xref: /sqlite-3.40.0/src/util.c (revision d4530979)
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 #ifdef 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 !defined(SQLITE_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 defined(SQLITE_HAVE_ISNAN) */
92   rc = isnan(x);
93 #endif /* SQLITE_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   const char *z2 = z;
109   if( z==0 ) return 0;
110   while( *z2 ){ z2++; }
111   return 0x3fffffff & (int)(z2 - z);
112 }
113 
114 /*
115 ** Set the current error code to err_code and clear any prior error message.
116 */
117 void sqlite3Error(sqlite3 *db, int err_code){
118   assert( db!=0 );
119   db->errCode = err_code;
120   if( db->pErr ) sqlite3ValueSetNull(db->pErr);
121 }
122 
123 /*
124 ** Set the most recent error code and error string for the sqlite
125 ** handle "db". The error code is set to "err_code".
126 **
127 ** If it is not NULL, string zFormat specifies the format of the
128 ** error string in the style of the printf functions: The following
129 ** format characters are allowed:
130 **
131 **      %s      Insert a string
132 **      %z      A string that should be freed after use
133 **      %d      Insert an integer
134 **      %T      Insert a token
135 **      %S      Insert the first element of a SrcList
136 **
137 ** zFormat and any string tokens that follow it are assumed to be
138 ** encoded in UTF-8.
139 **
140 ** To clear the most recent error for sqlite handle "db", sqlite3Error
141 ** should be called with err_code set to SQLITE_OK and zFormat set
142 ** to NULL.
143 */
144 void sqlite3ErrorWithMsg(sqlite3 *db, int err_code, const char *zFormat, ...){
145   assert( db!=0 );
146   db->errCode = err_code;
147   if( zFormat==0 ){
148     sqlite3Error(db, err_code);
149   }else if( db->pErr || (db->pErr = sqlite3ValueNew(db))!=0 ){
150     char *z;
151     va_list ap;
152     va_start(ap, zFormat);
153     z = sqlite3VMPrintf(db, zFormat, ap);
154     va_end(ap);
155     sqlite3ValueSetStr(db->pErr, -1, z, SQLITE_UTF8, SQLITE_DYNAMIC);
156   }
157 }
158 
159 /*
160 ** Add an error message to pParse->zErrMsg and increment pParse->nErr.
161 ** The following formatting characters are allowed:
162 **
163 **      %s      Insert a string
164 **      %z      A string that should be freed after use
165 **      %d      Insert an integer
166 **      %T      Insert a token
167 **      %S      Insert the first element of a SrcList
168 **
169 ** This function should be used to report any error that occurs while
170 ** compiling an SQL statement (i.e. within sqlite3_prepare()). The
171 ** last thing the sqlite3_prepare() function does is copy the error
172 ** stored by this function into the database handle using sqlite3Error().
173 ** Functions sqlite3Error() or sqlite3ErrorWithMsg() should be used
174 ** during statement execution (sqlite3_step() etc.).
175 */
176 void sqlite3ErrorMsg(Parse *pParse, const char *zFormat, ...){
177   char *zMsg;
178   va_list ap;
179   sqlite3 *db = pParse->db;
180   va_start(ap, zFormat);
181   zMsg = sqlite3VMPrintf(db, zFormat, ap);
182   va_end(ap);
183   if( db->suppressErr ){
184     sqlite3DbFree(db, zMsg);
185   }else{
186     pParse->nErr++;
187     sqlite3DbFree(db, pParse->zErrMsg);
188     pParse->zErrMsg = zMsg;
189     pParse->rc = SQLITE_ERROR;
190   }
191 }
192 
193 /*
194 ** Convert an SQL-style quoted string into a normal string by removing
195 ** the quote characters.  The conversion is done in-place.  If the
196 ** input does not begin with a quote character, then this routine
197 ** is a no-op.
198 **
199 ** The input string must be zero-terminated.  A new zero-terminator
200 ** is added to the dequoted string.
201 **
202 ** The return value is -1 if no dequoting occurs or the length of the
203 ** dequoted string, exclusive of the zero terminator, if dequoting does
204 ** occur.
205 **
206 ** 2002-Feb-14: This routine is extended to remove MS-Access style
207 ** brackets from around identifiers.  For example:  "[a-b-c]" becomes
208 ** "a-b-c".
209 */
210 int sqlite3Dequote(char *z){
211   char quote;
212   int i, j;
213   if( z==0 ) return -1;
214   quote = z[0];
215   switch( quote ){
216     case '\'':  break;
217     case '"':   break;
218     case '`':   break;                /* For MySQL compatibility */
219     case '[':   quote = ']';  break;  /* For MS SqlServer compatibility */
220     default:    return -1;
221   }
222   for(i=1, j=0;; i++){
223     assert( z[i] );
224     if( z[i]==quote ){
225       if( z[i+1]==quote ){
226         z[j++] = quote;
227         i++;
228       }else{
229         break;
230       }
231     }else{
232       z[j++] = z[i];
233     }
234   }
235   z[j] = 0;
236   return j;
237 }
238 
239 /* Convenient short-hand */
240 #define UpperToLower sqlite3UpperToLower
241 
242 /*
243 ** Some systems have stricmp().  Others have strcasecmp().  Because
244 ** there is no consistency, we will define our own.
245 **
246 ** IMPLEMENTATION-OF: R-30243-02494 The sqlite3_stricmp() and
247 ** sqlite3_strnicmp() APIs allow applications and extensions to compare
248 ** the contents of two buffers containing UTF-8 strings in a
249 ** case-independent fashion, using the same definition of "case
250 ** independence" that SQLite uses internally when comparing identifiers.
251 */
252 int sqlite3_stricmp(const char *zLeft, const char *zRight){
253   register unsigned char *a, *b;
254   a = (unsigned char *)zLeft;
255   b = (unsigned char *)zRight;
256   while( *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
257   return UpperToLower[*a] - UpperToLower[*b];
258 }
259 int sqlite3_strnicmp(const char *zLeft, const char *zRight, int N){
260   register unsigned char *a, *b;
261   a = (unsigned char *)zLeft;
262   b = (unsigned char *)zRight;
263   while( N-- > 0 && *a!=0 && UpperToLower[*a]==UpperToLower[*b]){ a++; b++; }
264   return N<0 ? 0 : UpperToLower[*a] - UpperToLower[*b];
265 }
266 
267 /*
268 ** The string z[] is an text representation of a real number.
269 ** Convert this string to a double and write it into *pResult.
270 **
271 ** The string z[] is length bytes in length (bytes, not characters) and
272 ** uses the encoding enc.  The string is not necessarily zero-terminated.
273 **
274 ** Return TRUE if the result is a valid real number (or integer) and FALSE
275 ** if the string is empty or contains extraneous text.  Valid numbers
276 ** are in one of these formats:
277 **
278 **    [+-]digits[E[+-]digits]
279 **    [+-]digits.[digits][E[+-]digits]
280 **    [+-].digits[E[+-]digits]
281 **
282 ** Leading and trailing whitespace is ignored for the purpose of determining
283 ** validity.
284 **
285 ** If some prefix of the input string is a valid number, this routine
286 ** returns FALSE but it still converts the prefix and writes the result
287 ** into *pResult.
288 */
289 int sqlite3AtoF(const char *z, double *pResult, int length, u8 enc){
290 #ifndef SQLITE_OMIT_FLOATING_POINT
291   int incr;
292   const char *zEnd = z + length;
293   /* sign * significand * (10 ^ (esign * exponent)) */
294   int sign = 1;    /* sign of significand */
295   i64 s = 0;       /* significand */
296   int d = 0;       /* adjust exponent for shifting decimal point */
297   int esign = 1;   /* sign of exponent */
298   int e = 0;       /* exponent */
299   int eValid = 1;  /* True exponent is either not used or is well-formed */
300   double result;
301   int nDigits = 0;
302   int nonNum = 0;
303 
304   assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
305   *pResult = 0.0;   /* Default return value, in case of an error */
306 
307   if( enc==SQLITE_UTF8 ){
308     incr = 1;
309   }else{
310     int i;
311     incr = 2;
312     assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
313     for(i=3-enc; i<length && z[i]==0; i+=2){}
314     nonNum = i<length;
315     zEnd = z+i+enc-3;
316     z += (enc&1);
317   }
318 
319   /* skip leading spaces */
320   while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
321   if( z>=zEnd ) return 0;
322 
323   /* get sign of significand */
324   if( *z=='-' ){
325     sign = -1;
326     z+=incr;
327   }else if( *z=='+' ){
328     z+=incr;
329   }
330 
331   /* skip leading zeroes */
332   while( z<zEnd && z[0]=='0' ) z+=incr, nDigits++;
333 
334   /* copy max significant digits to significand */
335   while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
336     s = s*10 + (*z - '0');
337     z+=incr, nDigits++;
338   }
339 
340   /* skip non-significant significand digits
341   ** (increase exponent by d to shift decimal left) */
342   while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++, d++;
343   if( z>=zEnd ) goto do_atof_calc;
344 
345   /* if decimal point is present */
346   if( *z=='.' ){
347     z+=incr;
348     /* copy digits from after decimal to significand
349     ** (decrease exponent by d to shift decimal right) */
350     while( z<zEnd && sqlite3Isdigit(*z) && s<((LARGEST_INT64-9)/10) ){
351       s = s*10 + (*z - '0');
352       z+=incr, nDigits++, d--;
353     }
354     /* skip non-significant digits */
355     while( z<zEnd && sqlite3Isdigit(*z) ) z+=incr, nDigits++;
356   }
357   if( z>=zEnd ) goto do_atof_calc;
358 
359   /* if exponent is present */
360   if( *z=='e' || *z=='E' ){
361     z+=incr;
362     eValid = 0;
363     if( z>=zEnd ) goto do_atof_calc;
364     /* get sign of exponent */
365     if( *z=='-' ){
366       esign = -1;
367       z+=incr;
368     }else if( *z=='+' ){
369       z+=incr;
370     }
371     /* copy digits to exponent */
372     while( z<zEnd && sqlite3Isdigit(*z) ){
373       e = e<10000 ? (e*10 + (*z - '0')) : 10000;
374       z+=incr;
375       eValid = 1;
376     }
377   }
378 
379   /* skip trailing spaces */
380   if( nDigits && eValid ){
381     while( z<zEnd && sqlite3Isspace(*z) ) z+=incr;
382   }
383 
384 do_atof_calc:
385   /* adjust exponent by d, and update sign */
386   e = (e*esign) + d;
387   if( e<0 ) {
388     esign = -1;
389     e *= -1;
390   } else {
391     esign = 1;
392   }
393 
394   /* if 0 significand */
395   if( !s ) {
396     /* In the IEEE 754 standard, zero is signed.
397     ** Add the sign if we've seen at least one digit */
398     result = (sign<0 && nDigits) ? -(double)0 : (double)0;
399   } else {
400     /* attempt to reduce exponent */
401     if( esign>0 ){
402       while( s<(LARGEST_INT64/10) && e>0 ) e--,s*=10;
403     }else{
404       while( !(s%10) && e>0 ) e--,s/=10;
405     }
406 
407     /* adjust the sign of significand */
408     s = sign<0 ? -s : s;
409 
410     /* if exponent, scale significand as appropriate
411     ** and store in result. */
412     if( e ){
413       LONGDOUBLE_TYPE scale = 1.0;
414       /* attempt to handle extremely small/large numbers better */
415       if( e>307 && e<342 ){
416         while( e%308 ) { scale *= 1.0e+1; e -= 1; }
417         if( esign<0 ){
418           result = s / scale;
419           result /= 1.0e+308;
420         }else{
421           result = s * scale;
422           result *= 1.0e+308;
423         }
424       }else if( e>=342 ){
425         if( esign<0 ){
426           result = 0.0*s;
427         }else{
428           result = 1e308*1e308*s;  /* Infinity */
429         }
430       }else{
431         /* 1.0e+22 is the largest power of 10 than can be
432         ** represented exactly. */
433         while( e%22 ) { scale *= 1.0e+1; e -= 1; }
434         while( e>0 ) { scale *= 1.0e+22; e -= 22; }
435         if( esign<0 ){
436           result = s / scale;
437         }else{
438           result = s * scale;
439         }
440       }
441     } else {
442       result = (double)s;
443     }
444   }
445 
446   /* store the result */
447   *pResult = result;
448 
449   /* return true if number and no extra non-whitespace chracters after */
450   return z>=zEnd && nDigits>0 && eValid && nonNum==0;
451 #else
452   return !sqlite3Atoi64(z, pResult, length, enc);
453 #endif /* SQLITE_OMIT_FLOATING_POINT */
454 }
455 
456 /*
457 ** Compare the 19-character string zNum against the text representation
458 ** value 2^63:  9223372036854775808.  Return negative, zero, or positive
459 ** if zNum is less than, equal to, or greater than the string.
460 ** Note that zNum must contain exactly 19 characters.
461 **
462 ** Unlike memcmp() this routine is guaranteed to return the difference
463 ** in the values of the last digit if the only difference is in the
464 ** last digit.  So, for example,
465 **
466 **      compare2pow63("9223372036854775800", 1)
467 **
468 ** will return -8.
469 */
470 static int compare2pow63(const char *zNum, int incr){
471   int c = 0;
472   int i;
473                     /* 012345678901234567 */
474   const char *pow63 = "922337203685477580";
475   for(i=0; c==0 && i<18; i++){
476     c = (zNum[i*incr]-pow63[i])*10;
477   }
478   if( c==0 ){
479     c = zNum[18*incr] - '8';
480     testcase( c==(-1) );
481     testcase( c==0 );
482     testcase( c==(+1) );
483   }
484   return c;
485 }
486 
487 /*
488 ** Convert zNum to a 64-bit signed integer.  zNum must be decimal. This
489 ** routine does *not* accept hexadecimal notation.
490 **
491 ** If the zNum value is representable as a 64-bit twos-complement
492 ** integer, then write that value into *pNum and return 0.
493 **
494 ** If zNum is exactly 9223372036854775808, return 2.  This special
495 ** case is broken out because while 9223372036854775808 cannot be a
496 ** signed 64-bit integer, its negative -9223372036854775808 can be.
497 **
498 ** If zNum is too big for a 64-bit integer and is not
499 ** 9223372036854775808  or if zNum contains any non-numeric text,
500 ** then return 1.
501 **
502 ** length is the number of bytes in the string (bytes, not characters).
503 ** The string is not necessarily zero-terminated.  The encoding is
504 ** given by enc.
505 */
506 int sqlite3Atoi64(const char *zNum, i64 *pNum, int length, u8 enc){
507   int incr;
508   u64 u = 0;
509   int neg = 0; /* assume positive */
510   int i;
511   int c = 0;
512   int nonNum = 0;
513   const char *zStart;
514   const char *zEnd = zNum + length;
515   assert( enc==SQLITE_UTF8 || enc==SQLITE_UTF16LE || enc==SQLITE_UTF16BE );
516   if( enc==SQLITE_UTF8 ){
517     incr = 1;
518   }else{
519     incr = 2;
520     assert( SQLITE_UTF16LE==2 && SQLITE_UTF16BE==3 );
521     for(i=3-enc; i<length && zNum[i]==0; i+=2){}
522     nonNum = i<length;
523     zEnd = zNum+i+enc-3;
524     zNum += (enc&1);
525   }
526   while( zNum<zEnd && sqlite3Isspace(*zNum) ) zNum+=incr;
527   if( zNum<zEnd ){
528     if( *zNum=='-' ){
529       neg = 1;
530       zNum+=incr;
531     }else if( *zNum=='+' ){
532       zNum+=incr;
533     }
534   }
535   zStart = zNum;
536   while( zNum<zEnd && zNum[0]=='0' ){ zNum+=incr; } /* Skip leading zeros. */
537   for(i=0; &zNum[i]<zEnd && (c=zNum[i])>='0' && c<='9'; i+=incr){
538     u = u*10 + c - '0';
539   }
540   if( u>LARGEST_INT64 ){
541     *pNum = neg ? SMALLEST_INT64 : LARGEST_INT64;
542   }else if( neg ){
543     *pNum = -(i64)u;
544   }else{
545     *pNum = (i64)u;
546   }
547   testcase( i==18 );
548   testcase( i==19 );
549   testcase( i==20 );
550   if( (c!=0 && &zNum[i]<zEnd) || (i==0 && zStart==zNum) || i>19*incr || nonNum ){
551     /* zNum is empty or contains non-numeric text or is longer
552     ** than 19 digits (thus guaranteeing that it is too large) */
553     return 1;
554   }else if( i<19*incr ){
555     /* Less than 19 digits, so we know that it fits in 64 bits */
556     assert( u<=LARGEST_INT64 );
557     return 0;
558   }else{
559     /* zNum is a 19-digit numbers.  Compare it against 9223372036854775808. */
560     c = compare2pow63(zNum, incr);
561     if( c<0 ){
562       /* zNum is less than 9223372036854775808 so it fits */
563       assert( u<=LARGEST_INT64 );
564       return 0;
565     }else if( c>0 ){
566       /* zNum is greater than 9223372036854775808 so it overflows */
567       return 1;
568     }else{
569       /* zNum is exactly 9223372036854775808.  Fits if negative.  The
570       ** special case 2 overflow if positive */
571       assert( u-1==LARGEST_INT64 );
572       return neg ? 0 : 2;
573     }
574   }
575 }
576 
577 /*
578 ** Transform a UTF-8 integer literal, in either decimal or hexadecimal,
579 ** into a 64-bit signed integer.  This routine accepts hexadecimal literals,
580 ** whereas sqlite3Atoi64() does not.
581 **
582 ** Returns:
583 **
584 **     0    Successful transformation.  Fits in a 64-bit signed integer.
585 **     1    Integer too large for a 64-bit signed integer or is malformed
586 **     2    Special case of 9223372036854775808
587 */
588 int sqlite3DecOrHexToI64(const char *z, i64 *pOut){
589 #ifndef SQLITE_OMIT_HEX_INTEGER
590   if( z[0]=='0'
591    && (z[1]=='x' || z[1]=='X')
592    && sqlite3Isxdigit(z[2])
593   ){
594     u64 u = 0;
595     int i, k;
596     for(i=2; z[i]=='0'; i++){}
597     for(k=i; sqlite3Isxdigit(z[k]); k++){
598       u = u*16 + sqlite3HexToInt(z[k]);
599     }
600     memcpy(pOut, &u, 8);
601     return (z[k]==0 && k-i<=16) ? 0 : 1;
602   }else
603 #endif /* SQLITE_OMIT_HEX_INTEGER */
604   {
605     return sqlite3Atoi64(z, pOut, sqlite3Strlen30(z), SQLITE_UTF8);
606   }
607 }
608 
609 /*
610 ** If zNum represents an integer that will fit in 32-bits, then set
611 ** *pValue to that integer and return true.  Otherwise return false.
612 **
613 ** This routine accepts both decimal and hexadecimal notation for integers.
614 **
615 ** Any non-numeric characters that following zNum are ignored.
616 ** This is different from sqlite3Atoi64() which requires the
617 ** input number to be zero-terminated.
618 */
619 int sqlite3GetInt32(const char *zNum, int *pValue){
620   sqlite_int64 v = 0;
621   int i, c;
622   int neg = 0;
623   if( zNum[0]=='-' ){
624     neg = 1;
625     zNum++;
626   }else if( zNum[0]=='+' ){
627     zNum++;
628   }
629 #ifndef SQLITE_OMIT_HEX_INTEGER
630   else if( zNum[0]=='0'
631         && (zNum[1]=='x' || zNum[1]=='X')
632         && sqlite3Isxdigit(zNum[2])
633   ){
634     u32 u = 0;
635     zNum += 2;
636     while( zNum[0]=='0' ) zNum++;
637     for(i=0; sqlite3Isxdigit(zNum[i]) && i<8; i++){
638       u = u*16 + sqlite3HexToInt(zNum[i]);
639     }
640     if( (u&0x80000000)==0 && sqlite3Isxdigit(zNum[i])==0 ){
641       memcpy(pValue, &u, 4);
642       return 1;
643     }else{
644       return 0;
645     }
646   }
647 #endif
648   for(i=0; i<11 && (c = zNum[i] - '0')>=0 && c<=9; i++){
649     v = v*10 + c;
650   }
651 
652   /* The longest decimal representation of a 32 bit integer is 10 digits:
653   **
654   **             1234567890
655   **     2^31 -> 2147483648
656   */
657   testcase( i==10 );
658   if( i>10 ){
659     return 0;
660   }
661   testcase( v-neg==2147483647 );
662   if( v-neg>2147483647 ){
663     return 0;
664   }
665   if( neg ){
666     v = -v;
667   }
668   *pValue = (int)v;
669   return 1;
670 }
671 
672 /*
673 ** Return a 32-bit integer value extracted from a string.  If the
674 ** string is not an integer, just return 0.
675 */
676 int sqlite3Atoi(const char *z){
677   int x = 0;
678   if( z ) sqlite3GetInt32(z, &x);
679   return x;
680 }
681 
682 /*
683 ** The variable-length integer encoding is as follows:
684 **
685 ** KEY:
686 **         A = 0xxxxxxx    7 bits of data and one flag bit
687 **         B = 1xxxxxxx    7 bits of data and one flag bit
688 **         C = xxxxxxxx    8 bits of data
689 **
690 **  7 bits - A
691 ** 14 bits - BA
692 ** 21 bits - BBA
693 ** 28 bits - BBBA
694 ** 35 bits - BBBBA
695 ** 42 bits - BBBBBA
696 ** 49 bits - BBBBBBA
697 ** 56 bits - BBBBBBBA
698 ** 64 bits - BBBBBBBBC
699 */
700 
701 /*
702 ** Write a 64-bit variable-length integer to memory starting at p[0].
703 ** The length of data write will be between 1 and 9 bytes.  The number
704 ** of bytes written is returned.
705 **
706 ** A variable-length integer consists of the lower 7 bits of each byte
707 ** for all bytes that have the 8th bit set and one byte with the 8th
708 ** bit clear.  Except, if we get to the 9th byte, it stores the full
709 ** 8 bits and is the last byte.
710 */
711 static int SQLITE_NOINLINE putVarint64(unsigned char *p, u64 v){
712   int i, j, n;
713   u8 buf[10];
714   if( v & (((u64)0xff000000)<<32) ){
715     p[8] = (u8)v;
716     v >>= 8;
717     for(i=7; i>=0; i--){
718       p[i] = (u8)((v & 0x7f) | 0x80);
719       v >>= 7;
720     }
721     return 9;
722   }
723   n = 0;
724   do{
725     buf[n++] = (u8)((v & 0x7f) | 0x80);
726     v >>= 7;
727   }while( v!=0 );
728   buf[0] &= 0x7f;
729   assert( n<=9 );
730   for(i=0, j=n-1; j>=0; j--, i++){
731     p[i] = buf[j];
732   }
733   return n;
734 }
735 int sqlite3PutVarint(unsigned char *p, u64 v){
736   if( v<=0x7f ){
737     p[0] = v&0x7f;
738     return 1;
739   }
740   if( v<=0x3fff ){
741     p[0] = ((v>>7)&0x7f)|0x80;
742     p[1] = v&0x7f;
743     return 2;
744   }
745   return putVarint64(p,v);
746 }
747 
748 /*
749 ** Bitmasks used by sqlite3GetVarint().  These precomputed constants
750 ** are defined here rather than simply putting the constant expressions
751 ** inline in order to work around bugs in the RVT compiler.
752 **
753 ** SLOT_2_0     A mask for  (0x7f<<14) | 0x7f
754 **
755 ** SLOT_4_2_0   A mask for  (0x7f<<28) | SLOT_2_0
756 */
757 #define SLOT_2_0     0x001fc07f
758 #define SLOT_4_2_0   0xf01fc07f
759 
760 
761 /*
762 ** Read a 64-bit variable-length integer from memory starting at p[0].
763 ** Return the number of bytes read.  The value is stored in *v.
764 */
765 u8 sqlite3GetVarint(const unsigned char *p, u64 *v){
766   u32 a,b,s;
767 
768   a = *p;
769   /* a: p0 (unmasked) */
770   if (!(a&0x80))
771   {
772     *v = a;
773     return 1;
774   }
775 
776   p++;
777   b = *p;
778   /* b: p1 (unmasked) */
779   if (!(b&0x80))
780   {
781     a &= 0x7f;
782     a = a<<7;
783     a |= b;
784     *v = a;
785     return 2;
786   }
787 
788   /* Verify that constants are precomputed correctly */
789   assert( SLOT_2_0 == ((0x7f<<14) | (0x7f)) );
790   assert( SLOT_4_2_0 == ((0xfU<<28) | (0x7f<<14) | (0x7f)) );
791 
792   p++;
793   a = a<<14;
794   a |= *p;
795   /* a: p0<<14 | p2 (unmasked) */
796   if (!(a&0x80))
797   {
798     a &= SLOT_2_0;
799     b &= 0x7f;
800     b = b<<7;
801     a |= b;
802     *v = a;
803     return 3;
804   }
805 
806   /* CSE1 from below */
807   a &= SLOT_2_0;
808   p++;
809   b = b<<14;
810   b |= *p;
811   /* b: p1<<14 | p3 (unmasked) */
812   if (!(b&0x80))
813   {
814     b &= SLOT_2_0;
815     /* moved CSE1 up */
816     /* a &= (0x7f<<14)|(0x7f); */
817     a = a<<7;
818     a |= b;
819     *v = a;
820     return 4;
821   }
822 
823   /* a: p0<<14 | p2 (masked) */
824   /* b: p1<<14 | p3 (unmasked) */
825   /* 1:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
826   /* moved CSE1 up */
827   /* a &= (0x7f<<14)|(0x7f); */
828   b &= SLOT_2_0;
829   s = a;
830   /* s: p0<<14 | p2 (masked) */
831 
832   p++;
833   a = a<<14;
834   a |= *p;
835   /* a: p0<<28 | p2<<14 | p4 (unmasked) */
836   if (!(a&0x80))
837   {
838     /* we can skip these cause they were (effectively) done above in calc'ing s */
839     /* a &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
840     /* b &= (0x7f<<14)|(0x7f); */
841     b = b<<7;
842     a |= b;
843     s = s>>18;
844     *v = ((u64)s)<<32 | a;
845     return 5;
846   }
847 
848   /* 2:save off p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
849   s = s<<7;
850   s |= b;
851   /* s: p0<<21 | p1<<14 | p2<<7 | p3 (masked) */
852 
853   p++;
854   b = b<<14;
855   b |= *p;
856   /* b: p1<<28 | p3<<14 | p5 (unmasked) */
857   if (!(b&0x80))
858   {
859     /* we can skip this cause it was (effectively) done above in calc'ing s */
860     /* b &= (0x7f<<28)|(0x7f<<14)|(0x7f); */
861     a &= SLOT_2_0;
862     a = a<<7;
863     a |= b;
864     s = s>>18;
865     *v = ((u64)s)<<32 | a;
866     return 6;
867   }
868 
869   p++;
870   a = a<<14;
871   a |= *p;
872   /* a: p2<<28 | p4<<14 | p6 (unmasked) */
873   if (!(a&0x80))
874   {
875     a &= SLOT_4_2_0;
876     b &= SLOT_2_0;
877     b = b<<7;
878     a |= b;
879     s = s>>11;
880     *v = ((u64)s)<<32 | a;
881     return 7;
882   }
883 
884   /* CSE2 from below */
885   a &= SLOT_2_0;
886   p++;
887   b = b<<14;
888   b |= *p;
889   /* b: p3<<28 | p5<<14 | p7 (unmasked) */
890   if (!(b&0x80))
891   {
892     b &= SLOT_4_2_0;
893     /* moved CSE2 up */
894     /* a &= (0x7f<<14)|(0x7f); */
895     a = a<<7;
896     a |= b;
897     s = s>>4;
898     *v = ((u64)s)<<32 | a;
899     return 8;
900   }
901 
902   p++;
903   a = a<<15;
904   a |= *p;
905   /* a: p4<<29 | p6<<15 | p8 (unmasked) */
906 
907   /* moved CSE2 up */
908   /* a &= (0x7f<<29)|(0x7f<<15)|(0xff); */
909   b &= SLOT_2_0;
910   b = b<<8;
911   a |= b;
912 
913   s = s<<4;
914   b = p[-4];
915   b &= 0x7f;
916   b = b>>3;
917   s |= b;
918 
919   *v = ((u64)s)<<32 | a;
920 
921   return 9;
922 }
923 
924 /*
925 ** Read a 32-bit variable-length integer from memory starting at p[0].
926 ** Return the number of bytes read.  The value is stored in *v.
927 **
928 ** If the varint stored in p[0] is larger than can fit in a 32-bit unsigned
929 ** integer, then set *v to 0xffffffff.
930 **
931 ** A MACRO version, getVarint32, is provided which inlines the
932 ** single-byte case.  All code should use the MACRO version as
933 ** this function assumes the single-byte case has already been handled.
934 */
935 u8 sqlite3GetVarint32(const unsigned char *p, u32 *v){
936   u32 a,b;
937 
938   /* The 1-byte case.  Overwhelmingly the most common.  Handled inline
939   ** by the getVarin32() macro */
940   a = *p;
941   /* a: p0 (unmasked) */
942 #ifndef getVarint32
943   if (!(a&0x80))
944   {
945     /* Values between 0 and 127 */
946     *v = a;
947     return 1;
948   }
949 #endif
950 
951   /* The 2-byte case */
952   p++;
953   b = *p;
954   /* b: p1 (unmasked) */
955   if (!(b&0x80))
956   {
957     /* Values between 128 and 16383 */
958     a &= 0x7f;
959     a = a<<7;
960     *v = a | b;
961     return 2;
962   }
963 
964   /* The 3-byte case */
965   p++;
966   a = a<<14;
967   a |= *p;
968   /* a: p0<<14 | p2 (unmasked) */
969   if (!(a&0x80))
970   {
971     /* Values between 16384 and 2097151 */
972     a &= (0x7f<<14)|(0x7f);
973     b &= 0x7f;
974     b = b<<7;
975     *v = a | b;
976     return 3;
977   }
978 
979   /* A 32-bit varint is used to store size information in btrees.
980   ** Objects are rarely larger than 2MiB limit of a 3-byte varint.
981   ** A 3-byte varint is sufficient, for example, to record the size
982   ** of a 1048569-byte BLOB or string.
983   **
984   ** We only unroll the first 1-, 2-, and 3- byte cases.  The very
985   ** rare larger cases can be handled by the slower 64-bit varint
986   ** routine.
987   */
988 #if 1
989   {
990     u64 v64;
991     u8 n;
992 
993     p -= 2;
994     n = sqlite3GetVarint(p, &v64);
995     assert( n>3 && n<=9 );
996     if( (v64 & SQLITE_MAX_U32)!=v64 ){
997       *v = 0xffffffff;
998     }else{
999       *v = (u32)v64;
1000     }
1001     return n;
1002   }
1003 
1004 #else
1005   /* For following code (kept for historical record only) shows an
1006   ** unrolling for the 3- and 4-byte varint cases.  This code is
1007   ** slightly faster, but it is also larger and much harder to test.
1008   */
1009   p++;
1010   b = b<<14;
1011   b |= *p;
1012   /* b: p1<<14 | p3 (unmasked) */
1013   if (!(b&0x80))
1014   {
1015     /* Values between 2097152 and 268435455 */
1016     b &= (0x7f<<14)|(0x7f);
1017     a &= (0x7f<<14)|(0x7f);
1018     a = a<<7;
1019     *v = a | b;
1020     return 4;
1021   }
1022 
1023   p++;
1024   a = a<<14;
1025   a |= *p;
1026   /* a: p0<<28 | p2<<14 | p4 (unmasked) */
1027   if (!(a&0x80))
1028   {
1029     /* Values  between 268435456 and 34359738367 */
1030     a &= SLOT_4_2_0;
1031     b &= SLOT_4_2_0;
1032     b = b<<7;
1033     *v = a | b;
1034     return 5;
1035   }
1036 
1037   /* We can only reach this point when reading a corrupt database
1038   ** file.  In that case we are not in any hurry.  Use the (relatively
1039   ** slow) general-purpose sqlite3GetVarint() routine to extract the
1040   ** value. */
1041   {
1042     u64 v64;
1043     u8 n;
1044 
1045     p -= 4;
1046     n = sqlite3GetVarint(p, &v64);
1047     assert( n>5 && n<=9 );
1048     *v = (u32)v64;
1049     return n;
1050   }
1051 #endif
1052 }
1053 
1054 /*
1055 ** Return the number of bytes that will be needed to store the given
1056 ** 64-bit integer.
1057 */
1058 int sqlite3VarintLen(u64 v){
1059   int i = 0;
1060   do{
1061     i++;
1062     v >>= 7;
1063   }while( v!=0 && ALWAYS(i<9) );
1064   return i;
1065 }
1066 
1067 
1068 /*
1069 ** Read or write a four-byte big-endian integer value.
1070 */
1071 u32 sqlite3Get4byte(const u8 *p){
1072   testcase( p[0]&0x80 );
1073   return ((unsigned)p[0]<<24) | (p[1]<<16) | (p[2]<<8) | p[3];
1074 }
1075 void sqlite3Put4byte(unsigned char *p, u32 v){
1076   p[0] = (u8)(v>>24);
1077   p[1] = (u8)(v>>16);
1078   p[2] = (u8)(v>>8);
1079   p[3] = (u8)v;
1080 }
1081 
1082 
1083 
1084 /*
1085 ** Translate a single byte of Hex into an integer.
1086 ** This routine only works if h really is a valid hexadecimal
1087 ** character:  0..9a..fA..F
1088 */
1089 u8 sqlite3HexToInt(int h){
1090   assert( (h>='0' && h<='9') ||  (h>='a' && h<='f') ||  (h>='A' && h<='F') );
1091 #ifdef SQLITE_ASCII
1092   h += 9*(1&(h>>6));
1093 #endif
1094 #ifdef SQLITE_EBCDIC
1095   h += 9*(1&~(h>>4));
1096 #endif
1097   return (u8)(h & 0xf);
1098 }
1099 
1100 #if !defined(SQLITE_OMIT_BLOB_LITERAL) || defined(SQLITE_HAS_CODEC)
1101 /*
1102 ** Convert a BLOB literal of the form "x'hhhhhh'" into its binary
1103 ** value.  Return a pointer to its binary value.  Space to hold the
1104 ** binary value has been obtained from malloc and must be freed by
1105 ** the calling routine.
1106 */
1107 void *sqlite3HexToBlob(sqlite3 *db, const char *z, int n){
1108   char *zBlob;
1109   int i;
1110 
1111   zBlob = (char *)sqlite3DbMallocRaw(db, n/2 + 1);
1112   n--;
1113   if( zBlob ){
1114     for(i=0; i<n; i+=2){
1115       zBlob[i/2] = (sqlite3HexToInt(z[i])<<4) | sqlite3HexToInt(z[i+1]);
1116     }
1117     zBlob[i/2] = 0;
1118   }
1119   return zBlob;
1120 }
1121 #endif /* !SQLITE_OMIT_BLOB_LITERAL || SQLITE_HAS_CODEC */
1122 
1123 /*
1124 ** Log an error that is an API call on a connection pointer that should
1125 ** not have been used.  The "type" of connection pointer is given as the
1126 ** argument.  The zType is a word like "NULL" or "closed" or "invalid".
1127 */
1128 static void logBadConnection(const char *zType){
1129   sqlite3_log(SQLITE_MISUSE,
1130      "API call with %s database connection pointer",
1131      zType
1132   );
1133 }
1134 
1135 /*
1136 ** Check to make sure we have a valid db pointer.  This test is not
1137 ** foolproof but it does provide some measure of protection against
1138 ** misuse of the interface such as passing in db pointers that are
1139 ** NULL or which have been previously closed.  If this routine returns
1140 ** 1 it means that the db pointer is valid and 0 if it should not be
1141 ** dereferenced for any reason.  The calling function should invoke
1142 ** SQLITE_MISUSE immediately.
1143 **
1144 ** sqlite3SafetyCheckOk() requires that the db pointer be valid for
1145 ** use.  sqlite3SafetyCheckSickOrOk() allows a db pointer that failed to
1146 ** open properly and is not fit for general use but which can be
1147 ** used as an argument to sqlite3_errmsg() or sqlite3_close().
1148 */
1149 int sqlite3SafetyCheckOk(sqlite3 *db){
1150   u32 magic;
1151   if( db==0 ){
1152     logBadConnection("NULL");
1153     return 0;
1154   }
1155   magic = db->magic;
1156   if( magic!=SQLITE_MAGIC_OPEN ){
1157     if( sqlite3SafetyCheckSickOrOk(db) ){
1158       testcase( sqlite3GlobalConfig.xLog!=0 );
1159       logBadConnection("unopened");
1160     }
1161     return 0;
1162   }else{
1163     return 1;
1164   }
1165 }
1166 int sqlite3SafetyCheckSickOrOk(sqlite3 *db){
1167   u32 magic;
1168   magic = db->magic;
1169   if( magic!=SQLITE_MAGIC_SICK &&
1170       magic!=SQLITE_MAGIC_OPEN &&
1171       magic!=SQLITE_MAGIC_BUSY ){
1172     testcase( sqlite3GlobalConfig.xLog!=0 );
1173     logBadConnection("invalid");
1174     return 0;
1175   }else{
1176     return 1;
1177   }
1178 }
1179 
1180 /*
1181 ** Attempt to add, substract, or multiply the 64-bit signed value iB against
1182 ** the other 64-bit signed integer at *pA and store the result in *pA.
1183 ** Return 0 on success.  Or if the operation would have resulted in an
1184 ** overflow, leave *pA unchanged and return 1.
1185 */
1186 int sqlite3AddInt64(i64 *pA, i64 iB){
1187   i64 iA = *pA;
1188   testcase( iA==0 ); testcase( iA==1 );
1189   testcase( iB==-1 ); testcase( iB==0 );
1190   if( iB>=0 ){
1191     testcase( iA>0 && LARGEST_INT64 - iA == iB );
1192     testcase( iA>0 && LARGEST_INT64 - iA == iB - 1 );
1193     if( iA>0 && LARGEST_INT64 - iA < iB ) return 1;
1194   }else{
1195     testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 1 );
1196     testcase( iA<0 && -(iA + LARGEST_INT64) == iB + 2 );
1197     if( iA<0 && -(iA + LARGEST_INT64) > iB + 1 ) return 1;
1198   }
1199   *pA += iB;
1200   return 0;
1201 }
1202 int sqlite3SubInt64(i64 *pA, i64 iB){
1203   testcase( iB==SMALLEST_INT64+1 );
1204   if( iB==SMALLEST_INT64 ){
1205     testcase( (*pA)==(-1) ); testcase( (*pA)==0 );
1206     if( (*pA)>=0 ) return 1;
1207     *pA -= iB;
1208     return 0;
1209   }else{
1210     return sqlite3AddInt64(pA, -iB);
1211   }
1212 }
1213 #define TWOPOWER32 (((i64)1)<<32)
1214 #define TWOPOWER31 (((i64)1)<<31)
1215 int sqlite3MulInt64(i64 *pA, i64 iB){
1216   i64 iA = *pA;
1217   i64 iA1, iA0, iB1, iB0, r;
1218 
1219   iA1 = iA/TWOPOWER32;
1220   iA0 = iA % TWOPOWER32;
1221   iB1 = iB/TWOPOWER32;
1222   iB0 = iB % TWOPOWER32;
1223   if( iA1==0 ){
1224     if( iB1==0 ){
1225       *pA *= iB;
1226       return 0;
1227     }
1228     r = iA0*iB1;
1229   }else if( iB1==0 ){
1230     r = iA1*iB0;
1231   }else{
1232     /* If both iA1 and iB1 are non-zero, overflow will result */
1233     return 1;
1234   }
1235   testcase( r==(-TWOPOWER31)-1 );
1236   testcase( r==(-TWOPOWER31) );
1237   testcase( r==TWOPOWER31 );
1238   testcase( r==TWOPOWER31-1 );
1239   if( r<(-TWOPOWER31) || r>=TWOPOWER31 ) return 1;
1240   r *= TWOPOWER32;
1241   if( sqlite3AddInt64(&r, iA0*iB0) ) return 1;
1242   *pA = r;
1243   return 0;
1244 }
1245 
1246 /*
1247 ** Compute the absolute value of a 32-bit signed integer, of possible.  Or
1248 ** if the integer has a value of -2147483648, return +2147483647
1249 */
1250 int sqlite3AbsInt32(int x){
1251   if( x>=0 ) return x;
1252   if( x==(int)0x80000000 ) return 0x7fffffff;
1253   return -x;
1254 }
1255 
1256 #ifdef SQLITE_ENABLE_8_3_NAMES
1257 /*
1258 ** If SQLITE_ENABLE_8_3_NAMES is set at compile-time and if the database
1259 ** filename in zBaseFilename is a URI with the "8_3_names=1" parameter and
1260 ** if filename in z[] has a suffix (a.k.a. "extension") that is longer than
1261 ** three characters, then shorten the suffix on z[] to be the last three
1262 ** characters of the original suffix.
1263 **
1264 ** If SQLITE_ENABLE_8_3_NAMES is set to 2 at compile-time, then always
1265 ** do the suffix shortening regardless of URI parameter.
1266 **
1267 ** Examples:
1268 **
1269 **     test.db-journal    =>   test.nal
1270 **     test.db-wal        =>   test.wal
1271 **     test.db-shm        =>   test.shm
1272 **     test.db-mj7f3319fa =>   test.9fa
1273 */
1274 void sqlite3FileSuffix3(const char *zBaseFilename, char *z){
1275 #if SQLITE_ENABLE_8_3_NAMES<2
1276   if( sqlite3_uri_boolean(zBaseFilename, "8_3_names", 0) )
1277 #endif
1278   {
1279     int i, sz;
1280     sz = sqlite3Strlen30(z);
1281     for(i=sz-1; i>0 && z[i]!='/' && z[i]!='.'; i--){}
1282     if( z[i]=='.' && ALWAYS(sz>i+4) ) memmove(&z[i+1], &z[sz-3], 4);
1283   }
1284 }
1285 #endif
1286 
1287 /*
1288 ** Find (an approximate) sum of two LogEst values.  This computation is
1289 ** not a simple "+" operator because LogEst is stored as a logarithmic
1290 ** value.
1291 **
1292 */
1293 LogEst sqlite3LogEstAdd(LogEst a, LogEst b){
1294   static const unsigned char x[] = {
1295      10, 10,                         /* 0,1 */
1296       9, 9,                          /* 2,3 */
1297       8, 8,                          /* 4,5 */
1298       7, 7, 7,                       /* 6,7,8 */
1299       6, 6, 6,                       /* 9,10,11 */
1300       5, 5, 5,                       /* 12-14 */
1301       4, 4, 4, 4,                    /* 15-18 */
1302       3, 3, 3, 3, 3, 3,              /* 19-24 */
1303       2, 2, 2, 2, 2, 2, 2,           /* 25-31 */
1304   };
1305   if( a>=b ){
1306     if( a>b+49 ) return a;
1307     if( a>b+31 ) return a+1;
1308     return a+x[a-b];
1309   }else{
1310     if( b>a+49 ) return b;
1311     if( b>a+31 ) return b+1;
1312     return b+x[b-a];
1313   }
1314 }
1315 
1316 /*
1317 ** Convert an integer into a LogEst.  In other words, compute an
1318 ** approximation for 10*log2(x).
1319 */
1320 LogEst sqlite3LogEst(u64 x){
1321   static LogEst a[] = { 0, 2, 3, 5, 6, 7, 8, 9 };
1322   LogEst y = 40;
1323   if( x<8 ){
1324     if( x<2 ) return 0;
1325     while( x<8 ){  y -= 10; x <<= 1; }
1326   }else{
1327     while( x>255 ){ y += 40; x >>= 4; }
1328     while( x>15 ){  y += 10; x >>= 1; }
1329   }
1330   return a[x&7] + y - 10;
1331 }
1332 
1333 #ifndef SQLITE_OMIT_VIRTUALTABLE
1334 /*
1335 ** Convert a double into a LogEst
1336 ** In other words, compute an approximation for 10*log2(x).
1337 */
1338 LogEst sqlite3LogEstFromDouble(double x){
1339   u64 a;
1340   LogEst e;
1341   assert( sizeof(x)==8 && sizeof(a)==8 );
1342   if( x<=1 ) return 0;
1343   if( x<=2000000000 ) return sqlite3LogEst((u64)x);
1344   memcpy(&a, &x, 8);
1345   e = (a>>52) - 1022;
1346   return e*10;
1347 }
1348 #endif /* SQLITE_OMIT_VIRTUALTABLE */
1349 
1350 /*
1351 ** Convert a LogEst into an integer.
1352 */
1353 u64 sqlite3LogEstToInt(LogEst x){
1354   u64 n;
1355   if( x<10 ) return 1;
1356   n = x%10;
1357   x /= 10;
1358   if( n>=5 ) n -= 2;
1359   else if( n>=1 ) n -= 1;
1360   if( x>=3 ){
1361     return x>60 ? (u64)LARGEST_INT64 : (n+8)<<(x-3);
1362   }
1363   return (n+8)>>(3-x);
1364 }
1365