/ Check-in [9e810967]
Login

Many hyperlinks are disabled.
Use anonymous login to enable hyperlinks.

Overview
Comment:First attempt to store costs and row counts as a logarithm.
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | nextgen-query-plan-logcost
Files: files | file ages | folders
SHA1:9e8109673c3a87e379f5a5a97a8b0d5a1afe853d
User & Date: drh 2013-06-10 19:12:39
Context
2013-06-10
20:46
Fix some minor issues with logarithmic cost in NGQP. check-in: 69cf8772 user: drh tags: nextgen-query-plan-logcost
19:12
First attempt to store costs and row counts as a logarithm. check-in: 9e810967 user: drh tags: nextgen-query-plan-logcost
14:56
Simplification and performance tweak to the high-speed NGQP bypass. check-in: 0f8a38ee user: drh tags: nextgen-query-plan-exp
Changes
Hide Diffs Unified Diffs Ignore Whitespace Patch

Changes to src/where.c.

41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
....
1815
1816
1817
1818
1819
1820
1821










































1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
....
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
....
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516


2517


2518
2519
2520
2521
2522
2523
2524
....
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
....
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
....
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
....
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
....
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
....
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
....
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
....
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
....
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
....
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
....
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215

4216
4217
4218
4219
4220
4221
4222
4223
4224

4225
4226
4227
4228

4229
4230
4231


4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
....
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
....
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
....
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374

4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
....
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
....
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
....
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
....
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
....
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
....
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
....
5017
5018
5019
5020
5021
5022
5023
5024

5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
....
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
....
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
....
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
....
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
....
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
....
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
....
5402
5403
5404
5405
5406
5407
5408



5409
5410
5411
5412
5413
5414
5415
....
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
typedef struct WhereAndInfo WhereAndInfo;
typedef struct WhereLevel WhereLevel;
typedef struct WhereLoop WhereLoop;
typedef struct WherePath WherePath;
typedef struct WhereTerm WhereTerm;
typedef struct WhereLoopBuilder WhereLoopBuilder;
typedef struct WhereScan WhereScan;
typedef float WhereCost;

/*
** For each nested loop in a WHERE clause implementation, the WhereInfo
** structure contains a single instance of this structure.  This structure
** is intended to be private to the where.c module and should not be
** access or modified by other modules.
**
................................................................................
      /* This index implies that the DISTINCT qualifier is redundant. */
      return 1;
    }
  }

  return 0;
}











































/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
** logN is a little off.
*/
static WhereCost estLog(WhereCost N){
  u32 a;
  assert( sizeof(WhereCost)==4 );  /* 32-bit float input */
  if( N<=0.0 ) return 0.0;
  memcpy(&a, &N, 4);
  return ((a >>= 23)-127)*0.3;
}

/*
** Two routines for printing the content of an sqlite3_index_info
** structure.  Used for testing and debugging only.  If neither
** SQLITE_TEST or SQLITE_DEBUG are defined, then these routines
** are no-ops.
................................................................................
  tRowcnt *aStat              /* OUT: stats written here */
){
  tRowcnt n;
  IndexSample *aSample;
  int i, eType;
  int isEq = 0;
  i64 v;
  WhereCost r, rS;

  assert( roundUp==0 || roundUp==1 );
  assert( pIdx->nSample>0 );
  if( pVal==0 ) return SQLITE_ERROR;
  n = pIdx->aiRowEst[0];
  aSample = pIdx->aSample;
  eType = sqlite3_value_type(pVal);
................................................................................
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      if( iUpper<=iLower ){
        *pRangeDiv = (WhereCost)p->aiRowEst[0];
      }else{
        *pRangeDiv = (WhereCost)p->aiRowEst[0]/(WhereCost)(iUpper - iLower);
      }
      /*WHERETRACE(("range scan regions: %u..%u  div=%g\n",
                  (u32)iLower, (u32)iUpper, *pRangeDiv));*/
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = (WhereCost)1;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ) *pRangeDiv *= (WhereCost)4;


  if( pUpper ) *pRangeDiv *= (WhereCost)4;


  return rc;
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  WhereCost *pnRow     /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */

  assert( p->aSample!=0 );
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  WhereCost *pnRow     /* Write the revised row estimate here */
){
  int rc = SQLITE_OK;         /* Subfunction return code */
  WhereCost nEst;                /* Number of rows for a single term */
  WhereCost nRowEst = (WhereCost)0; /* New estimate of the number of rows */
  int i;                      /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, p, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
  }
................................................................................
  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */
){
  if( pParse->explain==2 ){
    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
    Vdbe *v = pParse->pVdbe;      /* VM being constructed */
    sqlite3 *db = pParse->db;     /* Database handle */
    char *zMsg;                   /* Text to add to EQP output */
    sqlite3_int64 nRow;           /* Expected number of rows visited by scan */
    int iId = pParse->iSelectId;  /* Select id (left-most output column) */
    int isSearch;                 /* True for a SEARCH. False for SCAN. */
    WhereLoop *pLoop;             /* The controlling WhereLoop object */
    u32 flags;                    /* Flags that describe this loop */

    pLoop = pLevel->pWLoop;
    flags = pLoop->wsFlags;
................................................................................
    }
#ifndef SQLITE_OMIT_VIRTUALTABLE
    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s VIRTUAL TABLE INDEX %d:%s", zMsg,
                  pLoop->u.vtab.idxNum, pLoop->u.vtab.idxStr);
    }
#endif
    if( wctrlFlags&(WHERE_ORDERBY_MIN|WHERE_ORDERBY_MAX) ){
      testcase( wctrlFlags & WHERE_ORDERBY_MIN );
      nRow = 1;
    }else{
      nRow = (sqlite3_int64)pLoop->nOut;
    }
    zMsg = sqlite3MAppendf(db, zMsg, "%s (~%lld rows)", zMsg, nRow);
    sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg, P4_DYNAMIC);
  }
}
#else
# define explainOneScan(u,v,w,x,y,z)
#endif /* SQLITE_OMIT_EXPLAIN */

................................................................................
}

#ifdef WHERETRACE_ENABLED
/*
** Print a WhereLoop object for debugging purposes
*/
static void whereLoopPrint(WhereLoop *p, SrcList *pTabList){
  int nb = 2*((pTabList->nSrc+15)/16);
  struct SrcList_item *pItem = pTabList->a + p->iTab;
  Table *pTab = pItem->pTab;
  sqlite3DebugPrintf("%c %2d.%0*llx.%0*llx", p->cId,
                     p->iTab, nb, p->maskSelf, nb, p->prereq);
  sqlite3DebugPrintf(" %8s",
                     pItem->zAlias ? pItem->zAlias : pTab->zName);
  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
................................................................................
    }else{
      z = sqlite3_mprintf("(%d,%x)", p->u.vtab.idxNum, p->u.vtab.omitMask);
    }
    sqlite3DebugPrintf(" %-15s", z);
    sqlite3_free(z);
  }
  sqlite3DebugPrintf(" fg %05x N %d", p->wsFlags, p->nLTerm);
  sqlite3DebugPrintf(" cost %.2g,%.2g,%.2g\n",
                     p->prereq, p->rSetup, p->rRun, p->nOut);
}
#endif

/*
** Convert bulk memory into a valid WhereLoop that can be passed
** to whereLoopClear harmlessly.
*/
................................................................................
  /* If pBuilder->pBest is defined, then only keep track of the single
  ** best WhereLoop.  pBuilder->pBest->maskSelf==0 indicates that no
  ** prior WhereLoops have been evaluated and that the current pTemplate
  ** is therefore the first and hence the best and should be retained.
  */
  if( (p = pBuilder->pBest)!=0 ){
    if( p->maskSelf!=0 ){
      WhereCost rCost = p->rRun + p->rSetup;
      WhereCost rTemplate = pTemplate->rRun + pTemplate->rSetup;
      if( rCost < rTemplate ){
        goto whereLoopInsert_noop;
      }
      if( rCost == rTemplate && p->prereq <= pTemplate->prereq ){
        goto whereLoopInsert_noop;
      }
    }
................................................................................
** If pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
*/
static int whereLoopAddBtreeIndex(
  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */
  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */
  Index *pProbe,                  /* An index on pSrc */
  int nInMul                      /* Number of iterations due to IN */
){
  WhereInfo *pWInfo = pBuilder->pWInfo;  /* WHERE analyse context */
  Parse *pParse = pWInfo->pParse;        /* Parsing context */
  sqlite3 *db = pParse->db;       /* Database connection malloc context */
  WhereLoop *pNew;                /* Template WhereLoop under construction */
  WhereTerm *pTerm;               /* A WhereTerm under consideration */
  int opMask;                     /* Valid operators for constraints */
................................................................................
  Bitmask saved_prereq;           /* Original value of pNew->prereq */
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  int saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
  WhereCost saved_nOut;           /* Original value of pNew->nOut */
  int iCol;                       /* Index of the column in the table */
  int rc = SQLITE_OK;             /* Return code */
  tRowcnt iRowEst;                /* Estimated index selectivity */
  WhereCost rLogSize;             /* Logarithm of table size */
  WhereTerm *pTop, *pBtm;         /* Top and bottom range constraints */

  pNew = pBuilder->pNew;
  if( db->mallocFailed ) return SQLITE_NOMEM;

  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );
................................................................................
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    iRowEst = pProbe->aiRowEst[pNew->u.btree.nEq+1];
  }else{
    iCol = -1;
    iRowEst = 1;
  }
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = (WhereCost)0;
  rLogSize = estLog(pProbe->aiRowEst[0]);
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 1;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
      pNew->wsFlags |= WHERE_COLUMN_IN;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
        nIn = 25;
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = pExpr->x.pList->nExpr;
      }
      pNew->rRun *= nIn;
      pNew->u.btree.nEq++;
      pNew->nOut = (WhereCost)iRowEst * nInMul * nIn;
    }else if( pTerm->eOperator & (WO_EQ) ){
      assert( (pNew->wsFlags & (WHERE_COLUMN_NULL|WHERE_COLUMN_IN))!=0
                  || nInMul==1 );
      pNew->wsFlags |= WHERE_COLUMN_EQ;
      if( iCol<0  
       || (pProbe->onError!=OE_None && nInMul==1
           && pNew->u.btree.nEq==pProbe->nColumn-1)
      ){
        testcase( pNew->wsFlags & WHERE_COLUMN_IN );
        pNew->wsFlags |= WHERE_ONEROW;
      }
      pNew->u.btree.nEq++;
      pNew->nOut = (WhereCost)iRowEst * nInMul;
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      nIn = 2;  /* Assume IS NULL matches two rows */
      pNew->nOut = (WhereCost)iRowEst * nInMul * nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else if( pTerm->eOperator & (WO_LT|WO_LE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
................................................................................
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      WhereCost rDiv;
      whereRangeScanEst(pParse, pProbe, pNew->u.btree.nEq,
                        pBtm, pTop, &rDiv);
      pNew->nOut = saved_nOut/rDiv;
    }
#ifdef SQLITE_ENABLE_STAT3
    if( pNew->u.btree.nEq==1 && pProbe->nSample ){

      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight,
                               &pNew->nOut);
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList,
                             &pNew->nOut);

      }

    }
#endif
    if( pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK) ){
      pNew->rRun += pNew->nOut;  /* Unit step cost to reach each row */

    }else{
      /* Each row involves a step of the index, then a binary search of
      ** the main table */


      pNew->rRun += pNew->nOut*(1 + rLogSize);
    }
    /* TBD: Adjust nOut for additional constraints */
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<=pProbe->nColumn
     && pProbe->zName!=0
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul*nIn);
    }
  }
  pNew->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->wsFlags = saved_wsFlags;
  pNew->nOut = saved_nOut;
  pNew->nLTerm = saved_nLTerm;
................................................................................
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  SrcList *pTabList;          /* The FROM clause */
  struct SrcList_item *pSrc;  /* The FROM clause btree term to add */
  WhereLoop *pNew;            /* Template WhereLoop object */
  int rc = SQLITE_OK;         /* Return code */
  int iSortIdx = 1;           /* Index number */
  int b;                      /* A boolean value */
  WhereCost rSize;               /* number of rows in the table */
  WhereCost rLogSize;            /* Logarithm of the number of rows in the table */
  
  pNew = pBuilder->pNew;
  pWInfo = pBuilder->pWInfo;
  pTabList = pWInfo->pTabList;
  pSrc = pTabList->a + pNew->iTab;
  assert( !IsVirtual(pSrc->pTab) );

................................................................................
    if( pSrc->notIndexed==0 ){
      /* The real indices of the table are only considered if the
      ** NOT INDEXED qualifier is omitted from the FROM clause */
      sPk.pNext = pFirst;
    }
    pProbe = &sPk;
  }
  rSize = (WhereCost)pSrc->pTab->nRowEst;
  rLogSize = estLog(rSize);

  /* Automatic indexes */
  if( !pBuilder->pBest
   && pTabList->nSrc>1
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0 
   && !pSrc->viaCoroutine
................................................................................
    for(pTerm=pWC->a; rc==SQLITE_OK && pTerm<pWCEnd; pTerm++){
      if( pTerm->prereqRight & pNew->maskSelf ) continue;
      if( termCanDriveIndex(pTerm, pSrc, 0) ){
        pNew->u.btree.nEq = 1;
        pNew->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        pNew->rSetup = 20*rLogSize*pSrc->pTab->nRowEst;
        pNew->nOut = (WhereCost)10;
        pNew->rRun = rLogSize + pNew->nOut;

        pNew->wsFlags = WHERE_TEMP_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }

  /* Loop over all indices
  */
  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
    pNew->u.btree.nEq = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = (WhereCost)0;
    pNew->prereq = mExtra;
    pNew->u.btree.pIndex = pProbe;
    b = indexMightHelpWithOrderBy(pBuilder, pProbe, pSrc->iCursor);
    if( pProbe->tnum<=0 ){
      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      pNew->nOut = rSize;
      pNew->rRun = (rSize + rLogSize)*(3+b); /* 4x penalty for a full-scan */
      rc = whereLoopInsert(pBuilder, pNew);
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsUsedByIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
................................................................................
       && pProbe->bUnordered==0
       && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
       && sqlite3GlobalConfig.bUseCis
       && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        pNew->nOut = rSize;
        pNew->rRun = (m==0) ? (rSize + rLogSize)*(1+b) : (rSize*rLogSize);
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 1);

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;
  }
  return rc;
}
................................................................................
      assert( pNew->nLTerm<=pNew->nLSlot );
      pNew->u.vtab.idxNum = pIdxInfo->idxNum;
      pNew->u.vtab.needFree = pIdxInfo->needToFreeIdxStr;
      pIdxInfo->needToFreeIdxStr = 0;
      pNew->u.vtab.idxStr = pIdxInfo->idxStr;
      pNew->u.vtab.isOrdered = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = (WhereCost)0;
      pNew->rRun = pIdxInfo->estimatedCost;
      pNew->nOut = (WhereCost)25;
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
    }
  }  
................................................................................
        sBest.rRun = 0;
        if( IsVirtual(pItem->pTab) ){
          rc = whereLoopAddVirtual(&sSubBuild, mExtra);
        }else{
          rc = whereLoopAddBtree(&sSubBuild, mExtra);
        }
        if( sBest.maskSelf==0 ) break;
        assert( sBest.rSetup==(WhereCost)0 );
        rTotal += sBest.rRun;
        nRow += sBest.nOut;
        prereq |= sBest.prereq;
      }
      assert( pNew->nLSlot>=1 );
      pNew->nLTerm = 1;
      pNew->aLTerm[0] = pTerm;
      pNew->wsFlags = WHERE_MULTI_OR;
      pNew->rSetup = (WhereCost)0;
      pNew->rRun = rTotal;
      pNew->nOut = nRow;
      pNew->prereq = prereq;
      memset(&pNew->u, 0, sizeof(pNew->u));
      rc = whereLoopInsert(pBuilder, pNew);
      whereLoopClear(pWInfo->pParse->db, &sBest);
    }
................................................................................
  Bitmask mPrior = 0;
  int iTab;
  SrcList *pTabList = pWInfo->pTabList;
  struct SrcList_item *pItem;
  sqlite3 *db = pWInfo->pParse->db;
  int nTabList = pWInfo->nLevel;
  int rc = SQLITE_OK;
  WhereLoop *pNew, sNew;

  /* Loop over the tables in the join, from left to right */
  pBuilder->pNew = pNew = &sNew;
  whereLoopInit(pNew);
  for(iTab=0, pItem=pTabList->a; iTab<nTabList; iTab++, pItem++){
    pNew->iTab = iTab;
    pNew->maskSelf = getMask(&pWInfo->sMaskSet, pItem->iCursor);
    if( (pItem->jointype & (JT_LEFT|JT_CROSS))!=0 ){
      mExtra = mPrior;
    }
................................................................................
    if( rc==SQLITE_OK ){
      rc = whereLoopAddOr(pBuilder, mExtra);
    }
    mPrior |= pNew->maskSelf;
    if( rc || db->mallocFailed ) break;
  }
  whereLoopClear(db, pNew);
  pBuilder->pNew = 0;
  return rc;
}

/*
** Examine a WherePath (with the addition of the extra WhereLoop of the 5th
** parameters) to see if it outputs rows in the requested ORDER BY
** (or GROUP BY) without requiring a separate source operation.  Return:
................................................................................
  memset(aFrom, 0, sizeof(aFrom[0]));
  pX = (WhereLoop**)(aFrom+mxChoice);
  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){
    pFrom->aLoop = pX;
  }

  /* Seed the search with a single WherePath containing zero WhereLoops */
  aFrom[0].nRow = (WhereCost)1;
  nFrom = 1;

  /* Precompute the cost of sorting the final result set, if the caller
  ** to sqlite3WhereBegin() was concerned about sorting */
  rSortCost = (WhereCost)0;
  if( pWInfo->pOrderBy==0 || nRowEst<=0.0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* Compute an estimate on the cost to sort the entire result set */
    rSortCost = nRowEst*estLog(nRowEst);
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- sort cost=%-7.2g\n", rSortCost);
    }
#endif
  }

  /* Compute successively longer WherePaths using the previous generation
  ** of WherePaths as the basis for the next.  Keep track of the mxChoice
  ** best paths at each generation */
................................................................................
        Bitmask revMask = 0;
        u8 isOrderedValid = pFrom->isOrderedValid;
        u8 isOrdered = pFrom->isOrdered;
        if( (pWLoop->prereq & ~pFrom->maskLoop)!=0 ) continue;
        if( (pWLoop->maskSelf & pFrom->maskLoop)!=0 ) continue;
        /* At this point, pWLoop is a candidate to be the next loop. 
        ** Compute its cost */
        rCost = pWLoop->rSetup + pWLoop->rRun*pFrom->nRow + pFrom->rCost;

        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( !isOrderedValid ){
          switch( wherePathSatisfiesOrderBy(pWInfo, pFrom, iLoop, iLoop==nLoop-1,
                                            pWLoop, &revMask) ){
            case 1:  /* Yes.  pFrom+pWLoop does satisfy the ORDER BY clause */
              isOrdered = 1;
              isOrderedValid = 1;
              break;
            case 0:  /* No.  pFrom+pWLoop will require a separate sort */
              isOrdered = 0;
              isOrderedValid = 1;
              rCost += rSortCost;
              break;
            default: /* Cannot tell yet.  Try again on the next iteration */
              break;
          }
        }else{
          revMask = pFrom->revLoop;
        }
................................................................................
            break;
          }
        }
        if( jj>=nTo ){
          if( nTo>=mxChoice && rCost>=mxCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf("Skip   %s cost=%-7.2g order=%c\n",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            continue;
          }
          /* Add a new Path to the aTo[] set */
................................................................................
          }else{
            /* New path replaces the prior worst to keep count below mxChoice */
            for(jj=nTo-1; aTo[jj].rCost<mxCost; jj--){ assert(jj>0); }
          }
          pTo = &aTo[jj];
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf("New    %s cost=%-7.2g order=%c\n",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
          }
#endif
        }else{
          if( pTo->rCost<=rCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf(
                  "Skip   %s cost=%-7.2g order=%c",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
              sqlite3DebugPrintf("   vs %s cost=%-7.2g order=%c\n",
                  wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                  pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            continue;
          }
          /* A new and better score for a previously created equivalent path */
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf(
                "Update %s cost=%-7.2g order=%c",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            sqlite3DebugPrintf("  was %s cost=%-7.2g order=%c\n",
                wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
          }
#endif
        }
        /* pWLoop is a winner.  Add it to the set of best so far */
        pTo->maskLoop = pFrom->maskLoop | pWLoop->maskSelf;
        pTo->revLoop = revMask;
        pTo->nRow = pFrom->nRow * pWLoop->nOut;
        pTo->rCost = rCost;
        pTo->isOrderedValid = isOrderedValid;
        pTo->isOrdered = isOrdered;
        memcpy(pTo->aLoop, pFrom->aLoop, sizeof(WhereLoop*)*iLoop);
        pTo->aLoop[iLoop] = pWLoop;
        if( nTo>=mxChoice ){
          mxCost = aTo[0].rCost;
................................................................................
      }
    }

#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- after round %d ----\n", iLoop);
      for(ii=0, pTo=aTo; ii<nTo; ii++, pTo++){
        sqlite3DebugPrintf(" %s cost=%-7.2g nrow=%-7.2g order=%c",
           wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
           pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
        if( pTo->isOrderedValid && pTo->isOrdered ){
          sqlite3DebugPrintf(" rev=0x%llx\n", pTo->revLoop);
        }else{
          sqlite3DebugPrintf("\n");
        }
................................................................................
** general-purpose query planner, and thereby yield faster sqlite3_prepare()
** times for the common case.
**
** Return non-zero on success, if this query can be handled by this
** no-frills query planner.  Return zero if this query needs the 
** general-purpose query planner.
*/
static int whereSimpleFastCase(WhereLoopBuilder *pBuilder){
  WhereInfo *pWInfo;
  struct SrcList_item *pItem;
  WhereClause *pWC;
  WhereTerm *pTerm;
  WhereLoop *pLoop;
  int iCur;
  int j;
................................................................................
  pLoop->wsFlags = 0;
  pTerm = findTerm(pWC, iCur, -1, 0, WO_EQ, 0);
  if( pTerm ){
    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;
    pLoop->aLTerm[0] = pTerm;
    pLoop->nLTerm = 1;
    pLoop->u.btree.nEq = 1;
    pLoop->rRun = (WhereCost)10;
  }else{
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      if( pIdx->onError==OE_None ) continue;
      for(j=0; j<pIdx->nColumn; j++){
        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
        if( pTerm==0 ) break;
        whereLoopResize(pWInfo->pParse->db, pLoop, j);
................................................................................
      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
      if( (pItem->colUsed & ~columnsUsedByIndex(pIdx))==0 ){
        pLoop->wsFlags |= WHERE_IDX_ONLY;
      }
      pLoop->nLTerm = j;
      pLoop->u.btree.nEq = j;
      pLoop->u.btree.pIndex = pIdx;
      pLoop->rRun = (WhereCost)15;
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (WhereCost)1;
    pWInfo->a[0].pWLoop = pLoop;
    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);
................................................................................
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = &pWInfo->sMaskSet;
  sWLB.pWInfo = pWInfo;
  sWLB.pWC = &pWInfo->sWC;
  sWLB.pNew = (WhereLoop*)&pWInfo->a[nTabList];
  whereLoopInit(sWLB.pNew);




  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
  if( OptimizationDisabled(db, SQLITE_DistinctOpt) ) pDistinct = 0;

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
................................................................................
  if( pDistinct && isDistinctRedundant(pParse,pTabList,&pWInfo->sWC,pDistinct) ){
    pDistinct = 0;
    pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
  }

  /* Construct the WhereLoop objects */
  WHERETRACE(("*** Optimizer Start ***\n"));
  if( nTabList!=1 || whereSimpleFastCase(&sWLB)==0 ){
    rc = whereLoopAddAll(&sWLB);
    if( rc ) goto whereBeginError;
  
    /* Display all of the WhereLoop objects if wheretrace is enabled */
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace ){
      WhereLoop *p;







|







 







>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>









|
<
<
<
<







 







|







 







|
|
|
|
|











|
|
>
>
|
>
>







 







|







 







|

|
|
|
|







 







<







 







<
<
<
<
<
<
|







 







|







 







<
|







 







|
|







 







|







 







|







 







|


|








|
|

|













|


|

|

|


|


|






|



|
|







 







|



>

|
<


|
<
|
<
>



|
>



>
>
|







|







 







|
|







 







|







 







|
|
|
>













|










|







 







|




|







 







|
|
|







 







|
|
|






|







 







|


|







 







<







 







|




|
|



|


|







 







|
>











|







 







|







 







|









|


|










|


|








|







 







|







 







|







 







|







 







|







 







>
>
>







 







|







41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
....
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873




1874
1875
1876
1877
1878
1879
1880
....
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
....
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
....
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
....
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
....
3020
3021
3022
3023
3024
3025
3026

3027
3028
3029
3030
3031
3032
3033
....
3074
3075
3076
3077
3078
3079
3080






3081
3082
3083
3084
3085
3086
3087
3088
....
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
....
3891
3892
3893
3894
3895
3896
3897

3898
3899
3900
3901
3902
3903
3904
3905
....
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
....
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
....
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
....
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
....
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252

4253
4254
4255

4256

4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
....
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
....
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
....
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
....
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
....
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
....
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
....
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
....
4735
4736
4737
4738
4739
4740
4741

4742
4743
4744
4745
4746
4747
4748
....
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
....
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
....
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
....
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
....
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
....
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
....
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
....
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
....
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
....
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
typedef struct WhereAndInfo WhereAndInfo;
typedef struct WhereLevel WhereLevel;
typedef struct WhereLoop WhereLoop;
typedef struct WherePath WherePath;
typedef struct WhereTerm WhereTerm;
typedef struct WhereLoopBuilder WhereLoopBuilder;
typedef struct WhereScan WhereScan;
typedef unsigned short int WhereCost;  /* 10 times log2() of run-time */

/*
** For each nested loop in a WHERE clause implementation, the WhereInfo
** structure contains a single instance of this structure.  This structure
** is intended to be private to the where.c module and should not be
** access or modified by other modules.
**
................................................................................
      /* This index implies that the DISTINCT qualifier is redundant. */
      return 1;
    }
  }

  return 0;
}

/* 
** The sum of two WhereCosts
*/
static WhereCost whereCostAdd(WhereCost a, WhereCost b){
  static const unsigned char x[] = {
     10, 10,                         /* 0,1 */
      9, 9,                          /* 2,3 */
      8, 8,                          /* 4,5 */
      7, 7, 7,                       /* 6,7,8 */
      6, 6, 6,                       /* 9,10,11 */
      5, 5, 5,                       /* 12-14 */
      4, 4, 4, 4,                    /* 15-18 */
      3, 3, 3, 3, 3, 3,              /* 19-24 */
      2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
  };
  if( a>=b ){
    if( a>b+49 ) return a;
    if( a>b+31 ) return a+1;
    return a+x[a-b];
  }else{
    if( b>a+49 ) return b;
    if( b>a+31 ) return b+1;
    return b+x[b-a];
  }
}

/*
** Convert an integer into a WhereCost
*/
static WhereCost whereCostFromInt(tRowcnt x){
  static WhereCost a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
  WhereCost y = 40;
  if( x<8 ){
    if( x<2 ) return 0;
    while( x<8 ){  y -= 10; x <<= 1; }
  }else{
    while( x>255 ){ y += 40; x >>= 4; }
    while( x>15 ){  y += 10; x >>= 1; }
  }
  return a[x&7] + y - 10;
}

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operations with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
** logN is a little off.
*/
static WhereCost estLog(WhereCost N){
  return whereCostFromInt(N) - 33;




}

/*
** Two routines for printing the content of an sqlite3_index_info
** structure.  Used for testing and debugging only.  If neither
** SQLITE_TEST or SQLITE_DEBUG are defined, then these routines
** are no-ops.
................................................................................
  tRowcnt *aStat              /* OUT: stats written here */
){
  tRowcnt n;
  IndexSample *aSample;
  int i, eType;
  int isEq = 0;
  i64 v;
  double r, rS;

  assert( roundUp==0 || roundUp==1 );
  assert( pIdx->nSample>0 );
  if( pVal==0 ) return SQLITE_ERROR;
  n = pIdx->aiRowEst[0];
  aSample = pIdx->aSample;
  eType = sqlite3_value_type(pVal);
................................................................................
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      WhereCost iBase = whereCostFromInt(p->aiRowEst[0]);
      if( iUpper>iLower ){
        iBase -= whereCostFromInt(iUpper - iLower);
      }
      *pRangeDiv = iBase;
      /*WHERETRACE(("range scan regions: %u..%u  div=%g\n",
                  (u32)iLower, (u32)iUpper, *pRangeDiv));*/
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = 0;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
    *pRangeDiv += 20;  assert( 20==whereCostFromInt(4) );
  }
  if( pUpper ){
    *pRangeDiv += 20;  assert( 20==whereCostFromInt(4) );
  }
  return rc;
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */

  assert( p->aSample!=0 );
................................................................................
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  int rc = SQLITE_OK;     /* Subfunction return code */
  tRowcnt nEst;           /* Number of rows for a single term */
  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, p, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
  }
................................................................................
  u16 wctrlFlags                  /* Flags passed to sqlite3WhereBegin() */
){
  if( pParse->explain==2 ){
    struct SrcList_item *pItem = &pTabList->a[pLevel->iFrom];
    Vdbe *v = pParse->pVdbe;      /* VM being constructed */
    sqlite3 *db = pParse->db;     /* Database handle */
    char *zMsg;                   /* Text to add to EQP output */

    int iId = pParse->iSelectId;  /* Select id (left-most output column) */
    int isSearch;                 /* True for a SEARCH. False for SCAN. */
    WhereLoop *pLoop;             /* The controlling WhereLoop object */
    u32 flags;                    /* Flags that describe this loop */

    pLoop = pLevel->pWLoop;
    flags = pLoop->wsFlags;
................................................................................
    }
#ifndef SQLITE_OMIT_VIRTUALTABLE
    else if( (flags & WHERE_VIRTUALTABLE)!=0 ){
      zMsg = sqlite3MAppendf(db, zMsg, "%s VIRTUAL TABLE INDEX %d:%s", zMsg,
                  pLoop->u.vtab.idxNum, pLoop->u.vtab.idxStr);
    }
#endif






    zMsg = sqlite3MAppendf(db, zMsg, "%s", zMsg);
    sqlite3VdbeAddOp4(v, OP_Explain, iId, iLevel, iFrom, zMsg, P4_DYNAMIC);
  }
}
#else
# define explainOneScan(u,v,w,x,y,z)
#endif /* SQLITE_OMIT_EXPLAIN */

................................................................................
}

#ifdef WHERETRACE_ENABLED
/*
** Print a WhereLoop object for debugging purposes
*/
static void whereLoopPrint(WhereLoop *p, SrcList *pTabList){
  int nb = 1+(pTabList->nSrc+7)/8;
  struct SrcList_item *pItem = pTabList->a + p->iTab;
  Table *pTab = pItem->pTab;
  sqlite3DebugPrintf("%c %2d.%0*llx.%0*llx", p->cId,
                     p->iTab, nb, p->maskSelf, nb, p->prereq);
  sqlite3DebugPrintf(" %8s",
                     pItem->zAlias ? pItem->zAlias : pTab->zName);
  if( (p->wsFlags & WHERE_VIRTUALTABLE)==0 ){
................................................................................
    }else{
      z = sqlite3_mprintf("(%d,%x)", p->u.vtab.idxNum, p->u.vtab.omitMask);
    }
    sqlite3DebugPrintf(" %-15s", z);
    sqlite3_free(z);
  }
  sqlite3DebugPrintf(" fg %05x N %d", p->wsFlags, p->nLTerm);

  sqlite3DebugPrintf(" cost %d,%d,%d\n", p->rSetup, p->rRun, p->nOut);
}
#endif

/*
** Convert bulk memory into a valid WhereLoop that can be passed
** to whereLoopClear harmlessly.
*/
................................................................................
  /* If pBuilder->pBest is defined, then only keep track of the single
  ** best WhereLoop.  pBuilder->pBest->maskSelf==0 indicates that no
  ** prior WhereLoops have been evaluated and that the current pTemplate
  ** is therefore the first and hence the best and should be retained.
  */
  if( (p = pBuilder->pBest)!=0 ){
    if( p->maskSelf!=0 ){
      WhereCost rCost = whereCostAdd(p->rRun,p->rSetup);
      WhereCost rTemplate = whereCostAdd(pTemplate->rRun,pTemplate->rSetup);
      if( rCost < rTemplate ){
        goto whereLoopInsert_noop;
      }
      if( rCost == rTemplate && p->prereq <= pTemplate->prereq ){
        goto whereLoopInsert_noop;
      }
    }
................................................................................
** If pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
*/
static int whereLoopAddBtreeIndex(
  WhereLoopBuilder *pBuilder,     /* The WhereLoop factory */
  struct SrcList_item *pSrc,      /* FROM clause term being analyzed */
  Index *pProbe,                  /* An index on pSrc */
  WhereCost nInMul                /* log(Number of iterations due to IN) */
){
  WhereInfo *pWInfo = pBuilder->pWInfo;  /* WHERE analyse context */
  Parse *pParse = pWInfo->pParse;        /* Parsing context */
  sqlite3 *db = pParse->db;       /* Database connection malloc context */
  WhereLoop *pNew;                /* Template WhereLoop under construction */
  WhereTerm *pTerm;               /* A WhereTerm under consideration */
  int opMask;                     /* Valid operators for constraints */
................................................................................
  Bitmask saved_prereq;           /* Original value of pNew->prereq */
  u16 saved_nLTerm;               /* Original value of pNew->nLTerm */
  int saved_nEq;                  /* Original value of pNew->u.btree.nEq */
  u32 saved_wsFlags;              /* Original value of pNew->wsFlags */
  WhereCost saved_nOut;           /* Original value of pNew->nOut */
  int iCol;                       /* Index of the column in the table */
  int rc = SQLITE_OK;             /* Return code */
  WhereCost nRowEst;              /* Estimated index selectivity */
  WhereCost rLogSize;             /* Logarithm of table size */
  WhereTerm *pTop, *pBtm;         /* Top and bottom range constraints */

  pNew = pBuilder->pNew;
  if( db->mallocFailed ) return SQLITE_NOMEM;

  assert( (pNew->wsFlags & WHERE_VIRTUALTABLE)==0 );
................................................................................
  }else{
    opMask = WO_EQ|WO_IN|WO_ISNULL|WO_GT|WO_GE|WO_LT|WO_LE;
  }
  if( pProbe->bUnordered ) opMask &= ~(WO_GT|WO_GE|WO_LT|WO_LE);

  if( pNew->u.btree.nEq < pProbe->nColumn ){
    iCol = pProbe->aiColumn[pNew->u.btree.nEq];
    nRowEst = whereCostFromInt(pProbe->aiRowEst[pNew->u.btree.nEq+1]);
  }else{
    iCol = -1;
    nRowEst = 0;
  }
  pTerm = whereScanInit(&scan, pBuilder->pWC, pSrc->iCursor, iCol,
                        opMask, pProbe);
  saved_nEq = pNew->u.btree.nEq;
  saved_nLTerm = pNew->nLTerm;
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(whereCostFromInt(pProbe->aiRowEst[0]));
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize;
    if( pTerm->eOperator & WO_IN ){
      Expr *pExpr = pTerm->pExpr;
      pNew->wsFlags |= WHERE_COLUMN_IN;
      if( ExprHasProperty(pExpr, EP_xIsSelect) ){
        /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
        nIn = 46;  /* whereCostFromInt(25) */
      }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
        /* "x IN (value, value, ...)" */
        nIn = whereCostFromInt(pExpr->x.pList->nExpr);
      }
      pNew->rRun += nIn;
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_EQ) ){
      assert( (pNew->wsFlags & (WHERE_COLUMN_NULL|WHERE_COLUMN_IN))!=0
                  || nInMul==0 );
      pNew->wsFlags |= WHERE_COLUMN_EQ;
      if( iCol<0  
       || (pProbe->onError!=OE_None && nInMul==0
           && pNew->u.btree.nEq==pProbe->nColumn-1)
      ){
        testcase( pNew->wsFlags & WHERE_COLUMN_IN );
        pNew->wsFlags |= WHERE_ONEROW;
      }
      pNew->u.btree.nEq++;
      pNew->nOut = nRowEst + nInMul;
    }else if( pTerm->eOperator & (WO_ISNULL) ){
      pNew->wsFlags |= WHERE_COLUMN_NULL;
      pNew->u.btree.nEq++;
      nIn = 10;  /* Assume IS NULL matches two rows */
      pNew->nOut = nRowEst + nInMul + nIn;
    }else if( pTerm->eOperator & (WO_GT|WO_GE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_BTM_LIMIT;
      pBtm = pTerm;
      pTop = 0;
    }else if( pTerm->eOperator & (WO_LT|WO_LE) ){
      pNew->wsFlags |= WHERE_COLUMN_RANGE|WHERE_TOP_LIMIT;
      pTop = pTerm;
................................................................................
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      WhereCost rDiv;
      whereRangeScanEst(pParse, pProbe, pNew->u.btree.nEq,
                        pBtm, pTop, &rDiv);
      pNew->nOut = saved_nOut - rDiv;
    }
#ifdef SQLITE_ENABLE_STAT3
    if( pNew->u.btree.nEq==1 && pProbe->nSample ){
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight, &nOut);

      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList, &nOut);

      }

      pNew->nOut = whereCostFromInt(nOut);
    }
#endif
    if( pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK) ){
      /* Step cost for each output row */
      pNew->rRun = whereCostAdd(pNew->rRun, pNew->nOut);
    }else{
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun = rLogSize>90 ? 
                        whereCostAdd(pNew->rRun, pNew->nOut+rLogSize-90) :
                        pNew->rRun;
    }
    /* TBD: Adjust nOut for additional constraints */
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<=pProbe->nColumn
     && pProbe->zName!=0
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }
  }
  pNew->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->wsFlags = saved_wsFlags;
  pNew->nOut = saved_nOut;
  pNew->nLTerm = saved_nLTerm;
................................................................................
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  SrcList *pTabList;          /* The FROM clause */
  struct SrcList_item *pSrc;  /* The FROM clause btree term to add */
  WhereLoop *pNew;            /* Template WhereLoop object */
  int rc = SQLITE_OK;         /* Return code */
  int iSortIdx = 1;           /* Index number */
  int b;                      /* A boolean value */
  WhereCost rSize;            /* number of rows in the table */
  WhereCost rLogSize;         /* Logarithm of the number of rows in the table */
  
  pNew = pBuilder->pNew;
  pWInfo = pBuilder->pWInfo;
  pTabList = pWInfo->pTabList;
  pSrc = pTabList->a + pNew->iTab;
  assert( !IsVirtual(pSrc->pTab) );

................................................................................
    if( pSrc->notIndexed==0 ){
      /* The real indices of the table are only considered if the
      ** NOT INDEXED qualifier is omitted from the FROM clause */
      sPk.pNext = pFirst;
    }
    pProbe = &sPk;
  }
  rSize = whereCostFromInt(pSrc->pTab->nRowEst);
  rLogSize = estLog(rSize);

  /* Automatic indexes */
  if( !pBuilder->pBest
   && pTabList->nSrc>1
   && (pWInfo->pParse->db->flags & SQLITE_AutoIndex)!=0 
   && !pSrc->viaCoroutine
................................................................................
    for(pTerm=pWC->a; rc==SQLITE_OK && pTerm<pWCEnd; pTerm++){
      if( pTerm->prereqRight & pNew->maskSelf ) continue;
      if( termCanDriveIndex(pTerm, pSrc, 0) ){
        pNew->u.btree.nEq = 1;
        pNew->u.btree.pIndex = 0;
        pNew->nLTerm = 1;
        pNew->aLTerm[0] = pTerm;
        assert( 43==whereCostFromInt(20) );
        pNew->rSetup = 43 + rLogSize + rSize;
        pNew->nOut = 33;  assert( 33==whereCostFromInt(10) );
        pNew->rRun = whereCostAdd(rLogSize,pNew->nOut);
        pNew->wsFlags = WHERE_TEMP_INDEX;
        pNew->prereq = mExtra | pTerm->prereqRight;
        rc = whereLoopInsert(pBuilder, pNew);
      }
    }
  }

  /* Loop over all indices
  */
  for(; rc==SQLITE_OK && pProbe; pProbe=pProbe->pNext, iSortIdx++){
    pNew->u.btree.nEq = 0;
    pNew->nLTerm = 0;
    pNew->iSortIdx = 0;
    pNew->rSetup = 0;
    pNew->prereq = mExtra;
    pNew->u.btree.pIndex = pProbe;
    b = indexMightHelpWithOrderBy(pBuilder, pProbe, pSrc->iCursor);
    if( pProbe->tnum<=0 ){
      /* Integer primary key index */
      pNew->wsFlags = WHERE_IPK;

      /* Full table scan */
      pNew->iSortIdx = b ? iSortIdx : 0;
      pNew->nOut = rSize;
      pNew->rRun = whereCostAdd(rSize,rLogSize) + 16 + b*4;
      rc = whereLoopInsert(pBuilder, pNew);
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsUsedByIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
................................................................................
       && pProbe->bUnordered==0
       && (pWInfo->wctrlFlags & WHERE_ONEPASS_DESIRED)==0
       && sqlite3GlobalConfig.bUseCis
       && OptimizationEnabled(pWInfo->pParse->db, SQLITE_CoverIdxScan)
      ){
        pNew->iSortIdx = b ? iSortIdx : 0;
        pNew->nOut = rSize;
        pNew->rRun = whereCostAdd(rSize,rLogSize) + ((m==0 && b) ? 10 : 0);
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }
    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;
  }
  return rc;
}
................................................................................
      assert( pNew->nLTerm<=pNew->nLSlot );
      pNew->u.vtab.idxNum = pIdxInfo->idxNum;
      pNew->u.vtab.needFree = pIdxInfo->needToFreeIdxStr;
      pIdxInfo->needToFreeIdxStr = 0;
      pNew->u.vtab.idxStr = pIdxInfo->idxStr;
      pNew->u.vtab.isOrdered = (u8)((pIdxInfo->nOrderBy!=0)
                                     && pIdxInfo->orderByConsumed);
      pNew->rSetup = 0;
      pNew->rRun = whereCostFromInt((tRowcnt)pIdxInfo->estimatedCost);
      pNew->nOut = 46;  assert( 46 == whereCostFromInt(25) );
      whereLoopInsert(pBuilder, pNew);
      if( pNew->u.vtab.needFree ){
        sqlite3_free(pNew->u.vtab.idxStr);
        pNew->u.vtab.needFree = 0;
      }
    }
  }  
................................................................................
        sBest.rRun = 0;
        if( IsVirtual(pItem->pTab) ){
          rc = whereLoopAddVirtual(&sSubBuild, mExtra);
        }else{
          rc = whereLoopAddBtree(&sSubBuild, mExtra);
        }
        if( sBest.maskSelf==0 ) break;
        assert( sBest.rSetup==0 );
        rTotal = whereCostAdd(rTotal, sBest.rRun);
        nRow = whereCostAdd(nRow, sBest.nOut);
        prereq |= sBest.prereq;
      }
      assert( pNew->nLSlot>=1 );
      pNew->nLTerm = 1;
      pNew->aLTerm[0] = pTerm;
      pNew->wsFlags = WHERE_MULTI_OR;
      pNew->rSetup = 0;
      pNew->rRun = rTotal;
      pNew->nOut = nRow;
      pNew->prereq = prereq;
      memset(&pNew->u, 0, sizeof(pNew->u));
      rc = whereLoopInsert(pBuilder, pNew);
      whereLoopClear(pWInfo->pParse->db, &sBest);
    }
................................................................................
  Bitmask mPrior = 0;
  int iTab;
  SrcList *pTabList = pWInfo->pTabList;
  struct SrcList_item *pItem;
  sqlite3 *db = pWInfo->pParse->db;
  int nTabList = pWInfo->nLevel;
  int rc = SQLITE_OK;
  WhereLoop *pNew;

  /* Loop over the tables in the join, from left to right */
  pNew = pBuilder->pNew;
  whereLoopInit(pNew);
  for(iTab=0, pItem=pTabList->a; iTab<nTabList; iTab++, pItem++){
    pNew->iTab = iTab;
    pNew->maskSelf = getMask(&pWInfo->sMaskSet, pItem->iCursor);
    if( (pItem->jointype & (JT_LEFT|JT_CROSS))!=0 ){
      mExtra = mPrior;
    }
................................................................................
    if( rc==SQLITE_OK ){
      rc = whereLoopAddOr(pBuilder, mExtra);
    }
    mPrior |= pNew->maskSelf;
    if( rc || db->mallocFailed ) break;
  }
  whereLoopClear(db, pNew);

  return rc;
}

/*
** Examine a WherePath (with the addition of the extra WhereLoop of the 5th
** parameters) to see if it outputs rows in the requested ORDER BY
** (or GROUP BY) without requiring a separate source operation.  Return:
................................................................................
  memset(aFrom, 0, sizeof(aFrom[0]));
  pX = (WhereLoop**)(aFrom+mxChoice);
  for(ii=mxChoice*2, pFrom=aTo; ii>0; ii--, pFrom++, pX += nLoop){
    pFrom->aLoop = pX;
  }

  /* Seed the search with a single WherePath containing zero WhereLoops */
  aFrom[0].nRow = 0;
  nFrom = 1;

  /* Precompute the cost of sorting the final result set, if the caller
  ** to sqlite3WhereBegin() was concerned about sorting */
  rSortCost = 0;
  if( pWInfo->pOrderBy==0 || nRowEst==0 ){
    aFrom[0].isOrderedValid = 1;
  }else{
    /* Compute an estimate on the cost to sort the entire result set */
    rSortCost = nRowEst + estLog(nRowEst);
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- sort cost=%-3d\n", rSortCost);
    }
#endif
  }

  /* Compute successively longer WherePaths using the previous generation
  ** of WherePaths as the basis for the next.  Keep track of the mxChoice
  ** best paths at each generation */
................................................................................
        Bitmask revMask = 0;
        u8 isOrderedValid = pFrom->isOrderedValid;
        u8 isOrdered = pFrom->isOrdered;
        if( (pWLoop->prereq & ~pFrom->maskLoop)!=0 ) continue;
        if( (pWLoop->maskSelf & pFrom->maskLoop)!=0 ) continue;
        /* At this point, pWLoop is a candidate to be the next loop. 
        ** Compute its cost */
        rCost = whereCostAdd(pWLoop->rSetup,pWLoop->rRun + pFrom->nRow);
        rCost = whereCostAdd(rCost, pFrom->rCost);
        maskNew = pFrom->maskLoop | pWLoop->maskSelf;
        if( !isOrderedValid ){
          switch( wherePathSatisfiesOrderBy(pWInfo, pFrom, iLoop, iLoop==nLoop-1,
                                            pWLoop, &revMask) ){
            case 1:  /* Yes.  pFrom+pWLoop does satisfy the ORDER BY clause */
              isOrdered = 1;
              isOrderedValid = 1;
              break;
            case 0:  /* No.  pFrom+pWLoop will require a separate sort */
              isOrdered = 0;
              isOrderedValid = 1;
              rCost = whereCostAdd(rCost, rSortCost);
              break;
            default: /* Cannot tell yet.  Try again on the next iteration */
              break;
          }
        }else{
          revMask = pFrom->revLoop;
        }
................................................................................
            break;
          }
        }
        if( jj>=nTo ){
          if( nTo>=mxChoice && rCost>=mxCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf("Skip   %s cost=%3d order=%c\n",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            continue;
          }
          /* Add a new Path to the aTo[] set */
................................................................................
          }else{
            /* New path replaces the prior worst to keep count below mxChoice */
            for(jj=nTo-1; aTo[jj].rCost<mxCost; jj--){ assert(jj>0); }
          }
          pTo = &aTo[jj];
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf("New    %s cost=%-3d order=%c\n",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
          }
#endif
        }else{
          if( pTo->rCost<=rCost ){
#ifdef WHERETRACE_ENABLED
            if( sqlite3WhereTrace&0x4 ){
              sqlite3DebugPrintf(
                  "Skip   %s cost=%-3d order=%c",
                  wherePathName(pFrom, iLoop, pWLoop), rCost,
                  isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
              sqlite3DebugPrintf("   vs %s cost=%-3d order=%c\n",
                  wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                  pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
            }
#endif
            continue;
          }
          /* A new and better score for a previously created equivalent path */
#ifdef WHERETRACE_ENABLED
          if( sqlite3WhereTrace&0x4 ){
            sqlite3DebugPrintf(
                "Update %s cost=%-3d order=%c",
                wherePathName(pFrom, iLoop, pWLoop), rCost,
                isOrderedValid ? (isOrdered ? 'Y' : 'N') : '?');
            sqlite3DebugPrintf("  was %s cost=%-3d order=%c\n",
                wherePathName(pTo, iLoop+1, 0), pTo->rCost,
                pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
          }
#endif
        }
        /* pWLoop is a winner.  Add it to the set of best so far */
        pTo->maskLoop = pFrom->maskLoop | pWLoop->maskSelf;
        pTo->revLoop = revMask;
        pTo->nRow = pFrom->nRow + pWLoop->nOut;
        pTo->rCost = rCost;
        pTo->isOrderedValid = isOrderedValid;
        pTo->isOrdered = isOrdered;
        memcpy(pTo->aLoop, pFrom->aLoop, sizeof(WhereLoop*)*iLoop);
        pTo->aLoop[iLoop] = pWLoop;
        if( nTo>=mxChoice ){
          mxCost = aTo[0].rCost;
................................................................................
      }
    }

#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace>=2 ){
      sqlite3DebugPrintf("---- after round %d ----\n", iLoop);
      for(ii=0, pTo=aTo; ii<nTo; ii++, pTo++){
        sqlite3DebugPrintf(" %s cost=%-3d nrow=%-3d order=%c",
           wherePathName(pTo, iLoop+1, 0), pTo->rCost, pTo->nRow,
           pTo->isOrderedValid ? (pTo->isOrdered ? 'Y' : 'N') : '?');
        if( pTo->isOrderedValid && pTo->isOrdered ){
          sqlite3DebugPrintf(" rev=0x%llx\n", pTo->revLoop);
        }else{
          sqlite3DebugPrintf("\n");
        }
................................................................................
** general-purpose query planner, and thereby yield faster sqlite3_prepare()
** times for the common case.
**
** Return non-zero on success, if this query can be handled by this
** no-frills query planner.  Return zero if this query needs the 
** general-purpose query planner.
*/
static int whereShortCut(WhereLoopBuilder *pBuilder){
  WhereInfo *pWInfo;
  struct SrcList_item *pItem;
  WhereClause *pWC;
  WhereTerm *pTerm;
  WhereLoop *pLoop;
  int iCur;
  int j;
................................................................................
  pLoop->wsFlags = 0;
  pTerm = findTerm(pWC, iCur, -1, 0, WO_EQ, 0);
  if( pTerm ){
    pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_IPK|WHERE_ONEROW;
    pLoop->aLTerm[0] = pTerm;
    pLoop->nLTerm = 1;
    pLoop->u.btree.nEq = 1;
    pLoop->rRun = 33;  /* 33 == whereCostFromInt(10) */
  }else{
    for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
      if( pIdx->onError==OE_None ) continue;
      for(j=0; j<pIdx->nColumn; j++){
        pTerm = findTerm(pWC, iCur, pIdx->aiColumn[j], 0, WO_EQ, pIdx);
        if( pTerm==0 ) break;
        whereLoopResize(pWInfo->pParse->db, pLoop, j);
................................................................................
      pLoop->wsFlags = WHERE_COLUMN_EQ|WHERE_ONEROW|WHERE_INDEXED;
      if( (pItem->colUsed & ~columnsUsedByIndex(pIdx))==0 ){
        pLoop->wsFlags |= WHERE_IDX_ONLY;
      }
      pLoop->nLTerm = j;
      pLoop->u.btree.nEq = j;
      pLoop->u.btree.pIndex = pIdx;
      pLoop->rRun = 39;  /* 39 == whereCostFromInt(15) */
      break;
    }
  }
  if( pLoop->wsFlags ){
    pLoop->nOut = (WhereCost)1;
    pWInfo->a[0].pWLoop = pLoop;
    pLoop->maskSelf = getMask(&pWInfo->sMaskSet, iCur);
................................................................................
  pWInfo->wctrlFlags = wctrlFlags;
  pWInfo->savedNQueryLoop = pParse->nQueryLoop;
  pMaskSet = &pWInfo->sMaskSet;
  sWLB.pWInfo = pWInfo;
  sWLB.pWC = &pWInfo->sWC;
  sWLB.pNew = (WhereLoop*)&pWInfo->a[nTabList];
  whereLoopInit(sWLB.pNew);
#ifdef SQLITE_DEBUG
  sWLB.pNew->cId = '*';
#endif

  /* Disable the DISTINCT optimization if SQLITE_DistinctOpt is set via
  ** sqlite3_test_ctrl(SQLITE_TESTCTRL_OPTIMIZATIONS,...) */
  if( OptimizationDisabled(db, SQLITE_DistinctOpt) ) pDistinct = 0;

  /* Split the WHERE clause into separate subexpressions where each
  ** subexpression is separated by an AND operator.
................................................................................
  if( pDistinct && isDistinctRedundant(pParse,pTabList,&pWInfo->sWC,pDistinct) ){
    pDistinct = 0;
    pWInfo->eDistinct = WHERE_DISTINCT_UNIQUE;
  }

  /* Construct the WhereLoop objects */
  WHERETRACE(("*** Optimizer Start ***\n"));
  if( nTabList!=1 || whereShortCut(&sWLB)==0 ){
    rc = whereLoopAddAll(&sWLB);
    if( rc ) goto whereBeginError;
  
    /* Display all of the WhereLoop objects if wheretrace is enabled */
#ifdef WHERETRACE_ENABLED
    if( sqlite3WhereTrace ){
      WhereLoop *p;