/*

 ** 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 what pages a database file have been

 ** journalled during a transaction.  Usually only a few pages are

 ** journalled.  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 get journalled.  In those cases, the bitmap becomes

 ** dense.  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.

 **

 ** @(#) $Id: bitvec.c,v 1.6 2008/06/20 14:59:51 danielk1977 Exp $

 */

 #include "sqliteInt.h"

 #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-12)/sizeof(Bitvec*))*sizeof(Bitvec*))

 #define BITVEC_NCHAR     BITVEC_USIZE

 #define BITVEC_NBIT      (BITVEC_NCHAR*8)

 #define BITVEC_NINT      (BITVEC_USIZE/4)

 #define BITVEC_MXHASH    (BITVEC_NINT/2)

 #define BITVEC_NPTR      (BITVEC_USIZE/sizeof(Bitvec *))

 #define BITVEC_HASH(X)   (((X)*37)%BITVEC_NINT)

 /*

 ** A bitmap is an instance of the following structure.

 **

 ** This bitmap records the existance 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 */

   u32 nSet;       /* Number of bits that are set */

   u32 iDivisor;   /* Number of bits handled by each apSub[] entry */

   union {

     u8 aBitmap[BITVEC_NCHAR];    /* 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 sqlite3BitvecTest(Bitvec *p, u32 i){

   if( p==0 ) return 0;

   if( i>p->iSize || i==0 ) return 0;

   if( p->iSize<=BITVEC_NBIT ){

     i--;

     return (p->u.aBitmap[i/8] & (1<<(i&7)))!=0;

   }

   if( p->iDivisor>0 ){

     u32 bin = (i-1)/p->iDivisor;

     i = (i-1)%p->iDivisor + 1;

     return sqlite3BitvecTest(p->u.apSub[bin], i);

   }else{

     u32 h = BITVEC_HASH(i);

     while( p->u.aHash[h] ){

       if( p->u.aHash[h]==i ) return 1;

       h++;

       if( h>=BITVEC_NINT ) h = 0;

     }

     return 0;

   }

 }

 /*

 ** Set the i-th bit.  Return 0 on success and an error code if

 ** anything goes wrong.

 */

 int sqlite3BitvecSet(Bitvec *p, u32 i){

   u32 h;

   assert( p!=0 );

   assert( i>0 );

   assert( i<=p->iSize );

   if( p->iSize<=BITVEC_NBIT ){

     i--;

     p->u.aBitmap[i/8] |= 1 << (i&7);

     return SQLITE_OK;

   }

   if( p->iDivisor ){

     u32 bin = (i-1)/p->iDivisor;

     i = (i-1)%p->iDivisor + 1;

     if( p->u.apSub[bin]==0 ){

       sqlite3BeginBenignMalloc();

       p->u.apSub[bin] = sqlite3BitvecCreate( p->iDivisor );

       sqlite3EndBenignMalloc();

       if( p->u.apSub[bin]==0 ) return SQLITE_NOMEM;

     }

     return sqlite3BitvecSet(p->u.apSub[bin], i);

   }

   h = BITVEC_HASH(i);

   while( p->u.aHash[h] ){

     if( p->u.aHash[h]==i ) return SQLITE_OK;

     h++;

     if( h==BITVEC_NINT ) h = 0;

   }

   p->nSet++;

   if( p->nSet>=BITVEC_MXHASH ){

     int j, rc;

     u32 aiValues[BITVEC_NINT];

     memcpy(aiValues, p->u.aHash, sizeof(aiValues));

     memset(p->u.apSub, 0, sizeof(p->u.apSub[0])*BITVEC_NPTR);

     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]);

     }

     return rc;

   }

   p->u.aHash[h] = i;

   return SQLITE_OK;

 }

 /*

 ** Clear the i-th bit.  Return 0 on success and an error code if

 ** anything goes wrong.

 */

 void sqlite3BitvecClear(Bitvec *p, u32 i){

   assert( p!=0 );

   assert( i>0 );

   if( p->iSize<=BITVEC_NBIT ){

     i--;

     p->u.aBitmap[i/8] &= ~(1 << (i&7));

   }else if( p->iDivisor ){

     u32 bin = (i-1)/p->iDivisor;

     i = (i-1)%p->iDivisor + 1;

     if( p->u.apSub[bin] ){

       sqlite3BitvecClear(p->u.apSub[bin], i);

     }

   }else{

     int j;

     u32 aiValues[BITVEC_NINT];

     memcpy(aiValues, p->u.aHash, sizeof(aiValues));

     memset(p->u.aHash, 0, sizeof(p->u.aHash[0])*BITVEC_NINT);

     p->nSet = 0;

     for(j=0; j<BITVEC_NINT; j++){

       if( aiValues[j] && aiValues[j]!=i ){

         sqlite3BitvecSet(p, aiValues[j]);

       }

     }

   }

 }

 /*

 ** Destroy a bitmap object.  Reclaim all memory used.

 */

 void sqlite3BitvecDestroy(Bitvec *p){

   if( p==0 ) return;

   if( p->iDivisor ){

     int i;

     for(i=0; i<BITVEC_NPTR; i++){

       sqlite3BitvecDestroy(p->u.apSub[i]);

     }

   }

   sqlite3_free(p);

 }

 #ifndef SQLITE_OMIT_BUILTIN_TEST

 /*

 ** 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;

   /* Allocate the Bitvec to be tested and a linear array of

   ** bits to act as the reference */

   pBitvec = sqlite3BitvecCreate( sz );

   pV = sqlite3_malloc( (sz+7)/8 + 1 );

   if( pBitvec==0 || pV==0 ) goto bitvec_end;

   memset(pV, 0, (sz+7)/8 + 1);

   /* 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);

     }

   }

   /* 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);

   for(i=1; i<=sz; i++){

     if(  (TESTBIT(pV,i))!=sqlite3BitvecTest(pBitvec,i) ){

       rc = i;

       break;

     }

   }

   /* Free allocated structure */

 bitvec_end:

   sqlite3_free(pV);

   sqlite3BitvecDestroy(pBitvec);

   return rc;

 }

 #endif /* SQLITE_OMIT_BUILTIN_TEST */