/*
** 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 ((u32)(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] &= ~(BITVEC_TELEM)(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] &= ~(BITVEC_TELEM)(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( (7+(i64)sz)/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 */