xref: /sqlite-3.40.0/src/util.c (revision 7aa3ebee)
1 /*
2 ** 2001 September 15
3 **
4 ** The author disclaims copyright to this source code.  In place of
5 ** a legal notice, here is a blessing:
6 **
7 **    May you do good and not evil.
8 **    May you find forgiveness for yourself and forgive others.
9 **    May you share freely, never taking more than you give.
10 **
11 *************************************************************************
12 ** Utility functions used throughout sqlite.
13 **
14 ** This file contains functions for allocating memory, comparing
15 ** strings, and stuff like that.
16 **
17 */
18 #include "sqliteInt.h"
19 #include <stdarg.h>
20 #if HAVE_ISNAN || SQLITE_HAVE_ISNAN
21 # include <math.h>
22 #endif
23 
24 /*
25 ** Routine needed to support the testcase() macro.
26 */
27 #ifdef SQLITE_COVERAGE_TEST
28 void sqlite3Coverage(int x){
29   static unsigned dummy = 0;
30   dummy += (unsigned)x;
31 }
32 #endif
33 
34 /*
35 ** Give a callback to the test harness that can be used to simulate faults
36 ** in places where it is difficult or expensive to do so purely by means
37 ** of inputs.
38 **
39 ** The intent of the integer argument is to let the fault simulator know
40 ** which of multiple sqlite3FaultSim() calls has been hit.
41 **
42 ** Return whatever integer value the test callback returns, or return
43 ** SQLITE_OK if no test callback is installed.
44 */
45 #ifndef SQLITE_OMIT_BUILTIN_TEST
46 int sqlite3FaultSim(int iTest){
47   int (*xCallback)(int) = sqlite3GlobalConfig.xTestCallback;
48   return xCallback ? xCallback(iTest) : SQLITE_OK;
49 }
50 #endif
51 
52 #ifndef SQLITE_OMIT_FLOATING_POINT
53 /*
54 ** Return true if the floating point value is Not a Number (NaN).
55 **
56 ** Use the math library isnan() function if compiled with SQLITE_HAVE_ISNAN.
57 ** Otherwise, we have our own implementation that works on most systems.
58 */
59 int sqlite3IsNaN(double x){
60   int rc;   /* The value return */
61 #if !SQLITE_HAVE_ISNAN && !HAVE_ISNAN
62   /*
63   ** Systems that support the isnan() library function should probably
64   ** make use of it by compiling with -DSQLITE_HAVE_ISNAN.  But we have
65   ** found that many systems do not have a working isnan() function so
66   ** this implementation is provided as an alternative.
67   **
68   ** This NaN test sometimes fails if compiled on GCC with -ffast-math.
69   ** On the other hand, the use of -ffast-math comes with the following
70   ** warning:
71   **
72   **      This option [-ffast-math] should never be turned on by any
73   **      -O option since it can result in incorrect output for programs
74   **      which depend on an exact implementation of IEEE or ISO
75   **      rules/specifications for math functions.
76   **
77   ** Under MSVC, this NaN test may fail if compiled with a floating-
78   ** point precision mode other than /fp:precise.  From the MSDN
79   ** documentation:
80   **
81   **      The compiler [with /fp:precise] will properly handle comparisons
82   **      involving NaN. For example, x != x evaluates to true if x is NaN
83   **      ...
84   */
85 #ifdef __FAST_MATH__
86 # error SQLite will not work correctly with the -ffast-math option of GCC.
87 #endif
88   volatile double y = x;
89   volatile double z = y;
90   rc = (y!=z);
91 #else  /* if HAVE_ISNAN */
92   rc = isnan(x);
93 #endif /* HAVE_ISNAN */
94   testcase( rc );
95   return rc;
96 }
97 #endif /* SQLITE_OMIT_FLOATING_POINT */
98 
99 /*
100 ** Compute a string length that is limited to what can be stored in
101 ** lower 30 bits of a 32-bit signed integer.
102 **
103 ** The value returned will never be negative.  Nor will it ever be greater
104 ** than the actual length of the string.  For very long strings (greater
105 ** than 1GiB) the value returned might be less than the true string length.
106 */
107 int sqlite3Strlen30(const char *z){
108   if( z==0 ) return 0;
109   return 0x3fffffff & (int)strlen(z);
110 }
111 
112 /*
113 ** Set the current error code to err_code and clear any prior error message.
114 */
115 void sqlite3Error(sqlite3 *db, int err_code){
116   assert( db!=0 );
117   db->errCode = err_code;
118   if( db->pErr ) sqlite3ValueSetNull(db->pErr);
119 }
120 
121 /*
122 ** Set the most recent error code and error string for the sqlite
123 ** handle "db". The error code is set to "err_code".
124 **
125 ** If it is not NULL, string zFormat specifies the format of the
126 ** error string in the style of the printf functions: The following
127 ** format characters are allowed:
128 **
129 **      %s      Insert a string
130 **      %z      A string that should be freed after use
131 **      %d      Insert an integer
132 **      %T      Insert a token
133 **      %S      Insert the first element of a SrcList
134 **
135 ** zFormat and any string tokens that follow it are assumed to be
136 ** encoded in UTF-8.
137 **
138 ** To clear the most recent error for sqlite handle "db", sqlite3Error
139 ** should be called with err_code set to SQLITE_OK and zFormat set
140 ** to NULL.
141 */
142 void sqlite3ErrorWithMsg(sqlite3 *db, int err_code, const char *zFormat, ...){
143   assert( db!=0 );
144   db->errCode = err_code;
145   if( zFormat==0 ){
146     sqlite3Error(db, err_code);
147   }else if( db->pErr || (db->pErr = sqlite3ValueNew(db))!=0 ){
148     char *z;
149     va_list ap;
150     va_start(ap, zFormat);
151     z = sqlite3VMPrintf(db, zFormat, ap);
152     va_end(ap);
153     sqlite3ValueSetStr(db->pErr, -1, z, SQLITE_UTF8, SQLITE_DYNAMIC);
154   }
155 }
156 
157 /*
158 ** Add an error message to pParse->zErrMsg and increment pParse->nErr.
159 ** The following formatting characters are allowed:
160 **
161 **      %s      Insert a string
162 **      %z      A string that should be freed after use
163 **      %d      Insert an integer
164 **      %T      Insert a token
165 **      %S      Insert the first element of a SrcList
166 **
167 ** This function should be used to report any error that occurs while
168 ** compiling an SQL statement (i.e. within sqlite3_prepare()). The
169 ** last thing the sqlite3_prepare() function does is copy the error
170 ** stored by this function into the database handle using sqlite3Error().
171 ** Functions sqlite3Error() or sqlite3ErrorWithMsg() should be used
172 ** during statement execution (sqlite3_step() etc.).
173 */
174 void sqlite3ErrorMsg(Parse *pParse, const char *zFormat, ...){
175   char *zMsg;
176   va_list ap;
177   sqlite3 *db = pParse->db;
178   va_start(ap, zFormat);
179   zMsg = sqlite3VMPrintf(db, zFormat, ap);
180   va_end(ap);
181   if( db->suppressErr ){
182     sqlite3DbFree(db, zMsg);
183   }else{
184     pParse->nErr++;
185     sqlite3DbFree(db, pParse->zErrMsg);
186     pParse->zErrMsg = zMsg;
187     pParse->rc = SQLITE_ERROR;
188   }
189 }
190 
191 /*
192 ** Convert an SQL-style quoted string into a normal string by removing
193 ** the quote characters.  The conversion is done in-place.  If the
194 ** input does not begin with a quote character, then this routine
195 ** is a no-op.
196 **
197 ** The input string must be zero-terminated.  A new zero-terminator
198 ** is added to the dequoted string.
199 **
200 ** The return value is -1 if no dequoting occurs or the length of the
201 ** dequoted string, exclusive of the zero terminator, if dequoting does
202 ** occur.
203 **
204 ** 2002-Feb-14: This routine is extended to remove MS-Access style
205 ** brackets from around identifiers.  For example:  "[a-b-c]" becomes
206 ** "a-b-c".
207 */
208 int sqlite3Dequote(char *z){
209   char quote;
210   int i, j;
211   if( z==0 ) return -1;
212   quote = z[0];
213   switch( quote ){
214     case '\'':  break;
215     case '"':   break;
216     case '`':   break;                /* For MySQL compatibility */
217     case '[':   quote = ']';  break;  /* For MS SqlServer compatibility */
218     default:    return -1;
219   }
220   for(i=1, j=0;; i++){
221     assert( z[i] );
222     if( z[i]==quote ){
223       if( z[i+1]==quote ){
224         z[j++] = quote;
225         i++;
226       }else{
227         break;
228       }
229     }else{
230       z[j++] = z[i];
231     }
232   }
233   z[j] = 0;
234   return j;
235 }
236 
237 /*
238 ** Generate a Token object from a string
239 */
240 void sqlite3TokenInit(Token *p, char *z){
241   p->z = z;
242   p->n = sqlite3Strlen30(z);
243 }
244 
245 /* Convenient short-hand */
246 #define UpperToLower sqlite3UpperToLower
247 
248 /*
249 ** Some systems have stricmp().  Others have strcasecmp().  Because
250 ** there is no consistency, we will define our own.
251 **
252 ** IMPLEMENTATION-OF: R-30243-02494 The sqlite3_stricmp() and
253 ** sqlite3_strnicmp() APIs allow applications and extensions to compare
254 ** the contents of two buffers containing UTF-8 strings in a
255 ** case-independent fashion, using the same definition of "case
256 ** independence" that SQLite uses internally when comparing identifiers.
257 */
258 int sqlite3_stricmp(const char *zLeft, const char *zRight){
259   if( zLeft==0 ){
260     return zRight ? -1 : 0;
261   }else if( zRight==0 ){
262     return 1;
263   }
264   return sqlite3StrICmp(zLeft, zRight);
265 }
266 int sqlite3StrICmp(const char *zLeft, const char *zRight){
267   unsigned char *a, *b;
268   int c;
269   a = (unsigned char *)zLeft;
270   b = (unsigned char *)zRight;
271   for(;;){
272     c = (int)UpperToLower[*a] - (int)UpperToLower[*b];
273     if( c || *a==0 ) break;
274     a++;
275     b++;
276   }
277   return c;
278 }
279 int sqlite3_strnicmp(const char *zLeft, const char *zRight, int N){
280   register unsigned char *a, *b;
281   if( zLeft==0 ){
282     return zRight ? -1 : 0;
283   }else if( zRight==0 ){
284     return 1;
285   }
286   a = (unsigned char *)zLeft;
287   b = (unsigned char *)zRight;
288   while( N-- > 0 && *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
289   return N<0 ? 0 : UpperToLower[*a] - UpperToLower[*b];
290 }
291 
292 /*
293 ** The string z[] is an text representation of a real number.
294 ** Convert this string to a double and write it into *pResult.
295 **
296 ** The string z[] is length bytes in length (bytes, not characters) and
297 ** uses the encoding enc.  The string is not necessarily zero-terminated.
298 **
299 ** Return TRUE if the result is a valid real number (or integer) and FALSE
300 ** if the string is empty or contains extraneous text.  Valid numbers
301 ** are in one of these formats:
302 **
303 **    [+-]digits[E[+-]digits]
304 **    [+-]digits.[digits][E[+-]digits]
305 **    [+-].digits[E[+-]digits]
306 **
307 ** Leading and trailing whitespace is ignored for the purpose of determining
308 ** validity.
309 **
310 ** If some prefix of the input string is a valid number, this routine
311 ** returns FALSE but it still converts the prefix and writes the result
312 ** into *pResult.
313 */
314 int sqlite3AtoF(const char *z, double *pResult, int length, u8 enc){
315 #ifndef SQLITE_OMIT_FLOATING_POINT
316   int incr;
317   const char *zEnd = z + length;
318   /* sign * significand * (10 ^ (esign * exponent)) */
319   int sign = 1;    /* sign of significand */
320   i64 s = 0;       /* significand */
321   int d = 0;       /* adjust exponent for shifting decimal point */
322   int esign = 1;   /* sign of exponent */
323   int e = 0;       /* exponent */
324   int eValid = 1;  /* True exponent is either not used or is well-formed */
325   double result;
326   int nDigits = 0;
327   int nonNum = 0;
328 
329   assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
330   *pResult = 0.0;   /* Default return value, in case of an error */
331 
332   if( enc==SQLITE_UTF8 ){
333     incr = 1;
334   }else{
335     int i;
336     incr = 2;
337     assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
338     for(i=3-enc; i<length && z[i]==0; i+=2){}
339     nonNum = i<length;
340     zEnd = z+i+enc-3;
341     z += (enc&1);
342   }
343 
344   /* skip leading spaces */
345   while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
346   if( z>=zEnd ) return 0;
347 
348   /* get sign of significand */
349   if( *z=='-' ){
350     sign = -1;
351     z+=incr;
352   }else if( *z=='+' ){
353     z+=incr;
354   }
355 
356   /* skip leading zeroes */
357   while( z<zEnd && z[0]=='0' ) z+=incr, nDigits++;
358 
359   /* copy max significant digits to significand */
360   while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
361     s = s*10 + (*z - '0');
362     z+=incr, nDigits++;
363   }
364 
365   /* skip non-significant significand digits
366   ** (increase exponent by d to shift decimal left) */
367   while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++, d++;
368   if( z>=zEnd ) goto do_atof_calc;
369 
370   /* if decimal point is present */
371   if( *z=='.' ){
372     z+=incr;
373     /* copy digits from after decimal to significand
374     ** (decrease exponent by d to shift decimal right) */
375     while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
376       s = s*10 + (*z - '0');
377       z+=incr, nDigits++, d--;
378     }
379     /* skip non-significant digits */
380     while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++;
381   }
382   if( z>=zEnd ) goto do_atof_calc;
383 
384   /* if exponent is present */
385   if( *z=='e' || *z=='E' ){
386     z+=incr;
387     eValid = 0;
388     if( z>=zEnd ) goto do_atof_calc;
389     /* get sign of exponent */
390     if( *z=='-' ){
391       esign = -1;
392       z+=incr;
393     }else if( *z=='+' ){
394       z+=incr;
395     }
396     /* copy digits to exponent */
397     while( z<zEnd && sqlite3Isdigit(*z) ){
398       e = e<10000 ? (e*10 + (*z - '0')) : 10000;
399       z+=incr;
400       eValid = 1;
401     }
402   }
403 
404   /* skip trailing spaces */
405   if( nDigits && eValid ){
406     while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
407   }
408 
409 do_atof_calc:
410   /* adjust exponent by d, and update sign */
411   e = (e*esign) + d;
412   if( e<0 ) {
413     esign = -1;
414     e *= -1;
415   } else {
416     esign = 1;
417   }
418 
419   /* if 0 significand */
420   if( !s ) {
421     /* In the IEEE 754 standard, zero is signed.
422     ** Add the sign if we've seen at least one digit */
423     result = (sign<0 && nDigits) ? -(double)0 : (double)0;
424   } else {
425     /* attempt to reduce exponent */
426     if( esign>0 ){
427       while( s<(LARGEST_INT64/10) && e>0 ) e--,s*=10;
428     }else{
429       while( !(s%10) && e>0 ) e--,s/=10;
430     }
431 
432     /* adjust the sign of significand */
433     s = sign<0 ? -s : s;
434 
435     /* if exponent, scale significand as appropriate
436     ** and store in result. */
437     if( e ){
438       LONGDOUBLE_TYPE scale = 1.0;
439       /* attempt to handle extremely small/large numbers better */
440       if( e>307 && e<342 ){
441         while( e%308 ) { scale *= 1.0e+1; e -= 1; }
442         if( esign<0 ){
443           result = s / scale;
444           result /= 1.0e+308;
445         }else{
446           result = s * scale;
447           result *= 1.0e+308;
448         }
449       }else if( e>=342 ){
450         if( esign<0 ){
451           result = 0.0*s;
452         }else{
453           result = 1e308*1e308*s;  /* Infinity */
454         }
455       }else{
456         /* 1.0e+22 is the largest power of 10 than can be
457         ** represented exactly. */
458         while( e%22 ) { scale *= 1.0e+1; e -= 1; }
459         while( e>0 ) { scale *= 1.0e+22; e -= 22; }
460         if( esign<0 ){
461           result = s / scale;
462         }else{
463           result = s * scale;
464         }
465       }
466     } else {
467       result = (double)s;
468     }
469   }
470 
471   /* store the result */
472   *pResult = result;
473 
474   /* return true if number and no extra non-whitespace chracters after */
475   return z>=zEnd && nDigits>0 && eValid && nonNum==0;
476 #else
477   return !sqlite3Atoi64(z, pResult, length, enc);
478 #endif /* SQLITE_OMIT_FLOATING_POINT */
479 }
480 
481 /*
482 ** Compare the 19-character string zNum against the text representation
483 ** value 2^63:  9223372036854775808.  Return negative, zero, or positive
484 ** if zNum is less than, equal to, or greater than the string.
485 ** Note that zNum must contain exactly 19 characters.
486 **
487 ** Unlike memcmp() this routine is guaranteed to return the difference
488 ** in the values of the last digit if the only difference is in the
489 ** last digit.  So, for example,
490 **
491 **      compare2pow63("9223372036854775800", 1)
492 **
493 ** will return -8.
494 */
495 static int compare2pow63(const char *zNum, int incr){
496   int c = 0;
497   int i;
498                     /* 012345678901234567 */
499   const char *pow63 = "922337203685477580";
500   for(i=0; c==0 && i<18; i++){
501     c = (zNum[i*incr]-pow63[i])*10;
502   }
503   if( c==0 ){
504     c = zNum[18*incr] - '8';
505     testcase( c==(-1) );
506     testcase( c==0 );
507     testcase( c==(+1) );
508   }
509   return c;
510 }
511 
512 /*
513 ** Convert zNum to a 64-bit signed integer.  zNum must be decimal. This
514 ** routine does *not* accept hexadecimal notation.
515 **
516 ** If the zNum value is representable as a 64-bit twos-complement
517 ** integer, then write that value into *pNum and return 0.
518 **
519 ** If zNum is exactly 9223372036854775808, return 2.  This special
520 ** case is broken out because while 9223372036854775808 cannot be a
521 ** signed 64-bit integer, its negative -9223372036854775808 can be.
522 **
523 ** If zNum is too big for a 64-bit integer and is not
524 ** 9223372036854775808  or if zNum contains any non-numeric text,
525 ** then return 1.
526 **
527 ** length is the number of bytes in the string (bytes, not characters).
528 ** The string is not necessarily zero-terminated.  The encoding is
529 ** given by enc.
530 */
531 int sqlite3Atoi64(const char *zNum, i64 *pNum, int length, u8 enc){
532   int incr;
533   u64 u = 0;
534   int neg = 0; /* assume positive */
535   int i;
536   int c = 0;
537   int nonNum = 0;
538   const char *zStart;
539   const char *zEnd = zNum + length;
540   assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
541   if( enc==SQLITE_UTF8 ){
542     incr = 1;
543   }else{
544     incr = 2;
545     assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
546     for(i=3-enc; i<length && zNum[i]==0; i+=2){}
547     nonNum = i<length;
548     zEnd = zNum+i+enc-3;
549     zNum += (enc&1);
550   }
551   while( zNum<zEnd && sqlite3Isspace(*zNum) ) zNum+=incr;
552   if( zNum<zEnd ){
553     if( *zNum=='-' ){
554       neg = 1;
555       zNum+=incr;
556     }else if( *zNum=='+' ){
557       zNum+=incr;
558     }
559   }
560   zStart = zNum;
561   while( zNum<zEnd && zNum[0]=='0' ){ zNum+=incr; } /* Skip leading zeros. */
562   for(i=0; &zNum[i]<zEnd && (c=zNum[i])>='0' && c<='9'; i+=incr){
563     u = u*10 + c - '0';
564   }
565   if( u>LARGEST_INT64 ){
566     *pNum = neg ? SMALLEST_INT64 : LARGEST_INT64;
567   }else if( neg ){
568     *pNum = -(i64)u;
569   }else{
570     *pNum = (i64)u;
571   }
572   testcase( i==18 );
573   testcase( i==19 );
574   testcase( i==20 );
575   if( (c!=0 && &zNum[i]<zEnd) || (i==0 && zStart==zNum)
576        || i>19*incr || nonNum ){
577     /* zNum is empty or contains non-numeric text or is longer
578     ** than 19 digits (thus guaranteeing that it is too large) */
579     return 1;
580   }else if( i<19*incr ){
581     /* Less than 19 digits, so we know that it fits in 64 bits */
582     assert( u<=LARGEST_INT64 );
583     return 0;
584   }else{
585     /* zNum is a 19-digit numbers.  Compare it against 9223372036854775808. */
586     c = compare2pow63(zNum, incr);
587     if( c<0 ){
588       /* zNum is less than 9223372036854775808 so it fits */
589       assert( u<=LARGEST_INT64 );
590       return 0;
591     }else if( c>0 ){
592       /* zNum is greater than 9223372036854775808 so it overflows */
593       return 1;
594     }else{
595       /* zNum is exactly 9223372036854775808.  Fits if negative.  The
596       ** special case 2 overflow if positive */
597       assert( u-1==LARGEST_INT64 );
598       return neg ? 0 : 2;
599     }
600   }
601 }
602 
603 /*
604 ** Transform a UTF-8 integer literal, in either decimal or hexadecimal,
605 ** into a 64-bit signed integer.  This routine accepts hexadecimal literals,
606 ** whereas sqlite3Atoi64() does not.
607 **
608 ** Returns:
609 **
610 **     0    Successful transformation.  Fits in a 64-bit signed integer.
611 **     1    Integer too large for a 64-bit signed integer or is malformed
612 **     2    Special case of 9223372036854775808
613 */
614 int sqlite3DecOrHexToI64(const char *z, i64 *pOut){
615 #ifndef SQLITE_OMIT_HEX_INTEGER
616   if( z[0]=='0'
617    && (z[1]=='x' || z[1]=='X')
618    && sqlite3Isxdigit(z[2])
619   ){
620     u64 u = 0;
621     int i, k;
622     for(i=2; z[i]=='0'; i++){}
623     for(k=i; sqlite3Isxdigit(z[k]); k++){
624       u = u*16 + sqlite3HexToInt(z[k]);
625     }
626     memcpy(pOut, &u, 8);
627     return (z[k]==0 && k-i<=16) ? 0 : 1;
628   }else
629 #endif /* SQLITE_OMIT_HEX_INTEGER */
630   {
631     return sqlite3Atoi64(z, pOut, sqlite3Strlen30(z), SQLITE_UTF8);
632   }
633 }
634 
635 /*
636 ** If zNum represents an integer that will fit in 32-bits, then set
637 ** *pValue to that integer and return true.  Otherwise return false.
638 **
639 ** This routine accepts both decimal and hexadecimal notation for integers.
640 **
641 ** Any non-numeric characters that following zNum are ignored.
642 ** This is different from sqlite3Atoi64() which requires the
643 ** input number to be zero-terminated.
644 */
645 int sqlite3GetInt32(const char *zNum, int *pValue){
646   sqlite_int64 v = 0;
647   int i, c;
648   int neg = 0;
649   if( zNum[0]=='-' ){
650     neg = 1;
651     zNum++;
652   }else if( zNum[0]=='+' ){
653     zNum++;
654   }
655 #ifndef SQLITE_OMIT_HEX_INTEGER
656   else if( zNum[0]=='0'
657         && (zNum[1]=='x' || zNum[1]=='X')
658         && sqlite3Isxdigit(zNum[2])
659   ){
660     u32 u = 0;
661     zNum += 2;
662     while( zNum[0]=='0' ) zNum++;
663     for(i=0; sqlite3Isxdigit(zNum[i]) && i<8; i++){
664       u = u*16 + sqlite3HexToInt(zNum[i]);
665     }
666     if( (u&0x80000000)==0 && sqlite3Isxdigit(zNum[i])==0 ){
667       memcpy(pValue, &u, 4);
668       return 1;
669     }else{
670       return 0;
671     }
672   }
673 #endif
674   while( zNum[0]=='0' ) zNum++;
675   for(i=0; i<11 && (c = zNum[i] - '0')>=0 && c<=9; i++){
676     v = v*10 + c;
677   }
678 
679   /* The longest decimal representation of a 32 bit integer is 10 digits:
680   **
681   **             1234567890
682   **     2^31 -> 2147483648
683   */
684   testcase( i==10 );
685   if( i>10 ){
686     return 0;
687   }
688   testcase( v-neg==2147483647 );
689   if( v-neg>2147483647 ){
690     return 0;
691   }
692   if( neg ){
693     v = -v;
694   }
695   *pValue = (int)v;
696   return 1;
697 }
698 
699 /*
700 ** Return a 32-bit integer value extracted from a string.  If the
701 ** string is not an integer, just return 0.
702 */
703 int sqlite3Atoi(const char *z){
704   int x = 0;
705   if( z ) sqlite3GetInt32(z, &x);
706   return x;
707 }
708 
709 /*
710 ** The variable-length integer encoding is as follows:
711 **
712 ** KEY:
713 **         A = 0xxxxxxx    7 bits of data and one flag bit
714 **         B = 1xxxxxxx    7 bits of data and one flag bit
715 **         C = xxxxxxxx    8 bits of data
716 **
717 **  7 bits - A
718 ** 14 bits - BA
719 ** 21 bits - BBA
720 ** 28 bits - BBBA
721 ** 35 bits - BBBBA
722 ** 42 bits - BBBBBA
723 ** 49 bits - BBBBBBA
724 ** 56 bits - BBBBBBBA
725 ** 64 bits - BBBBBBBBC
726 */
727 
728 /*
729 ** Write a 64-bit variable-length integer to memory starting at p[0].
730 ** The length of data write will be between 1 and 9 bytes.  The number
731 ** of bytes written is returned.
732 **
733 ** A variable-length integer consists of the lower 7 bits of each byte
734 ** for all bytes that have the 8th bit set and one byte with the 8th
735 ** bit clear.  Except, if we get to the 9th byte, it stores the full
736 ** 8 bits and is the last byte.
737 */
738 static int SQLITE_NOINLINE putVarint64(unsigned char *p, u64 v){
739   int i, j, n;
740   u8 buf[10];
741   if( v & (((u64)0xff000000)<<32) ){
742     p[8] = (u8)v;
743     v >>= 8;
744     for(i=7; i>=0; i--){
745       p[i] = (u8)((v & 0x7f) | 0x80);
746       v >>= 7;
747     }
748     return 9;
749   }
750   n = 0;
751   do{
752     buf[n++] = (u8)((v & 0x7f) | 0x80);
753     v >>= 7;
754   }while( v!=0 );
755   buf[0] &= 0x7f;
756   assert( n<=9 );
757   for(i=0, j=n-1; j>=0; j--, i++){
758     p[i] = buf[j];
759   }
760   return n;
761 }
762 int sqlite3PutVarint(unsigned char *p, u64 v){
763   if( v<=0x7f ){
764     p[0] = v&0x7f;
765     return 1;
766   }
767   if( v<=0x3fff ){
768     p[0] = ((v>>7)&0x7f)|0x80;
769     p[1] = v&0x7f;
770     return 2;
771   }
772   return putVarint64(p,v);
773 }
774 
775 /*
776 ** Bitmasks used by sqlite3GetVarint().  These precomputed constants
777 ** are defined here rather than simply putting the constant expressions
778 ** inline in order to work around bugs in the RVT compiler.
779 **
780 ** SLOT_2_0     A mask for  (0x7f<<14) | 0x7f
781 **
782 ** SLOT_4_2_0   A mask for  (0x7f<<28) | SLOT_2_0
783 */
784 #define SLOT_2_0     0x001fc07f
785 #define SLOT_4_2_0   0xf01fc07f
786 
787 
788 /*
789 ** Read a 64-bit variable-length integer from memory starting at p[0].
790 ** Return the number of bytes read.  The value is stored in *v.
791 */
792 u8 sqlite3GetVarint(const unsigned char *p, u64 *v){
793   u32 a,b,s;
794 
795   a = *p;
796   /* a: p0 (unmasked) */
797   if (!(a&0x80))
798   {
799     *v = a;
800     return 1;
801   }
802 
803   p++;
804   b = *p;
805   /* b: p1 (unmasked) */
806   if (!(b&0x80))
807   {
808     a &= 0x7f;
809     a = a<<7;
810     a |= b;
811     *v = a;
812     return 2;
813   }
814 
815   /* Verify that constants are precomputed correctly */
816   assert( SLOT_2_0 == ((0x7f<<14) | (0x7f)) );
817   assert( SLOT_4_2_0 == ((0xfU<<28) | (0x7f<<14) | (0x7f)) );
818 
819   p++;
820   a = a<<14;
821   a |= *p;
822   /* a: p0<<14 | p2 (unmasked) */
823   if (!(a&0x80))
824   {
825     a &= SLOT_2_0;
826     b &= 0x7f;
827     b = b<<7;
828     a |= b;
829     *v = a;
830     return 3;
831   }
832 
833   /* CSE1 from below */
834   a &= SLOT_2_0;
835   p++;
836   b = b<<14;
837   b |= *p;
838   /* b: p1<<14 | p3 (unmasked) */
839   if (!(b&0x80))
840   {
841     b &= SLOT_2_0;
842     /* moved CSE1 up */
843     /* a &= (0x7f<<14)|(0x7f); */
844     a = a<<7;
845     a |= b;
846     *v = a;
847     return 4;
848   }
849 
850   /* a: p0<<14 | p2 (masked) */
851   /* b: p1<<14 | p3 (unmasked) */
852   /* 1:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
853   /* moved CSE1 up */
854   /* a &= (0x7f<<14)|(0x7f); */
855   b &= SLOT_2_0;
856   s = a;
857   /* s: p0<<14 | p2 (masked) */
858 
859   p++;
860   a = a<<14;
861   a |= *p;
862   /* a: p0<<28 | p2<<14 | p4 (unmasked) */
863   if (!(a&0x80))
864   {
865     /* we can skip these cause they were (effectively) done above
866     ** while calculating s */
867     /* a &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
868     /* b &= (0x7f<<14)|(0x7f); */
869     b = b<<7;
870     a |= b;
871     s = s>>18;
872     *v = ((u64)s)<<32 | a;
873     return 5;
874   }
875 
876   /* 2:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
877   s = s<<7;
878   s |= b;
879   /* s: p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
880 
881   p++;
882   b = b<<14;
883   b |= *p;
884   /* b: p1<<28 | p3<<14 | p5 (unmasked) */
885   if (!(b&0x80))
886   {
887     /* we can skip this cause it was (effectively) done above in calc'ing s */
888     /* b &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
889     a &= SLOT_2_0;
890     a = a<<7;
891     a |= b;
892     s = s>>18;
893     *v = ((u64)s)<<32 | a;
894     return 6;
895   }
896 
897   p++;
898   a = a<<14;
899   a |= *p;
900   /* a: p2<<28 | p4<<14 | p6 (unmasked) */
901   if (!(a&0x80))
902   {
903     a &= SLOT_4_2_0;
904     b &= SLOT_2_0;
905     b = b<<7;
906     a |= b;
907     s = s>>11;
908     *v = ((u64)s)<<32 | a;
909     return 7;
910   }
911 
912   /* CSE2 from below */
913   a &= SLOT_2_0;
914   p++;
915   b = b<<14;
916   b |= *p;
917   /* b: p3<<28 | p5<<14 | p7 (unmasked) */
918   if (!(b&0x80))
919   {
920     b &= SLOT_4_2_0;
921     /* moved CSE2 up */
922     /* a &= (0x7f<<14)|(0x7f); */
923     a = a<<7;
924     a |= b;
925     s = s>>4;
926     *v = ((u64)s)<<32 | a;
927     return 8;
928   }
929 
930   p++;
931   a = a<<15;
932   a |= *p;
933   /* a: p4<<29 | p6<<15 | p8 (unmasked) */
934 
935   /* moved CSE2 up */
936   /* a &= (0x7f<<29)|(0x7f<<15)|(0xff); */
937   b &= SLOT_2_0;
938   b = b<<8;
939   a |= b;
940 
941   s = s<<4;
942   b = p[-4];
943   b &= 0x7f;
944   b = b>>3;
945   s |= b;
946 
947   *v = ((u64)s)<<32 | a;
948 
949   return 9;
950 }
951 
952 /*
953 ** Read a 32-bit variable-length integer from memory starting at p[0].
954 ** Return the number of bytes read.  The value is stored in *v.
955 **
956 ** If the varint stored in p[0] is larger than can fit in a 32-bit unsigned
957 ** integer, then set *v to 0xffffffff.
958 **
959 ** A MACRO version, getVarint32, is provided which inlines the
960 ** single-byte case.  All code should use the MACRO version as
961 ** this function assumes the single-byte case has already been handled.
962 */
963 u8 sqlite3GetVarint32(const unsigned char *p, u32 *v){
964   u32 a,b;
965 
966   /* The 1-byte case.  Overwhelmingly the most common.  Handled inline
967   ** by the getVarin32() macro */
968   a = *p;
969   /* a: p0 (unmasked) */
970 #ifndef getVarint32
971   if (!(a&0x80))
972   {
973     /* Values between 0 and 127 */
974     *v = a;
975     return 1;
976   }
977 #endif
978 
979   /* The 2-byte case */
980   p++;
981   b = *p;
982   /* b: p1 (unmasked) */
983   if (!(b&0x80))
984   {
985     /* Values between 128 and 16383 */
986     a &= 0x7f;
987     a = a<<7;
988     *v = a | b;
989     return 2;
990   }
991 
992   /* The 3-byte case */
993   p++;
994   a = a<<14;
995   a |= *p;
996   /* a: p0<<14 | p2 (unmasked) */
997   if (!(a&0x80))
998   {
999     /* Values between 16384 and 2097151 */
1000     a &= (0x7f<<14)|(0x7f);
1001     b &= 0x7f;
1002     b = b<<7;
1003     *v = a | b;
1004     return 3;
1005   }
1006 
1007   /* A 32-bit varint is used to store size information in btrees.
1008   ** Objects are rarely larger than 2MiB limit of a 3-byte varint.
1009   ** A 3-byte varint is sufficient, for example, to record the size
1010   ** of a 1048569-byte BLOB or string.
1011   **
1012   ** We only unroll the first 1-, 2-, and 3- byte cases.  The very
1013   ** rare larger cases can be handled by the slower 64-bit varint
1014   ** routine.
1015   */
1016 #if 1
1017   {
1018     u64 v64;
1019     u8 n;
1020 
1021     p -= 2;
1022     n = sqlite3GetVarint(p, &v64);
1023     assert( n>3 && n<=9 );
1024     if( (v64 & SQLITE_MAX_U32)!=v64 ){
1025       *v = 0xffffffff;
1026     }else{
1027       *v = (u32)v64;
1028     }
1029     return n;
1030   }
1031 
1032 #else
1033   /* For following code (kept for historical record only) shows an
1034   ** unrolling for the 3- and 4-byte varint cases.  This code is
1035   ** slightly faster, but it is also larger and much harder to test.
1036   */
1037   p++;
1038   b = b<<14;
1039   b |= *p;
1040   /* b: p1<<14 | p3 (unmasked) */
1041   if (!(b&0x80))
1042   {
1043     /* Values between 2097152 and 268435455 */
1044     b &= (0x7f<<14)|(0x7f);
1045     a &= (0x7f<<14)|(0x7f);
1046     a = a<<7;
1047     *v = a | b;
1048     return 4;
1049   }
1050 
1051   p++;
1052   a = a<<14;
1053   a |= *p;
1054   /* a: p0<<28 | p2<<14 | p4 (unmasked) */
1055   if (!(a&0x80))
1056   {
1057     /* Values  between 268435456 and 34359738367 */
1058     a &= SLOT_4_2_0;
1059     b &= SLOT_4_2_0;
1060     b = b<<7;
1061     *v = a | b;
1062     return 5;
1063   }
1064 
1065   /* We can only reach this point when reading a corrupt database
1066   ** file.  In that case we are not in any hurry.  Use the (relatively
1067   ** slow) general-purpose sqlite3GetVarint() routine to extract the
1068   ** value. */
1069   {
1070     u64 v64;
1071     u8 n;
1072 
1073     p -= 4;
1074     n = sqlite3GetVarint(p, &v64);
1075     assert( n>5 && n<=9 );
1076     *v = (u32)v64;
1077     return n;
1078   }
1079 #endif
1080 }
1081 
1082 /*
1083 ** Return the number of bytes that will be needed to store the given
1084 ** 64-bit integer.
1085 */
1086 int sqlite3VarintLen(u64 v){
1087   int i;
1088   for(i=1; (v >>= 7)!=0; i++){ assert( i<9 ); }
1089   return i;
1090 }
1091 
1092 
1093 /*
1094 ** Read or write a four-byte big-endian integer value.
1095 */
1096 u32 sqlite3Get4byte(const u8 *p){
1097 #if SQLITE_BYTEORDER==4321
1098   u32 x;
1099   memcpy(&x,p,4);
1100   return x;
1101 #elif SQLITE_BYTEORDER==1234 && !defined(SQLITE_DISABLE_INTRINSIC) \
1102     && defined(__GNUC__) && GCC_VERSION>=4003000
1103   u32 x;
1104   memcpy(&x,p,4);
1105   return __builtin_bswap32(x);
1106 #elif SQLITE_BYTEORDER==1234 && !defined(SQLITE_DISABLE_INTRINSIC) \
1107     && defined(_MSC_VER) && _MSC_VER>=1300
1108   u32 x;
1109   memcpy(&x,p,4);
1110   return _byteswap_ulong(x);
1111 #else
1112   testcase( p[0]&0x80 );
1113   return ((unsigned)p[0]<<24) | (p[1]<<16) | (p[2]<<8) | p[3];
1114 #endif
1115 }
1116 void sqlite3Put4byte(unsigned char *p, u32 v){
1117 #if SQLITE_BYTEORDER==4321
1118   memcpy(p,&v,4);
1119 #elif SQLITE_BYTEORDER==1234 && !defined(SQLITE_DISABLE_INTRINSIC) \
1120     && defined(__GNUC__) && GCC_VERSION>=4003000
1121   u32 x = __builtin_bswap32(v);
1122   memcpy(p,&x,4);
1123 #elif SQLITE_BYTEORDER==1234 && !defined(SQLITE_DISABLE_INTRINSIC) \
1124     && defined(_MSC_VER) && _MSC_VER>=1300
1125   u32 x = _byteswap_ulong(v);
1126   memcpy(p,&x,4);
1127 #else
1128   p[0] = (u8)(v>>24);
1129   p[1] = (u8)(v>>16);
1130   p[2] = (u8)(v>>8);
1131   p[3] = (u8)v;
1132 #endif
1133 }
1134 
1135 
1136 
1137 /*
1138 ** Translate a single byte of Hex into an integer.
1139 ** This routine only works if h really is a valid hexadecimal
1140 ** character:  0..9a..fA..F
1141 */
1142 u8 sqlite3HexToInt(int h){
1143   assert( (h>='0' && h<='9') ||  (h>='a' && h<='f') ||  (h>='A' && h<='F') );
1144 #ifdef SQLITE_ASCII
1145   h += 9*(1&(h>>6));
1146 #endif
1147 #ifdef SQLITE_EBCDIC
1148   h += 9*(1&~(h>>4));
1149 #endif
1150   return (u8)(h & 0xf);
1151 }
1152 
1153 #if !defined(SQLITE_OMIT_BLOB_LITERAL) || defined(SQLITE_HAS_CODEC)
1154 /*
1155 ** Convert a BLOB literal of the form "x'hhhhhh'" into its binary
1156 ** value.  Return a pointer to its binary value.  Space to hold the
1157 ** binary value has been obtained from malloc and must be freed by
1158 ** the calling routine.
1159 */
1160 void *sqlite3HexToBlob(sqlite3 *db, const char *z, int n){
1161   char *zBlob;
1162   int i;
1163 
1164   zBlob = (char *)sqlite3DbMallocRawNN(db, n/2 + 1);
1165   n--;
1166   if( zBlob ){
1167     for(i=0; i<n; i+=2){
1168       zBlob[i/2] = (sqlite3HexToInt(z[i])<<4) | sqlite3HexToInt(z[i+1]);
1169     }
1170     zBlob[i/2] = 0;
1171   }
1172   return zBlob;
1173 }
1174 #endif /* !SQLITE_OMIT_BLOB_LITERAL || SQLITE_HAS_CODEC */
1175 
1176 /*
1177 ** Log an error that is an API call on a connection pointer that should
1178 ** not have been used.  The "type" of connection pointer is given as the
1179 ** argument.  The zType is a word like "NULL" or "closed" or "invalid".
1180 */
1181 static void logBadConnection(const char *zType){
1182   sqlite3_log(SQLITE_MISUSE,
1183      "API call with %s database connection pointer",
1184      zType
1185   );
1186 }
1187 
1188 /*
1189 ** Check to make sure we have a valid db pointer.  This test is not
1190 ** foolproof but it does provide some measure of protection against
1191 ** misuse of the interface such as passing in db pointers that are
1192 ** NULL or which have been previously closed.  If this routine returns
1193 ** 1 it means that the db pointer is valid and 0 if it should not be
1194 ** dereferenced for any reason.  The calling function should invoke
1195 ** SQLITE_MISUSE immediately.
1196 **
1197 ** sqlite3SafetyCheckOk() requires that the db pointer be valid for
1198 ** use.  sqlite3SafetyCheckSickOrOk() allows a db pointer that failed to
1199 ** open properly and is not fit for general use but which can be
1200 ** used as an argument to sqlite3_errmsg() or sqlite3_close().
1201 */
1202 int sqlite3SafetyCheckOk(sqlite3 *db){
1203   u32 magic;
1204   if( db==0 ){
1205     logBadConnection("NULL");
1206     return 0;
1207   }
1208   magic = db->magic;
1209   if( magic!=SQLITE_MAGIC_OPEN ){
1210     if( sqlite3SafetyCheckSickOrOk(db) ){
1211       testcase( sqlite3GlobalConfig.xLog!=0 );
1212       logBadConnection("unopened");
1213     }
1214     return 0;
1215   }else{
1216     return 1;
1217   }
1218 }
1219 int sqlite3SafetyCheckSickOrOk(sqlite3 *db){
1220   u32 magic;
1221   magic = db->magic;
1222   if( magic!=SQLITE_MAGIC_SICK &&
1223       magic!=SQLITE_MAGIC_OPEN &&
1224       magic!=SQLITE_MAGIC_BUSY ){
1225     testcase( sqlite3GlobalConfig.xLog!=0 );
1226     logBadConnection("invalid");
1227     return 0;
1228   }else{
1229     return 1;
1230   }
1231 }
1232 
1233 /*
1234 ** Attempt to add, substract, or multiply the 64-bit signed value iB against
1235 ** the other 64-bit signed integer at *pA and store the result in *pA.
1236 ** Return 0 on success.  Or if the operation would have resulted in an
1237 ** overflow, leave *pA unchanged and return 1.
1238 */
1239 int sqlite3AddInt64(i64 *pA, i64 iB){
1240   i64 iA = *pA;
1241   testcase( iA==0 ); testcase( iA==1 );
1242   testcase( iB==-1 ); testcase( iB==0 );
1243   if( iB>=0 ){
1244     testcase( iA>0 && LARGEST_INT64 - iA == iB );
1245     testcase( iA>0 && LARGEST_INT64 - iA == iB - 1 );
1246     if( iA>0 && LARGEST_INT64 - iA < iB ) return 1;
1247   }else{
1248     testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 1 );
1249     testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 2 );
1250     if( iA<0 && -(iA + LARGEST_INT64) > iB + 1 ) return 1;
1251   }
1252   *pA += iB;
1253   return 0;
1254 }
1255 int sqlite3SubInt64(i64 *pA, i64 iB){
1256   testcase( iB==SMALLEST_INT64+1 );
1257   if( iB==SMALLEST_INT64 ){
1258     testcase( (*pA)==(-1) ); testcase( (*pA)==0 );
1259     if( (*pA)>=0 ) return 1;
1260     *pA -= iB;
1261     return 0;
1262   }else{
1263     return sqlite3AddInt64(pA, -iB);
1264   }
1265 }
1266 #define TWOPOWER32 (((i64)1)<<32)
1267 #define TWOPOWER31 (((i64)1)<<31)
1268 int sqlite3MulInt64(i64 *pA, i64 iB){
1269   i64 iA = *pA;
1270   i64 iA1, iA0, iB1, iB0, r;
1271 
1272   iA1 = iA/TWOPOWER32;
1273   iA0 = iA % TWOPOWER32;
1274   iB1 = iB/TWOPOWER32;
1275   iB0 = iB % TWOPOWER32;
1276   if( iA1==0 ){
1277     if( iB1==0 ){
1278       *pA *= iB;
1279       return 0;
1280     }
1281     r = iA0*iB1;
1282   }else if( iB1==0 ){
1283     r = iA1*iB0;
1284   }else{
1285     /* If both iA1 and iB1 are non-zero, overflow will result */
1286     return 1;
1287   }
1288   testcase( r==(-TWOPOWER31)-1 );
1289   testcase( r==(-TWOPOWER31) );
1290   testcase( r==TWOPOWER31 );
1291   testcase( r==TWOPOWER31-1 );
1292   if( r<(-TWOPOWER31) || r>=TWOPOWER31 ) return 1;
1293   r *= TWOPOWER32;
1294   if( sqlite3AddInt64(&r, iA0*iB0) ) return 1;
1295   *pA = r;
1296   return 0;
1297 }
1298 
1299 /*
1300 ** Compute the absolute value of a 32-bit signed integer, of possible.  Or
1301 ** if the integer has a value of -2147483648, return +2147483647
1302 */
1303 int sqlite3AbsInt32(int x){
1304   if( x>=0 ) return x;
1305   if( x==(int)0x80000000 ) return 0x7fffffff;
1306   return -x;
1307 }
1308 
1309 #ifdef SQLITE_ENABLE_8_3_NAMES
1310 /*
1311 ** If SQLITE_ENABLE_8_3_NAMES is set at compile-time and if the database
1312 ** filename in zBaseFilename is a URI with the "8_3_names=1" parameter and
1313 ** if filename in z[] has a suffix (a.k.a. "extension") that is longer than
1314 ** three characters, then shorten the suffix on z[] to be the last three
1315 ** characters of the original suffix.
1316 **
1317 ** If SQLITE_ENABLE_8_3_NAMES is set to 2 at compile-time, then always
1318 ** do the suffix shortening regardless of URI parameter.
1319 **
1320 ** Examples:
1321 **
1322 **     test.db-journal    =>   test.nal
1323 **     test.db-wal        =>   test.wal
1324 **     test.db-shm        =>   test.shm
1325 **     test.db-mj7f3319fa =>   test.9fa
1326 */
1327 void sqlite3FileSuffix3(const char *zBaseFilename, char *z){
1328 #if SQLITE_ENABLE_8_3_NAMES<2
1329   if( sqlite3_uri_boolean(zBaseFilename, "8_3_names", 0) )
1330 #endif
1331   {
1332     int i, sz;
1333     sz = sqlite3Strlen30(z);
1334     for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}
1335     if( z[i]=='.' && ALWAYS(sz>i+4) ) memmove(&z[i+1], &z[sz-3], 4);
1336   }
1337 }
1338 #endif
1339 
1340 /*
1341 ** Find (an approximate) sum of two LogEst values.  This computation is
1342 ** not a simple "+" operator because LogEst is stored as a logarithmic
1343 ** value.
1344 **
1345 */
1346 LogEst sqlite3LogEstAdd(LogEst a, LogEst b){
1347   static const unsigned char x[] = {
1348      10, 10,                         /* 0,1 */
1349       9, 9,                          /* 2,3 */
1350       8, 8,                          /* 4,5 */
1351       7, 7, 7,                       /* 6,7,8 */
1352       6, 6, 6,                       /* 9,10,11 */
1353       5, 5, 5,                       /* 12-14 */
1354       4, 4, 4, 4,                    /* 15-18 */
1355       3, 3, 3, 3, 3, 3,              /* 19-24 */
1356       2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
1357   };
1358   if( a>=b ){
1359     if( a>b+49 ) return a;
1360     if( a>b+31 ) return a+1;
1361     return a+x[a-b];
1362   }else{
1363     if( b>a+49 ) return b;
1364     if( b>a+31 ) return b+1;
1365     return b+x[b-a];
1366   }
1367 }
1368 
1369 /*
1370 ** Convert an integer into a LogEst.  In other words, compute an
1371 ** approximation for 10*log2(x).
1372 */
1373 LogEst sqlite3LogEst(u64 x){
1374   static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
1375   LogEst y = 40;
1376   if( x<8 ){
1377     if( x<2 ) return 0;
1378     while( x<8 ){  y -= 10; x <<= 1; }
1379   }else{
1380     while( x>255 ){ y += 40; x >>= 4; }
1381     while( x>15 ){  y += 10; x >>= 1; }
1382   }
1383   return a[x&7] + y - 10;
1384 }
1385 
1386 #ifndef SQLITE_OMIT_VIRTUALTABLE
1387 /*
1388 ** Convert a double into a LogEst
1389 ** In other words, compute an approximation for 10*log2(x).
1390 */
1391 LogEst sqlite3LogEstFromDouble(double x){
1392   u64 a;
1393   LogEst e;
1394   assert( sizeof(x)==8 && sizeof(a)==8 );
1395   if( x<=1 ) return 0;
1396   if( x<=2000000000 ) return sqlite3LogEst((u64)x);
1397   memcpy(&a, &x, 8);
1398   e = (a>>52) - 1022;
1399   return e*10;
1400 }
1401 #endif /* SQLITE_OMIT_VIRTUALTABLE */
1402 
1403 /*
1404 ** Convert a LogEst into an integer.
1405 */
1406 u64 sqlite3LogEstToInt(LogEst x){
1407   u64 n;
1408   if( x<10 ) return 1;
1409   n = x%10;
1410   x /= 10;
1411   if( n>=5 ) n -= 2;
1412   else if( n>=1 ) n -= 1;
1413   if( x>=3 ){
1414     return x>60 ? (u64)LARGEST_INT64 : (n+8)<<(x-3);
1415   }
1416   return (n+8)>>(3-x);
1417 }
1418