[sql] Import reference version of SQLite 3.17..

third_party/sqlite/sqlite-src-3170000/src/util.c

+/*
+** 2001 September 15
+**
+** The author disclaims copyright to this source code.  In place of
+** a legal notice, here is a blessing:
+**
+**    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.
+**
+*************************************************************************
+** Utility functions used throughout sqlite.
+**
+** This file contains functions for allocating memory, comparing
+** strings, and stuff like that.
+**
+*/
+#include "sqliteInt.h"
+#include <stdarg.h>
+#if HAVE_ISNAN || SQLITE_HAVE_ISNAN
+# include <math.h>
+#endif
+
+/*
+** Routine needed to support the testcase() macro.
+*/
+#ifdef SQLITE_COVERAGE_TEST
+void sqlite3Coverage(int x){
+  static unsigned dummy = 0;
+  dummy += (unsigned)x;
+}
+#endif
+
+/*
+** Give a callback to the test harness that can be used to simulate faults
+** in places where it is difficult or expensive to do so purely by means
+** of inputs.
+**
+** The intent of the integer argument is to let the fault simulator know
+** which of multiple sqlite3FaultSim() calls has been hit.
+**
+** Return whatever integer value the test callback returns, or return
+** SQLITE_OK if no test callback is installed.
+*/
+#ifndef SQLITE_UNTESTABLE
+int sqlite3FaultSim(int iTest){
+  int (*xCallback)(int) = sqlite3GlobalConfig.xTestCallback;
+  return xCallback ? xCallback(iTest) : SQLITE_OK;
+}
+#endif
+
+#ifndef SQLITE_OMIT_FLOATING_POINT
+/*
+** Return true if the floating point value is Not a Number (NaN).
+**
+** Use the math library isnan() function if compiled with SQLITE_HAVE_ISNAN.
+** Otherwise, we have our own implementation that works on most systems.
+*/
+int sqlite3IsNaN(double x){
+  int rc;   /* The value return */
+#if !SQLITE_HAVE_ISNAN && !HAVE_ISNAN
+  /*
+  ** Systems that support the isnan() library function should probably
+  ** make use of it by compiling with -DSQLITE_HAVE_ISNAN.  But we have
+  ** found that many systems do not have a working isnan() function so
+  ** this implementation is provided as an alternative.
+  **
+  ** This NaN test sometimes fails if compiled on GCC with -ffast-math.
+  ** On the other hand, the use of -ffast-math comes with the following
+  ** warning:
+  **
+  **      This option [-ffast-math] should never be turned on by any
+  **      -O option since it can result in incorrect output for programs
+  **      which depend on an exact implementation of IEEE or ISO 
+  **      rules/specifications for math functions.
+  **
+  ** Under MSVC, this NaN test may fail if compiled with a floating-
+  ** point precision mode other than /fp:precise.  From the MSDN 
+  ** documentation:
+  **
+  **      The compiler [with /fp:precise] will properly handle comparisons 
+  **      involving NaN. For example, x != x evaluates to true if x is NaN 
+  **      ...
+  */
+#ifdef __FAST_MATH__
+# error SQLite will not work correctly with the -ffast-math option of GCC.
+#endif
+  volatile double y = x;
+  volatile double z = y;
+  rc = (y!=z);
+#else  /* if HAVE_ISNAN */
+  rc = isnan(x);
+#endif /* HAVE_ISNAN */
+  testcase( rc );
+  return rc;
+}
+#endif /* SQLITE_OMIT_FLOATING_POINT */
+
+/*
+** Compute a string length that is limited to what can be stored in
+** lower 30 bits of a 32-bit signed integer.
+**
+** The value returned will never be negative.  Nor will it ever be greater
+** than the actual length of the string.  For very long strings (greater
+** than 1GiB) the value returned might be less than the true string length.
+*/
+int sqlite3Strlen30(const char *z){
+  if( z==0 ) return 0;
+  return 0x3fffffff & (int)strlen(z);
+}
+
+/*
+** Return the declared type of a column.  Or return zDflt if the column 
+** has no declared type.
+**
+** The column type is an extra string stored after the zero-terminator on
+** the column name if and only if the COLFLAG_HASTYPE flag is set.
+*/
+char *sqlite3ColumnType(Column *pCol, char *zDflt){
+  if( (pCol->colFlags & COLFLAG_HASTYPE)==0 ) return zDflt;
+  return pCol->zName + strlen(pCol->zName) + 1;
+}
+
+/*
+** Helper function for sqlite3Error() - called rarely.  Broken out into
+** a separate routine to avoid unnecessary register saves on entry to
+** sqlite3Error().
+*/
+static SQLITE_NOINLINE void  sqlite3ErrorFinish(sqlite3 *db, int err_code){
+  if( db->pErr ) sqlite3ValueSetNull(db->pErr);
+  sqlite3SystemError(db, err_code);
+}
+
+/*
+** Set the current error code to err_code and clear any prior error message.
+** Also set iSysErrno (by calling sqlite3System) if the err_code indicates
+** that would be appropriate.
+*/
+void sqlite3Error(sqlite3 *db, int err_code){
+  assert( db!=0 );
+  db->errCode = err_code;
+  if( err_code || db->pErr ) sqlite3ErrorFinish(db, err_code);
+}
+
+/*
+** Load the sqlite3.iSysErrno field if that is an appropriate thing
+** to do based on the SQLite error code in rc.
+*/
+void sqlite3SystemError(sqlite3 *db, int rc){
+  if( rc==SQLITE_IOERR_NOMEM ) return;
+  rc &= 0xff;
+  if( rc==SQLITE_CANTOPEN || rc==SQLITE_IOERR ){
+    db->iSysErrno = sqlite3OsGetLastError(db->pVfs);
+  }
+}
+
+/*
+** Set the most recent error code and error string for the sqlite
+** handle "db". The error code is set to "err_code".
+**
+** If it is not NULL, string zFormat specifies the format of the
+** error string in the style of the printf functions: The following
+** format characters are allowed:
+**
+**      %s      Insert a string
+**      %z      A string that should be freed after use
+**      %d      Insert an integer
+**      %T      Insert a token
+**      %S      Insert the first element of a SrcList
+**
+** zFormat and any string tokens that follow it are assumed to be
+** encoded in UTF-8.
+**
+** To clear the most recent error for sqlite handle "db", sqlite3Error
+** should be called with err_code set to SQLITE_OK and zFormat set
+** to NULL.
+*/
+void sqlite3ErrorWithMsg(sqlite3 *db, int err_code, const char *zFormat, ...){
+  assert( db!=0 );
+  db->errCode = err_code;
+  sqlite3SystemError(db, err_code);
+  if( zFormat==0 ){
+    sqlite3Error(db, err_code);
+  }else if( db->pErr || (db->pErr = sqlite3ValueNew(db))!=0 ){
+    char *z;
+    va_list ap;
+    va_start(ap, zFormat);
+    z = sqlite3VMPrintf(db, zFormat, ap);
+    va_end(ap);
+    sqlite3ValueSetStr(db->pErr, -1, z, SQLITE_UTF8, SQLITE_DYNAMIC);
+  }
+}
+
+/*
+** Add an error message to pParse->zErrMsg and increment pParse->nErr.
+** The following formatting characters are allowed:
+**
+**      %s      Insert a string
+**      %z      A string that should be freed after use
+**      %d      Insert an integer
+**      %T      Insert a token
+**      %S      Insert the first element of a SrcList
+**
+** This function should be used to report any error that occurs while
+** compiling an SQL statement (i.e. within sqlite3_prepare()). The
+** last thing the sqlite3_prepare() function does is copy the error
+** stored by this function into the database handle using sqlite3Error().
+** Functions sqlite3Error() or sqlite3ErrorWithMsg() should be used
+** during statement execution (sqlite3_step() etc.).
+*/
+void sqlite3ErrorMsg(Parse *pParse, const char *zFormat, ...){
+  char *zMsg;
+  va_list ap;
+  sqlite3 *db = pParse->db;
+  va_start(ap, zFormat);
+  zMsg = sqlite3VMPrintf(db, zFormat, ap);
+  va_end(ap);
+  if( db->suppressErr ){
+    sqlite3DbFree(db, zMsg);
+  }else{
+    pParse->nErr++;
+    sqlite3DbFree(db, pParse->zErrMsg);
+    pParse->zErrMsg = zMsg;
+    pParse->rc = SQLITE_ERROR;
+  }
+}
+
+/*
+** Convert an SQL-style quoted string into a normal string by removing
+** the quote characters.  The conversion is done in-place.  If the
+** input does not begin with a quote character, then this routine
+** is a no-op.
+**
+** The input string must be zero-terminated.  A new zero-terminator
+** is added to the dequoted string.
+**
+** The return value is -1 if no dequoting occurs or the length of the
+** dequoted string, exclusive of the zero terminator, if dequoting does
+** occur.
+**
+** 2002-Feb-14: This routine is extended to remove MS-Access style
+** brackets from around identifiers.  For example:  "[a-b-c]" becomes
+** "a-b-c".
+*/
+void sqlite3Dequote(char *z){
+  char quote;
+  int i, j;
+  if( z==0 ) return;
+  quote = z[0];
+  if( !sqlite3Isquote(quote) ) return;
+  if( quote=='[' ) quote = ']';
+  for(i=1, j=0;; i++){
+    assert( z[i] );
+    if( z[i]==quote ){
+      if( z[i+1]==quote ){
+        z[j++] = quote;
+        i++;
+      }else{
+        break;
+      }
+    }else{
+      z[j++] = z[i];
+    }
+  }
+  z[j] = 0;
+}
+
+/*
+** Generate a Token object from a string
+*/
+void sqlite3TokenInit(Token *p, char *z){
+  p->z = z;
+  p->n = sqlite3Strlen30(z);
+}
+
+/* Convenient short-hand */
+#define UpperToLower sqlite3UpperToLower
+
+/*
+** Some systems have stricmp().  Others have strcasecmp().  Because
+** there is no consistency, we will define our own.
+**
+** IMPLEMENTATION-OF: R-30243-02494 The sqlite3_stricmp() and
+** sqlite3_strnicmp() APIs allow applications and extensions to compare
+** the contents of two buffers containing UTF-8 strings in a
+** case-independent fashion, using the same definition of "case
+** independence" that SQLite uses internally when comparing identifiers.
+*/
+int sqlite3_stricmp(const char *zLeft, const char *zRight){
+  if( zLeft==0 ){
+    return zRight ? -1 : 0;
+  }else if( zRight==0 ){
+    return 1;
+  }
+  return sqlite3StrICmp(zLeft, zRight);
+}
+int sqlite3StrICmp(const char *zLeft, const char *zRight){
+  unsigned char *a, *b;
+  int c;
+  a = (unsigned char *)zLeft;
+  b = (unsigned char *)zRight;
+  for(;;){
+    c = (int)UpperToLower[*a] - (int)UpperToLower[*b];
+    if( c || *a==0 ) break;
+    a++;
+    b++;
+  }
+  return c;
+}
+int sqlite3_strnicmp(const char *zLeft, const char *zRight, int N){
+  register unsigned char *a, *b;
+  if( zLeft==0 ){
+    return zRight ? -1 : 0;
+  }else if( zRight==0 ){
+    return 1;
+  }
+  a = (unsigned char *)zLeft;
+  b = (unsigned char *)zRight;
+  while( N-- > 0 && *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
+  return N<0 ? 0 : UpperToLower[*a] - UpperToLower[*b];
+}
+
+/*
+** The string z[] is an text representation of a real number.
+** Convert this string to a double and write it into *pResult.
+**
+** The string z[] is length bytes in length (bytes, not characters) and
+** uses the encoding enc.  The string is not necessarily zero-terminated.
+**
+** Return TRUE if the result is a valid real number (or integer) and FALSE
+** if the string is empty or contains extraneous text.  Valid numbers
+** are in one of these formats:
+**
+**    [+-]digits[E[+-]digits]
+**    [+-]digits.[digits][E[+-]digits]
+**    [+-].digits[E[+-]digits]
+**
+** Leading and trailing whitespace is ignored for the purpose of determining
+** validity.
+**
+** If some prefix of the input string is a valid number, this routine
+** returns FALSE but it still converts the prefix and writes the result
+** into *pResult.
+*/
+int sqlite3AtoF(const char *z, double *pResult, int length, u8 enc){
+#ifndef SQLITE_OMIT_FLOATING_POINT
+  int incr;
+  const char *zEnd = z + length;
+  /* sign * significand * (10 ^ (esign * exponent)) */
+  int sign = 1;    /* sign of significand */
+  i64 s = 0;       /* significand */
+  int d = 0;       /* adjust exponent for shifting decimal point */
+  int esign = 1;   /* sign of exponent */
+  int e = 0;       /* exponent */
+  int eValid = 1;  /* True exponent is either not used or is well-formed */
+  double result;
+  int nDigits = 0;
+  int nonNum = 0;  /* True if input contains UTF16 with high byte non-zero */
+
+  assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
+  *pResult = 0.0;   /* Default return value, in case of an error */
+
+  if( enc==SQLITE_UTF8 ){
+    incr = 1;
+  }else{
+    int i;
+    incr = 2;
+    assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
+    for(i=3-enc; i<length && z[i]==0; i+=2){}
+    nonNum = i<length;
+    zEnd = &z[i^1];
+    z += (enc&1);
+  }
+
+  /* skip leading spaces */
+  while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
+  if( z>=zEnd ) return 0;
+
+  /* get sign of significand */
+  if( *z=='-' ){
+    sign = -1;
+    z+=incr;
+  }else if( *z=='+' ){
+    z+=incr;
+  }
+
+  /* copy max significant digits to significand */
+  while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
+    s = s*10 + (*z - '0');
+    z+=incr, nDigits++;
+  }
+
+  /* skip non-significant significand digits
+  ** (increase exponent by d to shift decimal left) */
+  while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++, d++;
+  if( z>=zEnd ) goto do_atof_calc;
+
+  /* if decimal point is present */
+  if( *z=='.' ){
+    z+=incr;
+    /* copy digits from after decimal to significand
+    ** (decrease exponent by d to shift decimal right) */
+    while( z<zEnd && sqlite3Isdigit(*z) ){
+      if( s<((LARGEST_INT64-9)/10) ){
+        s = s*10 + (*z - '0');
+        d--;
+      }
+      z+=incr, nDigits++;
+    }
+  }
+  if( z>=zEnd ) goto do_atof_calc;
+
+  /* if exponent is present */
+  if( *z=='e' || *z=='E' ){
+    z+=incr;
+    eValid = 0;
+
+    /* This branch is needed to avoid a (harmless) buffer overread.  The 
+    ** special comment alerts the mutation tester that the correct answer
+    ** is obtained even if the branch is omitted */
+    if( z>=zEnd ) goto do_atof_calc;              /*PREVENTS-HARMLESS-OVERREAD*/
+
+    /* get sign of exponent */
+    if( *z=='-' ){
+      esign = -1;
+      z+=incr;
+    }else if( *z=='+' ){
+      z+=incr;
+    }
+    /* copy digits to exponent */
+    while( z<zEnd && sqlite3Isdigit(*z) ){
+      e = e<10000 ? (e*10 + (*z - '0')) : 10000;
+      z+=incr;
+      eValid = 1;
+    }
+  }
+
+  /* skip trailing spaces */
+  while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
+
+do_atof_calc:
+  /* adjust exponent by d, and update sign */
+  e = (e*esign) + d;
+  if( e<0 ) {
+    esign = -1;
+    e *= -1;
+  } else {
+    esign = 1;
+  }
+
+  if( s==0 ) {
+    /* In the IEEE 754 standard, zero is signed. */
+    result = sign<0 ? -(double)0 : (double)0;
+  } else {
+    /* Attempt to reduce exponent.
+    **
+    ** Branches that are not required for the correct answer but which only
+    ** help to obtain the correct answer faster are marked with special
+    ** comments, as a hint to the mutation tester.
+    */
+    while( e>0 ){                                       /*OPTIMIZATION-IF-TRUE*/
+      if( esign>0 ){
+        if( s>=(LARGEST_INT64/10) ) break;             /*OPTIMIZATION-IF-FALSE*/
+        s *= 10;
+      }else{
+        if( s%10!=0 ) break;                           /*OPTIMIZATION-IF-FALSE*/
+        s /= 10;
+      }
+      e--;
+    }
+
+    /* adjust the sign of significand */
+    s = sign<0 ? -s : s;
+
+    if( e==0 ){                                         /*OPTIMIZATION-IF-TRUE*/
+      result = (double)s;
+    }else{
+      LONGDOUBLE_TYPE scale = 1.0;
+      /* attempt to handle extremely small/large numbers better */
+      if( e>307 ){                                      /*OPTIMIZATION-IF-TRUE*/
+        if( e<342 ){                                    /*OPTIMIZATION-IF-TRUE*/
+          while( e%308 ) { scale *= 1.0e+1; e -= 1; }
+          if( esign<0 ){
+            result = s / scale;
+            result /= 1.0e+308;
+          }else{
+            result = s * scale;
+            result *= 1.0e+308;
+          }
+        }else{ assert( e>=342 );
+          if( esign<0 ){
+            result = 0.0*s;
+          }else{
+            result = 1e308*1e308*s;  /* Infinity */
+          }
+        }
+      }else{
+        /* 1.0e+22 is the largest power of 10 than can be 
+        ** represented exactly. */
+        while( e%22 ) { scale *= 1.0e+1; e -= 1; }
+        while( e>0 ) { scale *= 1.0e+22; e -= 22; }
+        if( esign<0 ){
+          result = s / scale;
+        }else{
+          result = s * scale;
+        }
+      }
+    }
+  }
+
+  /* store the result */
+  *pResult = result;
+
+  /* return true if number and no extra non-whitespace chracters after */
+  return z==zEnd && nDigits>0 && eValid && nonNum==0;
+#else
+  return !sqlite3Atoi64(z, pResult, length, enc);
+#endif /* SQLITE_OMIT_FLOATING_POINT */
+}
+
+/*
+** Compare the 19-character string zNum against the text representation
+** value 2^63:  9223372036854775808.  Return negative, zero, or positive
+** if zNum is less than, equal to, or greater than the string.
+** Note that zNum must contain exactly 19 characters.
+**
+** Unlike memcmp() this routine is guaranteed to return the difference
+** in the values of the last digit if the only difference is in the
+** last digit.  So, for example,
+**
+**      compare2pow63("9223372036854775800", 1)
+**
+** will return -8.
+*/
+static int compare2pow63(const char *zNum, int incr){
+  int c = 0;
+  int i;
+                    /* 012345678901234567 */
+  const char *pow63 = "922337203685477580";
+  for(i=0; c==0 && i<18; i++){
+    c = (zNum[i*incr]-pow63[i])*10;
+  }
+  if( c==0 ){
+    c = zNum[18*incr] - '8';
+    testcase( c==(-1) );
+    testcase( c==0 );
+    testcase( c==(+1) );
+  }
+  return c;
+}
+
+/*
+** Convert zNum to a 64-bit signed integer.  zNum must be decimal. This
+** routine does *not* accept hexadecimal notation.
+**
+** If the zNum value is representable as a 64-bit twos-complement 
+** integer, then write that value into *pNum and return 0.
+**
+** If zNum is exactly 9223372036854775808, return 2.  This special
+** case is broken out because while 9223372036854775808 cannot be a 
+** signed 64-bit integer, its negative -9223372036854775808 can be.
+**
+** If zNum is too big for a 64-bit integer and is not
+** 9223372036854775808  or if zNum contains any non-numeric text,
+** then return 1.
+**
+** length is the number of bytes in the string (bytes, not characters).
+** The string is not necessarily zero-terminated.  The encoding is
+** given by enc.
+*/
+int sqlite3Atoi64(const char *zNum, i64 *pNum, int length, u8 enc){
+  int incr;
+  u64 u = 0;
+  int neg = 0; /* assume positive */
+  int i;
+  int c = 0;
+  int nonNum = 0;  /* True if input contains UTF16 with high byte non-zero */
+  const char *zStart;
+  const char *zEnd = zNum + length;
+  assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
+  if( enc==SQLITE_UTF8 ){
+    incr = 1;
+  }else{
+    incr = 2;
+    assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
+    for(i=3-enc; i<length && zNum[i]==0; i+=2){}
+    nonNum = i<length;
+    zEnd = &zNum[i^1];
+    zNum += (enc&1);
+  }
+  while( zNum<zEnd && sqlite3Isspace(*zNum) ) zNum+=incr;
+  if( zNum<zEnd ){
+    if( *zNum=='-' ){
+      neg = 1;
+      zNum+=incr;
+    }else if( *zNum=='+' ){
+      zNum+=incr;
+    }
+  }
+  zStart = zNum;
+  while( zNum<zEnd && zNum[0]=='0' ){ zNum+=incr; } /* Skip leading zeros. */
+  for(i=0; &zNum[i]<zEnd && (c=zNum[i])>='0' && c<='9'; i+=incr){
+    u = u*10 + c - '0';
+  }
+  if( u>LARGEST_INT64 ){
+    *pNum = neg ? SMALLEST_INT64 : LARGEST_INT64;
+  }else if( neg ){
+    *pNum = -(i64)u;
+  }else{
+    *pNum = (i64)u;
+  }
+  testcase( i==18 );
+  testcase( i==19 );
+  testcase( i==20 );
+  if( &zNum[i]<zEnd              /* Extra bytes at the end */
+   || (i==0 && zStart==zNum)     /* No digits */
+   || i>19*incr                  /* Too many digits */
+   || nonNum                     /* UTF16 with high-order bytes non-zero */
+  ){
+    /* zNum is empty or contains non-numeric text or is longer
+    ** than 19 digits (thus guaranteeing that it is too large) */
+    return 1;
+  }else if( i<19*incr ){
+    /* Less than 19 digits, so we know that it fits in 64 bits */
+    assert( u<=LARGEST_INT64 );
+    return 0;
+  }else{
+    /* zNum is a 19-digit numbers.  Compare it against 9223372036854775808. */
+    c = compare2pow63(zNum, incr);
+    if( c<0 ){
+      /* zNum is less than 9223372036854775808 so it fits */
+      assert( u<=LARGEST_INT64 );
+      return 0;
+    }else if( c>0 ){
+      /* zNum is greater than 9223372036854775808 so it overflows */
+      return 1;
+    }else{
+      /* zNum is exactly 9223372036854775808.  Fits if negative.  The
+      ** special case 2 overflow if positive */
+      assert( u-1==LARGEST_INT64 );
+      return neg ? 0 : 2;
+    }
+  }
+}
+
+/*
+** Transform a UTF-8 integer literal, in either decimal or hexadecimal,
+** into a 64-bit signed integer.  This routine accepts hexadecimal literals,
+** whereas sqlite3Atoi64() does not.
+**
+** Returns:
+**
+**     0    Successful transformation.  Fits in a 64-bit signed integer.
+**     1    Integer too large for a 64-bit signed integer or is malformed
+**     2    Special case of 9223372036854775808
+*/
+int sqlite3DecOrHexToI64(const char *z, i64 *pOut){
+#ifndef SQLITE_OMIT_HEX_INTEGER
+  if( z[0]=='0'
+   && (z[1]=='x' || z[1]=='X')
+  ){
+    u64 u = 0;
+    int i, k;
+    for(i=2; z[i]=='0'; i++){}
+    for(k=i; sqlite3Isxdigit(z[k]); k++){
+      u = u*16 + sqlite3HexToInt(z[k]);
+    }
+    memcpy(pOut, &u, 8);
+    return (z[k]==0 && k-i<=16) ? 0 : 1;
+  }else
+#endif /* SQLITE_OMIT_HEX_INTEGER */
+  {
+    return sqlite3Atoi64(z, pOut, sqlite3Strlen30(z), SQLITE_UTF8);
+  }
+}
+
+/*
+** If zNum represents an integer that will fit in 32-bits, then set
+** *pValue to that integer and return true.  Otherwise return false.
+**
+** This routine accepts both decimal and hexadecimal notation for integers.
+**
+** Any non-numeric characters that following zNum are ignored.
+** This is different from sqlite3Atoi64() which requires the
+** input number to be zero-terminated.
+*/
+int sqlite3GetInt32(const char *zNum, int *pValue){
+  sqlite_int64 v = 0;
+  int i, c;
+  int neg = 0;
+  if( zNum[0]=='-' ){
+    neg = 1;
+    zNum++;
+  }else if( zNum[0]=='+' ){
+    zNum++;
+  }
+#ifndef SQLITE_OMIT_HEX_INTEGER
+  else if( zNum[0]=='0'
+        && (zNum[1]=='x' || zNum[1]=='X')
+        && sqlite3Isxdigit(zNum[2])
+  ){
+    u32 u = 0;
+    zNum += 2;
+    while( zNum[0]=='0' ) zNum++;
+    for(i=0; sqlite3Isxdigit(zNum[i]) && i<8; i++){
+      u = u*16 + sqlite3HexToInt(zNum[i]);
+    }
+    if( (u&0x80000000)==0 && sqlite3Isxdigit(zNum[i])==0 ){
+      memcpy(pValue, &u, 4);
+      return 1;
+    }else{
+      return 0;
+    }
+  }
+#endif
+  while( zNum[0]=='0' ) zNum++;
+  for(i=0; i<11 && (c = zNum[i] - '0')>=0 && c<=9; i++){
+    v = v*10 + c;
+  }
+
+  /* The longest decimal representation of a 32 bit integer is 10 digits:
+  **
+  **             1234567890
+  **     2^31 -> 2147483648
+  */
+  testcase( i==10 );
+  if( i>10 ){
+    return 0;
+  }
+  testcase( v-neg==2147483647 );
+  if( v-neg>2147483647 ){
+    return 0;
+  }
+  if( neg ){
+    v = -v;
+  }
+  *pValue = (int)v;
+  return 1;
+}
+
+/*
+** Return a 32-bit integer value extracted from a string.  If the
+** string is not an integer, just return 0.
+*/
+int sqlite3Atoi(const char *z){
+  int x = 0;
+  if( z ) sqlite3GetInt32(z, &x);
+  return x;
+}
+
+/*
+** The variable-length integer encoding is as follows:
+**
+** KEY:
+**         A = 0xxxxxxx    7 bits of data and one flag bit
+**         B = 1xxxxxxx    7 bits of data and one flag bit
+**         C = xxxxxxxx    8 bits of data
+**
+**  7 bits - A
+** 14 bits - BA
+** 21 bits - BBA
+** 28 bits - BBBA
+** 35 bits - BBBBA
+** 42 bits - BBBBBA
+** 49 bits - BBBBBBA
+** 56 bits - BBBBBBBA
+** 64 bits - BBBBBBBBC
+*/
+
+/*
+** Write a 64-bit variable-length integer to memory starting at p[0].
+** The length of data write will be between 1 and 9 bytes.  The number
+** of bytes written is returned.
+**
+** A variable-length integer consists of the lower 7 bits of each byte
+** for all bytes that have the 8th bit set and one byte with the 8th
+** bit clear.  Except, if we get to the 9th byte, it stores the full
+** 8 bits and is the last byte.
+*/
+static int SQLITE_NOINLINE putVarint64(unsigned char *p, u64 v){
+  int i, j, n;
+  u8 buf[10];
+  if( v & (((u64)0xff000000)<<32) ){
+    p[8] = (u8)v;
+    v >>= 8;
+    for(i=7; i>=0; i--){
+      p[i] = (u8)((v & 0x7f) | 0x80);
+      v >>= 7;
+    }
+    return 9;
+  }    
+  n = 0;
+  do{
+    buf[n++] = (u8)((v & 0x7f) | 0x80);
+    v >>= 7;
+  }while( v!=0 );
+  buf[0] &= 0x7f;
+  assert( n<=9 );
+  for(i=0, j=n-1; j>=0; j--, i++){
+    p[i] = buf[j];
+  }
+  return n;
+}
+int sqlite3PutVarint(unsigned char *p, u64 v){
+  if( v<=0x7f ){
+    p[0] = v&0x7f;
+    return 1;
+  }
+  if( v<=0x3fff ){
+    p[0] = ((v>>7)&0x7f)|0x80;
+    p[1] = v&0x7f;
+    return 2;
+  }
+  return putVarint64(p,v);
+}
+
+/*
+** Bitmasks used by sqlite3GetVarint().  These precomputed constants
+** are defined here rather than simply putting the constant expressions
+** inline in order to work around bugs in the RVT compiler.
+**
+** SLOT_2_0     A mask for  (0x7f<<14) | 0x7f
+**
+** SLOT_4_2_0   A mask for  (0x7f<<28) | SLOT_2_0
+*/
+#define SLOT_2_0     0x001fc07f
+#define SLOT_4_2_0   0xf01fc07f
+
+
+/*
+** Read a 64-bit variable-length integer from memory starting at p[0].
+** Return the number of bytes read.  The value is stored in *v.
+*/
+u8 sqlite3GetVarint(const unsigned char *p, u64 *v){
+  u32 a,b,s;
+
+  a = *p;
+  /* a: p0 (unmasked) */
+  if (!(a&0x80))
+  {
+    *v = a;
+    return 1;
+  }
+
+  p++;
+  b = *p;
+  /* b: p1 (unmasked) */
+  if (!(b&0x80))
+  {
+    a &= 0x7f;
+    a = a<<7;
+    a |= b;
+    *v = a;
+    return 2;
+  }
+
+  /* Verify that constants are precomputed correctly */
+  assert( SLOT_2_0 == ((0x7f<<14) | (0x7f)) );
+  assert( SLOT_4_2_0 == ((0xfU<<28) | (0x7f<<14) | (0x7f)) );
+
+  p++;
+  a = a<<14;
+  a |= *p;
+  /* a: p0<<14 | p2 (unmasked) */
+  if (!(a&0x80))
+  {
+    a &= SLOT_2_0;
+    b &= 0x7f;
+    b = b<<7;
+    a |= b;
+    *v = a;
+    return 3;
+  }
+
+  /* CSE1 from below */
+  a &= SLOT_2_0;
+  p++;
+  b = b<<14;
+  b |= *p;
+  /* b: p1<<14 | p3 (unmasked) */
+  if (!(b&0x80))
+  {
+    b &= SLOT_2_0;
+    /* moved CSE1 up */
+    /* a &= (0x7f<<14)|(0x7f); */
+    a = a<<7;
+    a |= b;
+    *v = a;
+    return 4;
+  }
+
+  /* a: p0<<14 | p2 (masked) */
+  /* b: p1<<14 | p3 (unmasked) */
+  /* 1:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
+  /* moved CSE1 up */
+  /* a &= (0x7f<<14)|(0x7f); */
+  b &= SLOT_2_0;
+  s = a;
+  /* s: p0<<14 | p2 (masked) */
+
+  p++;
+  a = a<<14;
+  a |= *p;
+  /* a: p0<<28 | p2<<14 | p4 (unmasked) */
+  if (!(a&0x80))
+  {
+    /* we can skip these cause they were (effectively) done above
+    ** while calculating s */
+    /* a &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
+    /* b &= (0x7f<<14)|(0x7f); */
+    b = b<<7;
+    a |= b;
+    s = s>>18;
+    *v = ((u64)s)<<32 | a;
+    return 5;
+  }
+
+  /* 2:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
+  s = s<<7;
+  s |= b;
+  /* s: p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
+
+  p++;
+  b = b<<14;
+  b |= *p;
+  /* b: p1<<28 | p3<<14 | p5 (unmasked) */
+  if (!(b&0x80))
+  {
+    /* we can skip this cause it was (effectively) done above in calc'ing s */
+    /* b &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
+    a &= SLOT_2_0;
+    a = a<<7;
+    a |= b;
+    s = s>>18;
+    *v = ((u64)s)<<32 | a;
+    return 6;
+  }
+
+  p++;
+  a = a<<14;
+  a |= *p;
+  /* a: p2<<28 | p4<<14 | p6 (unmasked) */
+  if (!(a&0x80))
+  {
+    a &= SLOT_4_2_0;
+    b &= SLOT_2_0;
+    b = b<<7;
+    a |= b;
+    s = s>>11;
+    *v = ((u64)s)<<32 | a;
+    return 7;
+  }
+
+  /* CSE2 from below */
+  a &= SLOT_2_0;
+  p++;
+  b = b<<14;
+  b |= *p;
+  /* b: p3<<28 | p5<<14 | p7 (unmasked) */
+  if (!(b&0x80))
+  {
+    b &= SLOT_4_2_0;
+    /* moved CSE2 up */
+    /* a &= (0x7f<<14)|(0x7f); */
+    a = a<<7;
+    a |= b;
+    s = s>>4;
+    *v = ((u64)s)<<32 | a;
+    return 8;
+  }
+
+  p++;
+  a = a<<15;
+  a |= *p;
+  /* a: p4<<29 | p6<<15 | p8 (unmasked) */
+
+  /* moved CSE2 up */
+  /* a &= (0x7f<<29)|(0x7f<<15)|(0xff); */
+  b &= SLOT_2_0;
+  b = b<<8;
+  a |= b;
+
+  s = s<<4;
+  b = p[-4];
+  b &= 0x7f;
+  b = b>>3;
+  s |= b;
+
+  *v = ((u64)s)<<32 | a;
+
+  return 9;
+}
+
+/*
+** Read a 32-bit variable-length integer from memory starting at p[0].
+** Return the number of bytes read.  The value is stored in *v.
+**
+** If the varint stored in p[0] is larger than can fit in a 32-bit unsigned
+** integer, then set *v to 0xffffffff.
+**
+** A MACRO version, getVarint32, is provided which inlines the 
+** single-byte case.  All code should use the MACRO version as 
+** this function assumes the single-byte case has already been handled.
+*/
+u8 sqlite3GetVarint32(const unsigned char *p, u32 *v){
+  u32 a,b;
+
+  /* The 1-byte case.  Overwhelmingly the most common.  Handled inline
+  ** by the getVarin32() macro */
+  a = *p;
+  /* a: p0 (unmasked) */
+#ifndef getVarint32
+  if (!(a&0x80))
+  {
+    /* Values between 0 and 127 */
+    *v = a;
+    return 1;
+  }
+#endif
+
+  /* The 2-byte case */
+  p++;
+  b = *p;
+  /* b: p1 (unmasked) */
+  if (!(b&0x80))
+  {
+    /* Values between 128 and 16383 */
+    a &= 0x7f;
+    a = a<<7;
+    *v = a | b;
+    return 2;
+  }
+
+  /* The 3-byte case */
+  p++;
+  a = a<<14;
+  a |= *p;
+  /* a: p0<<14 | p2 (unmasked) */
+  if (!(a&0x80))
+  {
+    /* Values between 16384 and 2097151 */
+    a &= (0x7f<<14)|(0x7f);
+    b &= 0x7f;
+    b = b<<7;
+    *v = a | b;
+    return 3;
+  }
+
+  /* A 32-bit varint is used to store size information in btrees.
+  ** Objects are rarely larger than 2MiB limit of a 3-byte varint.
+  ** A 3-byte varint is sufficient, for example, to record the size
+  ** of a 1048569-byte BLOB or string.
+  **
+  ** We only unroll the first 1-, 2-, and 3- byte cases.  The very
+  ** rare larger cases can be handled by the slower 64-bit varint
+  ** routine.
+  */
+#if 1
+  {
+    u64 v64;
+    u8 n;
+
+    p -= 2;
+    n = sqlite3GetVarint(p, &v64);
+    assert( n>3 && n<=9 );
+    if( (v64 & SQLITE_MAX_U32)!=v64 ){
+      *v = 0xffffffff;
+    }else{
+      *v = (u32)v64;
+    }
+    return n;
+  }
+
+#else
+  /* For following code (kept for historical record only) shows an
+  ** unrolling for the 3- and 4-byte varint cases.  This code is
+  ** slightly faster, but it is also larger and much harder to test.
+  */
+  p++;
+  b = b<<14;
+  b |= *p;
+  /* b: p1<<14 | p3 (unmasked) */
+  if (!(b&0x80))
+  {
+    /* Values between 2097152 and 268435455 */
+    b &= (0x7f<<14)|(0x7f);
+    a &= (0x7f<<14)|(0x7f);
+    a = a<<7;
+    *v = a | b;
+    return 4;
+  }
+
+  p++;
+  a = a<<14;
+  a |= *p;
+  /* a: p0<<28 | p2<<14 | p4 (unmasked) */
+  if (!(a&0x80))
+  {
+    /* Values  between 268435456 and 34359738367 */
+    a &= SLOT_4_2_0;
+    b &= SLOT_4_2_0;
+    b = b<<7;
+    *v = a | b;
+    return 5;
+  }
+
+  /* We can only reach this point when reading a corrupt database
+  ** file.  In that case we are not in any hurry.  Use the (relatively
+  ** slow) general-purpose sqlite3GetVarint() routine to extract the
+  ** value. */
+  {
+    u64 v64;
+    u8 n;
+
+    p -= 4;
+    n = sqlite3GetVarint(p, &v64);
+    assert( n>5 && n<=9 );
+    *v = (u32)v64;
+    return n;
+  }
+#endif
+}
+
+/*
+** Return the number of bytes that will be needed to store the given
+** 64-bit integer.
+*/
+int sqlite3VarintLen(u64 v){
+  int i;
+  for(i=1; (v >>= 7)!=0; i++){ assert( i<10 ); }
+  return i;
+}
+
+
+/*
+** Read or write a four-byte big-endian integer value.
+*/
+u32 sqlite3Get4byte(const u8 *p){
+#if SQLITE_BYTEORDER==4321
+  u32 x;
+  memcpy(&x,p,4);
+  return x;
+#elif SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+  u32 x;
+  memcpy(&x,p,4);
+  return __builtin_bswap32(x);
+#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  u32 x;
+  memcpy(&x,p,4);
+  return _byteswap_ulong(x);
+#else
+  testcase( p[0]&0x80 );
+  return ((unsigned)p[0]<<24) | (p[1]<<16) | (p[2]<<8) | p[3];
+#endif
+}
+void sqlite3Put4byte(unsigned char *p, u32 v){
+#if SQLITE_BYTEORDER==4321
+  memcpy(p,&v,4);
+#elif SQLITE_BYTEORDER==1234 && (GCC_VERSION>=4003000 || CLANG_VERSION>=3000000)
+  u32 x = __builtin_bswap32(v);
+  memcpy(p,&x,4);
+#elif SQLITE_BYTEORDER==1234 && MSVC_VERSION>=1300
+  u32 x = _byteswap_ulong(v);
+  memcpy(p,&x,4);
+#else
+  p[0] = (u8)(v>>24);
+  p[1] = (u8)(v>>16);
+  p[2] = (u8)(v>>8);
+  p[3] = (u8)v;
+#endif
+}
+
+
+
+/*
+** Translate a single byte of Hex into an integer.
+** This routine only works if h really is a valid hexadecimal
+** character:  0..9a..fA..F
+*/
+u8 sqlite3HexToInt(int h){
+  assert( (h>='0' && h<='9') ||  (h>='a' && h<='f') ||  (h>='A' && h<='F') );
+#ifdef SQLITE_ASCII
+  h += 9*(1&(h>>6));
+#endif
+#ifdef SQLITE_EBCDIC
+  h += 9*(1&~(h>>4));
+#endif
+  return (u8)(h & 0xf);
+}
+
+#if !defined(SQLITE_OMIT_BLOB_LITERAL) || defined(SQLITE_HAS_CODEC)
+/*
+** Convert a BLOB literal of the form "x'hhhhhh'" into its binary
+** value.  Return a pointer to its binary value.  Space to hold the
+** binary value has been obtained from malloc and must be freed by
+** the calling routine.
+*/
+void *sqlite3HexToBlob(sqlite3 *db, const char *z, int n){
+  char *zBlob;
+  int i;
+
+  zBlob = (char *)sqlite3DbMallocRawNN(db, n/2 + 1);
+  n--;
+  if( zBlob ){
+    for(i=0; i<n; i+=2){
+      zBlob[i/2] = (sqlite3HexToInt(z[i])<<4) | sqlite3HexToInt(z[i+1]);
+    }
+    zBlob[i/2] = 0;
+  }
+  return zBlob;
+}
+#endif /* !SQLITE_OMIT_BLOB_LITERAL || SQLITE_HAS_CODEC */
+
+/*
+** Log an error that is an API call on a connection pointer that should
+** not have been used.  The "type" of connection pointer is given as the
+** argument.  The zType is a word like "NULL" or "closed" or "invalid".
+*/
+static void logBadConnection(const char *zType){
+  sqlite3_log(SQLITE_MISUSE, 
+     "API call with %s database connection pointer",
+     zType
+  );
+}
+
+/*
+** Check to make sure we have a valid db pointer.  This test is not
+** foolproof but it does provide some measure of protection against
+** misuse of the interface such as passing in db pointers that are
+** NULL or which have been previously closed.  If this routine returns
+** 1 it means that the db pointer is valid and 0 if it should not be
+** dereferenced for any reason.  The calling function should invoke
+** SQLITE_MISUSE immediately.
+**
+** sqlite3SafetyCheckOk() requires that the db pointer be valid for
+** use.  sqlite3SafetyCheckSickOrOk() allows a db pointer that failed to
+** open properly and is not fit for general use but which can be
+** used as an argument to sqlite3_errmsg() or sqlite3_close().
+*/
+int sqlite3SafetyCheckOk(sqlite3 *db){
+  u32 magic;
+  if( db==0 ){
+    logBadConnection("NULL");
+    return 0;
+  }
+  magic = db->magic;
+  if( magic!=SQLITE_MAGIC_OPEN ){
+    if( sqlite3SafetyCheckSickOrOk(db) ){
+      testcase( sqlite3GlobalConfig.xLog!=0 );
+      logBadConnection("unopened");
+    }
+    return 0;
+  }else{
+    return 1;
+  }
+}
+int sqlite3SafetyCheckSickOrOk(sqlite3 *db){
+  u32 magic;
+  magic = db->magic;
+  if( magic!=SQLITE_MAGIC_SICK &&
+      magic!=SQLITE_MAGIC_OPEN &&
+      magic!=SQLITE_MAGIC_BUSY ){
+    testcase( sqlite3GlobalConfig.xLog!=0 );
+    logBadConnection("invalid");
+    return 0;
+  }else{
+    return 1;
+  }
+}
+
+/*
+** Attempt to add, substract, or multiply the 64-bit signed value iB against
+** the other 64-bit signed integer at *pA and store the result in *pA.
+** Return 0 on success.  Or if the operation would have resulted in an
+** overflow, leave *pA unchanged and return 1.
+*/
+int sqlite3AddInt64(i64 *pA, i64 iB){
+#if GCC_VERSION>=5004000 || CLANG_VERSION>=4000000
+  return __builtin_add_overflow(*pA, iB, pA);
+#else
+  i64 iA = *pA;
+  testcase( iA==0 ); testcase( iA==1 );
+  testcase( iB==-1 ); testcase( iB==0 );
+  if( iB>=0 ){
+    testcase( iA>0 && LARGEST_INT64 - iA == iB );
+    testcase( iA>0 && LARGEST_INT64 - iA == iB - 1 );
+    if( iA>0 && LARGEST_INT64 - iA < iB ) return 1;
+  }else{
+    testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 1 );
+    testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 2 );
+    if( iA<0 && -(iA + LARGEST_INT64) > iB + 1 ) return 1;
+  }
+  *pA += iB;
+  return 0; 
+#endif
+}
+int sqlite3SubInt64(i64 *pA, i64 iB){
+#if GCC_VERSION>=5004000 || CLANG_VERSION>=4000000
+  return __builtin_sub_overflow(*pA, iB, pA);
+#else
+  testcase( iB==SMALLEST_INT64+1 );
+  if( iB==SMALLEST_INT64 ){
+    testcase( (*pA)==(-1) ); testcase( (*pA)==0 );
+    if( (*pA)>=0 ) return 1;
+    *pA -= iB;
+    return 0;
+  }else{
+    return sqlite3AddInt64(pA, -iB);
+  }
+#endif
+}
+int sqlite3MulInt64(i64 *pA, i64 iB){
+#if GCC_VERSION>=5004000 || CLANG_VERSION>=4000000
+  return __builtin_mul_overflow(*pA, iB, pA);
+#else
+  i64 iA = *pA;
+  if( iB>0 ){
+    if( iA>LARGEST_INT64/iB ) return 1;
+    if( iA<SMALLEST_INT64/iB ) return 1;
+  }else if( iB<0 ){
+    if( iA>0 ){
+      if( iB<SMALLEST_INT64/iA ) return 1;
+    }else if( iA<0 ){
+      if( iB==SMALLEST_INT64 ) return 1;
+      if( iA==SMALLEST_INT64 ) return 1;
+      if( -iA>LARGEST_INT64/-iB ) return 1;
+    }
+  }
+  *pA = iA*iB;
+  return 0;
+#endif
+}
+
+/*
+** Compute the absolute value of a 32-bit signed integer, of possible.  Or 
+** if the integer has a value of -2147483648, return +2147483647
+*/
+int sqlite3AbsInt32(int x){
+  if( x>=0 ) return x;
+  if( x==(int)0x80000000 ) return 0x7fffffff;
+  return -x;
+}
+
+#ifdef SQLITE_ENABLE_8_3_NAMES
+/*
+** If SQLITE_ENABLE_8_3_NAMES is set at compile-time and if the database
+** filename in zBaseFilename is a URI with the "8_3_names=1" parameter and
+** if filename in z[] has a suffix (a.k.a. "extension") that is longer than
+** three characters, then shorten the suffix on z[] to be the last three
+** characters of the original suffix.
+**
+** If SQLITE_ENABLE_8_3_NAMES is set to 2 at compile-time, then always
+** do the suffix shortening regardless of URI parameter.
+**
+** Examples:
+**
+**     test.db-journal    =>   test.nal
+**     test.db-wal        =>   test.wal
+**     test.db-shm        =>   test.shm
+**     test.db-mj7f3319fa =>   test.9fa
+*/
+void sqlite3FileSuffix3(const char *zBaseFilename, char *z){
+#if SQLITE_ENABLE_8_3_NAMES<2
+  if( sqlite3_uri_boolean(zBaseFilename, "8_3_names", 0) )
+#endif
+  {
+    int i, sz;
+    sz = sqlite3Strlen30(z);
+    for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}
+    if( z[i]=='.' && ALWAYS(sz>i+4) ) memmove(&z[i+1], &z[sz-3], 4);
+  }
+}
+#endif
+
+/* 
+** Find (an approximate) sum of two LogEst values.  This computation is
+** not a simple "+" operator because LogEst is stored as a logarithmic
+** value.
+** 
+*/
+LogEst sqlite3LogEstAdd(LogEst a, LogEst 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 LogEst.  In other words, compute an
+** approximation for 10*log2(x).
+*/
+LogEst sqlite3LogEst(u64 x){
+  static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
+  LogEst 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; }  /*OPTIMIZATION-IF-TRUE*/
+    while( x>15 ){  y += 10; x >>= 1; }
+  }
+  return a[x&7] + y - 10;
+}
+
+#ifndef SQLITE_OMIT_VIRTUALTABLE
+/*
+** Convert a double into a LogEst
+** In other words, compute an approximation for 10*log2(x).
+*/
+LogEst sqlite3LogEstFromDouble(double x){
+  u64 a;
+  LogEst e;
+  assert( sizeof(x)==8 && sizeof(a)==8 );
+  if( x<=1 ) return 0;
+  if( x<=2000000000 ) return sqlite3LogEst((u64)x);
+  memcpy(&a, &x, 8);
+  e = (a>>52) - 1022;
+  return e*10;
+}
+#endif /* SQLITE_OMIT_VIRTUALTABLE */
+
+#if defined(SQLITE_ENABLE_STMT_SCANSTATUS) || \
+    defined(SQLITE_ENABLE_STAT3_OR_STAT4) || \
+    defined(SQLITE_EXPLAIN_ESTIMATED_ROWS)
+/*
+** Convert a LogEst into an integer.
+**
+** Note that this routine is only used when one or more of various
+** non-standard compile-time options is enabled.
+*/
+u64 sqlite3LogEstToInt(LogEst x){
+  u64 n;
+  n = x%10;
+  x /= 10;
+  if( n>=5 ) n -= 2;
+  else if( n>=1 ) n -= 1;
+#if defined(SQLITE_ENABLE_STMT_SCANSTATUS) || \
+    defined(SQLITE_EXPLAIN_ESTIMATED_ROWS)
+  if( x>60 ) return (u64)LARGEST_INT64;
+#else
+  /* If only SQLITE_ENABLE_STAT3_OR_STAT4 is on, then the largest input
+  ** possible to this routine is 310, resulting in a maximum x of 31 */
+  assert( x<=60 );
+#endif
+  return x>=3 ? (n+8)<<(x-3) : (n+8)>>(3-x);
+}
+#endif /* defined SCANSTAT or STAT4 or ESTIMATED_ROWS */
+
+/*
+** Add a new name/number pair to a VList.  This might require that the
+** VList object be reallocated, so return the new VList.  If an OOM
+** error occurs, the original VList returned and the
+** db->mallocFailed flag is set.
+**
+** A VList is really just an array of integers.  To destroy a VList,
+** simply pass it to sqlite3DbFree().
+**
+** The first integer is the number of integers allocated for the whole
+** VList.  The second integer is the number of integers actually used.
+** Each name/number pair is encoded by subsequent groups of 3 or more
+** integers.
+**
+** Each name/number pair starts with two integers which are the numeric
+** value for the pair and the size of the name/number pair, respectively.
+** The text name overlays one or more following integers.  The text name
+** is always zero-terminated.
+**
+** Conceptually:
+**
+**    struct VList {
+**      int nAlloc;   // Number of allocated slots 
+**      int nUsed;    // Number of used slots 
+**      struct VListEntry {
+**        int iValue;    // Value for this entry
+**        int nSlot;     // Slots used by this entry
+**        // ... variable name goes here
+**      } a[0];
+**    }
+**
+** During code generation, pointers to the variable names within the
+** VList are taken.  When that happens, nAlloc is set to zero as an 
+** indication that the VList may never again be enlarged, since the
+** accompanying realloc() would invalidate the pointers.
+*/
+VList *sqlite3VListAdd(
+  sqlite3 *db,           /* The database connection used for malloc() */
+  VList *pIn,            /* The input VList.  Might be NULL */
+  const char *zName,     /* Name of symbol to add */
+  int nName,             /* Bytes of text in zName */
+  int iVal               /* Value to associate with zName */
+){
+  int nInt;              /* number of sizeof(int) objects needed for zName */
+  char *z;               /* Pointer to where zName will be stored */
+  int i;                 /* Index in pIn[] where zName is stored */
+
+  nInt = nName/4 + 3;
+  assert( pIn==0 || pIn[0]>=3 );  /* Verify ok to add new elements */
+  if( pIn==0 || pIn[1]+nInt > pIn[0] ){
+    /* Enlarge the allocation */
+    int nAlloc = (pIn ? pIn[0]*2 : 10) + nInt;
+    VList *pOut = sqlite3DbRealloc(db, pIn, nAlloc*sizeof(int));
+    if( pOut==0 ) return pIn;
+    if( pIn==0 ) pOut[1] = 2;
+    pIn = pOut;
+    pIn[0] = nAlloc;
+  }
+  i = pIn[1];
+  pIn[i] = iVal;
+  pIn[i+1] = nInt;
+  z = (char*)&pIn[i+2];
+  pIn[1] = i+nInt;
+  assert( pIn[1]<=pIn[0] );
+  memcpy(z, zName, nName);
+  z[nName] = 0;
+  return pIn;
+}
+
+/*
+** Return a pointer to the name of a variable in the given VList that
+** has the value iVal.  Or return a NULL if there is no such variable in
+** the list
+*/
+const char *sqlite3VListNumToName(VList *pIn, int iVal){
+  int i, mx;
+  if( pIn==0 ) return 0;
+  mx = pIn[1];
+  i = 2;
+  do{
+    if( pIn[i]==iVal ) return (char*)&pIn[i+2];
+    i += pIn[i+1];
+  }while( i<mx );
+  return 0;
+}
+
+/*
+** Return the number of the variable named zName, if it is in VList.
+** or return 0 if there is no such variable.
+*/
+int sqlite3VListNameToNum(VList *pIn, const char *zName, int nName){
+  int i, mx;
+  if( pIn==0 ) return 0;
+  mx = pIn[1];
+  i = 2;
+  do{
+    const char *z = (const char*)&pIn[i+2];
+    if( strncmp(z,zName,nName)==0 && z[nName]==0 ) return pIn[i];
+    i += pIn[i+1];
+  }while( i<mx );
+  return 0;
+}