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-/*
-** 2008 February 16
-**
-** The author disclaims copyright to this source code. In place of
-** a legal notice, here is a blessing:
-**
-** May you do good and not evil.
-** May you find forgiveness for yourself and forgive others.
-** May you share freely, never taking more than you give.
-**
-*************************************************************************
-** This file implements an object that represents a fixed-length
-** bitmap. Bits are numbered starting with 1.
-**
-** A bitmap is used to record which pages of a database file have been
-** journalled during a transaction, or which pages have the "dont-write"
-** property. Usually only a few pages are meet either condition.
-** So the bitmap is usually sparse and has low cardinality.
-** But sometimes (for example when during a DROP of a large table) most
-** or all of the pages in a database can get journalled. In those cases,
-** the bitmap becomes dense with high cardinality. The algorithm needs
-** to handle both cases well.
-**
-** The size of the bitmap is fixed when the object is created.
-**
-** All bits are clear when the bitmap is created. Individual bits
-** may be set or cleared one at a time.
-**
-** Test operations are about 100 times more common that set operations.
-** Clear operations are exceedingly rare. There are usually between
-** 5 and 500 set operations per Bitvec object, though the number of sets can
-** sometimes grow into tens of thousands or larger. The size of the
-** Bitvec object is the number of pages in the database file at the
-** start of a transaction, and is thus usually less than a few thousand,
-** but can be as large as 2 billion for a really big database.
-*/
-#include "sqliteInt.h"
-
-/* Size of the Bitvec structure in bytes. */
-#define BITVEC_SZ 512
-
-/* Round the union size down to the nearest pointer boundary, since that's how
-** it will be aligned within the Bitvec struct. */
-#define BITVEC_USIZE \
- (((BITVEC_SZ-(3*sizeof(u32)))/sizeof(Bitvec*))*sizeof(Bitvec*))
-
-/* Type of the array "element" for the bitmap representation.
-** Should be a power of 2, and ideally, evenly divide into BITVEC_USIZE.
-** Setting this to the "natural word" size of your CPU may improve
-** performance. */
-#define BITVEC_TELEM u8
-/* Size, in bits, of the bitmap element. */
-#define BITVEC_SZELEM 8
-/* Number of elements in a bitmap array. */
-#define BITVEC_NELEM (BITVEC_USIZE/sizeof(BITVEC_TELEM))
-/* Number of bits in the bitmap array. */
-#define BITVEC_NBIT (BITVEC_NELEM*BITVEC_SZELEM)
-
-/* Number of u32 values in hash table. */
-#define BITVEC_NINT (BITVEC_USIZE/sizeof(u32))
-/* Maximum number of entries in hash table before
-** sub-dividing and re-hashing. */
-#define BITVEC_MXHASH (BITVEC_NINT/2)
-/* Hashing function for the aHash representation.
-** Empirical testing showed that the *37 multiplier
-** (an arbitrary prime)in the hash function provided
-** no fewer collisions than the no-op *1. */
-#define BITVEC_HASH(X) (((X)*1)%BITVEC_NINT)
-
-#define BITVEC_NPTR (BITVEC_USIZE/sizeof(Bitvec *))
-
-
-/*
-** A bitmap is an instance of the following structure.
-**
-** This bitmap records the existence of zero or more bits
-** with values between 1 and iSize, inclusive.
-**
-** There are three possible representations of the bitmap.
-** If iSize<=BITVEC_NBIT, then Bitvec.u.aBitmap[] is a straight
-** bitmap. The least significant bit is bit 1.
-**
-** If iSize>BITVEC_NBIT and iDivisor==0 then Bitvec.u.aHash[] is
-** a hash table that will hold up to BITVEC_MXHASH distinct values.
-**
-** Otherwise, the value i is redirected into one of BITVEC_NPTR
-** sub-bitmaps pointed to by Bitvec.u.apSub[]. Each subbitmap
-** handles up to iDivisor separate values of i. apSub[0] holds
-** values between 1 and iDivisor. apSub[1] holds values between
-** iDivisor+1 and 2*iDivisor. apSub[N] holds values between
-** N*iDivisor+1 and (N+1)*iDivisor. Each subbitmap is normalized
-** to hold deal with values between 1 and iDivisor.
-*/
-struct Bitvec {
- u32 iSize; /* Maximum bit index. Max iSize is 4,294,967,296. */
- u32 nSet; /* Number of bits that are set - only valid for aHash
- ** element. Max is BITVEC_NINT. For BITVEC_SZ of 512,
- ** this would be 125. */
- u32 iDivisor; /* Number of bits handled by each apSub[] entry. */
- /* Should >=0 for apSub element. */
- /* Max iDivisor is max(u32) / BITVEC_NPTR + 1. */
- /* For a BITVEC_SZ of 512, this would be 34,359,739. */
- union {
- BITVEC_TELEM aBitmap[BITVEC_NELEM]; /* Bitmap representation */
- u32 aHash[BITVEC_NINT]; /* Hash table representation */
- Bitvec *apSub[BITVEC_NPTR]; /* Recursive representation */
- } u;
-};
-
-/*
-** Create a new bitmap object able to handle bits between 0 and iSize,
-** inclusive. Return a pointer to the new object. Return NULL if
-** malloc fails.
-*/
-Bitvec *sqlite3BitvecCreate(u32 iSize){
- Bitvec *p;
- assert( sizeof(*p)==BITVEC_SZ );
- p = sqlite3MallocZero( sizeof(*p) );
- if( p ){
- p->iSize = iSize;
- }
- return p;
-}
-
-/*
-** Check to see if the i-th bit is set. Return true or false.
-** If p is NULL (if the bitmap has not been created) or if
-** i is out of range, then return false.
-*/
-int sqlite3BitvecTestNotNull(Bitvec *p, u32 i){
- assert( p!=0 );
- i--;
- if( i>=p->iSize ) return 0;
- while( p->iDivisor ){
- u32 bin = i/p->iDivisor;
- i = i%p->iDivisor;
- p = p->u.apSub[bin];
- if (!p) {
- return 0;
- }
- }
- if( p->iSize<=BITVEC_NBIT ){
- return (p->u.aBitmap[i/BITVEC_SZELEM] & (1<<(i&(BITVEC_SZELEM-1))))!=0;
- } else{
- u32 h = BITVEC_HASH(i++);
- while( p->u.aHash[h] ){
- if( p->u.aHash[h]==i ) return 1;
- h = (h+1) % BITVEC_NINT;
- }
- return 0;
- }
-}
-int sqlite3BitvecTest(Bitvec *p, u32 i){
- return p!=0 && sqlite3BitvecTestNotNull(p,i);
-}
-
-/*
-** Set the i-th bit. Return 0 on success and an error code if
-** anything goes wrong.
-**
-** This routine might cause sub-bitmaps to be allocated. Failing
-** to get the memory needed to hold the sub-bitmap is the only
-** that can go wrong with an insert, assuming p and i are valid.
-**
-** The calling function must ensure that p is a valid Bitvec object
-** and that the value for "i" is within range of the Bitvec object.
-** Otherwise the behavior is undefined.
-*/
-int sqlite3BitvecSet(Bitvec *p, u32 i){
- u32 h;
- if( p==0 ) return SQLITE_OK;
- assert( i>0 );
- assert( i<=p->iSize );
- i--;
- while((p->iSize > BITVEC_NBIT) && p->iDivisor) {
- u32 bin = i/p->iDivisor;
- i = i%p->iDivisor;
- if( p->u.apSub[bin]==0 ){
- p->u.apSub[bin] = sqlite3BitvecCreate( p->iDivisor );
- if( p->u.apSub[bin]==0 ) return SQLITE_NOMEM_BKPT;
- }
- p = p->u.apSub[bin];
- }
- if( p->iSize<=BITVEC_NBIT ){
- p->u.aBitmap[i/BITVEC_SZELEM] |= 1 << (i&(BITVEC_SZELEM-1));
- return SQLITE_OK;
- }
- h = BITVEC_HASH(i++);
- /* if there wasn't a hash collision, and this doesn't */
- /* completely fill the hash, then just add it without */
- /* worring about sub-dividing and re-hashing. */
- if( !p->u.aHash[h] ){
- if (p->nSet<(BITVEC_NINT-1)) {
- goto bitvec_set_end;
- } else {
- goto bitvec_set_rehash;
- }
- }
- /* there was a collision, check to see if it's already */
- /* in hash, if not, try to find a spot for it */
- do {
- if( p->u.aHash[h]==i ) return SQLITE_OK;
- h++;
- if( h>=BITVEC_NINT ) h = 0;
- } while( p->u.aHash[h] );
- /* we didn't find it in the hash. h points to the first */
- /* available free spot. check to see if this is going to */
- /* make our hash too "full". */
-bitvec_set_rehash:
- if( p->nSet>=BITVEC_MXHASH ){
- unsigned int j;
- int rc;
- u32 *aiValues = sqlite3StackAllocRaw(0, sizeof(p->u.aHash));
- if( aiValues==0 ){
- return SQLITE_NOMEM_BKPT;
- }else{
- memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));
- memset(p->u.apSub, 0, sizeof(p->u.apSub));
- p->iDivisor = (p->iSize + BITVEC_NPTR - 1)/BITVEC_NPTR;
- rc = sqlite3BitvecSet(p, i);
- for(j=0; j<BITVEC_NINT; j++){
- if( aiValues[j] ) rc |= sqlite3BitvecSet(p, aiValues[j]);
- }
- sqlite3StackFree(0, aiValues);
- return rc;
- }
- }
-bitvec_set_end:
- p->nSet++;
- p->u.aHash[h] = i;
- return SQLITE_OK;
-}
-
-/*
-** Clear the i-th bit.
-**
-** pBuf must be a pointer to at least BITVEC_SZ bytes of temporary storage
-** that BitvecClear can use to rebuilt its hash table.
-*/
-void sqlite3BitvecClear(Bitvec *p, u32 i, void *pBuf){
- if( p==0 ) return;
- assert( i>0 );
- i--;
- while( p->iDivisor ){
- u32 bin = i/p->iDivisor;
- i = i%p->iDivisor;
- p = p->u.apSub[bin];
- if (!p) {
- return;
- }
- }
- if( p->iSize<=BITVEC_NBIT ){
- p->u.aBitmap[i/BITVEC_SZELEM] &= ~(1 << (i&(BITVEC_SZELEM-1)));
- }else{
- unsigned int j;
- u32 *aiValues = pBuf;
- memcpy(aiValues, p->u.aHash, sizeof(p->u.aHash));
- memset(p->u.aHash, 0, sizeof(p->u.aHash));
- p->nSet = 0;
- for(j=0; j<BITVEC_NINT; j++){
- if( aiValues[j] && aiValues[j]!=(i+1) ){
- u32 h = BITVEC_HASH(aiValues[j]-1);
- p->nSet++;
- while( p->u.aHash[h] ){
- h++;
- if( h>=BITVEC_NINT ) h = 0;
- }
- p->u.aHash[h] = aiValues[j];
- }
- }
- }
-}
-
-/*
-** Destroy a bitmap object. Reclaim all memory used.
-*/
-void sqlite3BitvecDestroy(Bitvec *p){
- if( p==0 ) return;
- if( p->iDivisor ){
- unsigned int i;
- for(i=0; i<BITVEC_NPTR; i++){
- sqlite3BitvecDestroy(p->u.apSub[i]);
- }
- }
- sqlite3_free(p);
-}
-
-/*
-** Return the value of the iSize parameter specified when Bitvec *p
-** was created.
-*/
-u32 sqlite3BitvecSize(Bitvec *p){
- return p->iSize;
-}
-
-#ifndef SQLITE_UNTESTABLE
-/*
-** Let V[] be an array of unsigned characters sufficient to hold
-** up to N bits. Let I be an integer between 0 and N. 0<=I<N.
-** Then the following macros can be used to set, clear, or test
-** individual bits within V.
-*/
-#define SETBIT(V,I) V[I>>3] |= (1<<(I&7))
-#define CLEARBIT(V,I) V[I>>3] &= ~(1<<(I&7))
-#define TESTBIT(V,I) (V[I>>3]&(1<<(I&7)))!=0
-
-/*
-** This routine runs an extensive test of the Bitvec code.
-**
-** The input is an array of integers that acts as a program
-** to test the Bitvec. The integers are opcodes followed
-** by 0, 1, or 3 operands, depending on the opcode. Another
-** opcode follows immediately after the last operand.
-**
-** There are 6 opcodes numbered from 0 through 5. 0 is the
-** "halt" opcode and causes the test to end.
-**
-** 0 Halt and return the number of errors
-** 1 N S X Set N bits beginning with S and incrementing by X
-** 2 N S X Clear N bits beginning with S and incrementing by X
-** 3 N Set N randomly chosen bits
-** 4 N Clear N randomly chosen bits
-** 5 N S X Set N bits from S increment X in array only, not in bitvec
-**
-** The opcodes 1 through 4 perform set and clear operations are performed
-** on both a Bitvec object and on a linear array of bits obtained from malloc.
-** Opcode 5 works on the linear array only, not on the Bitvec.
-** Opcode 5 is used to deliberately induce a fault in order to
-** confirm that error detection works.
-**
-** At the conclusion of the test the linear array is compared
-** against the Bitvec object. If there are any differences,
-** an error is returned. If they are the same, zero is returned.
-**
-** If a memory allocation error occurs, return -1.
-*/
-int sqlite3BitvecBuiltinTest(int sz, int *aOp){
- Bitvec *pBitvec = 0;
- unsigned char *pV = 0;
- int rc = -1;
- int i, nx, pc, op;
- void *pTmpSpace;
-
- /* Allocate the Bitvec to be tested and a linear array of
- ** bits to act as the reference */
- pBitvec = sqlite3BitvecCreate( sz );
- pV = sqlite3MallocZero( (sz+7)/8 + 1 );
- pTmpSpace = sqlite3_malloc64(BITVEC_SZ);
- if( pBitvec==0 || pV==0 || pTmpSpace==0 ) goto bitvec_end;
-
- /* NULL pBitvec tests */
- sqlite3BitvecSet(0, 1);
- sqlite3BitvecClear(0, 1, pTmpSpace);
-
- /* Run the program */
- pc = 0;
- while( (op = aOp[pc])!=0 ){
- switch( op ){
- case 1:
- case 2:
- case 5: {
- nx = 4;
- i = aOp[pc+2] - 1;
- aOp[pc+2] += aOp[pc+3];
- break;
- }
- case 3:
- case 4:
- default: {
- nx = 2;
- sqlite3_randomness(sizeof(i), &i);
- break;
- }
- }
- if( (--aOp[pc+1]) > 0 ) nx = 0;
- pc += nx;
- i = (i & 0x7fffffff)%sz;
- if( (op & 1)!=0 ){
- SETBIT(pV, (i+1));
- if( op!=5 ){
- if( sqlite3BitvecSet(pBitvec, i+1) ) goto bitvec_end;
- }
- }else{
- CLEARBIT(pV, (i+1));
- sqlite3BitvecClear(pBitvec, i+1, pTmpSpace);
- }
- }
-
- /* Test to make sure the linear array exactly matches the
- ** Bitvec object. Start with the assumption that they do
- ** match (rc==0). Change rc to non-zero if a discrepancy
- ** is found.
- */
- rc = sqlite3BitvecTest(0,0) + sqlite3BitvecTest(pBitvec, sz+1)
- + sqlite3BitvecTest(pBitvec, 0)
- + (sqlite3BitvecSize(pBitvec) - sz);
- for(i=1; i<=sz; i++){
- if( (TESTBIT(pV,i))!=sqlite3BitvecTest(pBitvec,i) ){
- rc = i;
- break;
- }
- }
-
- /* Free allocated structure */
-bitvec_end:
- sqlite3_free(pTmpSpace);
- sqlite3_free(pV);
- sqlite3BitvecDestroy(pBitvec);
- return rc;
-}
-#endif /* SQLITE_UNTESTABLE */
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