/*
** 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 */
/* worrying 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 = i = 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 */