree(workstr_const);
5572                 }
5573
5574                 /* restore last byte so we don't confuse pg_mbcliplen */
5575                 *lastchar = savelastchar;
5576
5577                 /*
5578                  * Truncate off the last character, which might be more than 1 byte,
5579                  * depending on the character encoding.
5580                  */
5581                 if (datatype != BYTEAOID && pg_database_encoding_max_length() > 1)
5582                         len = pg_mbcliplen(workstr, len, len - 1);
5583                 else
5584                         len -= 1;
5585
5586                 if (datatype != BYTEAOID)
5587                         workstr[len] = '\0';
5588         }
5589
5590         /* Failed... */
5591         if (cmptxt)
5592                 pfree(cmptxt);
5593         pfree(workstr);
5594
5595         return NULL;
5596 }
5597
5598 /*
5599  * Generate a Datum of the appropriate type from a C string.
5600  * Note that all of the supported types are pass-by-ref, so the
5601  * returned value should be pfree'd if no longer needed.
5602  */
5603 static Datum
5604 string_to_datum(const char *str, Oid datatype)
5605 {
5606         Assert(str != NULL);
5607
5608         /*
5609          * We cheat a little by assuming that CStringGetTextDatum() will do for
5610          * bpchar and varchar constants too...
5611          */
5612         if (datatype == NAMEOID)
5613                 return DirectFunctionCall1(namein, CStringGetDatum(str));
5614         else if (datatype == BYTEAOID)
5615                 return DirectFunctionCall1(byteain, CStringGetDatum(str));
5616         else
5617                 return CStringGetTextDatum(str);
5618 }
5619
5620 /*
5621  * Generate a Const node of the appropriate type from a C string.
5622  */
5623 static Const *
5624 string_to_const(const char *str, Oid datatype)
5625 {
5626         Datum           conval = string_to_datum(str, datatype);
5627         Oid                     collation;
5628         int                     constlen;
5629
5630         /*
5631          * We only need to support a few datatypes here, so hard-wire properties
5632          * instead of incurring the expense of catalog lookups.
5633          */
5634         switch (datatype)
5635         {
5636                 case TEXTOID:
5637                 case VARCHAROID:
5638                 case BPCHAROID:
5639                         collation = DEFAULT_COLLATION_OID;
5640                         constlen = -1;
5641                         break;
5642
5643                 case NAMEOID:
5644                         collation = InvalidOid;
5645                         constlen = NAMEDATALEN;
5646                         break;
5647
5648                 case BYTEAOID:
5649                         collation = InvalidOid;
5650                         constlen = -1;
5651                         break;
5652
5653                 default:
5654                         elog(ERROR, "unexpected datatype in string_to_const: %u",
5655                                  datatype);
5656                         return NULL;
5657         }
5658
5659         return makeConst(datatype, -1, collation, constlen,
5660                                          conval, false, false);
5661 }
5662
5663 /*
5664  * Generate a Const node of bytea type from a binary C string and a length.
5665  */
5666 static Const *
5667 string_to_bytea_const(const char *str, size_t str_len)
5668 {
5669         bytea      *bstr = palloc(VARHDRSZ + str_len);
5670         Datum           conval;
5671
5672         memcpy(VARDATA(bstr), str, str_len);
5673         SET_VARSIZE(bstr, VARHDRSZ + str_len);
5674         conval = PointerGetDatum(bstr);
5675
5676         return makeConst(BYTEAOID, -1, InvalidOid, -1, conval, false, false);
5677 }
5678
5679 /*-------------------------------------------------------------------------
5680  *
5681  * Index cost estimation functions
5682  *
5683  * genericcostestimate is a general-purpose estimator for use when we
5684  * don't have any better idea about how to estimate.  Index-type-specific
5685  * knowledge can be incorporated in the type-specific routines.
5686  *
5687  * One bit of index-type-specific knowledge we can relatively easily use
5688  * in genericcostestimate is the estimate of the number of index tuples
5689  * visited.  If numIndexTuples is not 0 then it is used as the estimate,
5690  * otherwise we compute a generic estimate.
5691  *
5692  *-------------------------------------------------------------------------
5693  */
5694
5695 static void
5696 genericcostestimate(PlannerInfo *root,
5697                                         IndexOptInfo *index,
5698                                         List *indexQuals,
5699                                         List *indexOrderBys,
5700                                         RelOptInfo *outer_rel,
5701                                         double numIndexTuples,
5702                                         Cost *indexStartupCost,
5703                                         Cost *indexTotalCost,
5704                                         Selectivity *indexSelectivity,
5705                                         double *indexCorrelation)
5706 {
5707         double          numIndexPages;
5708         double          num_sa_scans;
5709         double          num_outer_scans;
5710         double          num_scans;
5711         QualCost        index_qual_cost;
5712         double          qual_op_cost;
5713         double          qual_arg_cost;
5714         double          spc_random_page_cost;
5715         List       *selectivityQuals;
5716         ListCell   *l;
5717
5718         /*----------
5719          * If the index is partial, AND the index predicate with the explicitly
5720          * given indexquals to produce a more accurate idea of the index
5721          * selectivity.  However, we need to be careful not to insert redundant
5722          * clauses, because clauselist_selectivity() is easily fooled into
5723          * computing a too-low selectivity estimate.  Our approach is to add
5724          * only the index predicate clause(s) that cannot be proven to be implied
5725          * by the given indexquals.  This successfully handles cases such as a
5726          * qual "x = 42" used with a partial index "WHERE x >= 40 AND x < 50".
5727          * There are many other cases where we won't detect redundancy, leading
5728          * to a too-low selectivity estimate, which will bias the system in favor
5729          * of using partial indexes where possible.  That is not necessarily bad
5730          * though.
5731          *
5732          * Note that indexQuals contains RestrictInfo nodes while the indpred
5733          * does not.  This is OK for both predicate_implied_by() and
5734          * clauselist_selectivity().
5735          *----------
5736          */
5737         if (index->indpred != NIL)
5738         {
5739                 List       *predExtraQuals = NIL;
5740
5741                 foreach(l, index->indpred)
5742                 {
5743                         Node       *predQual = (Node *) lfirst(l);
5744                         List       *oneQual = list_make1(predQual);
5745
5746                         if (!predicate_implied_by(oneQual, indexQuals))
5747                                 predExtraQuals = list_concat(predExtraQuals, oneQual);
5748                 }
5749                 /* list_concat avoids modifying the passed-in indexQuals list */
5750                 selectivityQuals = list_concat(predExtraQuals, indexQuals);
5751         }
5752         else
5753                 selectivityQuals = indexQuals;
5754
5755         /*
5756          * Check for ScalarArrayOpExpr index quals, and estimate the number of
5757          * index scans that will be performed.
5758          */
5759         num_sa_scans = 1;
5760         foreach(l, indexQuals)
5761         {
5762                 RestrictInfo *rinfo = (RestrictInfo *) lfirst(l);
5763
5764                 if (IsA(rinfo->clause, ScalarArrayOpExpr))
5765                 {
5766                         ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) rinfo->clause;
5767                         int                     alength = estimate_array_length(lsecond(saop->args));
5768
5769                         if (alength > 1)
5770                                 num_sa_scans *= alength;
5771                 }
5772         }
5773
5774         /* Estimate the fraction of main-table tuples that will be visited */
5775         *indexSelectivity = clauselist_selectivity(root, selectivityQuals,
5776                                                                                            index->rel->relid,
5777                                                                                            JOIN_INNER,
5778                                                                                            NULL);
5779
5780         /*
5781          * If caller didn't give us an estimate, estimate the number of index
5782          * tuples that will be visited.  We do it in this rather peculiar-looking
5783          * way in order to get the right answer for partial indexes.
5784          */
5785         if (numIndexTuples <= 0.0)
5786         {
5787                 numIndexTuples = *indexSelectivity * index->rel->tuples;
5788
5789                 /*
5790                  * The above calculation counts all the tuples visited across all
5791                  * scans induced by ScalarArrayOpExpr nodes.  We want to consider the
5792                  * average per-indexscan number, so adjust.  This is a handy place to
5793                  * round to integer, too.  (If caller supplied tuple estimate, it's
5794                  * responsible for handling these considerations.)
5795                  */
5796                 numIndexTuples = rint(numIndexTuples / num_sa_scans);
5797         }
5798
5799         /*
5800          * We can bound the number of tuples by the index size in any case. Also,
5801          * always estimate at least one tuple is touched, even when
5802          * indexSelectivity estimate is tiny.
5803          */
5804         if (numIndexTuples > index->tuples)
5805                 numIndexTuples = index->tuples;
5806         if (numIndexTuples < 1.0)
5807                 numIndexTuples = 1.0;
5808
5809         /*
5810          * Estimate the number of index pages that will be retrieved.
5811          *
5812          * We use the simplistic method of taking a pro-rata fraction of the total
5813          * number of index pages.  In effect, this counts only leaf pages and not
5814          * any overhead such as index metapage or upper tree levels. In practice
5815          * this seems a better approximation than charging for access to the upper
5816          * levels, perhaps because those tend to stay in cache under load.
5817          */
5818         if (index->pages > 1 && index->tuples > 1)
5819                 numIndexPages = ceil(numIndexTuples * index->pages / index->tuples);
5820         else
5821                 numIndexPages = 1.0;
5822
5823         /* fetch estimated page cost for schema containing index */
5824         get_tablespace_page_costs(index->reltablespace,
5825                                                           &spc_random_page_cost,
5826                                                           NULL);
5827
5828         /*
5829          * Now compute the disk access costs.
5830          *
5831          * The above calculations are all per-index-scan.  However, if we are in a
5832          * nestloop inner scan, we can expect the scan to be repeated (with
5833          * different search keys) for each row of the outer relation.  Likewise,
5834          * ScalarArrayOpExpr quals result in multiple index scans.      This creates
5835          * the potential for cache effects to reduce the number of disk page
5836          * fetches needed.      We want to estimate the average per-scan I/O cost in
5837          * the presence of caching.
5838          *
5839          * We use the Mackert-Lohman formula (see costsize.c for details) to
5840          * estimate the total number of page fetches that occur.  While this
5841          * wasn't what it was designed for, it seems a reasonable model anyway.
5842          * Note that we are counting pages not tuples anymore, so we take N = T =
5843          * index size, as if there were one "tuple" per page.
5844          */
5845         if (outer_rel != NULL && outer_rel->rows > 1)
5846         {
5847                 num_outer_scans = outer_rel->rows;
5848                 num_scans = num_sa_scans * num_outer_scans;
5849         }
5850         else
5851         {
5852                 num_outer_scans = 1;
5853                 num_scans = num_sa_scans;
5854         }
5855
5856         if (num_scans > 1)
5857         {
5858                 double          pages_fetched;
5859
5860                 /* total page fetches ignoring cache effects */
5861                 pages_fetched = numIndexPages * num_scans;
5862
5863                 /* use Mackert and Lohman formula to adjust for cache effects */
5864                 pages_fetched = index_pages_fetched(pages_fetched,
5865                                                                                         index->pages,
5866                                                                                         (double) index->pages,
5867                                                                                         root);
5868
5869                 /*
5870                  * Now compute the total disk access cost, and then report a pro-rated
5871                  * share for each outer scan.  (Don't pro-rate for ScalarArrayOpExpr,
5872                  * since that's internal to the indexscan.)
5873                  */
5874                 *indexTotalCost = (pages_fetched * spc_random_page_cost)
5875                         / num_outer_scans;
5876         }
5877         else
5878         {
5879                 /*
5880                  * For a single index scan, we just charge spc_random_page_cost per
5881                  * page touched.
5882                  */
5883                 *indexTotalCost = numIndexPages * spc_random_page_cost;
5884         }
5885
5886         /*
5887          * A difficulty with the leaf-pages-only cost approach is that for small
5888          * selectivities (eg, single index tuple fetched) all indexes will look
5889          * equally attractive because we will estimate exactly 1 leaf page to be
5890          * fetched.  All else being equal, we should prefer physically smaller
5891          * indexes over larger ones.  (An index might be smaller because it is
5892          * partial or because it contains fewer columns; presumably the other
5893          * columns in the larger index aren't useful to the query, or the larger
5894          * index would have better selectivity.)
5895          *
5896          * We can deal with this by adding a very small "fudge factor" that
5897          * depends on the index size.  The fudge factor used here is one
5898          * spc_random_page_cost per 100000 index pages, which should be small
5899          * enough to not alter index-vs-seqscan decisions, but will prevent
5900          * indexes of different sizes from looking exactly equally attractive.
5901          */
5902         *indexTotalCost += index->pages * spc_random_page_cost / 100000.0;
5903
5904         /*
5905          * CPU cost: any complex expressions in the indexquals will need to be
5906          * evaluated once at the start of the scan to reduce them to runtime keys
5907          * to pass to the index AM (see nodeIndexscan.c).  We model the per-tuple
5908          * CPU costs as cpu_index_tuple_cost plus one cpu_operator_cost per
5909          * indexqual operator.  Because we have numIndexTuples as a per-scan
5910          * number, we have to multiply by num_sa_scans to get the correct result
5911          * for ScalarArrayOpExpr cases.  Similarly add in costs for any index
5912          * ORDER BY expressions.
5913          *
5914          * Note: this neglects the possible costs of rechecking lossy operators
5915          * and OR-clause expressions.  Detecting that that might be needed seems
5916          * more expensive than it's worth, though, considering all the other
5917          * inaccuracies here ...
5918          */
5919         cost_qual_eval(&index_qual_cost, indexQuals, root);
5920         qual_arg_cost = index_qual_cost.startup + index_qual_cost.per_tuple;
5921         cost_qual_eval(&index_qual_cost, indexOrderBys, root);
5922         qual_arg_cost += index_qual_cost.startup + index_qual_cost.per_tuple;
5923         qual_op_cost = cpu_operator_cost *
5924                 (list_length(indexQuals) + list_length(indexOrderBys));
5925         qual_arg_cost -= qual_op_cost;
5926         if (qual_arg_cost < 0)          /* just in case... */
5927                 qual_arg_cost = 0;
5928
5929         *indexStartupCost = qual_arg_cost;
5930         *indexTotalCost += qual_arg_cost;
5931         *indexTotalCost += numIndexTuples * num_sa_scans * (cpu_index_tuple_cost + qual_op_cost);
5932
5933         /*
5934          * We also add a CPU-cost component to represent the general costs of
5935          * starting an indexscan, such as analysis of btree index keys and initial
5936          * tree descent.  This is estimated at 100x cpu_operator_cost, which is a
5937          * bit arbitrary but seems the right order of magnitude. (As noted above,
5938          * we don't charge any I/O for touching upper tree levels, but charging
5939          * nothing at all has been found too optimistic.)
5940          *
5941          * Although this is startup cost with respect to any one scan, we add it
5942          * to the "total" cost component because it's only very interesting in the
5943          * many-ScalarArrayOpExpr-scan case, and there it will be paid over the
5944          * life of the scan node.
5945          */
5946         *indexTotalCost += num_sa_scans * 100.0 * cpu_operator_cost;
5947
5948         /*
5949          * Generic assumption about index correlation: there isn't any.
5950          */
5951         *indexCorrelation = 0.0;
5952 }
5953
5954
5955 Datum
5956 btcostestimate(PG_FUNCTION_ARGS)
5957 {
5958         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
5959         IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(1);
5960         List       *indexQuals = (List *) PG_GETARG_POINTER(2);
5961         List       *indexOrderBys = (List *) PG_GETARG_POINTER(3);
5962         RelOptInfo *outer_rel = (RelOptInfo *) PG_GETARG_POINTER(4);
5963         Cost       *indexStartupCost = (Cost *) PG_GETARG_POINTER(5);
5964         Cost       *indexTotalCost = (Cost *) PG_GETARG_POINTER(6);
5965         Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(7);
5966         double     *indexCorrelation = (double *) PG_GETARG_POINTER(8);
5967         Oid                     relid;
5968         AttrNumber      colnum;
5969         VariableStatData vardata;
5970         double          numIndexTuples;
5971         List       *indexBoundQuals;
5972         int                     indexcol;
5973         bool            eqQualHere;
5974         bool            found_saop;
5975         bool            found_is_null_op;
5976         double          num_sa_scans;
5977         ListCell   *l;
5978
5979         /*
5980          * For a btree scan, only leading '=' quals plus inequality quals for the
5981          * immediately next attribute contribute to index selectivity (these are
5982          * the "boundary quals" that determine the starting and stopping points of
5983          * the index scan).  Additional quals can suppress visits to the heap, so
5984          * it's OK to count them in indexSelectivity, but they should not count
5985          * for estimating numIndexTuples.  So we must examine the given indexQuals
5986          * to find out which ones count as boundary quals.      We rely on the
5987          * knowledge that they are given in index column order.
5988          *
5989          * For a RowCompareExpr, we consider only the first column, just as
5990          * rowcomparesel() does.
5991          *
5992          * If there's a ScalarArrayOpExpr in the quals, we'll actually perform N
5993          * index scans not one, but the ScalarArrayOpExpr's operator can be
5994          * considered to act the same as it normally does.
5995          */
5996         indexBoundQuals = NIL;
5997         indexcol = 0;
5998         eqQualHere = false;
5999         found_saop = false;
6000         found_is_null_op = false;
6001         num_sa_scans = 1;
6002         foreach(l, indexQuals)
6003         {
6004                 RestrictInfo *rinfo = (RestrictInfo *) lfirst(l);
6005                 Expr       *clause;
6006                 Node       *leftop,
6007                                    *rightop;
6008                 Oid                     clause_op;
6009                 int                     op_strategy;
6010                 bool            is_null_op = false;
6011
6012                 Assert(IsA(rinfo, RestrictInfo));
6013                 clause = rinfo->clause;
6014                 if (IsA(clause, OpExpr))
6015                 {
6016                         leftop = get_leftop(clause);
6017                         rightop = get_rightop(clause);
6018                         clause_op = ((OpExpr *) clause)->opno;
6019                 }
6020                 else if (IsA(clause, RowCompareExpr))
6021                 {
6022                         RowCompareExpr *rc = (RowCompareExpr *) clause;
6023
6024                         leftop = (Node *) linitial(rc->largs);
6025                         rightop = (Node *) linitial(rc->rargs);
6026                         clause_op = linitial_oid(rc->opnos);
6027                 }
6028                 else if (IsA(clause, ScalarArrayOpExpr))
6029                 {
6030                         ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
6031
6032                         leftop = (Node *) linitial(saop->args);
6033                         rightop = (Node *) lsecond(saop->args);
6034                         clause_op = saop->opno;
6035                         found_saop = true;
6036                 }
6037                 else if (IsA(clause, NullTest))
6038                 {
6039                         NullTest   *nt = (NullTest *) clause;
6040
6041                         leftop = (Node *) nt->arg;
6042                         rightop = NULL;
6043                         clause_op = InvalidOid;
6044                         if (nt->nulltesttype == IS_NULL)
6045                         {
6046                                 found_is_null_op = true;
6047                                 is_null_op = true;
6048                         }
6049                 }
6050                 else
6051                 {
6052                         elog(ERROR, "unsupported indexqual type: %d",
6053                                  (int) nodeTag(clause));
6054                         continue;                       /* keep compiler quiet */
6055                 }
6056                 if (match_index_to_operand(leftop, indexcol, index))
6057                 {
6058                         /* clause_op is correct */
6059                 }
6060                 else if (match_index_to_operand(rightop, indexcol, index))
6061                 {
6062                         /* Must flip operator to get the opfamily member */
6063                         clause_op = get_commutator(clause_op);
6064                 }
6065                 else
6066                 {
6067                         /* Must be past the end of quals for indexcol, try next */
6068                         if (!eqQualHere)
6069                                 break;                  /* done if no '=' qual for indexcol */
6070                         indexcol++;
6071                         eqQualHere = false;
6072                         if (match_index_to_operand(leftop, indexcol, index))
6073                         {
6074                                 /* clause_op is correct */
6075                         }
6076                         else if (match_index_to_operand(rightop, indexcol, index))
6077                         {
6078                                 /* Must flip operator to get the opfamily member */
6079                                 clause_op = get_commutator(clause_op);
6080                         }
6081                         else
6082                         {
6083                                 /* No quals for new indexcol, so we are done */
6084                                 break;
6085                         }
6086                 }
6087                 /* check for equality operator */
6088                 if (OidIsValid(clause_op))
6089                 {
6090                         op_strategy = get_op_opfamily_strategy(clause_op,
6091                                                                                                    index->opfamily[indexcol]);
6092                         Assert(op_strategy != 0);       /* not a member of opfamily?? */
6093                         if (op_strategy == BTEqualStrategyNumber)
6094                                 eqQualHere = true;
6095                 }
6096                 else if (is_null_op)
6097                 {
6098                         /* IS NULL is like = for purposes of selectivity determination */
6099                         eqQualHere = true;
6100                 }
6101                 /* count up number of SA scans induced by indexBoundQuals only */
6102                 if (IsA(clause, ScalarArrayOpExpr))
6103                 {
6104                         ScalarArrayOpExpr *saop = (ScalarArrayOpExpr *) clause;
6105                         int                     alength = estimate_array_length(lsecond(saop->args));
6106
6107                         if (alength > 1)
6108                                 num_sa_scans *= alength;
6109                 }
6110                 indexBoundQuals = lappend(indexBoundQuals, rinfo);
6111         }
6112
6113         /*
6114          * If index is unique and we found an '=' clause for each column, we can
6115          * just assume numIndexTuples = 1 and skip the expensive
6116          * clauselist_selectivity calculations.  However, a ScalarArrayOp or
6117          * NullTest invalidates that theory, even though it sets eqQualHere.
6118          */
6119         if (index->unique &&
6120                 indexcol == index->ncolumns - 1 &&
6121                 eqQualHere &&
6122                 !found_saop &&
6123                 !found_is_null_op)
6124                 numIndexTuples = 1.0;
6125         else
6126         {
6127                 Selectivity btreeSelectivity;
6128
6129                 btreeSelectivity = clauselist_selectivity(root, indexBoundQuals,
6130                                                                                                   index->rel->relid,
6131                                                                                                   JOIN_INNER,
6132                                                                                                   NULL);
6133                 numIndexTuples = btreeSelectivity * index->rel->tuples;
6134
6135                 /*
6136                  * As in genericcostestimate(), we have to adjust for any
6137                  * ScalarArrayOpExpr quals included in indexBoundQuals, and then round
6138                  * to integer.
6139                  */
6140                 numIndexTuples = rint(numIndexTuples / num_sa_scans);
6141         }
6142
6143         genericcostestimate(root, index, indexQuals, indexOrderBys,
6144                                                 outer_rel, numIndexTuples,
6145                                                 indexStartupCost, indexTotalCost,
6146                                                 indexSelectivity, indexCorrelation);
6147
6148         /*
6149          * If we can get an estimate of the first column's ordering correlation C
6150          * from pg_statistic, estimate the index correlation as C for a
6151          * single-column index, or C * 0.75 for multiple columns. (The idea here
6152          * is that multiple columns dilute the importance of the first column's
6153          * ordering, but don't negate it entirely.  Before 8.0 we divided the
6154          * correlation by the number of columns, but that seems too strong.)
6155          *
6156          * We can skip all this if we found a ScalarArrayOpExpr, because then the
6157          * call must be for a bitmap index scan, and the caller isn't going to
6158          * care what the index correlation is.
6159          */
6160         if (found_saop)
6161                 PG_RETURN_VOID();
6162
6163         MemSet(&vardata, 0, sizeof(vardata));
6164
6165         if (index->indexkeys[0] != 0)
6166         {
6167                 /* Simple variable --- look to stats for the underlying table */
6168                 RangeTblEntry *rte = planner_rt_fetch(index->rel->relid, root);
6169
6170                 Assert(rte->rtekind == RTE_RELATION);
6171                 relid = rte->relid;
6172                 Assert(relid != InvalidOid);
6173                 colnum = index->indexkeys[0];
6174
6175                 if (get_relation_stats_hook &&
6176                         (*get_relation_stats_hook) (root, rte, colnum, &vardata))
6177                 {
6178                         /*
6179                          * The hook took control of acquiring a stats tuple.  If it did
6180                          * supply a tuple, it'd better have supplied a freefunc.
6181                          */
6182                         if (HeapTupleIsValid(vardata.statsTuple) &&
6183                                 !vardata.freefunc)
6184                                 elog(ERROR, "no function provided to release variable stats with");
6185                 }
6186                 else
6187                 {
6188                         vardata.statsTuple = SearchSysCache3(STATRELATTINH,
6189                                                                                                  ObjectIdGetDatum(relid),
6190                                                                                                  Int16GetDatum(colnum),
6191                                                                                                  BoolGetDatum(rte->inh));
6192                         vardata.freefunc = ReleaseSysCache;
6193                 }
6194         }
6195         else
6196         {
6197                 /* Expression --- maybe there are stats for the index itself */
6198                 relid = index->indexoid;
6199                 colnum = 1;
6200
6201                 if (get_index_stats_hook &&
6202                         (*get_index_stats_hook) (root, relid, colnum, &vardata))
6203                 {
6204                         /*
6205                          * The hook took control of acquiring a stats tuple.  If it did
6206                          * supply a tuple, it'd better have supplied a freefunc.
6207                          */
6208                         if (HeapTupleIsValid(vardata.statsTuple) &&
6209                                 !vardata.freefunc)
6210                                 elog(ERROR, "no function provided to release variable stats with");
6211                 }
6212                 else
6213                 {
6214                         vardata.statsTuple = SearchSysCache3(STATRELATTINH,
6215                                                                                                  ObjectIdGetDatum(relid),
6216                                                                                                  Int16GetDatum(colnum),
6217                                                                                                  BoolGetDatum(false));
6218                         vardata.freefunc = ReleaseSysCache;
6219                 }
6220         }
6221
6222         if (HeapTupleIsValid(vardata.statsTuple))
6223         {
6224                 Oid                     sortop;
6225                 float4     *numbers;
6226                 int                     nnumbers;
6227
6228                 sortop = get_opfamily_member(index->opfamily[0],
6229                                                                          index->opcintype[0],
6230                                                                          index->opcintype[0],
6231                                                                          BTLessStrategyNumber);
6232                 if (OidIsValid(sortop) &&
6233                         get_attstatsslot(vardata.statsTuple, InvalidOid, 0,
6234                                                          STATISTIC_KIND_CORRELATION,
6235                                                          sortop,
6236                                                          NULL,
6237                                                          NULL, NULL,
6238                                                          &numbers, &nnumbers))
6239                 {
6240                         double          varCorrelation;
6241
6242                         Assert(nnumbers == 1);
6243                         varCorrelation = numbers[0];
6244
6245                         if (index->reverse_sort[0])
6246                                 varCorrelation = -varCorrelation;
6247
6248                         if (index->ncolumns > 1)
6249                                 *indexCorrelation = varCorrelation * 0.75;
6250                         else
6251                                 *indexCorrelation = varCorrelation;
6252
6253                         free_attstatsslot(InvalidOid, NULL, 0, numbers, nnumbers);
6254                 }
6255         }
6256
6257         ReleaseVariableStats(vardata);
6258
6259         PG_RETURN_VOID();
6260 }
6261
6262 Datum
6263 hashcostestimate(PG_FUNCTION_ARGS)
6264 {
6265         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
6266         IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(1);
6267         List       *indexQuals = (List *) PG_GETARG_POINTER(2);
6268         List       *indexOrderBys = (List *) PG_GETARG_POINTER(3);
6269         RelOptInfo *outer_rel = (RelOptInfo *) PG_GETARG_POINTER(4);
6270         Cost       *indexStartupCost = (Cost *) PG_GETARG_POINTER(5);
6271         Cost       *indexTotalCost = (Cost *) PG_GETARG_POINTER(6);
6272         Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(7);
6273         double     *indexCorrelation = (double *) PG_GETARG_POINTER(8);
6274
6275         genericcostestimate(root, index, indexQuals, indexOrderBys, outer_rel, 0.0,
6276                                                 indexStartupCost, indexTotalCost,
6277                                                 indexSelectivity, indexCorrelation);
6278
6279         PG_RETURN_VOID();
6280 }
6281
6282 Datum
6283 gistcostestimate(PG_FUNCTION_ARGS)
6284 {
6285         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
6286         IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(1);
6287         List       *indexQuals = (List *) PG_GETARG_POINTER(2);
6288         List       *indexOrderBys = (List *) PG_GETARG_POINTER(3);
6289         RelOptInfo *outer_rel = (RelOptInfo *) PG_GETARG_POINTER(4);
6290         Cost       *indexStartupCost = (Cost *) PG_GETARG_POINTER(5);
6291         Cost       *indexTotalCost = (Cost *) PG_GETARG_POINTER(6);
6292         Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(7);
6293         double     *indexCorrelation = (double *) PG_GETARG_POINTER(8);
6294
6295         genericcostestimate(root, index, indexQuals, indexOrderBys, outer_rel, 0.0,
6296                                                 indexStartupCost, indexTotalCost,
6297                                                 indexSelectivity, indexCorrelation);
6298
6299         PG_RETURN_VOID();
6300 }
6301
6302 /* Find the index column matching "op"; return its index, or -1 if no match */
6303 static int
6304 find_index_column(Node *op, IndexOptInfo *index)
6305 {
6306         int                     i;
6307
6308         for (i = 0; i < index->ncolumns; i++)
6309         {
6310                 if (match_index_to_operand(op, i, index))
6311                         return i;
6312         }
6313
6314         return -1;
6315 }
6316
6317 /*
6318  * GIN has search behavior completely different from other index types
6319  */
6320 Datum
6321 gincostestimate(PG_FUNCTION_ARGS)
6322 {
6323         PlannerInfo *root = (PlannerInfo *) PG_GETARG_POINTER(0);
6324         IndexOptInfo *index = (IndexOptInfo *) PG_GETARG_POINTER(1);
6325         List       *indexQuals = (List *) PG_GETARG_POINTER(2);
6326         List       *indexOrderBys = (List *) PG_GETARG_POINTER(3);
6327         RelOptInfo *outer_rel = (RelOptInfo *) PG_GETARG_POINTER(4);
6328         Cost       *indexStartupCost = (Cost *) PG_GETARG_POINTER(5);
6329         Cost       *indexTotalCost = (Cost *) PG_GETARG_POINTER(6);
6330         Selectivity *indexSelectivity = (Selectivity *) PG_GETARG_POINTER(7);
6331         double     *indexCorrelation = (double *) PG_GETARG_POINTER(8);
6332         ListCell   *l;
6333         List       *selectivityQuals;
6334         double          numPages = index->pages,
6335                                 numTuples = index->tuples;
6336         double          numEntryPages,
6337                                 numDataPages,
6338                                 numPendingPages,
6339                                 numEntries;
6340         bool            haveFullScan = false;
6341         double          partialEntriesInQuals = 0.0;
6342         double          searchEntriesInQuals = 0.0;
6343         double          exactEntriesInQuals = 0.0;
6344         double          entryPagesFetched,
6345                                 dataPagesFetched,
6346                                 dataPagesFetchedBySel;
6347         double          qual_op_cost,
6348                                 qual_arg_cost,
6349                                 spc_random_page_cost,
6350                                 num_scans;
6351         QualCost        index_qual_cost;
6352         Relation        indexRel;
6353         GinStatsData ginStats;
6354
6355         /*
6356          * Obtain statistic information from the meta page
6357          */
6358         indexRel = index_open(index->indexoid, AccessShareLock);
6359         ginGetStats(indexRel, &ginStats);
6360         index_close(indexRel, AccessShareLock);
6361
6362         numEntryPages = ginStats.nEntryPages;
6363         numDataPages = ginStats.nDataPages;
6364         numPendingPages = ginStats.nPendingPages;
6365         numEntries = ginStats.nEntries;
6366
6367         /*
6368          * nPendingPages can be trusted, but the other fields are as of the last
6369          * VACUUM.      Scale them by the ratio numPages / nTotalPages to account for
6370          * growth since then.  If the fields are zero (implying no VACUUM at all,
6371          * and an index created pre-9.1), assume all pages are entry pages.
6372          */
6373         if (ginStats.nTotalPages == 0 || ginStats.nEntryPages == 0)
6374         {
6375                 numEntryPages = numPages;
6376                 numDataPages = 0;
6377                 numEntries = numTuples; /* bogus, but no other info available */
6378         }
6379         else
6380         {
6381                 double          scale = numPages / ginStats.nTotalPages;
6382
6383                 numEntryPages = ceil(numEntryPages * scale);
6384                 numDataPages = ceil(numDataPages * scale);
6385                 numEntries = ceil(numEntries * scale);
6386                 /* ensure we didn't round up too much */
6387                 numEntryPages = Min(numEntryPages, numPages);
6388                 numDataPages = Min(numDataPages, numPages - numEntryPages);
6389         }
6390
6391         /*
6392          * Include predicate in selectivityQuals (should match
6393          * genericcostestimate)
6394          */
6395         if (index->indpred != NIL)
6396         {
6397                 List       *predExtraQuals = NIL;
6398
6399                 foreach(l, index->indpred)
6400                 {
6401                         Node       *predQual = (Node *) lfirst(l);
6402                         List       *oneQual = list_make1(predQual);
6403
6404                         if (!predicate_implied_by(oneQual, indexQuals))
6405                                 predExtraQuals = list_concat(predExtraQuals, oneQual);
6406                 }
6407                 /* list_concat avoids modifying the passed-in indexQuals list */
6408                 selectivityQuals = list_concat(predExtraQuals, indexQuals);
6409         }
6410         else
6411                 selectivityQuals = indexQuals;
6412
6413         /* Estimate the fraction of main-table tuples that will be visited */
6414         *indexSelectivity = clauselist_selectivity(root, selectivityQuals,
6415                                                                                            index->rel->relid,
6416                                                                                            JOIN_INNER,
6417                                                                                            NULL);
6418
6419         /* fetch estimated page cost for schema containing index */
6420         get_tablespace_page_costs(index->reltablespace,
6421                                                           &spc_random_page_cost,
6422                                                           NULL);
6423
6424         /*
6425          * Generic assumption about index correlation: there isn't any.
6426          */
6427         *indexCorrelation = 0.0;
6428
6429         /*
6430          * Examine quals to estimate number of search entries & partial matches
6431          */
6432         foreach(l, indexQuals)
6433         {
6434                 RestrictInfo *rinfo = (RestrictInfo *) lfirst(l);
6435                 Expr       *clause;
6436                 Node       *leftop,
6437                                    *rightop,
6438                                    *operand;
6439                 Oid                     extractProcOid;
6440                 Oid                     clause_op;
6441                 int                     strategy_op;
6442                 Oid                     lefttype,
6443                                         righttype;
6444                 int32           nentries = 0;
6445                 bool       *partial_matches = NULL;
6446                 Pointer    *extra_data = NULL;
6447                 bool       *nullFlags = NULL;
6448                 int32           searchMode = GIN_SEARCH_MODE_DEFAULT;
6449                 int                     indexcol;
6450
6451                 Assert(IsA(rinfo, RestrictInfo));
6452                 clause = rinfo->clause;
6453                 Assert(IsA(clause, OpExpr));
6454                 leftop = get_leftop(clause);
6455                 rightop = get_rightop(clause);
6456                 clause_op = ((OpExpr *) clause)->opno;
6457
6458                 if ((indexcol = find_index_column(leftop, index)) >= 0)
6459                 {
6460                         operand = rightop;
6461                 }
6462                 else if ((indexcol = find_index_column(rightop, index)) >= 0)
6463                 {
6464                         operand = leftop;
6465                         clause_op = get_commutator(clause_op);
6466                 }
6467                 else
6468                 {
6469                         elog(ERROR, "could not match index to operand");
6470                         operand = NULL;         /* keep compiler quiet */
6471                 }
6472
6473                 if (IsA(operand, RelabelType))
6474                         operand = (Node *) ((RelabelType *) operand)->arg;
6475
6476                 /*
6477                  * It's impossible to call extractQuery method for unknown operand. So
6478                  * unless operand is a Const we can't do much; just assume there will
6479                  * be one ordinary search entry from the operand at runtime.
6480                  */
6481                 if (!IsA(operand, Const))
6482                 {
6483                         searchEntriesInQuals++;
6484                         continue;
6485                 }
6486
6487                 /* If Const is null, there can be no matches */
6488                 if (((Const *) operand)->constisnull)
6489                 {
6490                         *indexStartupCost = 0;
6491                         *indexTotalCost = 0;
6492                         *indexSelectivity = 0;
6493                         PG_RETURN_VOID();
6494                 }
6495
6496                 /*
6497                  * Get the operator's strategy number and declared input data types
6498                  * within the index opfamily.  (We don't need the latter, but we use
6499                  * get_op_opfamily_properties because it will throw error if it fails
6500                  * to find a matching pg_amop entry.)
6501                  */
6502                 get_op_opfamily_properties(clause_op, index->opfamily[indexcol], false,
6503                                                                    &strategy_op, &lefttype, &righttype);
6504
6505                 /*
6506                  * GIN always uses the "default" support functions, which are those
6507                  * with lefttype == righttype == the opclass' opcintype (see
6508                  * IndexSupportInitialize in relcache.c).
6509                  */
6510                 extractProcOid = get_opfamily_proc(index->opfamily[indexcol],
6511                                                                                    index->opcintype[indexcol],
6512                                                                                    index->opcintype[indexcol],
6513                                                                                    GIN_EXTRACTQUERY_PROC);
6514
6515                 if (!OidIsValid(extractProcOid))
6516                 {
6517                         /* should not happen; throw same error as index_getprocinfo */
6518                         elog(ERROR, "missing support function %d for attribute %d of index \"%s\"",
6519                                  GIN_EXTRACTQUERY_PROC, indexcol + 1,
6520                                  get_rel_name(index->indexoid));
6521                 }
6522
6523                 OidFunctionCall7(extractProcOid,
6524                                                  ((Const *) operand)->constvalue,
6525                                                  PointerGetDatum(&nentries),
6526                                                  UInt16GetDatum(strategy_op),
6527                                                  PointerGetDatum(&partial_matches),
6528                                                  PointerGetDatum(&extra_data),
6529                                                  PointerGetDatum(&nullFlags),
6530                                                  PointerGetDatum(&searchMode));
6531
6532                 if (nentries <= 0 && searchMode == GIN_SEARCH_MODE_DEFAULT)
6533                 {
6534                         /* No match is possible */
6535                         *indexStartupCost = 0;
6536                         *indexTotalCost = 0;
6537                         *indexSelectivity = 0;
6538                         PG_RETURN_VOID();
6539                 }
6540                 else
6541                 {
6542                         int32           i;
6543
6544                         for (i = 0; i < nentries; i++)
6545                         {
6546                                 /*
6547                                  * For partial match we haven't any information to estimate
6548                                  * number of matched entries in index, so, we just estimate it
6549                                  * as 100
6550                                  */
6551                                 if (partial_matches && partial_matches[i])
6552                                         partialEntriesInQuals += 100;
6553                                 else
6554                                         exactEntriesInQuals++;
6555
6556                                 searchEntriesInQuals++;
6557                         }
6558                 }
6559
6560                 if (searchMode == GIN_SEARCH_MODE_INCLUDE_EMPTY)
6561                 {
6562                         /* Treat "include empty" like an exact-match item */
6563                         exactEntriesInQuals++;
6564                         searchEntriesInQuals++;
6565                 }
6566                 else if (searchMode != GIN_SEARCH_MODE_DEFAULT)
6567                 {
6568                         /* It's GIN_SEARCH_MODE_ALL */
6569                         haveFullScan = true;
6570                 }
6571         }
6572
6573         if (haveFullScan || indexQuals == NIL)
6574         {
6575                 /*
6576                  * Full index scan will be required.  We treat this as if every key in
6577                  * the index had been listed in the query; is that reasonable?
6578                  */
6579                 searchEntriesInQuals = numEntries;
6580         }
6581
6582         /* Will we have more than one iteration of a nestloop scan? */
6583         if (outer_rel != NULL && outer_rel->rows > 1)
6584                 num_scans = outer_rel->rows;
6585         else
6586                 num_scans = 1;
6587
6588         /*
6589          * cost to begin scan, first of all, pay attention to pending list.
6590          */
6591         entryPagesFetched = numPendingPages;
6592
6593         /*
6594          * Estimate number of entry pages read.  We need to do
6595          * searchEntriesInQuals searches.  Use a power function as it should be,
6596          * but tuples on leaf pages usually is much greater. Here we include all
6597          * searches in entry tree, including search of first entry in partial
6598          * match algorithm
6599          */
6600         entryPagesFetched += ceil(searchEntriesInQuals * rint(pow(numEntryPages, 0.15)));
6601
6602         /*
6603          * Add an estimate of entry pages read by partial match algorithm. It's a
6604          * scan over leaf pages in entry tree.  We haven't any useful stats here,
6605          * so estimate it as proportion.
6606          */
6607         entryPagesFetched += ceil(numEntryPages * partialEntriesInQuals / numEntries);
6608
6609         /*
6610          * Partial match algorithm reads all data pages before doing actual scan,
6611          * so it's a startup cost. Again, we havn't any useful stats here, so,
6612          * estimate it as proportion
6613          */
6614         dataPagesFetched = ceil(numDataPages * partialEntriesInQuals / numEntries);
6615
6616         /* calculate cache effects */
6617         if (num_scans > 1 || searchEntriesInQuals > 1)
6618         {
6619                 entryPagesFetched = index_pages_fetched(entryPagesFetched,
6620                                                                                                 (BlockNumber) numEntryPages,
6621                                                                                                 numEntryPages, root);
6622                 dataPagesFetched = index_pages_fetched(dataPagesFetched,
6623                                                                                            (BlockNumber) numDataPages,
6624                                                                                            numDataPages, root);
6625         }
6626
6627         /*
6628          * Here we use random page cost because logically-close pages could be far
6629          * apart on disk.
6630          */
6631         *indexStartupCost = (entryPagesFetched + dataPagesFetched) * spc_random_page_cost;
6632
6633         /* cost to scan data pages for each exact (non-partial) matched entry */
6634         dataPagesFetched = ceil(numDataPages * exactEntriesInQuals / numEntries);
6635
6636         /*
6637          * Estimate number of data pages read, using selectivity estimation and
6638          * capacity of data page.
6639          */
6640         dataPagesFetchedBySel = ceil(*indexSelectivity *
6641                                                                  (numTuples / (BLCKSZ / SizeOfIptrData)));
6642
6643         if (dataPagesFetchedBySel > dataPagesFetched)
6644         {
6645                 /*
6646                  * At least one of entries is very frequent and, unfortunately, we
6647                  * couldn't get statistic about entries (only tsvector has such
6648                  * statistics). So, we obviously have too small estimation of pages
6649                  * fetched from data tree. Re-estimate it from known capacity of data
6650                  * pages
6651                  */
6652                 dataPagesFetched = dataPagesFetchedBySel;
6653         }
6654
6655         if (num_scans > 1)
6656                 dataPagesFetched = index_pages_fetched(dataPagesFetched,
6657                                                                                            (BlockNumber) numDataPages,
6658                                                                                            numDataPages, root);
6659         *indexTotalCost = *indexStartupCost +
6660                 dataPagesFetched * spc_random_page_cost;
6661
6662         /*
6663          * Add on index qual eval costs, much as in genericcostestimate
6664          */
6665         cost_qual_eval(&index_qual_cost, indexQuals, root);
6666         qual_arg_cost = index_qual_cost.startup + index_qual_cost.per_tuple;
6667         cost_qual_eval(&index_qual_cost, indexOrderBys, root);
6668         qual_arg_cost += index_qual_cost.startup + index_qual_cost.per_tuple;
6669         qual_op_cost = cpu_operator_cost *
6670                 (list_length(indexQuals) + list_length(indexOrderBys));
6671         qual_arg_cost -= qual_op_cost;
6672         if (qual_arg_cost < 0)          /* just in case... */
6673                 qual_arg_cost = 0;
6674
6675         *indexStartupCost += qual_arg_cost;
6676         *indexTotalCost += qual_arg_cost;
6677         *indexTotalCost += (numTuples * *indexSelectivity) * (cpu_index_tuple_cost + qual_op_cost);
6678
6679         PG_RETURN_VOID();
6680 }