xref: /sqlite-3.40.0/src/util.c (revision cd423525)
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   register unsigned char *a, *b;
260   if( zLeft==0 ){
261     return zRight ? -1 : 0;
262   }else if( zRight==0 ){
263     return 1;
264   }
265   a = (unsigned char *)zLeft;
266   b = (unsigned char *)zRight;
267   while( *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
268   return UpperToLower[*a] - UpperToLower[*b];
269 }
270 int sqlite3_strnicmp(const char *zLeft, const char *zRight, int N){
271   register unsigned char *a, *b;
272   if( zLeft==0 ){
273     return zRight ? -1 : 0;
274   }else if( zRight==0 ){
275     return 1;
276   }
277   a = (unsigned char *)zLeft;
278   b = (unsigned char *)zRight;
279   while( N-- > 0 && *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
280   return N<0 ? 0 : UpperToLower[*a] - UpperToLower[*b];
281 }
282 
283 /*
284 ** The string z[] is an text representation of a real number.
285 ** Convert this string to a double and write it into *pResult.
286 **
287 ** The string z[] is length bytes in length (bytes, not characters) and
288 ** uses the encoding enc.  The string is not necessarily zero-terminated.
289 **
290 ** Return TRUE if the result is a valid real number (or integer) and FALSE
291 ** if the string is empty or contains extraneous text.  Valid numbers
292 ** are in one of these formats:
293 **
294 **    [+-]digits[E[+-]digits]
295 **    [+-]digits.[digits][E[+-]digits]
296 **    [+-].digits[E[+-]digits]
297 **
298 ** Leading and trailing whitespace is ignored for the purpose of determining
299 ** validity.
300 **
301 ** If some prefix of the input string is a valid number, this routine
302 ** returns FALSE but it still converts the prefix and writes the result
303 ** into *pResult.
304 */
305 int sqlite3AtoF(const char *z, double *pResult, int length, u8 enc){
306 #ifndef SQLITE_OMIT_FLOATING_POINT
307   int incr;
308   const char *zEnd = z + length;
309   /* sign * significand * (10 ^ (esign * exponent)) */
310   int sign = 1;    /* sign of significand */
311   i64 s = 0;       /* significand */
312   int d = 0;       /* adjust exponent for shifting decimal point */
313   int esign = 1;   /* sign of exponent */
314   int e = 0;       /* exponent */
315   int eValid = 1;  /* True exponent is either not used or is well-formed */
316   double result;
317   int nDigits = 0;
318   int nonNum = 0;
319 
320   assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
321   *pResult = 0.0;   /* Default return value, in case of an error */
322 
323   if( enc==SQLITE_UTF8 ){
324     incr = 1;
325   }else{
326     int i;
327     incr = 2;
328     assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
329     for(i=3-enc; i<length && z[i]==0; i+=2){}
330     nonNum = i<length;
331     zEnd = z+i+enc-3;
332     z += (enc&1);
333   }
334 
335   /* skip leading spaces */
336   while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
337   if( z>=zEnd ) return 0;
338 
339   /* get sign of significand */
340   if( *z=='-' ){
341     sign = -1;
342     z+=incr;
343   }else if( *z=='+' ){
344     z+=incr;
345   }
346 
347   /* skip leading zeroes */
348   while( z<zEnd && z[0]=='0' ) z+=incr, nDigits++;
349 
350   /* copy max significant digits to significand */
351   while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
352     s = s*10 + (*z - '0');
353     z+=incr, nDigits++;
354   }
355 
356   /* skip non-significant significand digits
357   ** (increase exponent by d to shift decimal left) */
358   while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++, d++;
359   if( z>=zEnd ) goto do_atof_calc;
360 
361   /* if decimal point is present */
362   if( *z=='.' ){
363     z+=incr;
364     /* copy digits from after decimal to significand
365     ** (decrease exponent by d to shift decimal right) */
366     while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
367       s = s*10 + (*z - '0');
368       z+=incr, nDigits++, d--;
369     }
370     /* skip non-significant digits */
371     while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++;
372   }
373   if( z>=zEnd ) goto do_atof_calc;
374 
375   /* if exponent is present */
376   if( *z=='e' || *z=='E' ){
377     z+=incr;
378     eValid = 0;
379     if( z>=zEnd ) goto do_atof_calc;
380     /* get sign of exponent */
381     if( *z=='-' ){
382       esign = -1;
383       z+=incr;
384     }else if( *z=='+' ){
385       z+=incr;
386     }
387     /* copy digits to exponent */
388     while( z<zEnd && sqlite3Isdigit(*z) ){
389       e = e<10000 ? (e*10 + (*z - '0')) : 10000;
390       z+=incr;
391       eValid = 1;
392     }
393   }
394 
395   /* skip trailing spaces */
396   if( nDigits && eValid ){
397     while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
398   }
399 
400 do_atof_calc:
401   /* adjust exponent by d, and update sign */
402   e = (e*esign) + d;
403   if( e<0 ) {
404     esign = -1;
405     e *= -1;
406   } else {
407     esign = 1;
408   }
409 
410   /* if 0 significand */
411   if( !s ) {
412     /* In the IEEE 754 standard, zero is signed.
413     ** Add the sign if we've seen at least one digit */
414     result = (sign<0 && nDigits) ? -(double)0 : (double)0;
415   } else {
416     /* attempt to reduce exponent */
417     if( esign>0 ){
418       while( s<(LARGEST_INT64/10) && e>0 ) e--,s*=10;
419     }else{
420       while( !(s%10) && e>0 ) e--,s/=10;
421     }
422 
423     /* adjust the sign of significand */
424     s = sign<0 ? -s : s;
425 
426     /* if exponent, scale significand as appropriate
427     ** and store in result. */
428     if( e ){
429       LONGDOUBLE_TYPE scale = 1.0;
430       /* attempt to handle extremely small/large numbers better */
431       if( e>307 && e<342 ){
432         while( e%308 ) { scale *= 1.0e+1; e -= 1; }
433         if( esign<0 ){
434           result = s / scale;
435           result /= 1.0e+308;
436         }else{
437           result = s * scale;
438           result *= 1.0e+308;
439         }
440       }else if( e>=342 ){
441         if( esign<0 ){
442           result = 0.0*s;
443         }else{
444           result = 1e308*1e308*s;  /* Infinity */
445         }
446       }else{
447         /* 1.0e+22 is the largest power of 10 than can be
448         ** represented exactly. */
449         while( e%22 ) { scale *= 1.0e+1; e -= 1; }
450         while( e>0 ) { scale *= 1.0e+22; e -= 22; }
451         if( esign<0 ){
452           result = s / scale;
453         }else{
454           result = s * scale;
455         }
456       }
457     } else {
458       result = (double)s;
459     }
460   }
461 
462   /* store the result */
463   *pResult = result;
464 
465   /* return true if number and no extra non-whitespace chracters after */
466   return z>=zEnd && nDigits>0 && eValid && nonNum==0;
467 #else
468   return !sqlite3Atoi64(z, pResult, length, enc);
469 #endif /* SQLITE_OMIT_FLOATING_POINT */
470 }
471 
472 /*
473 ** Compare the 19-character string zNum against the text representation
474 ** value 2^63:  9223372036854775808.  Return negative, zero, or positive
475 ** if zNum is less than, equal to, or greater than the string.
476 ** Note that zNum must contain exactly 19 characters.
477 **
478 ** Unlike memcmp() this routine is guaranteed to return the difference
479 ** in the values of the last digit if the only difference is in the
480 ** last digit.  So, for example,
481 **
482 **      compare2pow63("9223372036854775800", 1)
483 **
484 ** will return -8.
485 */
486 static int compare2pow63(const char *zNum, int incr){
487   int c = 0;
488   int i;
489                     /* 012345678901234567 */
490   const char *pow63 = "922337203685477580";
491   for(i=0; c==0 && i<18; i++){
492     c = (zNum[i*incr]-pow63[i])*10;
493   }
494   if( c==0 ){
495     c = zNum[18*incr] - '8';
496     testcase( c==(-1) );
497     testcase( c==0 );
498     testcase( c==(+1) );
499   }
500   return c;
501 }
502 
503 /*
504 ** Convert zNum to a 64-bit signed integer.  zNum must be decimal. This
505 ** routine does *not* accept hexadecimal notation.
506 **
507 ** If the zNum value is representable as a 64-bit twos-complement
508 ** integer, then write that value into *pNum and return 0.
509 **
510 ** If zNum is exactly 9223372036854775808, return 2.  This special
511 ** case is broken out because while 9223372036854775808 cannot be a
512 ** signed 64-bit integer, its negative -9223372036854775808 can be.
513 **
514 ** If zNum is too big for a 64-bit integer and is not
515 ** 9223372036854775808  or if zNum contains any non-numeric text,
516 ** then return 1.
517 **
518 ** length is the number of bytes in the string (bytes, not characters).
519 ** The string is not necessarily zero-terminated.  The encoding is
520 ** given by enc.
521 */
522 int sqlite3Atoi64(const char *zNum, i64 *pNum, int length, u8 enc){
523   int incr;
524   u64 u = 0;
525   int neg = 0; /* assume positive */
526   int i;
527   int c = 0;
528   int nonNum = 0;
529   const char *zStart;
530   const char *zEnd = zNum + length;
531   assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
532   if( enc==SQLITE_UTF8 ){
533     incr = 1;
534   }else{
535     incr = 2;
536     assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
537     for(i=3-enc; i<length && zNum[i]==0; i+=2){}
538     nonNum = i<length;
539     zEnd = zNum+i+enc-3;
540     zNum += (enc&1);
541   }
542   while( zNum<zEnd && sqlite3Isspace(*zNum) ) zNum+=incr;
543   if( zNum<zEnd ){
544     if( *zNum=='-' ){
545       neg = 1;
546       zNum+=incr;
547     }else if( *zNum=='+' ){
548       zNum+=incr;
549     }
550   }
551   zStart = zNum;
552   while( zNum<zEnd && zNum[0]=='0' ){ zNum+=incr; } /* Skip leading zeros. */
553   for(i=0; &zNum[i]<zEnd && (c=zNum[i])>='0' && c<='9'; i+=incr){
554     u = u*10 + c - '0';
555   }
556   if( u>LARGEST_INT64 ){
557     *pNum = neg ? SMALLEST_INT64 : LARGEST_INT64;
558   }else if( neg ){
559     *pNum = -(i64)u;
560   }else{
561     *pNum = (i64)u;
562   }
563   testcase( i==18 );
564   testcase( i==19 );
565   testcase( i==20 );
566   if( (c!=0 && &zNum[i]<zEnd) || (i==0 && zStart==zNum)
567        || i>19*incr || nonNum ){
568     /* zNum is empty or contains non-numeric text or is longer
569     ** than 19 digits (thus guaranteeing that it is too large) */
570     return 1;
571   }else if( i<19*incr ){
572     /* Less than 19 digits, so we know that it fits in 64 bits */
573     assert( u<=LARGEST_INT64 );
574     return 0;
575   }else{
576     /* zNum is a 19-digit numbers.  Compare it against 9223372036854775808. */
577     c = compare2pow63(zNum, incr);
578     if( c<0 ){
579       /* zNum is less than 9223372036854775808 so it fits */
580       assert( u<=LARGEST_INT64 );
581       return 0;
582     }else if( c>0 ){
583       /* zNum is greater than 9223372036854775808 so it overflows */
584       return 1;
585     }else{
586       /* zNum is exactly 9223372036854775808.  Fits if negative.  The
587       ** special case 2 overflow if positive */
588       assert( u-1==LARGEST_INT64 );
589       return neg ? 0 : 2;
590     }
591   }
592 }
593 
594 /*
595 ** Transform a UTF-8 integer literal, in either decimal or hexadecimal,
596 ** into a 64-bit signed integer.  This routine accepts hexadecimal literals,
597 ** whereas sqlite3Atoi64() does not.
598 **
599 ** Returns:
600 **
601 **     0    Successful transformation.  Fits in a 64-bit signed integer.
602 **     1    Integer too large for a 64-bit signed integer or is malformed
603 **     2    Special case of 9223372036854775808
604 */
605 int sqlite3DecOrHexToI64(const char *z, i64 *pOut){
606 #ifndef SQLITE_OMIT_HEX_INTEGER
607   if( z[0]=='0'
608    && (z[1]=='x' || z[1]=='X')
609    && sqlite3Isxdigit(z[2])
610   ){
611     u64 u = 0;
612     int i, k;
613     for(i=2; z[i]=='0'; i++){}
614     for(k=i; sqlite3Isxdigit(z[k]); k++){
615       u = u*16 + sqlite3HexToInt(z[k]);
616     }
617     memcpy(pOut, &u, 8);
618     return (z[k]==0 && k-i<=16) ? 0 : 1;
619   }else
620 #endif /* SQLITE_OMIT_HEX_INTEGER */
621   {
622     return sqlite3Atoi64(z, pOut, sqlite3Strlen30(z), SQLITE_UTF8);
623   }
624 }
625 
626 /*
627 ** If zNum represents an integer that will fit in 32-bits, then set
628 ** *pValue to that integer and return true.  Otherwise return false.
629 **
630 ** This routine accepts both decimal and hexadecimal notation for integers.
631 **
632 ** Any non-numeric characters that following zNum are ignored.
633 ** This is different from sqlite3Atoi64() which requires the
634 ** input number to be zero-terminated.
635 */
636 int sqlite3GetInt32(const char *zNum, int *pValue){
637   sqlite_int64 v = 0;
638   int i, c;
639   int neg = 0;
640   if( zNum[0]=='-' ){
641     neg = 1;
642     zNum++;
643   }else if( zNum[0]=='+' ){
644     zNum++;
645   }
646 #ifndef SQLITE_OMIT_HEX_INTEGER
647   else if( zNum[0]=='0'
648         && (zNum[1]=='x' || zNum[1]=='X')
649         && sqlite3Isxdigit(zNum[2])
650   ){
651     u32 u = 0;
652     zNum += 2;
653     while( zNum[0]=='0' ) zNum++;
654     for(i=0; sqlite3Isxdigit(zNum[i]) && i<8; i++){
655       u = u*16 + sqlite3HexToInt(zNum[i]);
656     }
657     if( (u&0x80000000)==0 && sqlite3Isxdigit(zNum[i])==0 ){
658       memcpy(pValue, &u, 4);
659       return 1;
660     }else{
661       return 0;
662     }
663   }
664 #endif
665   while( zNum[0]=='0' ) zNum++;
666   for(i=0; i<11 && (c = zNum[i] - '0')>=0 && c<=9; i++){
667     v = v*10 + c;
668   }
669 
670   /* The longest decimal representation of a 32 bit integer is 10 digits:
671   **
672   **             1234567890
673   **     2^31 -> 2147483648
674   */
675   testcase( i==10 );
676   if( i>10 ){
677     return 0;
678   }
679   testcase( v-neg==2147483647 );
680   if( v-neg>2147483647 ){
681     return 0;
682   }
683   if( neg ){
684     v = -v;
685   }
686   *pValue = (int)v;
687   return 1;
688 }
689 
690 /*
691 ** Return a 32-bit integer value extracted from a string.  If the
692 ** string is not an integer, just return 0.
693 */
694 int sqlite3Atoi(const char *z){
695   int x = 0;
696   if( z ) sqlite3GetInt32(z, &x);
697   return x;
698 }
699 
700 /*
701 ** The variable-length integer encoding is as follows:
702 **
703 ** KEY:
704 **         A = 0xxxxxxx    7 bits of data and one flag bit
705 **         B = 1xxxxxxx    7 bits of data and one flag bit
706 **         C = xxxxxxxx    8 bits of data
707 **
708 **  7 bits - A
709 ** 14 bits - BA
710 ** 21 bits - BBA
711 ** 28 bits - BBBA
712 ** 35 bits - BBBBA
713 ** 42 bits - BBBBBA
714 ** 49 bits - BBBBBBA
715 ** 56 bits - BBBBBBBA
716 ** 64 bits - BBBBBBBBC
717 */
718 
719 /*
720 ** Write a 64-bit variable-length integer to memory starting at p[0].
721 ** The length of data write will be between 1 and 9 bytes.  The number
722 ** of bytes written is returned.
723 **
724 ** A variable-length integer consists of the lower 7 bits of each byte
725 ** for all bytes that have the 8th bit set and one byte with the 8th
726 ** bit clear.  Except, if we get to the 9th byte, it stores the full
727 ** 8 bits and is the last byte.
728 */
729 static int SQLITE_NOINLINE putVarint64(unsigned char *p, u64 v){
730   int i, j, n;
731   u8 buf[10];
732   if( v & (((u64)0xff000000)<<32) ){
733     p[8] = (u8)v;
734     v >>= 8;
735     for(i=7; i>=0; i--){
736       p[i] = (u8)((v & 0x7f) | 0x80);
737       v >>= 7;
738     }
739     return 9;
740   }
741   n = 0;
742   do{
743     buf[n++] = (u8)((v & 0x7f) | 0x80);
744     v >>= 7;
745   }while( v!=0 );
746   buf[0] &= 0x7f;
747   assert( n<=9 );
748   for(i=0, j=n-1; j>=0; j--, i++){
749     p[i] = buf[j];
750   }
751   return n;
752 }
753 int sqlite3PutVarint(unsigned char *p, u64 v){
754   if( v<=0x7f ){
755     p[0] = v&0x7f;
756     return 1;
757   }
758   if( v<=0x3fff ){
759     p[0] = ((v>>7)&0x7f)|0x80;
760     p[1] = v&0x7f;
761     return 2;
762   }
763   return putVarint64(p,v);
764 }
765 
766 /*
767 ** Bitmasks used by sqlite3GetVarint().  These precomputed constants
768 ** are defined here rather than simply putting the constant expressions
769 ** inline in order to work around bugs in the RVT compiler.
770 **
771 ** SLOT_2_0     A mask for  (0x7f<<14) | 0x7f
772 **
773 ** SLOT_4_2_0   A mask for  (0x7f<<28) | SLOT_2_0
774 */
775 #define SLOT_2_0     0x001fc07f
776 #define SLOT_4_2_0   0xf01fc07f
777 
778 
779 /*
780 ** Read a 64-bit variable-length integer from memory starting at p[0].
781 ** Return the number of bytes read.  The value is stored in *v.
782 */
783 u8 sqlite3GetVarint(const unsigned char *p, u64 *v){
784   u32 a,b,s;
785 
786   a = *p;
787   /* a: p0 (unmasked) */
788   if (!(a&0x80))
789   {
790     *v = a;
791     return 1;
792   }
793 
794   p++;
795   b = *p;
796   /* b: p1 (unmasked) */
797   if (!(b&0x80))
798   {
799     a &= 0x7f;
800     a = a<<7;
801     a |= b;
802     *v = a;
803     return 2;
804   }
805 
806   /* Verify that constants are precomputed correctly */
807   assert( SLOT_2_0 == ((0x7f<<14) | (0x7f)) );
808   assert( SLOT_4_2_0 == ((0xfU<<28) | (0x7f<<14) | (0x7f)) );
809 
810   p++;
811   a = a<<14;
812   a |= *p;
813   /* a: p0<<14 | p2 (unmasked) */
814   if (!(a&0x80))
815   {
816     a &= SLOT_2_0;
817     b &= 0x7f;
818     b = b<<7;
819     a |= b;
820     *v = a;
821     return 3;
822   }
823 
824   /* CSE1 from below */
825   a &= SLOT_2_0;
826   p++;
827   b = b<<14;
828   b |= *p;
829   /* b: p1<<14 | p3 (unmasked) */
830   if (!(b&0x80))
831   {
832     b &= SLOT_2_0;
833     /* moved CSE1 up */
834     /* a &= (0x7f<<14)|(0x7f); */
835     a = a<<7;
836     a |= b;
837     *v = a;
838     return 4;
839   }
840 
841   /* a: p0<<14 | p2 (masked) */
842   /* b: p1<<14 | p3 (unmasked) */
843   /* 1:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
844   /* moved CSE1 up */
845   /* a &= (0x7f<<14)|(0x7f); */
846   b &= SLOT_2_0;
847   s = a;
848   /* s: p0<<14 | p2 (masked) */
849 
850   p++;
851   a = a<<14;
852   a |= *p;
853   /* a: p0<<28 | p2<<14 | p4 (unmasked) */
854   if (!(a&0x80))
855   {
856     /* we can skip these cause they were (effectively) done above
857     ** while calculating s */
858     /* a &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
859     /* b &= (0x7f<<14)|(0x7f); */
860     b = b<<7;
861     a |= b;
862     s = s>>18;
863     *v = ((u64)s)<<32 | a;
864     return 5;
865   }
866 
867   /* 2:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
868   s = s<<7;
869   s |= b;
870   /* s: p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
871 
872   p++;
873   b = b<<14;
874   b |= *p;
875   /* b: p1<<28 | p3<<14 | p5 (unmasked) */
876   if (!(b&0x80))
877   {
878     /* we can skip this cause it was (effectively) done above in calc'ing s */
879     /* b &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
880     a &= SLOT_2_0;
881     a = a<<7;
882     a |= b;
883     s = s>>18;
884     *v = ((u64)s)<<32 | a;
885     return 6;
886   }
887 
888   p++;
889   a = a<<14;
890   a |= *p;
891   /* a: p2<<28 | p4<<14 | p6 (unmasked) */
892   if (!(a&0x80))
893   {
894     a &= SLOT_4_2_0;
895     b &= SLOT_2_0;
896     b = b<<7;
897     a |= b;
898     s = s>>11;
899     *v = ((u64)s)<<32 | a;
900     return 7;
901   }
902 
903   /* CSE2 from below */
904   a &= SLOT_2_0;
905   p++;
906   b = b<<14;
907   b |= *p;
908   /* b: p3<<28 | p5<<14 | p7 (unmasked) */
909   if (!(b&0x80))
910   {
911     b &= SLOT_4_2_0;
912     /* moved CSE2 up */
913     /* a &= (0x7f<<14)|(0x7f); */
914     a = a<<7;
915     a |= b;
916     s = s>>4;
917     *v = ((u64)s)<<32 | a;
918     return 8;
919   }
920 
921   p++;
922   a = a<<15;
923   a |= *p;
924   /* a: p4<<29 | p6<<15 | p8 (unmasked) */
925 
926   /* moved CSE2 up */
927   /* a &= (0x7f<<29)|(0x7f<<15)|(0xff); */
928   b &= SLOT_2_0;
929   b = b<<8;
930   a |= b;
931 
932   s = s<<4;
933   b = p[-4];
934   b &= 0x7f;
935   b = b>>3;
936   s |= b;
937 
938   *v = ((u64)s)<<32 | a;
939 
940   return 9;
941 }
942 
943 /*
944 ** Read a 32-bit variable-length integer from memory starting at p[0].
945 ** Return the number of bytes read.  The value is stored in *v.
946 **
947 ** If the varint stored in p[0] is larger than can fit in a 32-bit unsigned
948 ** integer, then set *v to 0xffffffff.
949 **
950 ** A MACRO version, getVarint32, is provided which inlines the
951 ** single-byte case.  All code should use the MACRO version as
952 ** this function assumes the single-byte case has already been handled.
953 */
954 u8 sqlite3GetVarint32(const unsigned char *p, u32 *v){
955   u32 a,b;
956 
957   /* The 1-byte case.  Overwhelmingly the most common.  Handled inline
958   ** by the getVarin32() macro */
959   a = *p;
960   /* a: p0 (unmasked) */
961 #ifndef getVarint32
962   if (!(a&0x80))
963   {
964     /* Values between 0 and 127 */
965     *v = a;
966     return 1;
967   }
968 #endif
969 
970   /* The 2-byte case */
971   p++;
972   b = *p;
973   /* b: p1 (unmasked) */
974   if (!(b&0x80))
975   {
976     /* Values between 128 and 16383 */
977     a &= 0x7f;
978     a = a<<7;
979     *v = a | b;
980     return 2;
981   }
982 
983   /* The 3-byte case */
984   p++;
985   a = a<<14;
986   a |= *p;
987   /* a: p0<<14 | p2 (unmasked) */
988   if (!(a&0x80))
989   {
990     /* Values between 16384 and 2097151 */
991     a &= (0x7f<<14)|(0x7f);
992     b &= 0x7f;
993     b = b<<7;
994     *v = a | b;
995     return 3;
996   }
997 
998   /* A 32-bit varint is used to store size information in btrees.
999   ** Objects are rarely larger than 2MiB limit of a 3-byte varint.
1000   ** A 3-byte varint is sufficient, for example, to record the size
1001   ** of a 1048569-byte BLOB or string.
1002   **
1003   ** We only unroll the first 1-, 2-, and 3- byte cases.  The very
1004   ** rare larger cases can be handled by the slower 64-bit varint
1005   ** routine.
1006   */
1007 #if 1
1008   {
1009     u64 v64;
1010     u8 n;
1011 
1012     p -= 2;
1013     n = sqlite3GetVarint(p, &v64);
1014     assert( n>3 && n<=9 );
1015     if( (v64 & SQLITE_MAX_U32)!=v64 ){
1016       *v = 0xffffffff;
1017     }else{
1018       *v = (u32)v64;
1019     }
1020     return n;
1021   }
1022 
1023 #else
1024   /* For following code (kept for historical record only) shows an
1025   ** unrolling for the 3- and 4-byte varint cases.  This code is
1026   ** slightly faster, but it is also larger and much harder to test.
1027   */
1028   p++;
1029   b = b<<14;
1030   b |= *p;
1031   /* b: p1<<14 | p3 (unmasked) */
1032   if (!(b&0x80))
1033   {
1034     /* Values between 2097152 and 268435455 */
1035     b &= (0x7f<<14)|(0x7f);
1036     a &= (0x7f<<14)|(0x7f);
1037     a = a<<7;
1038     *v = a | b;
1039     return 4;
1040   }
1041 
1042   p++;
1043   a = a<<14;
1044   a |= *p;
1045   /* a: p0<<28 | p2<<14 | p4 (unmasked) */
1046   if (!(a&0x80))
1047   {
1048     /* Values  between 268435456 and 34359738367 */
1049     a &= SLOT_4_2_0;
1050     b &= SLOT_4_2_0;
1051     b = b<<7;
1052     *v = a | b;
1053     return 5;
1054   }
1055 
1056   /* We can only reach this point when reading a corrupt database
1057   ** file.  In that case we are not in any hurry.  Use the (relatively
1058   ** slow) general-purpose sqlite3GetVarint() routine to extract the
1059   ** value. */
1060   {
1061     u64 v64;
1062     u8 n;
1063 
1064     p -= 4;
1065     n = sqlite3GetVarint(p, &v64);
1066     assert( n>5 && n<=9 );
1067     *v = (u32)v64;
1068     return n;
1069   }
1070 #endif
1071 }
1072 
1073 /*
1074 ** Return the number of bytes that will be needed to store the given
1075 ** 64-bit integer.
1076 */
1077 int sqlite3VarintLen(u64 v){
1078   int i;
1079   for(i=1; (v >>= 7)!=0; i++){ assert( i<9 ); }
1080   return i;
1081 }
1082 
1083 
1084 /*
1085 ** Read or write a four-byte big-endian integer value.
1086 */
1087 u32 sqlite3Get4byte(const u8 *p){
1088 #if SQLITE_BYTEORDER==4321
1089   u32 x;
1090   memcpy(&x,p,4);
1091   return x;
1092 #elif SQLITE_BYTEORDER==1234 && !defined(SQLITE_DISABLE_INTRINSIC) \
1093     && defined(__GNUC__) && GCC_VERSION>=4003000
1094   u32 x;
1095   memcpy(&x,p,4);
1096   return __builtin_bswap32(x);
1097 #elif SQLITE_BYTEORDER==1234 && !defined(SQLITE_DISABLE_INTRINSIC) \
1098     && defined(_MSC_VER) && _MSC_VER>=1300
1099   u32 x;
1100   memcpy(&x,p,4);
1101   return _byteswap_ulong(x);
1102 #else
1103   testcase( p[0]&0x80 );
1104   return ((unsigned)p[0]<<24) | (p[1]<<16) | (p[2]<<8) | p[3];
1105 #endif
1106 }
1107 void sqlite3Put4byte(unsigned char *p, u32 v){
1108 #if SQLITE_BYTEORDER==4321
1109   memcpy(p,&v,4);
1110 #elif SQLITE_BYTEORDER==1234 && defined(__GNUC__) && GCC_VERSION>=4003000
1111   u32 x = __builtin_bswap32(v);
1112   memcpy(p,&x,4);
1113 #elif SQLITE_BYTEORDER==1234 && defined(_MSC_VER) && _MSC_VER>=1300
1114   u32 x = _byteswap_ulong(v);
1115   memcpy(p,&x,4);
1116 #else
1117   p[0] = (u8)(v>>24);
1118   p[1] = (u8)(v>>16);
1119   p[2] = (u8)(v>>8);
1120   p[3] = (u8)v;
1121 #endif
1122 }
1123 
1124 
1125 
1126 /*
1127 ** Translate a single byte of Hex into an integer.
1128 ** This routine only works if h really is a valid hexadecimal
1129 ** character:  0..9a..fA..F
1130 */
1131 u8 sqlite3HexToInt(int h){
1132   assert( (h>='0' && h<='9') ||  (h>='a' && h<='f') ||  (h>='A' && h<='F') );
1133 #ifdef SQLITE_ASCII
1134   h += 9*(1&(h>>6));
1135 #endif
1136 #ifdef SQLITE_EBCDIC
1137   h += 9*(1&~(h>>4));
1138 #endif
1139   return (u8)(h & 0xf);
1140 }
1141 
1142 #if !defined(SQLITE_OMIT_BLOB_LITERAL) || defined(SQLITE_HAS_CODEC)
1143 /*
1144 ** Convert a BLOB literal of the form "x'hhhhhh'" into its binary
1145 ** value.  Return a pointer to its binary value.  Space to hold the
1146 ** binary value has been obtained from malloc and must be freed by
1147 ** the calling routine.
1148 */
1149 void *sqlite3HexToBlob(sqlite3 *db, const char *z, int n){
1150   char *zBlob;
1151   int i;
1152 
1153   zBlob = (char *)sqlite3DbMallocRawNN(db, n/2 + 1);
1154   n--;
1155   if( zBlob ){
1156     for(i=0; i<n; i+=2){
1157       zBlob[i/2] = (sqlite3HexToInt(z[i])<<4) | sqlite3HexToInt(z[i+1]);
1158     }
1159     zBlob[i/2] = 0;
1160   }
1161   return zBlob;
1162 }
1163 #endif /* !SQLITE_OMIT_BLOB_LITERAL || SQLITE_HAS_CODEC */
1164 
1165 /*
1166 ** Log an error that is an API call on a connection pointer that should
1167 ** not have been used.  The "type" of connection pointer is given as the
1168 ** argument.  The zType is a word like "NULL" or "closed" or "invalid".
1169 */
1170 static void logBadConnection(const char *zType){
1171   sqlite3_log(SQLITE_MISUSE,
1172      "API call with %s database connection pointer",
1173      zType
1174   );
1175 }
1176 
1177 /*
1178 ** Check to make sure we have a valid db pointer.  This test is not
1179 ** foolproof but it does provide some measure of protection against
1180 ** misuse of the interface such as passing in db pointers that are
1181 ** NULL or which have been previously closed.  If this routine returns
1182 ** 1 it means that the db pointer is valid and 0 if it should not be
1183 ** dereferenced for any reason.  The calling function should invoke
1184 ** SQLITE_MISUSE immediately.
1185 **
1186 ** sqlite3SafetyCheckOk() requires that the db pointer be valid for
1187 ** use.  sqlite3SafetyCheckSickOrOk() allows a db pointer that failed to
1188 ** open properly and is not fit for general use but which can be
1189 ** used as an argument to sqlite3_errmsg() or sqlite3_close().
1190 */
1191 int sqlite3SafetyCheckOk(sqlite3 *db){
1192   u32 magic;
1193   if( db==0 ){
1194     logBadConnection("NULL");
1195     return 0;
1196   }
1197   magic = db->magic;
1198   if( magic!=SQLITE_MAGIC_OPEN ){
1199     if( sqlite3SafetyCheckSickOrOk(db) ){
1200       testcase( sqlite3GlobalConfig.xLog!=0 );
1201       logBadConnection("unopened");
1202     }
1203     return 0;
1204   }else{
1205     return 1;
1206   }
1207 }
1208 int sqlite3SafetyCheckSickOrOk(sqlite3 *db){
1209   u32 magic;
1210   magic = db->magic;
1211   if( magic!=SQLITE_MAGIC_SICK &&
1212       magic!=SQLITE_MAGIC_OPEN &&
1213       magic!=SQLITE_MAGIC_BUSY ){
1214     testcase( sqlite3GlobalConfig.xLog!=0 );
1215     logBadConnection("invalid");
1216     return 0;
1217   }else{
1218     return 1;
1219   }
1220 }
1221 
1222 /*
1223 ** Attempt to add, substract, or multiply the 64-bit signed value iB against
1224 ** the other 64-bit signed integer at *pA and store the result in *pA.
1225 ** Return 0 on success.  Or if the operation would have resulted in an
1226 ** overflow, leave *pA unchanged and return 1.
1227 */
1228 int sqlite3AddInt64(i64 *pA, i64 iB){
1229   i64 iA = *pA;
1230   testcase( iA==0 ); testcase( iA==1 );
1231   testcase( iB==-1 ); testcase( iB==0 );
1232   if( iB>=0 ){
1233     testcase( iA>0 && LARGEST_INT64 - iA == iB );
1234     testcase( iA>0 && LARGEST_INT64 - iA == iB - 1 );
1235     if( iA>0 && LARGEST_INT64 - iA < iB ) return 1;
1236   }else{
1237     testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 1 );
1238     testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 2 );
1239     if( iA<0 && -(iA + LARGEST_INT64) > iB + 1 ) return 1;
1240   }
1241   *pA += iB;
1242   return 0;
1243 }
1244 int sqlite3SubInt64(i64 *pA, i64 iB){
1245   testcase( iB==SMALLEST_INT64+1 );
1246   if( iB==SMALLEST_INT64 ){
1247     testcase( (*pA)==(-1) ); testcase( (*pA)==0 );
1248     if( (*pA)>=0 ) return 1;
1249     *pA -= iB;
1250     return 0;
1251   }else{
1252     return sqlite3AddInt64(pA, -iB);
1253   }
1254 }
1255 #define TWOPOWER32 (((i64)1)<<32)
1256 #define TWOPOWER31 (((i64)1)<<31)
1257 int sqlite3MulInt64(i64 *pA, i64 iB){
1258   i64 iA = *pA;
1259   i64 iA1, iA0, iB1, iB0, r;
1260 
1261   iA1 = iA/TWOPOWER32;
1262   iA0 = iA % TWOPOWER32;
1263   iB1 = iB/TWOPOWER32;
1264   iB0 = iB % TWOPOWER32;
1265   if( iA1==0 ){
1266     if( iB1==0 ){
1267       *pA *= iB;
1268       return 0;
1269     }
1270     r = iA0*iB1;
1271   }else if( iB1==0 ){
1272     r = iA1*iB0;
1273   }else{
1274     /* If both iA1 and iB1 are non-zero, overflow will result */
1275     return 1;
1276   }
1277   testcase( r==(-TWOPOWER31)-1 );
1278   testcase( r==(-TWOPOWER31) );
1279   testcase( r==TWOPOWER31 );
1280   testcase( r==TWOPOWER31-1 );
1281   if( r<(-TWOPOWER31) || r>=TWOPOWER31 ) return 1;
1282   r *= TWOPOWER32;
1283   if( sqlite3AddInt64(&r, iA0*iB0) ) return 1;
1284   *pA = r;
1285   return 0;
1286 }
1287 
1288 /*
1289 ** Compute the absolute value of a 32-bit signed integer, of possible.  Or
1290 ** if the integer has a value of -2147483648, return +2147483647
1291 */
1292 int sqlite3AbsInt32(int x){
1293   if( x>=0 ) return x;
1294   if( x==(int)0x80000000 ) return 0x7fffffff;
1295   return -x;
1296 }
1297 
1298 #ifdef SQLITE_ENABLE_8_3_NAMES
1299 /*
1300 ** If SQLITE_ENABLE_8_3_NAMES is set at compile-time and if the database
1301 ** filename in zBaseFilename is a URI with the "8_3_names=1" parameter and
1302 ** if filename in z[] has a suffix (a.k.a. "extension") that is longer than
1303 ** three characters, then shorten the suffix on z[] to be the last three
1304 ** characters of the original suffix.
1305 **
1306 ** If SQLITE_ENABLE_8_3_NAMES is set to 2 at compile-time, then always
1307 ** do the suffix shortening regardless of URI parameter.
1308 **
1309 ** Examples:
1310 **
1311 **     test.db-journal    =>   test.nal
1312 **     test.db-wal        =>   test.wal
1313 **     test.db-shm        =>   test.shm
1314 **     test.db-mj7f3319fa =>   test.9fa
1315 */
1316 void sqlite3FileSuffix3(const char *zBaseFilename, char *z){
1317 #if SQLITE_ENABLE_8_3_NAMES<2
1318   if( sqlite3_uri_boolean(zBaseFilename, "8_3_names", 0) )
1319 #endif
1320   {
1321     int i, sz;
1322     sz = sqlite3Strlen30(z);
1323     for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}
1324     if( z[i]=='.' && ALWAYS(sz>i+4) ) memmove(&z[i+1], &z[sz-3], 4);
1325   }
1326 }
1327 #endif
1328 
1329 /*
1330 ** Find (an approximate) sum of two LogEst values.  This computation is
1331 ** not a simple "+" operator because LogEst is stored as a logarithmic
1332 ** value.
1333 **
1334 */
1335 LogEst sqlite3LogEstAdd(LogEst a, LogEst b){
1336   static const unsigned char x[] = {
1337      10, 10,                         /* 0,1 */
1338       9, 9,                          /* 2,3 */
1339       8, 8,                          /* 4,5 */
1340       7, 7, 7,                       /* 6,7,8 */
1341       6, 6, 6,                       /* 9,10,11 */
1342       5, 5, 5,                       /* 12-14 */
1343       4, 4, 4, 4,                    /* 15-18 */
1344       3, 3, 3, 3, 3, 3,              /* 19-24 */
1345       2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
1346   };
1347   if( a>=b ){
1348     if( a>b+49 ) return a;
1349     if( a>b+31 ) return a+1;
1350     return a+x[a-b];
1351   }else{
1352     if( b>a+49 ) return b;
1353     if( b>a+31 ) return b+1;
1354     return b+x[b-a];
1355   }
1356 }
1357 
1358 /*
1359 ** Convert an integer into a LogEst.  In other words, compute an
1360 ** approximation for 10*log2(x).
1361 */
1362 LogEst sqlite3LogEst(u64 x){
1363   static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
1364   LogEst y = 40;
1365   if( x<8 ){
1366     if( x<2 ) return 0;
1367     while( x<8 ){  y -= 10; x <<= 1; }
1368   }else{
1369     while( x>255 ){ y += 40; x >>= 4; }
1370     while( x>15 ){  y += 10; x >>= 1; }
1371   }
1372   return a[x&7] + y - 10;
1373 }
1374 
1375 #ifndef SQLITE_OMIT_VIRTUALTABLE
1376 /*
1377 ** Convert a double into a LogEst
1378 ** In other words, compute an approximation for 10*log2(x).
1379 */
1380 LogEst sqlite3LogEstFromDouble(double x){
1381   u64 a;
1382   LogEst e;
1383   assert( sizeof(x)==8 && sizeof(a)==8 );
1384   if( x<=1 ) return 0;
1385   if( x<=2000000000 ) return sqlite3LogEst((u64)x);
1386   memcpy(&a, &x, 8);
1387   e = (a>>52) - 1022;
1388   return e*10;
1389 }
1390 #endif /* SQLITE_OMIT_VIRTUALTABLE */
1391 
1392 /*
1393 ** Convert a LogEst into an integer.
1394 */
1395 u64 sqlite3LogEstToInt(LogEst x){
1396   u64 n;
1397   if( x<10 ) return 1;
1398   n = x%10;
1399   x /= 10;
1400   if( n>=5 ) n -= 2;
1401   else if( n>=1 ) n -= 1;
1402   if( x>=3 ){
1403     return x>60 ? (u64)LARGEST_INT64 : (n+8)<<(x-3);
1404   }
1405   return (n+8)>>(3-x);
1406 }
1407