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SQLite training in Houston TX on 2019-11-05 (details)
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Overview
Comment:Allow the sqlite_stat2 table to contain a number of samples other than the default of 10.
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SHA1: b9d41c3490bf325915227a32b612e6772fb62fa9
User & Date: drh 2011-08-05 01:09:49
Context
2011-08-06
02:03
Merge together the fork in the query-planner-tweaks branch. check-in: 2daab6bd user: drh tags: query-planner-tweaks
2011-08-05
01:09
Allow the sqlite_stat2 table to contain a number of samples other than the default of 10. check-in: b9d41c34 user: drh tags: query-planner-tweaks
2011-08-03
01:07
Adjust the output row estimating logic when using STAT2. check-in: c8ba8855 user: drh tags: query-planner-tweaks
Changes
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Changes to src/analyze.c.

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** If the Index.aSample variable is not NULL, delete the aSample[] array
** and its contents.
*/
void sqlite3DeleteIndexSamples(sqlite3 *db, Index *pIdx){
#ifdef SQLITE_ENABLE_STAT2
  if( pIdx->aSample ){
    int j;
    for(j=0; j<SQLITE_INDEX_SAMPLES; j++){
      IndexSample *p = &pIdx->aSample[j];
      if( p->eType==SQLITE_TEXT || p->eType==SQLITE_BLOB ){
        sqlite3DbFree(db, p->u.z);
      }
    }
    sqlite3DbFree(db, pIdx->aSample);
  }
................................................................................
  /* Clear any prior statistics */
  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );
  for(i=sqliteHashFirst(&db->aDb[iDb].pSchema->idxHash);i;i=sqliteHashNext(i)){
    Index *pIdx = sqliteHashData(i);
    sqlite3DefaultRowEst(pIdx);
    sqlite3DeleteIndexSamples(db, pIdx);
    pIdx->aSample = 0;

  }

  /* Check to make sure the sqlite_stat1 table exists */
  sInfo.db = db;
  sInfo.zDatabase = db->aDb[iDb].zName;
  if( sqlite3FindTable(db, "sqlite_stat1", sInfo.zDatabase)==0 ){
    return SQLITE_ERROR;
................................................................................
  if( rc==SQLITE_OK && !sqlite3FindTable(db, "sqlite_stat2", sInfo.zDatabase) ){
    rc = SQLITE_ERROR;
  }
  if( rc==SQLITE_OK ){
    sqlite3_stmt *pStmt = 0;

    zSql = sqlite3MPrintf(db, 
        "SELECT idx,sampleno,sample FROM %Q.sqlite_stat2", sInfo.zDatabase);

    if( !zSql ){
      rc = SQLITE_NOMEM;
    }else{
      rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);
      sqlite3DbFree(db, zSql);
    }

    if( rc==SQLITE_OK ){
      while( sqlite3_step(pStmt)==SQLITE_ROW ){
        char *zIndex;   /* Index name */
        Index *pIdx;    /* Pointer to the index object */




        zIndex = (char *)sqlite3_column_text(pStmt, 0);

        pIdx = zIndex ? sqlite3FindIndex(db, zIndex, sInfo.zDatabase) : 0;
        if( pIdx ){
          int iSample = sqlite3_column_int(pStmt, 1);
          if( iSample<SQLITE_INDEX_SAMPLES && iSample>=0 ){
            int eType = sqlite3_column_type(pStmt, 2);


            if( pIdx->aSample==0 ){

              static const int sz = sizeof(IndexSample)*SQLITE_INDEX_SAMPLES;
              pIdx->aSample = (IndexSample *)sqlite3DbMallocRaw(0, sz);
              if( pIdx->aSample==0 ){


                db->mallocFailed = 1;
                break;
              }
	      memset(pIdx->aSample, 0, sz);

            }

            assert( pIdx->aSample );
            {

              IndexSample *pSample = &pIdx->aSample[iSample];
              pSample->eType = (u8)eType;
              if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
                pSample->u.r = sqlite3_column_double(pStmt, 2);
              }else if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){
                const char *z = (const char *)(
                    (eType==SQLITE_BLOB) ?
                    sqlite3_column_blob(pStmt, 2):
                    sqlite3_column_text(pStmt, 2)
                );
                int n = sqlite3_column_bytes(pStmt, 2);
                if( n>24 ){
                  n = 24;
                }
                pSample->nByte = (u8)n;
                if( n < 1){
                  pSample->u.z = 0;
                }else{
                  pSample->u.z = sqlite3DbStrNDup(0, z, n);
                  if( pSample->u.z==0 ){
                    db->mallocFailed = 1;
                    break;
                  }
                }
              }
            }
          }
        }
      }
      rc = sqlite3_finalize(pStmt);
    }
  }







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** If the Index.aSample variable is not NULL, delete the aSample[] array
** and its contents.
*/
void sqlite3DeleteIndexSamples(sqlite3 *db, Index *pIdx){
#ifdef SQLITE_ENABLE_STAT2
  if( pIdx->aSample ){
    int j;
    for(j=0; j<pIdx->nSample; j++){
      IndexSample *p = &pIdx->aSample[j];
      if( p->eType==SQLITE_TEXT || p->eType==SQLITE_BLOB ){
        sqlite3DbFree(db, p->u.z);
      }
    }
    sqlite3DbFree(db, pIdx->aSample);
  }
................................................................................
  /* Clear any prior statistics */
  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );
  for(i=sqliteHashFirst(&db->aDb[iDb].pSchema->idxHash);i;i=sqliteHashNext(i)){
    Index *pIdx = sqliteHashData(i);
    sqlite3DefaultRowEst(pIdx);
    sqlite3DeleteIndexSamples(db, pIdx);
    pIdx->aSample = 0;
    pIdx->nSample = 0;
  }

  /* Check to make sure the sqlite_stat1 table exists */
  sInfo.db = db;
  sInfo.zDatabase = db->aDb[iDb].zName;
  if( sqlite3FindTable(db, "sqlite_stat1", sInfo.zDatabase)==0 ){
    return SQLITE_ERROR;
................................................................................
  if( rc==SQLITE_OK && !sqlite3FindTable(db, "sqlite_stat2", sInfo.zDatabase) ){
    rc = SQLITE_ERROR;
  }
  if( rc==SQLITE_OK ){
    sqlite3_stmt *pStmt = 0;

    zSql = sqlite3MPrintf(db, 
        "SELECT idx, sampleno, sample FROM %Q.sqlite_stat2"
        " ORDER BY rowid DESC", sInfo.zDatabase);
    if( !zSql ){
      rc = SQLITE_NOMEM;
    }else{
      rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);
      sqlite3DbFree(db, zSql);
    }

    if( rc==SQLITE_OK ){
      while( sqlite3_step(pStmt)==SQLITE_ROW ){
        char *zIndex;   /* Index name */
        Index *pIdx;    /* Pointer to the index object */
        int iSample;
        int eType;
        IndexSample *pSample;

        zIndex = (char *)sqlite3_column_text(pStmt, 0);
        if( zIndex==0 ) continue;
        pIdx = sqlite3FindIndex(db, zIndex, sInfo.zDatabase);
        if( pIdx==0 ) continue;
        iSample = sqlite3_column_int(pStmt, 1);



        if( iSample>=SQLITE_MAX_SAMPLES || iSample<0 ) continue;
        if( pIdx->nSample<=iSample ){
          IndexSample *pNew;
          int sz = sizeof(IndexSample)*(iSample+1);


          pNew = (IndexSample*)sqlite3Realloc(pIdx->aSample, sz);
          if( pNew==0 ){
            db->mallocFailed = 1;
            break;
          }
          pIdx->aSample = pNew;
          pIdx->nSample = iSample+1;
        }



        eType = sqlite3_column_type(pStmt, 2);
        pSample = &pIdx->aSample[iSample];
        pSample->eType = (u8)eType;
        if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
          pSample->u.r = sqlite3_column_double(pStmt, 2);
        }else if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){
          const char *z = (const char *)(
             (eType==SQLITE_BLOB) ?
              sqlite3_column_blob(pStmt, 2):
              sqlite3_column_text(pStmt, 2)
          );
          int n = sqlite3_column_bytes(pStmt, 2);
          if( n>24 ) n = 24;


          pSample->nByte = (u8)n;
          if( n < 1){
            pSample->u.z = 0;
          }else{
            pSample->u.z = sqlite3DbStrNDup(0, z, n);
            if( pSample->u.z==0 ){
              db->mallocFailed = 1;
              break;



            }
          }
        }
      }
      rc = sqlite3_finalize(pStmt);
    }
  }

Changes to src/sqliteInt.h.

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** The number of samples of an index that SQLite takes in order to 
** construct a histogram of the table content when running ANALYZE
** and with SQLITE_ENABLE_STAT2
*/
#ifndef SQLITE_INDEX_SAMPLES
# define SQLITE_INDEX_SAMPLES 10
#endif


/*
** The following macros are used to cast pointers to integers and
** integers to pointers.  The way you do this varies from one compiler
** to the next, so we have developed the following set of #if statements
** to generate appropriate macros for a wide range of compilers.
**
................................................................................
  int *aiColumn;   /* Which columns are used by this index.  1st is 0 */
  unsigned *aiRowEst; /* Result of ANALYZE: Est. rows selected by each column */
  Table *pTable;   /* The SQL table being indexed */
  int tnum;        /* Page containing root of this index in database file */
  u8 onError;      /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */
  u8 autoIndex;    /* True if is automatically created (ex: by UNIQUE) */
  u8 bUnordered;   /* Use this index for == or IN queries only */

  char *zColAff;   /* String defining the affinity of each column */
  Index *pNext;    /* The next index associated with the same table */
  Schema *pSchema; /* Schema containing this index */
  u8 *aSortOrder;  /* Array of size Index.nColumn. True==DESC, False==ASC */
  char **azColl;   /* Array of collation sequence names for index */
  IndexSample *aSample;    /* Array of SQLITE_INDEX_SAMPLES samples */
};







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** The number of samples of an index that SQLite takes in order to 
** construct a histogram of the table content when running ANALYZE
** and with SQLITE_ENABLE_STAT2
*/
#ifndef SQLITE_INDEX_SAMPLES
# define SQLITE_INDEX_SAMPLES 10
#endif
#define SQLITE_MAX_SAMPLES 100

/*
** The following macros are used to cast pointers to integers and
** integers to pointers.  The way you do this varies from one compiler
** to the next, so we have developed the following set of #if statements
** to generate appropriate macros for a wide range of compilers.
**
................................................................................
  int *aiColumn;   /* Which columns are used by this index.  1st is 0 */
  unsigned *aiRowEst; /* Result of ANALYZE: Est. rows selected by each column */
  Table *pTable;   /* The SQL table being indexed */
  int tnum;        /* Page containing root of this index in database file */
  u8 onError;      /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */
  u8 autoIndex;    /* True if is automatically created (ex: by UNIQUE) */
  u8 bUnordered;   /* Use this index for == or IN queries only */
  u8 nSample;      /* Number of slots in aSample[] */
  char *zColAff;   /* String defining the affinity of each column */
  Index *pNext;    /* The next index associated with the same table */
  Schema *pSchema; /* Schema containing this index */
  u8 *aSortOrder;  /* Array of size Index.nColumn. True==DESC, False==ASC */
  char **azColl;   /* Array of collation sequence names for index */
  IndexSample *aSample;    /* Array of SQLITE_INDEX_SAMPLES samples */
};

Changes to src/where.c.

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  */
  bestOrClauseIndex(pParse, pWC, pSrc, notReady, notValid, pOrderBy, pCost);
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** Argument pIdx is a pointer to an index structure that has an array of
** SQLITE_INDEX_SAMPLES evenly spaced samples of the first indexed column
** stored in Index.aSample. These samples divide the domain of values stored
** the index into (SQLITE_INDEX_SAMPLES+1) regions.
** Region 0 contains all values less than the first sample value. Region
** 1 contains values between the first and second samples.  Region 2 contains
** values between samples 2 and 3.  And so on.  Region SQLITE_INDEX_SAMPLES
** contains values larger than the last sample.
**
** If the index contains many duplicates of a single value, then it is
** possible that two or more adjacent samples can hold the same value.
** When that is the case, the smallest possible region code is returned
** when roundUp is false and the largest possible region code is returned
** when roundUp is true.
**
** If successful, this function determines which of the regions value 
** pVal lies in, sets *piRegion to the region index (a value between 0
** and SQLITE_INDEX_SAMPLES+1, inclusive) and returns SQLITE_OK.
** Or, if an OOM occurs while converting text values between encodings,
** SQLITE_NOMEM is returned and *piRegion is undefined.
*/
#ifdef SQLITE_ENABLE_STAT2
static int whereRangeRegion(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
................................................................................
  sqlite3_value *pVal,        /* Value to consider */
  int roundUp,                /* Return largest valid region if true */
  int *piRegion               /* OUT: Region of domain in which value lies */
){
  assert( roundUp==0 || roundUp==1 );
  if( ALWAYS(pVal) ){
    IndexSample *aSample = pIdx->aSample;

    int i = 0;
    int eType = sqlite3_value_type(pVal);


    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
      double r = sqlite3_value_double(pVal);
      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){

        if( aSample[i].eType==SQLITE_NULL ) continue;
        if( aSample[i].eType>=SQLITE_TEXT ) break;
        if( roundUp ){
          if( aSample[i].u.r>r ) break;
        }else{
          if( aSample[i].u.r>=r ) break;
        }
      }
    }else if( eType==SQLITE_NULL ){
      i = 0;
      if( roundUp ){
        while( i<SQLITE_INDEX_SAMPLES && aSample[i].eType==SQLITE_NULL ) i++;
      }
    }else{ 
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;

................................................................................
        if( !z ){
          return SQLITE_NOMEM;
        }
        assert( z && pColl && pColl->xCmp );
      }
      n = sqlite3ValueBytes(pVal, pColl->enc);

      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        int c;
        int eSampletype = aSample[i].eType;
        if( eSampletype==SQLITE_NULL || eSampletype<eType ) continue;
        if( (eSampletype!=eType) ) break;
#ifndef SQLITE_OMIT_UTF16
        if( pColl->enc!=SQLITE_UTF8 ){
          int nSample;
................................................................................
        {
          c = pColl->xCmp(pColl->pUser, aSample[i].nByte, aSample[i].u.z, n, z);
        }
        if( c-roundUp>=0 ) break;
      }
    }

    assert( i>=0 && i<=SQLITE_INDEX_SAMPLES );
    *piRegion = i;
  }
  return SQLITE_OK;
}
#endif   /* #ifdef SQLITE_ENABLE_STAT2 */

/*
................................................................................
#ifdef SQLITE_ENABLE_STAT2

  if( nEq==0 && p->aSample ){
    sqlite3_value *pLowerVal = 0;
    sqlite3_value *pUpperVal = 0;
    int iEst;
    int iLower = 0;

    int iUpper = SQLITE_INDEX_SAMPLES;
    int roundUpUpper = 0;
    int roundUpLower = 0;
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    if( pLower ){
      Expr *pExpr = pLower->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pLowerVal);
................................................................................
      sqlite3ValueFree(pUpperVal);
      goto range_est_fallback;
    }else if( pLowerVal==0 ){
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( pLower ) iLower = iUpper/2;
    }else if( pUpperVal==0 ){
      rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      if( pUpper ) iUpper = (iLower + SQLITE_INDEX_SAMPLES + 1)/2;
    }else{
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( rc==SQLITE_OK ){
        rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      }
    }
    WHERETRACE(("range scan regions: %d..%d\n", iLower, iUpper));

    iEst = iUpper - iLower;
    testcase( iEst==SQLITE_INDEX_SAMPLES );
    assert( iEst<=SQLITE_INDEX_SAMPLES );

    if( iEst<1 ){
      *piEst = 50/SQLITE_INDEX_SAMPLES;
    }else{
      *piEst = (iEst*100)/SQLITE_INDEX_SAMPLES;
    }
    sqlite3ValueFree(pLowerVal);
    sqlite3ValueFree(pUpperVal);
    return rc;
  }
range_est_fallback:
#else
................................................................................
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */

  assert( p->aSample!=0 );

  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  if( pExpr ){
    rc = valueFromExpr(pParse, pExpr, aff, &pRhs);
    if( rc ) goto whereEqualScanEst_cancel;
  }else{
    pRhs = sqlite3ValueNew(pParse->db);
  }
................................................................................
  if( pRhs==0 ) return SQLITE_NOTFOUND;
  rc = whereRangeRegion(pParse, p, pRhs, 0, &iLower);
  if( rc ) goto whereEqualScanEst_cancel;
  rc = whereRangeRegion(pParse, p, pRhs, 1, &iUpper);
  if( rc ) goto whereEqualScanEst_cancel;
  WHERETRACE(("equality scan regions: %d..%d\n", iLower, iUpper));
  if( iLower>=iUpper ){
    nRowEst = p->aiRowEst[0]/(SQLITE_INDEX_SAMPLES*3);
    if( nRowEst<*pnRow ) *pnRow = nRowEst;
  }else{
    nRowEst = (iUpper-iLower)*p->aiRowEst[0]/SQLITE_INDEX_SAMPLES;
    *pnRow = nRowEst;
  }

whereEqualScanEst_cancel:
  sqlite3ValueFree(pRhs);
  return rc;
}
................................................................................
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc = SQLITE_OK;       /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */
  int nSpan = 0;            /* Number of histogram regions spanned */
  int nSingle = 0;          /* Histogram regions hit by a single value */
  int nNotFound = 0;        /* Count of values that are not constants */
  int i;                               /* Loop counter */

  u8 aSpan[SQLITE_INDEX_SAMPLES+1];    /* Histogram regions that are spanned */
  u8 aSingle[SQLITE_INDEX_SAMPLES+1];  /* Histogram regions hit once */

  assert( p->aSample!=0 );

  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  memset(aSpan, 0, sizeof(aSpan));
  memset(aSingle, 0, sizeof(aSingle));
  for(i=0; i<pList->nExpr; i++){
    sqlite3ValueFree(pVal);
    rc = valueFromExpr(pParse, pList->a[i].pExpr, aff, &pVal);
    if( rc ) break;
    if( pVal==0 || sqlite3_value_type(pVal)==SQLITE_NULL ){
      nNotFound++;
      continue;
................................................................................
    rc = whereRangeRegion(pParse, p, pVal, 0, &iLower);
    if( rc ) break;
    rc = whereRangeRegion(pParse, p, pVal, 1, &iUpper);
    if( rc ) break;
    if( iLower>=iUpper ){
      aSingle[iLower] = 1;
    }else{
      assert( iLower>=0 && iUpper<=SQLITE_INDEX_SAMPLES );
      while( iLower<iUpper ) aSpan[iLower++] = 1;
    }
  }
  if( rc==SQLITE_OK ){
    for(i=nSpan=0; i<=SQLITE_INDEX_SAMPLES; i++){
      if( aSpan[i] ){
        nSpan++;
      }else if( aSingle[i] ){
        nSingle++;
      }
    }
    nRowEst = (nSpan*3+nSingle)*p->aiRowEst[0]/(3*SQLITE_INDEX_SAMPLES)
               + nNotFound*p->aiRowEst[1];
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: nSpan=%d, nSingle=%d, nNotFound=%d, est=%g\n",
                 nSpan, nSingle, nNotFound, nRowEst));
  }
  sqlite3ValueFree(pVal);







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2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
....
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462

2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
....
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
....
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
....
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
....
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
....
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
....
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
....
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
....
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
  */
  bestOrClauseIndex(pParse, pWC, pSrc, notReady, notValid, pOrderBy, pCost);
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** Argument pIdx is a pointer to an index structure that has an array of
** pIdx->nSample evenly spaced samples of the first indexed column
** stored in Index.aSample. These samples divide the domain of values stored
** the index into (pIdx->nSample+1) regions.
** Region 0 contains all values less than the first sample value. Region
** 1 contains values between the first and second samples.  Region 2 contains
** values between samples 2 and 3.  And so on.  Region pIdx->nSample
** contains values larger than the last sample.
**
** If the index contains many duplicates of a single value, then it is
** possible that two or more adjacent samples can hold the same value.
** When that is the case, the smallest possible region code is returned
** when roundUp is false and the largest possible region code is returned
** when roundUp is true.
**
** If successful, this function determines which of the regions value 
** pVal lies in, sets *piRegion to the region index (a value between 0
** and S+1, inclusive) and returns SQLITE_OK.
** Or, if an OOM occurs while converting text values between encodings,
** SQLITE_NOMEM is returned and *piRegion is undefined.
*/
#ifdef SQLITE_ENABLE_STAT2
static int whereRangeRegion(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
................................................................................
  sqlite3_value *pVal,        /* Value to consider */
  int roundUp,                /* Return largest valid region if true */
  int *piRegion               /* OUT: Region of domain in which value lies */
){
  assert( roundUp==0 || roundUp==1 );
  if( ALWAYS(pVal) ){
    IndexSample *aSample = pIdx->aSample;
    int nSample = pIdx->nSample;
    int i = 0;
    int eType = sqlite3_value_type(pVal);

    assert( nSample>0 );
    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
      double r = sqlite3_value_double(pVal);

      for(i=0; i<nSample; i++){
        if( aSample[i].eType==SQLITE_NULL ) continue;
        if( aSample[i].eType>=SQLITE_TEXT ) break;
        if( roundUp ){
          if( aSample[i].u.r>r ) break;
        }else{
          if( aSample[i].u.r>=r ) break;
        }
      }
    }else if( eType==SQLITE_NULL ){
      i = 0;
      if( roundUp ){
        while( i<nSample && aSample[i].eType==SQLITE_NULL ) i++;
      }
    }else{ 
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;

................................................................................
        if( !z ){
          return SQLITE_NOMEM;
        }
        assert( z && pColl && pColl->xCmp );
      }
      n = sqlite3ValueBytes(pVal, pColl->enc);

      for(i=0; i<nSample; i++){
        int c;
        int eSampletype = aSample[i].eType;
        if( eSampletype==SQLITE_NULL || eSampletype<eType ) continue;
        if( (eSampletype!=eType) ) break;
#ifndef SQLITE_OMIT_UTF16
        if( pColl->enc!=SQLITE_UTF8 ){
          int nSample;
................................................................................
        {
          c = pColl->xCmp(pColl->pUser, aSample[i].nByte, aSample[i].u.z, n, z);
        }
        if( c-roundUp>=0 ) break;
      }
    }

    assert( i>=0 && i<=pIdx->nSample );
    *piRegion = i;
  }
  return SQLITE_OK;
}
#endif   /* #ifdef SQLITE_ENABLE_STAT2 */

/*
................................................................................
#ifdef SQLITE_ENABLE_STAT2

  if( nEq==0 && p->aSample ){
    sqlite3_value *pLowerVal = 0;
    sqlite3_value *pUpperVal = 0;
    int iEst;
    int iLower = 0;
    int nSample = p->nSample;
    int iUpper = p->nSample;
    int roundUpUpper = 0;
    int roundUpLower = 0;
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    if( pLower ){
      Expr *pExpr = pLower->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pLowerVal);
................................................................................
      sqlite3ValueFree(pUpperVal);
      goto range_est_fallback;
    }else if( pLowerVal==0 ){
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( pLower ) iLower = iUpper/2;
    }else if( pUpperVal==0 ){
      rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      if( pUpper ) iUpper = (iLower + p->nSample + 1)/2;
    }else{
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( rc==SQLITE_OK ){
        rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      }
    }
    WHERETRACE(("range scan regions: %d..%d\n", iLower, iUpper));

    iEst = iUpper - iLower;
    testcase( iEst==nSample );
    assert( iEst<=nSample );
    assert( nSample>0 );
    if( iEst<1 ){
      *piEst = 50/nSample;
    }else{
      *piEst = (iEst*100)/nSample;
    }
    sqlite3ValueFree(pLowerVal);
    sqlite3ValueFree(pUpperVal);
    return rc;
  }
range_est_fallback:
#else
................................................................................
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */

  assert( p->aSample!=0 );
  assert( p->nSample>0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  if( pExpr ){
    rc = valueFromExpr(pParse, pExpr, aff, &pRhs);
    if( rc ) goto whereEqualScanEst_cancel;
  }else{
    pRhs = sqlite3ValueNew(pParse->db);
  }
................................................................................
  if( pRhs==0 ) return SQLITE_NOTFOUND;
  rc = whereRangeRegion(pParse, p, pRhs, 0, &iLower);
  if( rc ) goto whereEqualScanEst_cancel;
  rc = whereRangeRegion(pParse, p, pRhs, 1, &iUpper);
  if( rc ) goto whereEqualScanEst_cancel;
  WHERETRACE(("equality scan regions: %d..%d\n", iLower, iUpper));
  if( iLower>=iUpper ){
    nRowEst = p->aiRowEst[0]/(p->nSample*3);
    if( nRowEst<*pnRow ) *pnRow = nRowEst;
  }else{
    nRowEst = (iUpper-iLower)*p->aiRowEst[0]/p->nSample;
    *pnRow = nRowEst;
  }

whereEqualScanEst_cancel:
  sqlite3ValueFree(pRhs);
  return rc;
}
................................................................................
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc = SQLITE_OK;       /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */
  int nSpan = 0;            /* Number of histogram regions spanned */
  int nSingle = 0;          /* Histogram regions hit by a single value */
  int nNotFound = 0;        /* Count of values that are not constants */
  int i;                             /* Loop counter */
  int nSample = p->nSample;          /* Number of samples */
  u8 aSpan[SQLITE_MAX_SAMPLES+1];    /* Histogram regions that are spanned */
  u8 aSingle[SQLITE_MAX_SAMPLES+1];  /* Histogram regions hit once */

  assert( p->aSample!=0 );
  assert( nSample>0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  memset(aSpan, 0, nSample+1);
  memset(aSingle, 0, nSample+1);
  for(i=0; i<pList->nExpr; i++){
    sqlite3ValueFree(pVal);
    rc = valueFromExpr(pParse, pList->a[i].pExpr, aff, &pVal);
    if( rc ) break;
    if( pVal==0 || sqlite3_value_type(pVal)==SQLITE_NULL ){
      nNotFound++;
      continue;
................................................................................
    rc = whereRangeRegion(pParse, p, pVal, 0, &iLower);
    if( rc ) break;
    rc = whereRangeRegion(pParse, p, pVal, 1, &iUpper);
    if( rc ) break;
    if( iLower>=iUpper ){
      aSingle[iLower] = 1;
    }else{
      assert( iLower>=0 && iUpper<=nSample );
      while( iLower<iUpper ) aSpan[iLower++] = 1;
    }
  }
  if( rc==SQLITE_OK ){
    for(i=nSpan=0; i<=nSample; i++){
      if( aSpan[i] ){
        nSpan++;
      }else if( aSingle[i] ){
        nSingle++;
      }
    }
    nRowEst = (nSpan*3+nSingle)*p->aiRowEst[0]/(3*nSample)
               + nNotFound*p->aiRowEst[1];
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: nSpan=%d, nSingle=%d, nNotFound=%d, est=%g\n",
                 nSpan, nSingle, nNotFound, nRowEst));
  }
  sqlite3ValueFree(pVal);