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Diffstat (limited to 'src/bitvec.c')
-rw-r--r-- | src/bitvec.c | 411 |
1 files changed, 411 insertions, 0 deletions
diff --git a/src/bitvec.c b/src/bitvec.c new file mode 100644 index 0000000..13f87d5 --- /dev/null +++ b/src/bitvec.c @@ -0,0 +1,411 @@ +/* +** 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 */ |