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SQLite training in Houston TX on 2019-11-05 (details)
Part of the 2019 Tcl Conference

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Overview
Comment:Attempt to fix the SQLite core so that no floating point operations are used anywhere if SQLITE_OMIT_FLOATING_POINT is defined at compile-time. This is useful to people who use SQLite on embedded processors that lack floating point support. (CVS 2749)
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | trunk
Files: files | file ages | folders
SHA1: a0bdb584680ce6400d9e8c57db9d91197cc7b776
User & Date: drh 2005-10-13 02:09:50
Context
2005-10-20
07:28
Changes to prevent various compiler warnings. (CVS 2750) check-in: e261b8b0 user: drh tags: trunk
2005-10-13
02:09
Attempt to fix the SQLite core so that no floating point operations are used anywhere if SQLITE_OMIT_FLOATING_POINT is defined at compile-time. This is useful to people who use SQLite on embedded processors that lack floating point support. (CVS 2749) check-in: a0bdb584 user: drh tags: trunk
2005-10-10
00:05
Make the default TEMP_STORE=1 (TEMP tables stored on disk) in the configure script. (CVS 2748) check-in: 9753af53 user: drh tags: trunk
Changes
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Changes to src/func.c.

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** This file contains the C functions that implement various SQL
** functions of SQLite.  
**
** There is only one exported symbol in this file - the function
** sqliteRegisterBuildinFunctions() found at the bottom of the file.
** All other code has file scope.
**
** $Id: func.c,v 1.110 2005/09/08 20:37:43 drh Exp $
*/
#include "sqliteInt.h"
#include <ctype.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>
#include "vdbeInt.h"
#include "os.h"

/*
** Return the collating function associated with a function.







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** This file contains the C functions that implement various SQL
** functions of SQLite.  
**
** There is only one exported symbol in this file - the function
** sqliteRegisterBuildinFunctions() found at the bottom of the file.
** All other code has file scope.
**
** $Id: func.c,v 1.111 2005/10/13 02:09:50 drh Exp $
*/
#include "sqliteInt.h"
#include <ctype.h>
/* #include <math.h> */
#include <stdlib.h>
#include <assert.h>
#include "vdbeInt.h"
#include "os.h"

/*
** Return the collating function associated with a function.

Changes to src/printf.c.

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  {  'q',  0, 4, etSQLESCAPE,  0,  0 },
  {  'Q',  0, 4, etSQLESCAPE2, 0,  0 },
  {  'c',  0, 0, etCHARX,      0,  0 },
  {  'o',  8, 0, etRADIX,      0,  2 },
  {  'u', 10, 0, etRADIX,      0,  0 },
  {  'x', 16, 0, etRADIX,      16, 1 },
  {  'X', 16, 0, etRADIX,      0,  4 },

  {  'f',  0, 1, etFLOAT,      0,  0 },
  {  'e',  0, 1, etEXP,        30, 0 },
  {  'E',  0, 1, etEXP,        14, 0 },
  {  'G',  0, 1, etGENERIC,    14, 0 },

  {  'i', 10, 1, etRADIX,      0,  0 },
  {  'n',  0, 0, etSIZE,       0,  0 },
  {  '%',  0, 0, etPERCENT,    0,  0 },
  {  'p', 16, 0, etPOINTER,    0,  1 },
  {  'T',  0, 2, etTOKEN,      0,  0 },
  {  'S',  0, 2, etSRCLIST,    0,  0 },
};
#define etNINFO  (sizeof(fmtinfo)/sizeof(fmtinfo[0]))

/*
** If NOFLOATINGPOINT is defined, then none of the floating point
** conversions will work.
*/
#ifndef etNOFLOATINGPOINT
/*
** "*val" is a double such that 0.1 <= *val < 10.0
** Return the ascii code for the leading digit of *val, then
** multiply "*val" by 10.0 to renormalize.
**
** Example:
**     input:     *val = 3.14159
................................................................................
  if( (*cnt)++ >= 16 ) return '0';
  digit = (int)*val;
  d = digit;
  digit += '0';
  *val = (*val - d)*10.0;
  return digit;
}
#endif

/*
** On machines with a small stack size, you can redefine the
** SQLITE_PRINT_BUF_SIZE to be less than 350.  But beware - for
** smaller values some %f conversions may go into an infinite loop.
*/
#ifndef SQLITE_PRINT_BUF_SIZE
................................................................................
  char prefix;               /* Prefix character.  "+" or "-" or " " or '\0'. */
  etByte errorflag = 0;      /* True if an error is encountered */
  etByte xtype;              /* Conversion paradigm */
  char *zExtra;              /* Extra memory used for etTCLESCAPE conversions */
  static const char spaces[] =
   "                                                                         ";
#define etSPACESIZE (sizeof(spaces)-1)
#ifndef etNOFLOATINGPOINT
  int  exp, e2;              /* exponent of real numbers */
  double rounder;            /* Used for rounding floating point values */
  etByte flag_dp;            /* True if decimal point should be shown */
  etByte flag_rtz;           /* True if trailing zeros should be removed */
  etByte flag_exp;           /* True to force display of the exponent */
  int nsd;                   /* Number of significant digits returned */
#endif
................................................................................
        }
        length = &buf[etBUFSIZE-1]-bufpt;
        break;
      case etFLOAT:
      case etEXP:
      case etGENERIC:
        realvalue = va_arg(ap,double);
#ifndef etNOFLOATINGPOINT
        if( precision<0 ) precision = 6;         /* Set default precision */
        if( precision>etBUFSIZE/2-10 ) precision = etBUFSIZE/2-10;
        if( realvalue<0.0 ){
          realvalue = -realvalue;
          prefix = '-';
        }else{
          if( flag_plussign )          prefix = '+';







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  {  'q',  0, 4, etSQLESCAPE,  0,  0 },
  {  'Q',  0, 4, etSQLESCAPE2, 0,  0 },
  {  'c',  0, 0, etCHARX,      0,  0 },
  {  'o',  8, 0, etRADIX,      0,  2 },
  {  'u', 10, 0, etRADIX,      0,  0 },
  {  'x', 16, 0, etRADIX,      16, 1 },
  {  'X', 16, 0, etRADIX,      0,  4 },
#ifndef SQLITE_OMIT_FLOATING_POINT
  {  'f',  0, 1, etFLOAT,      0,  0 },
  {  'e',  0, 1, etEXP,        30, 0 },
  {  'E',  0, 1, etEXP,        14, 0 },
  {  'G',  0, 1, etGENERIC,    14, 0 },
#endif
  {  'i', 10, 1, etRADIX,      0,  0 },
  {  'n',  0, 0, etSIZE,       0,  0 },
  {  '%',  0, 0, etPERCENT,    0,  0 },
  {  'p', 16, 0, etPOINTER,    0,  1 },
  {  'T',  0, 2, etTOKEN,      0,  0 },
  {  'S',  0, 2, etSRCLIST,    0,  0 },
};
#define etNINFO  (sizeof(fmtinfo)/sizeof(fmtinfo[0]))

/*
** If SQLITE_OMIT_FLOATING_POINT is defined, then none of the floating point
** conversions will work.
*/
#ifndef SQLITE_OMIT_FLOATING_POINT
/*
** "*val" is a double such that 0.1 <= *val < 10.0
** Return the ascii code for the leading digit of *val, then
** multiply "*val" by 10.0 to renormalize.
**
** Example:
**     input:     *val = 3.14159
................................................................................
  if( (*cnt)++ >= 16 ) return '0';
  digit = (int)*val;
  d = digit;
  digit += '0';
  *val = (*val - d)*10.0;
  return digit;
}
#endif /* SQLITE_OMIT_FLOATING_POINT */

/*
** On machines with a small stack size, you can redefine the
** SQLITE_PRINT_BUF_SIZE to be less than 350.  But beware - for
** smaller values some %f conversions may go into an infinite loop.
*/
#ifndef SQLITE_PRINT_BUF_SIZE
................................................................................
  char prefix;               /* Prefix character.  "+" or "-" or " " or '\0'. */
  etByte errorflag = 0;      /* True if an error is encountered */
  etByte xtype;              /* Conversion paradigm */
  char *zExtra;              /* Extra memory used for etTCLESCAPE conversions */
  static const char spaces[] =
   "                                                                         ";
#define etSPACESIZE (sizeof(spaces)-1)
#ifndef SQLITE_OMIT_FLOATING_POINT
  int  exp, e2;              /* exponent of real numbers */
  double rounder;            /* Used for rounding floating point values */
  etByte flag_dp;            /* True if decimal point should be shown */
  etByte flag_rtz;           /* True if trailing zeros should be removed */
  etByte flag_exp;           /* True to force display of the exponent */
  int nsd;                   /* Number of significant digits returned */
#endif
................................................................................
        }
        length = &buf[etBUFSIZE-1]-bufpt;
        break;
      case etFLOAT:
      case etEXP:
      case etGENERIC:
        realvalue = va_arg(ap,double);
#ifndef SQLITE_OMIT_FLOATING_POINT
        if( precision<0 ) precision = 6;         /* Set default precision */
        if( precision>etBUFSIZE/2-10 ) precision = etBUFSIZE/2-10;
        if( realvalue<0.0 ){
          realvalue = -realvalue;
          prefix = '-';
        }else{
          if( flag_plussign )          prefix = '+';

Changes to src/sqlite.h.in.

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**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This header file defines the interface that the SQLite library
** presents to client programs.
**
** @(#) $Id: sqlite.h.in,v 1.141 2005/09/08 10:58:52 drh Exp $
*/
#ifndef _SQLITE3_H_
#define _SQLITE3_H_
#include <stdarg.h>     /* Needed for the definition of va_list */

/*
** Make sure we can call this stuff from C++.
................................................................................
  typedef __int64 sqlite_int64;
  typedef unsigned __int64 sqlite_uint64;
#else
  typedef long long int sqlite_int64;
  typedef unsigned long long int sqlite_uint64;
#endif









/*
** A function to close the database.
**
** Call this function with a pointer to a structure that was previously
** returned from sqlite3_open() and the corresponding database will by closed.
**
................................................................................
** Return the sqlite3* database handle to which the prepared statement given
** in the argument belongs.  This is the same database handle that was
** the first argument to the sqlite3_prepare() that was used to create
** the statement in the first place.
*/
sqlite3 *sqlite3_db_handle(sqlite3_stmt*);









#ifdef __cplusplus
}  /* End of the 'extern "C"' block */
#endif
#endif







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**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This header file defines the interface that the SQLite library
** presents to client programs.
**
** @(#) $Id: sqlite.h.in,v 1.142 2005/10/13 02:09:50 drh Exp $
*/
#ifndef _SQLITE3_H_
#define _SQLITE3_H_
#include <stdarg.h>     /* Needed for the definition of va_list */

/*
** Make sure we can call this stuff from C++.
................................................................................
  typedef __int64 sqlite_int64;
  typedef unsigned __int64 sqlite_uint64;
#else
  typedef long long int sqlite_int64;
  typedef unsigned long long int sqlite_uint64;
#endif

/*
** If compiling for a processor that lacks floating point support,
** substitute integer for floating-point
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# define double sqlite_int64
#endif

/*
** A function to close the database.
**
** Call this function with a pointer to a structure that was previously
** returned from sqlite3_open() and the corresponding database will by closed.
**
................................................................................
** Return the sqlite3* database handle to which the prepared statement given
** in the argument belongs.  This is the same database handle that was
** the first argument to the sqlite3_prepare() that was used to create
** the statement in the first place.
*/
sqlite3 *sqlite3_db_handle(sqlite3_stmt*);

/*
** Undo the hack that converts floating point types to integer for
** builds on processors without floating point support.
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# undef double
#endif

#ifdef __cplusplus
}  /* End of the 'extern "C"' block */
#endif
#endif

Changes to src/sqliteInt.h.

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**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** Internal interface definitions for SQLite.
**
** @(#) $Id: sqliteInt.h,v 1.422 2005/10/06 16:53:15 drh Exp $
*/
#ifndef _SQLITEINT_H_
#define _SQLITEINT_H_

/*
** Many people are failing to set -DNDEBUG=1 when compiling SQLite.
** Setting NDEBUG makes the code smaller and run faster.  So the following
................................................................................
#include "parse.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <stddef.h>













/*
** The maximum number of in-memory pages to use for the main database
** table and for temporary tables. Internally, the MAX_PAGES and 
** TEMP_PAGES macros are used. To override the default values at
** compilation time, the SQLITE_DEFAULT_CACHE_SIZE and 
** SQLITE_DEFAULT_TEMP_CACHE_SIZE macros should be set.
*/
................................................................................
#define MAX_ATTACHED 10

/*
** The maximum value of a ?nnn wildcard that the parser will accept.
*/
#define SQLITE_MAX_VARIABLE_NUMBER 999

/*
** When building SQLite for embedded systems where memory is scarce,
** you can define one or more of the following macros to omit extra
** features of the library and thus keep the size of the library to
** a minimum.
*/
/* #define SQLITE_OMIT_AUTHORIZATION  1 */
/* #define SQLITE_OMIT_MEMORYDB     1 */
/* #define SQLITE_OMIT_VACUUM         1 */
/* #define SQLITE_OMIT_DATETIME_FUNCS 1 */
/* #define SQLITE_OMIT_PROGRESS_CALLBACK 1 */
/* #define SQLITE_OMIT_AUTOVACUUM */
/* #define SQLITE_OMIT_ALTERTABLE */

/*
** Provide a default value for TEMP_STORE in case it is not specified
** on the command-line
*/
#ifndef TEMP_STORE
# define TEMP_STORE 1
#endif







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**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** Internal interface definitions for SQLite.
**
** @(#) $Id: sqliteInt.h,v 1.423 2005/10/13 02:09:50 drh Exp $
*/
#ifndef _SQLITEINT_H_
#define _SQLITEINT_H_

/*
** Many people are failing to set -DNDEBUG=1 when compiling SQLite.
** Setting NDEBUG makes the code smaller and run faster.  So the following
................................................................................
#include "parse.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <stddef.h>

/*
** If compiling for a processor that lacks floating point support,
** substitute integer for floating-point
*/
#ifdef SQLITE_OMIT_FLOATING_POINT
# define double sqlite_int64
# define LONGDOUBLE_TYPE sqlite_int64
# define SQLITE_BIG_DBL (0x7fffffffffffffff)
# define SQLITE_OMIT_DATETIME_FUNCS 1
# define SQLITE_OMIT_TRACE 1
#endif

/*
** The maximum number of in-memory pages to use for the main database
** table and for temporary tables. Internally, the MAX_PAGES and 
** TEMP_PAGES macros are used. To override the default values at
** compilation time, the SQLITE_DEFAULT_CACHE_SIZE and 
** SQLITE_DEFAULT_TEMP_CACHE_SIZE macros should be set.
*/
................................................................................
#define MAX_ATTACHED 10

/*
** The maximum value of a ?nnn wildcard that the parser will accept.
*/
#define SQLITE_MAX_VARIABLE_NUMBER 999















/*
** Provide a default value for TEMP_STORE in case it is not specified
** on the command-line
*/
#ifndef TEMP_STORE
# define TEMP_STORE 1
#endif

Changes to src/util.c.

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**
*************************************************************************
** Utility functions used throughout sqlite.
**
** This file contains functions for allocating memory, comparing
** strings, and stuff like that.
**
** $Id: util.c,v 1.146 2005/09/17 18:34:11 drh Exp $
*/
#include "sqliteInt.h"
#include <stdarg.h>
#include <ctype.h>

#if SQLITE_MEMDEBUG>2 && defined(__GLIBC__)
#include <execinfo.h>
................................................................................
**
** This routine is used instead of the library atof() function because
** the library atof() might want to use "," as the decimal point instead
** of "." depending on how locale is set.  But that would cause problems
** for SQL.  So this routine always uses "." regardless of locale.
*/
int sqlite3AtoF(const char *z, double *pResult){

  int sign = 1;
  const char *zBegin = z;
  LONGDOUBLE_TYPE v1 = 0.0;
  if( *z=='-' ){
    sign = -1;
    z++;
  }else if( *z=='+' ){
................................................................................
      v1 /= scale;
    }else{
      v1 *= scale;
    }
  }
  *pResult = sign<0 ? -v1 : v1;
  return z - zBegin;



}

/*
** Return TRUE if zNum is a 64-bit signed integer and write
** the value of the integer into *pNum.  If zNum is not an integer
** or is an integer that is too large to be expressed with 64 bits,
** then return false.  If n>0 and the integer is string is not







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**
*************************************************************************
** Utility functions used throughout sqlite.
**
** This file contains functions for allocating memory, comparing
** strings, and stuff like that.
**
** $Id: util.c,v 1.147 2005/10/13 02:09:50 drh Exp $
*/
#include "sqliteInt.h"
#include <stdarg.h>
#include <ctype.h>

#if SQLITE_MEMDEBUG>2 && defined(__GLIBC__)
#include <execinfo.h>
................................................................................
**
** This routine is used instead of the library atof() function because
** the library atof() might want to use "," as the decimal point instead
** of "." depending on how locale is set.  But that would cause problems
** for SQL.  So this routine always uses "." regardless of locale.
*/
int sqlite3AtoF(const char *z, double *pResult){
#ifndef SQLITE_OMIT_FLOATING_POINT
  int sign = 1;
  const char *zBegin = z;
  LONGDOUBLE_TYPE v1 = 0.0;
  if( *z=='-' ){
    sign = -1;
    z++;
  }else if( *z=='+' ){
................................................................................
      v1 /= scale;
    }else{
      v1 *= scale;
    }
  }
  *pResult = sign<0 ? -v1 : v1;
  return z - zBegin;
#else
  return sqlite3atoi64(z, pResult);
#endif /* SQLITE_OMIT_FLOATING_POINT */
}

/*
** Return TRUE if zNum is a 64-bit signed integer and write
** the value of the integer into *pNum.  If zNum is not an integer
** or is an integer that is too large to be expressed with 64 bits,
** then return false.  If n>0 and the integer is string is not

Changes to src/where.c.

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** This module contains C code that generates VDBE code used to process
** the WHERE clause of SQL statements.  This module is reponsible for
** generating the code that loops through a table looking for applicable
** rows.  Indices are selected and used to speed the search when doing
** so is applicable.  Because this module is responsible for selecting
** indices, you might also think of this module as the "query optimizer".
**
** $Id: where.c,v 1.179 2005/09/20 17:42:23 drh Exp $
*/
#include "sqliteInt.h"

/*
** The number of bits in a Bitmask.  "BMS" means "BitMask Size".
*/
#define BMS  (sizeof(Bitmask)*8)
................................................................................
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
int sqlite3_where_trace = 0;
# define TRACE(X)  if(sqlite3_where_trace) sqlite3DebugPrintf X
#else
# define TRACE(X)
#endif











/* Forward reference
*/
typedef struct WhereClause WhereClause;

/*
** The query generator uses an array of instances of this structure to
** help it analyze the subexpressions of the WHERE clause.  Each WHERE
................................................................................
** 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 operatings 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 double estLog(double N){
  double logN = 1.0;
  double x = 10.0;
  while( N>x ){
    logN += 1.0;
    x *= 10;
  }
  return logN;
}

/*
** Find the best index for accessing a particular table.  Return a pointer
................................................................................
  ExprList *pOrderBy,         /* The order by clause */
  Index **ppIndex,            /* Make *ppIndex point to the best index */
  int *pFlags,                /* Put flags describing this choice in *pFlags */
  int *pnEq                   /* Put the number of == or IN constraints here */
){
  WhereTerm *pTerm;
  Index *bestIdx = 0;         /* Index that gives the lowest cost */
  double lowestCost = 1.0e99; /* The cost of using bestIdx */
  int bestFlags = 0;          /* Flags associated with bestIdx */
  int bestNEq = 0;            /* Best value for nEq */
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  int rev;                    /* True to scan in reverse order */
  int flags;                  /* Flags associated with pProbe */
  int nEq;                    /* Number of == or IN constraints */
  double cost;                /* Cost of using pProbe */

  TRACE(("bestIndex: tbl=%s notReady=%x\n", pSrc->pTab->zName, notReady));


  /* Check for a rowid=EXPR or rowid IN (...) constraints
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_EQ|WO_IN, 0);
  if( pTerm ){
    Expr *pExpr;
    *ppIndex = 0;
................................................................................
      ** elements.  */
      lowestCost = pExpr->pList->nExpr;
      lowestCost *= estLog(lowestCost);
    }else{
      /* Rowid IN (SELECT): cost is NlogN where N is the number of rows
      ** in the result of the inner select.  We have no way to estimate
      ** that value so make a wild guess. */
      lowestCost = 200.0;
    }
    TRACE(("... rowid IN cost: %.9g\n", lowestCost));
  }

  /* Estimate the cost of a table scan.  If we do not know how many
  ** entries are in the table, use 1 million as a guess.
  */
  pProbe = pSrc->pTab->pIndex;
  cost = pProbe ? pProbe->aiRowEst[0] : 1000000.0;
  TRACE(("... table scan base cost: %.9g\n", cost));
  flags = WHERE_ROWID_RANGE;

  /* Check for constraints on a range of rowids in a table scan.
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE|WO_GT|WO_GE, 0);
  if( pTerm ){
    if( findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE, 0) ){
      flags |= WHERE_TOP_LIMIT;
      cost *= 0.333;  /* Guess that rowid<EXPR eliminates two-thirds or rows */
    }
    if( findTerm(pWC, iCur, -1, notReady, WO_GT|WO_GE, 0) ){
      flags |= WHERE_BTM_LIMIT;
      cost *= 0.333;  /* Guess that rowid>EXPR eliminates two-thirds of rows */
    }
    TRACE(("... rowid range reduces cost to %.9g\n", cost));
  }else{
    flags = 0;
  }

  /* If the table scan does not satisfy the ORDER BY clause, increase
................................................................................
    bestFlags = flags;
  }

  /* Look at each index.
  */
  for(; pProbe; pProbe=pProbe->pNext){
    int i;                       /* Loop counter */
    double inMultiplier = 1.0;

    TRACE(("... index %s:\n", pProbe->zName));

    /* Count the number of columns in the index that are satisfied
    ** by x=EXPR constraints or x IN (...) constraints.
    */
    flags = 0;
................................................................................
      pTerm = findTerm(pWC, iCur, j, notReady, WO_EQ|WO_IN, pProbe);
      if( pTerm==0 ) break;
      flags |= WHERE_COLUMN_EQ;
      if( pTerm->operator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        flags |= WHERE_COLUMN_IN;
        if( pExpr->pSelect!=0 ){
          inMultiplier *= 100.0;
        }else if( pExpr->pList!=0 ){
          inMultiplier *= pExpr->pList->nExpr + 1.0;
        }
      }
    }
    cost = pProbe->aiRowEst[i] * inMultiplier * estLog(inMultiplier);
    nEq = i;
    if( pProbe->onError!=OE_None && (flags & WHERE_COLUMN_IN)==0
         && nEq==pProbe->nColumn ){
................................................................................
    if( nEq<pProbe->nColumn ){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pProbe);
      if( pTerm ){
        flags |= WHERE_COLUMN_RANGE;
        if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE, pProbe) ){
          flags |= WHERE_TOP_LIMIT;
          cost *= 0.333;
        }
        if( findTerm(pWC, iCur, j, notReady, WO_GT|WO_GE, pProbe) ){
          flags |= WHERE_BTM_LIMIT;
          cost *= 0.333;
        }
        TRACE(("...... range reduces cost to %.9g\n", cost));
      }
    }

    /* Add the additional cost of sorting if that is a factor.
    */
................................................................................
        int x = pProbe->aiColumn[j];
        if( x<BMS-1 ){
          m &= ~(((Bitmask)1)<<x);
        }
      }
      if( m==0 ){
        flags |= WHERE_IDX_ONLY;
        cost *= 0.5;
        TRACE(("...... idx-only reduces cost to %.9g\n", cost));
      }
    }

    /* If this index has achieved the lowest cost so far, then use it.
    */
    if( cost < lowestCost ){
................................................................................
    int flags;                  /* Flags asssociated with pIdx */
    int nEq;                    /* Number of == or IN constraints */
    double cost;                /* The cost for pIdx */
    int j;                      /* For looping over FROM tables */
    Index *pBest = 0;           /* The best index seen so far */
    int bestFlags = 0;          /* Flags associated with pBest */
    int bestNEq = 0;            /* nEq associated with pBest */
    double lowestCost = 1.0e99; /* Cost of the pBest */
    int bestJ;                  /* The value of j */
    Bitmask m;                  /* Bitmask value for j or bestJ */


    for(j=iFrom, pTabItem=&pTabList->a[j]; j<pTabList->nSrc; j++, pTabItem++){
      m = getMask(&maskSet, pTabItem->iCursor);
      if( (m & notReady)==0 ){
        if( j==iFrom ) iFrom++;
        continue;
      }
      cost = bestIndex(pParse, &wc, pTabItem, notReady,







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** This module contains C code that generates VDBE code used to process
** the WHERE clause of SQL statements.  This module is reponsible for
** generating the code that loops through a table looking for applicable
** rows.  Indices are selected and used to speed the search when doing
** so is applicable.  Because this module is responsible for selecting
** indices, you might also think of this module as the "query optimizer".
**
** $Id: where.c,v 1.180 2005/10/13 02:09:50 drh Exp $
*/
#include "sqliteInt.h"

/*
** The number of bits in a Bitmask.  "BMS" means "BitMask Size".
*/
#define BMS  (sizeof(Bitmask)*8)
................................................................................
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
int sqlite3_where_trace = 0;
# define TRACE(X)  if(sqlite3_where_trace) sqlite3DebugPrintf X
#else
# define TRACE(X)
#endif

/*
** A large value which is the maximum cost of using an index.
** By default this is a large floating point value.  When compiling
** SQLite for a processor that lacks floating point support, simply
** redefine this constant to a large integer.
*/
#ifndef SQLITE_BIG_DBL
# define SQLITE_BIG_DBL (1.0e+99)
#endif

/* Forward reference
*/
typedef struct WhereClause WhereClause;

/*
** The query generator uses an array of instances of this structure to
** help it analyze the subexpressions of the WHERE clause.  Each WHERE
................................................................................
** 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 operatings 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 double estLog(double N){
  double logN = 1;
  double x = 10;
  while( N>x ){
    logN += 1;
    x *= 10;
  }
  return logN;
}

/*
** Find the best index for accessing a particular table.  Return a pointer
................................................................................
  ExprList *pOrderBy,         /* The order by clause */
  Index **ppIndex,            /* Make *ppIndex point to the best index */
  int *pFlags,                /* Put flags describing this choice in *pFlags */
  int *pnEq                   /* Put the number of == or IN constraints here */
){
  WhereTerm *pTerm;
  Index *bestIdx = 0;         /* Index that gives the lowest cost */
  double lowestCost;          /* The cost of using bestIdx */
  int bestFlags = 0;          /* Flags associated with bestIdx */
  int bestNEq = 0;            /* Best value for nEq */
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  int rev;                    /* True to scan in reverse order */
  int flags;                  /* Flags associated with pProbe */
  int nEq;                    /* Number of == or IN constraints */
  double cost;                /* Cost of using pProbe */

  TRACE(("bestIndex: tbl=%s notReady=%x\n", pSrc->pTab->zName, notReady));
  lowestCost = SQLITE_BIG_DBL;

  /* Check for a rowid=EXPR or rowid IN (...) constraints
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_EQ|WO_IN, 0);
  if( pTerm ){
    Expr *pExpr;
    *ppIndex = 0;
................................................................................
      ** elements.  */
      lowestCost = pExpr->pList->nExpr;
      lowestCost *= estLog(lowestCost);
    }else{
      /* Rowid IN (SELECT): cost is NlogN where N is the number of rows
      ** in the result of the inner select.  We have no way to estimate
      ** that value so make a wild guess. */
      lowestCost = 200;
    }
    TRACE(("... rowid IN cost: %.9g\n", lowestCost));
  }

  /* Estimate the cost of a table scan.  If we do not know how many
  ** entries are in the table, use 1 million as a guess.
  */
  pProbe = pSrc->pTab->pIndex;
  cost = pProbe ? pProbe->aiRowEst[0] : 1000000;
  TRACE(("... table scan base cost: %.9g\n", cost));
  flags = WHERE_ROWID_RANGE;

  /* Check for constraints on a range of rowids in a table scan.
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE|WO_GT|WO_GE, 0);
  if( pTerm ){
    if( findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE, 0) ){
      flags |= WHERE_TOP_LIMIT;
      cost /= 3;  /* Guess that rowid<EXPR eliminates two-thirds or rows */
    }
    if( findTerm(pWC, iCur, -1, notReady, WO_GT|WO_GE, 0) ){
      flags |= WHERE_BTM_LIMIT;
      cost /= 3;  /* Guess that rowid>EXPR eliminates two-thirds of rows */
    }
    TRACE(("... rowid range reduces cost to %.9g\n", cost));
  }else{
    flags = 0;
  }

  /* If the table scan does not satisfy the ORDER BY clause, increase
................................................................................
    bestFlags = flags;
  }

  /* Look at each index.
  */
  for(; pProbe; pProbe=pProbe->pNext){
    int i;                       /* Loop counter */
    double inMultiplier = 1;

    TRACE(("... index %s:\n", pProbe->zName));

    /* Count the number of columns in the index that are satisfied
    ** by x=EXPR constraints or x IN (...) constraints.
    */
    flags = 0;
................................................................................
      pTerm = findTerm(pWC, iCur, j, notReady, WO_EQ|WO_IN, pProbe);
      if( pTerm==0 ) break;
      flags |= WHERE_COLUMN_EQ;
      if( pTerm->operator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        flags |= WHERE_COLUMN_IN;
        if( pExpr->pSelect!=0 ){
          inMultiplier *= 100;
        }else if( pExpr->pList!=0 ){
          inMultiplier *= pExpr->pList->nExpr + 1;
        }
      }
    }
    cost = pProbe->aiRowEst[i] * inMultiplier * estLog(inMultiplier);
    nEq = i;
    if( pProbe->onError!=OE_None && (flags & WHERE_COLUMN_IN)==0
         && nEq==pProbe->nColumn ){
................................................................................
    if( nEq<pProbe->nColumn ){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pProbe);
      if( pTerm ){
        flags |= WHERE_COLUMN_RANGE;
        if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE, pProbe) ){
          flags |= WHERE_TOP_LIMIT;
          cost /= 3;
        }
        if( findTerm(pWC, iCur, j, notReady, WO_GT|WO_GE, pProbe) ){
          flags |= WHERE_BTM_LIMIT;
          cost /= 3;
        }
        TRACE(("...... range reduces cost to %.9g\n", cost));
      }
    }

    /* Add the additional cost of sorting if that is a factor.
    */
................................................................................
        int x = pProbe->aiColumn[j];
        if( x<BMS-1 ){
          m &= ~(((Bitmask)1)<<x);
        }
      }
      if( m==0 ){
        flags |= WHERE_IDX_ONLY;
        cost /= 2;
        TRACE(("...... idx-only reduces cost to %.9g\n", cost));
      }
    }

    /* If this index has achieved the lowest cost so far, then use it.
    */
    if( cost < lowestCost ){
................................................................................
    int flags;                  /* Flags asssociated with pIdx */
    int nEq;                    /* Number of == or IN constraints */
    double cost;                /* The cost for pIdx */
    int j;                      /* For looping over FROM tables */
    Index *pBest = 0;           /* The best index seen so far */
    int bestFlags = 0;          /* Flags associated with pBest */
    int bestNEq = 0;            /* nEq associated with pBest */
    double lowestCost;          /* Cost of the pBest */
    int bestJ;                  /* The value of j */
    Bitmask m;                  /* Bitmask value for j or bestJ */

    lowestCost = SQLITE_BIG_DBL;
    for(j=iFrom, pTabItem=&pTabList->a[j]; j<pTabList->nSrc; j++, pTabItem++){
      m = getMask(&maskSet, pTabItem->iCursor);
      if( (m & notReady)==0 ){
        if( j==iFrom ) iFrom++;
        continue;
      }
      cost = bestIndex(pParse, &wc, pTabItem, notReady,