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>
#ifdef 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

#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 !defined(SQLITE_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 defined(SQLITE_HAVE_ISNAN) */
  rc = isnan(x);
#endif /* SQLITE_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){
  const char *z2 = z;
  if( z==0 ) return 0;
  while( *z2 ){ z2++; }
  return 0x3fffffff & (int)(z2 - z);
}

/*
** 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 sqlite3Error(sqlite3 *db, int err_code, const char *zFormat, ...){
  if( db && (db->pErr || (db->pErr = sqlite3ValueNew(db))!=0) ){
    db->errCode = err_code;
    if( zFormat ){
      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);
    }else{
      sqlite3ValueSetStr(db->pErr, 0, 0, SQLITE_UTF8, SQLITE_STATIC);
    }
  }
}

/*
** 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 whilst
** 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().
** Function sqlite3Error() 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 identifers.  For example:  "[a-b-c]" becomes
** "a-b-c".
*/
int sqlite3Dequote(char *z){
  char quote;
  int i, j;
  if( z==0 ) return -1;
  quote = z[0];
  switch( quote ){
    case '\'':  break;
    case '"':   break;
    case '`':   break;                /* For MySQL compatibility */
    case '[':   quote = ']';  break;  /* For MS SqlServer compatibility */
    default:    return -1;
  }
  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;
  return j;
}

/* 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){
  register unsigned char *a, *b;
  a = (unsigned char *)zLeft;
  b = (unsigned char *)zRight;
  while( *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
  return UpperToLower[*a] - UpperToLower[*b];
}
int sqlite3_strnicmp(const char *zLeft, const char *zRight, int N){
  register unsigned char *a, *b;
  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;

  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+enc-3;
    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;
  }

  /* skip leading zeroes */
  while( z<zEnd && z[0]=='0' ) z+=incr, nDigits++;

  /* 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) && s<((LARGEST_INT64-9)/10) ){
      s = s*10 + (*z - '0');
      z+=incr, nDigits++, d--;
    }
    /* skip non-significant digits */
    while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++;
  }
  if( z>=zEnd ) goto do_atof_calc;

  /* if exponent is present */
  if( *z=='e' || *z=='E' ){
    z+=incr;
    eValid = 0;
    if( z>=zEnd ) goto do_atof_calc;
    /* 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 */
  if( nDigits && eValid ){
    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 0 significand */
  if( !s ) {
    /* In the IEEE 754 standard, zero is signed.
    ** Add the sign if we've seen at least one digit */
    result = (sign<0 && nDigits) ? -(double)0 : (double)0;
  } else {
    /* attempt to reduce exponent */
    if( esign>0 ){
      while( s<(LARGEST_INT64/10) && e>0 ) e--,s*=10;
    }else{
      while( !(s%10) && e>0 ) e--,s/=10;
    }

    /* adjust the sign of significand */
    s = sign<0 ? -s : s;

    /* if exponent, scale significand as appropriate
    ** and store in result. */
    if( e ){
      LONGDOUBLE_TYPE scale = 1.0;
      /* attempt to handle extremely small/large numbers better */
      if( e>307 && e<342 ){
        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 if( 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;
        }
      }
    } else {
      result = (double)s;
    }
  }

  /* 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.
**
** 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;
  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+enc-3;
    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( (c!=0 && &zNum[i]<zEnd) || (i==0 && zStart==zNum) || i>19*incr || nonNum ){
    /* 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;
    }
  }
}

/*
** If zNum represents an integer that will fit in 32-bits, then set
** *pValue to that integer and return true.  Otherwise return false.
**
** 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++;
  }
  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.
*/
int sqlite3PutVarint(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;
}

/*
** This routine is a faster version of sqlite3PutVarint() that only
** works for 32-bit positive integers and which is optimized for
** the common case of small integers.  A MACRO version, putVarint32,
** 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.
*/
int sqlite3PutVarint32(unsigned char *p, u32 v){
#ifndef putVarint32
  if( (v & ~0x7f)==0 ){
    p[0] = v;
    return 1;
  }
#endif
  if( (v & ~0x3fff)==0 ){
    p[0] = (u8)((v>>7) | 0x80);
    p[1] = (u8)(v & 0x7f);
    return 2;
  }
  return sqlite3PutVarint(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 in calc'ing 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 = 0;
  do{
    i++;
    v >>= 7;
  }while( v!=0 && ALWAYS(i<9) );
  return i;
}


/*
** Read or write a four-byte big-endian integer value.
*/
u32 sqlite3Get4byte(const u8 *p){
  return (p[0]<<24) | (p[1]<<16) | (p[2]<<8) | p[3];
}
void sqlite3Put4byte(unsigned char *p, u32 v){
  p[0] = (u8)(v>>24);
  p[1] = (u8)(v>>16);
  p[2] = (u8)(v>>8);
  p[3] = (u8)v;
}



/*
** 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 *)sqlite3DbMallocRaw(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){
  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;
    *pA += iB;
  }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; 
}
int sqlite3SubInt64(i64 *pA, i64 iB){
  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);
  }
}
#define TWOPOWER32 (((i64)1)<<32)
#define TWOPOWER31 (((i64)1)<<31)
int sqlite3MulInt64(i64 *pA, i64 iB){
  i64 iA = *pA;
  i64 iA1, iA0, iB1, iB0, r;

  iA1 = iA/TWOPOWER32;
  iA0 = iA % TWOPOWER32;
  iB1 = iB/TWOPOWER32;
  iB0 = iB % TWOPOWER32;
  if( iA1*iB1 != 0 ) return 1;
  assert( iA1*iB0==0 || iA0*iB1==0 );
  r = iA1*iB0 + iA0*iB1;
  testcase( r==(-TWOPOWER31)-1 );
  testcase( r==(-TWOPOWER31) );
  testcase( r==TWOPOWER31 );
  testcase( r==TWOPOWER31-1 );
  if( r<(-TWOPOWER31) || r>=TWOPOWER31 ) return 1;
  r *= TWOPOWER32;
  if( sqlite3AddInt64(&r, iA0*iB0) ) return 1;
  *pA = r;
  return 0;
}

/*
** 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 a
** good approximatation 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; }
    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 */

/*
** Convert a LogEst into an integer.
*/
u64 sqlite3LogEstToInt(LogEst x){
  u64 n;
  if( x<10 ) return 1;
  n = x%10;
  x /= 10;
  if( n>=5 ) n -= 2;
  else if( n>=1 ) n -= 1;
  if( x>=3 ){
    return x>60 ? (u64)LARGEST_INT64 : (n+8)<<(x-3);
  }
  return (n+8)>>(3-x);
}