src/bitvec.c

   1 /*
   2 ** 2008 February 16
   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 ** This file implements an object that represents a fixed-length
  13 ** bitmap.  Bits are numbered starting with 1.
  14 **
  15 ** A bitmap is used to record which pages of a database file have been
  16 ** journalled during a transaction, or which pages have the "dont-write"
  17 ** property.  Usually only a few pages are meet either condition.
  18 ** So the bitmap is usually sparse and has low cardinality.
  19 ** But sometimes (for example when during a DROP of a large table) most
  20 ** or all of the pages in a database can get journalled.  In those cases,
  21 ** the bitmap becomes dense with high cardinality.  The algorithm needs
  22 ** to handle both cases well.
  23 **
  24 ** The size of the bitmap is fixed when the object is created.
  25 **
  26 ** All bits are clear when the bitmap is created.  Individual bits
  27 ** may be set or cleared one at a time.
  28 **
  29 ** Test operations are about 100 times more common that set operations.
  30 ** Clear operations are exceedingly rare.  There are usually between
  31 ** 5 and 500 set operations per Bitvec object, though the number of sets can
  32 ** sometimes grow into tens of thousands or larger.  The size of the
  33 ** Bitvec object is the number of pages in the database file at the
  34 ** start of a transaction, and is thus usually less than a few thousand,
  35 ** but can be as large as 2 billion for a really big database.
  36 */
  37 #include "sqliteInt.h"
  38
  39 /* Size of the Bitvec structure in bytes. */
  40 #define BITVEC_SZ        512
  41
  42 /* Round the union size down to the nearest pointer boundary, since that's how
  43 ** it will be aligned within the Bitvec struct. */
  44 #define BITVEC_USIZE     (((BITVEC_SZ-(3*sizeof(u32)))/sizeof(Bitvec*))*sizeof(Bitvec*))
  45
  46 /* Type of the array "element" for the bitmap representation.
  47 ** Should be a power of 2, and ideally, evenly divide into BITVEC_USIZE.
  48 ** Setting this to the "natural word" size of your CPU may improve
  49 ** performance. */
  50 #define BITVEC_TELEM     u8
  51 /* Size, in bits, of the bitmap element. */
  52 #define BITVEC_SZELEM    8
  53 /* Number of elements in a bitmap array. */
  54 #define BITVEC_NELEM     (BITVEC_USIZE/sizeof(BITVEC_TELEM))
  55 /* Number of bits in the bitmap array. */
  56 #define BITVEC_NBIT      (BITVEC_NELEM*BITVEC_SZELEM)
  57
  58 /* Number of u32 values in hash table. */
  59 #define BITVEC_NINT      (BITVEC_USIZE/sizeof(u32))
  60 /* Maximum number of entries in hash table before
  61 ** sub-dividing and re-hashing. */
  62 #define BITVEC_MXHASH    (BITVEC_NINT/2)
  63 /* Hashing function for the aHash representation.
  64 ** Empirical testing showed that the *37 multiplier
  65 ** (an arbitrary prime)in the hash function provided
  66 ** no fewer collisions than the no-op *1. */
  67 #define BITVEC_HASH(X)   (((X)*1)%BITVEC_NINT)
  68
  69 #define BITVEC_NPTR      (BITVEC_USIZE/sizeof(Bitvec *))
  70
  71
  72 /*
  73 ** A bitmap is an instance of the following structure.
  74 **
  75 ** This bitmap records the existence of zero or more bits
  76 ** with values between 1 and iSize, inclusive.
  77 **
  78 ** There are three possible representations of the bitmap.
  79 ** If iSize<=BITVEC_NBIT, then Bitvec.u.aBitmap[] is a straight
  80 ** bitmap.  The least significant bit is bit 1.
  81 **
  82 ** If iSize>BITVEC_NBIT and iDivisor==0 then Bitvec.u.aHash[] is
  83 ** a hash table that will hold up to BITVEC_MXHASH distinct values.
  84 **
  85 ** Otherwise, the value i is redirected into one of BITVEC_NPTR
  86 ** sub-bitmaps pointed to by Bitvec.u.apSub[].  Each subbitmap
  87 ** handles up to iDivisor separate values of i.  apSub[0] holds
  88 ** values between 1 and iDivisor.  apSub[1] holds values between
  89 ** iDivisor+1 and 2*iDivisor.  apSub[N] holds values between
  90 ** N*iDivisor+1 and (N+1)*iDivisor.  Each subbitmap is normalized
  91 ** to hold deal with values between 1 and iDivisor.
  92 */
  93 struct Bitvec {
  94   u32 iSize;      /* Maximum bit index.  Max iSize is 4,294,967,296. */
  95   u32 nSet;       /* Number of bits that are set - only valid for aHash
  96                   ** element.  Max is BITVEC_NINT.  For BITVEC_SZ of 512,
  97                   ** this would be 125. */
  98   u32 iDivisor;   /* Number of bits handled by each apSub[] entry. */
  99                   /* Should >=0 for apSub element. */
 100                   /* Max iDivisor is max(u32) / BITVEC_NPTR + 1.  */
 101                   /* For a BITVEC_SZ of 512, this would be 34,359,739. */
 102   union {
 103     BITVEC_TELEM aBitmap[BITVEC_NELEM];    /* Bitmap representation */
 104     u32 aHash[BITVEC_NINT];      /* Hash table representation */
 105     Bitvec *apSub[BITVEC_NPTR];  /* Recursive representation */
 106   } u;
 107 };
 108
 109 /*
 110 ** Create a new bitmap object able to handle bits between 0 and iSize,
 111 ** inclusive.  Return a pointer to the new object.  Return NULL if
 112 ** malloc fails.
 113 */
 114 Bitvec *sqlite3BitvecCreate(u32 iSize){
 115   Bitvec *p;
 116   assert( sizeof(*p)==BITVEC_SZ );
 117   p = sqlite3MallocZero( sizeof(*p) );
 118   if( p ){
 119     p->iSize = iSize;
 120   }
 121   return p;
 122 }
 123
 124 /*
 125 ** Check to see if the i-th bit is set.  Return true or false.
 126 ** If p is NULL (if the bitmap has not been created) or if
 127 ** i is out of range, then return false.
 128 */
 129 int sqlite3BitvecTest(Bitvec *p, u32 i){
 130   if( p==0 ) return 0;
 131   if( i>p->iSize || i==0 ) return 0;
 132   i--;
 133   while( p->iDivisor ){
 134     u32 bin = i/p->iDivisor;
 135     i = i%p->iDivisor;
 136     p = p->u.apSub[bin];
 137     if (!p) {
 138       return 0;
 139     }
 140   }
 141   if( p->iSize<=BITVEC_NBIT ){
 142     return (p->u.aBitmap[i/BITVEC_SZELEM] & (1<<(i&(BITVEC_SZELEM-1))))!=0;
 143   } else{
 144     u32 h = BITVEC_HASH(i++);
 145     while( p->u.aHash[h] ){
 146       if( p->u.aHash[h]==i ) return 1;
 147       h = (h+1) % BITVEC_NINT;
 148     }
 149     return 0;
 150   }
 151 }
 152
 153 /*
 154 ** Set the i-th bit.  Return 0 on success and an error code if
 155 ** anything goes wrong.
 156 **
 157 ** This routine might cause sub-bitmaps to be allocated.  Failing
 158 ** to get the memory needed to hold the sub-bitmap is the only
 159 ** that can go wrong with an insert, assuming p and i are valid.
 160 **
 161 ** The calling function must ensure that p is a valid Bitvec object
 162 ** and that the value for "i" is within range of the Bitvec object.
 163 ** Otherwise the behavior is undefined.
 164 */
 165 int sqlite3BitvecSet(Bitvec *p, u32 i){
 166   u32 h;
 167   if( p==0 ) return SQLITE_OK;
 168   assert( i>0 );
 169   assert( i<=p->iSize );
 170   i--;
 171   while((p->iSize > BITVEC_NBIT) && p->iDivisor) {
 172     u32 bin = i/p->iDivisor;
 173     i = i%p->iDivisor;
 174     if( p->u.apSub[bin]==0 ){
 175       p->u.apSub[bin] = sqlite3BitvecCreate( p->iDivisor );
 176       if( p->u.apSub[bin]==0 ) return SQLITE_NOMEM;
 177     }
 178     p = p->u.apSub[bin];
 179   }
 180   if( p->iSize<=BITVEC_NBIT ){
 181     p->u.aBitmap[i/BITVEC_SZELEM] |= 1 << (i&(BITVEC_SZELEM-1));
 182     return SQLITE_OK;
 183   }
 184   h = BITVEC_HASH(i++);
 185   /* if there wasn't a hash collision, and this doesn't */
 186   /* completely fill the hash, then just add it without */
 187   /* worring about sub-dividing and re-hashing. */
 188   if( !p->u.aHash[h] ){
 189     if (p->nSet<(BITVEC_NINT-1)) {
 190       goto bitvec_set_end;
 191     } else {
 192       goto bitvec_set_rehash;
 193     }
 194   }
 195   /* there was a collision, check to see if it's already */
 196   /* in hash, if not, try to find a spot for it */
 197   do {
 198     if( p->u.aHash[h]==i ) return SQLITE_OK;
 199     h++;
 200     if( h>=BITVEC_NINT ) h = 0;
 201   } while( p->u.aHash[h] );
 202   /* we didn't find it in the hash.  h points to the first */
 203   /* available free spot. check to see if this is going to */
 204   /* make our hash too "full".  */
 205 bitvec_set_rehash:
 206   if( p->nSet>=BITVEC_MXHASH ){
 207     unsigned int j;
 208     int rc;
 209     u32 *aiValues = sqlite3StackAllocRaw(0, sizeof(p->u.aHash));
 210     if( aiValues==0 ){
 211       return SQLITE_NOMEM;
 212     }else{
 213       memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));
 214       memset(p->u.apSub, 0, sizeof(p->u.apSub));
 215       p->iDivisor = (p->iSize + BITVEC_NPTR - 1)/BITVEC_NPTR;
 216       rc = sqlite3BitvecSet(p, i);
 217       for(j=0; j<BITVEC_NINT; j++){
 218         if( aiValues[j] ) rc |= sqlite3BitvecSet(p, aiValues[j]);
 219       }
 220       sqlite3StackFree(0, aiValues);
 221       return rc;
 222     }
 223   }
 224 bitvec_set_end:
 225   p->nSet++;
 226   p->u.aHash[h] = i;
 227   return SQLITE_OK;
 228 }
 229
 230 /*
 231 ** Clear the i-th bit.
 232 **
 233 ** pBuf must be a pointer to at least BITVEC_SZ bytes of temporary storage
 234 ** that BitvecClear can use to rebuilt its hash table.
 235 */
 236 void sqlite3BitvecClear(Bitvec *p, u32 i, void *pBuf){
 237   if( p==0 ) return;
 238   assert( i>0 );
 239   i--;
 240   while( p->iDivisor ){
 241     u32 bin = i/p->iDivisor;
 242     i = i%p->iDivisor;
 243     p = p->u.apSub[bin];
 244     if (!p) {
 245       return;
 246     }
 247   }
 248   if( p->iSize<=BITVEC_NBIT ){
 249     p->u.aBitmap[i/BITVEC_SZELEM] &= ~(1 << (i&(BITVEC_SZELEM-1)));
 250   }else{
 251     unsigned int j;
 252     u32 *aiValues = pBuf;
 253     memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));
 254     memset(p->u.aHash, 0, sizeof(p->u.aHash));
 255     p->nSet = 0;
 256     for(j=0; j<BITVEC_NINT; j++){
 257       if( aiValues[j] && aiValues[j]!=(i+1) ){
 258         u32 h = BITVEC_HASH(aiValues[j]-1);
 259         p->nSet++;
 260         while( p->u.aHash[h] ){
 261           h++;
 262           if( h>=BITVEC_NINT ) h = 0;
 263         }
 264         p->u.aHash[h] = aiValues[j];
 265       }
 266     }
 267   }
 268 }
 269
 270 /*
 271 ** Destroy a bitmap object.  Reclaim all memory used.
 272 */
 273 void sqlite3BitvecDestroy(Bitvec *p){
 274   if( p==0 ) return;
 275   if( p->iDivisor ){
 276     unsigned int i;
 277     for(i=0; i<BITVEC_NPTR; i++){
 278       sqlite3BitvecDestroy(p->u.apSub[i]);
 279     }
 280   }
 281   sqlite3_free(p);
 282 }
 283
 284 /*
 285 ** Return the value of the iSize parameter specified when Bitvec *p
 286 ** was created.
 287 */
 288 u32 sqlite3BitvecSize(Bitvec *p){
 289   return p->iSize;
 290 }
 291
 292 #ifndef SQLITE_OMIT_BUILTIN_TEST
 293 /*
 294 ** Let V[] be an array of unsigned characters sufficient to hold
 295 ** up to N bits.  Let I be an integer between 0 and N.  0<=I<N.
 296 ** Then the following macros can be used to set, clear, or test
 297 ** individual bits within V.
 298 */
 299 #define SETBIT(V,I)      V[I>>3] |= (1<<(I&7))
 300 #define CLEARBIT(V,I)    V[I>>3] &= ~(1<<(I&7))
 301 #define TESTBIT(V,I)     (V[I>>3]&(1<<(I&7)))!=0
 302
 303 /*
 304 ** This routine runs an extensive test of the Bitvec code.
 305 **
 306 ** The input is an array of integers that acts as a program
 307 ** to test the Bitvec.  The integers are opcodes followed
 308 ** by 0, 1, or 3 operands, depending on the opcode.  Another
 309 ** opcode follows immediately after the last operand.
 310 **
 311 ** There are 6 opcodes numbered from 0 through 5.  0 is the
 312 ** "halt" opcode and causes the test to end.
 313 **
 314 **    0          Halt and return the number of errors
 315 **    1 N S X    Set N bits beginning with S and incrementing by X
 316 **    2 N S X    Clear N bits beginning with S and incrementing by X
 317 **    3 N        Set N randomly chosen bits
 318 **    4 N        Clear N randomly chosen bits
 319 **    5 N S X    Set N bits from S increment X in array only, not in bitvec
 320 **
 321 ** The opcodes 1 through 4 perform set and clear operations are performed
 322 ** on both a Bitvec object and on a linear array of bits obtained from malloc.
 323 ** Opcode 5 works on the linear array only, not on the Bitvec.
 324 ** Opcode 5 is used to deliberately induce a fault in order to
 325 ** confirm that error detection works.
 326 **
 327 ** At the conclusion of the test the linear array is compared
 328 ** against the Bitvec object.  If there are any differences,
 329 ** an error is returned.  If they are the same, zero is returned.
 330 **
 331 ** If a memory allocation error occurs, return -1.
 332 */
 333 int sqlite3BitvecBuiltinTest(int sz, int *aOp){
 334   Bitvec *pBitvec = 0;
 335   unsigned char *pV = 0;
 336   int rc = -1;
 337   int i, nx, pc, op;
 338   void *pTmpSpace;
 339
 340   /* Allocate the Bitvec to be tested and a linear array of
 341   ** bits to act as the reference */
 342   pBitvec = sqlite3BitvecCreate( sz );
 343   pV = sqlite3MallocZero( (sz+7)/8 + 1 );
 344   pTmpSpace = sqlite3_malloc(BITVEC_SZ);
 345   if( pBitvec==0 || pV==0 || pTmpSpace==0  ) goto bitvec_end;
 346
 347   /* NULL pBitvec tests */
 348   sqlite3BitvecSet(0, 1);
 349   sqlite3BitvecClear(0, 1, pTmpSpace);
 350
 351   /* Run the program */
 352   pc = 0;
 353   while( (op = aOp[pc])!=0 ){
 354     switch( op ){
 355       case 1:
 356       case 2:
 357       case 5: {
 358         nx = 4;
 359         i = aOp[pc+2] - 1;
 360         aOp[pc+2] += aOp[pc+3];
 361         break;
 362       }
 363       case 3:
 364       case 4:
 365       default: {
 366         nx = 2;
 367         sqlite3_randomness(sizeof(i), &i);
 368         break;
 369       }
 370     }
 371     if( (--aOp[pc+1]) > 0 ) nx = 0;
 372     pc += nx;
 373     i = (i & 0x7fffffff)%sz;
 374     if( (op & 1)!=0 ){
 375       SETBIT(pV, (i+1));
 376       if( op!=5 ){
 377         if( sqlite3BitvecSet(pBitvec, i+1) ) goto bitvec_end;
 378       }
 379     }else{
 380       CLEARBIT(pV, (i+1));
 381       sqlite3BitvecClear(pBitvec, i+1, pTmpSpace);
 382     }
 383   }
 384
 385   /* Test to make sure the linear array exactly matches the
 386   ** Bitvec object.  Start with the assumption that they do
 387   ** match (rc==0).  Change rc to non-zero if a discrepancy
 388   ** is found.
 389   */
 390   rc = sqlite3BitvecTest(0,0) + sqlite3BitvecTest(pBitvec, sz+1)
 391           + sqlite3BitvecTest(pBitvec, 0)
 392           + (sqlite3BitvecSize(pBitvec) - sz);
 393   for(i=1; i<=sz; i++){
 394     if(  (TESTBIT(pV,i))!=sqlite3BitvecTest(pBitvec,i) ){
 395       rc = i;
 396       break;
 397     }
 398   }
 399
 400   /* Free allocated structure */
 401 bitvec_end:
 402   sqlite3_free(pTmpSpace);
 403   sqlite3_free(pV);
 404   sqlite3BitvecDestroy(pBitvec);
 405   return rc;
 406 }
 407 #endif /* SQLITE_OMIT_BUILTIN_TEST */