** 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.
**
*************************************************************************
** $Id: btree.c,v 1.140 2004/05/15 00:29:24 drh Exp $
**
** This file implements a external (disk-based) database using BTrees.
** For a detailed discussion of BTrees, refer to
**
**     Donald E. Knuth, THE ART OF COMPUTER PROGRAMMING, Volume 3:
**     "Sorting And Searching", pages 473-480. Addison-Wesley
**     Publishing Company, Reading, Massachusetts.
................................................................................
  /* 
  ** Return without doing any work if pPage is neither overfull nor
  ** underfull.
  */
  assert( pPage->isInit );
  assert( sqlite3pager_iswriteable(pPage->aData) );
  pBt = pPage->pBt;
  if( !pPage->isOverfull && pPage->nFree<pBt->usableSize*2/3 && pPage->nCell>=2){

    relinkCellList(pPage);
    return SQLITE_OK;
  }

  /*
  ** Find the parent of the page to be balanced.  If there is no parent,
  ** it means this page is the root page and special rules apply.
................................................................................
  ** Load pointers to all cells on sibling pages and the divider cells
  ** into the local apCell[] array.  Make copies of the divider cells
  ** into space obtained form aSpace[] and remove the the divider Cells
  ** from pParent.
  **
  ** If the siblings are on leaf pages, then the child pointers of the
  ** divider cells are stripped from the cells before they are copied
  ** into aSpace[].  In this wall, all cells in apCell[] are without
  ** child pointers.  If siblings are not leaves, then all cell in
  ** apCell[] include child pointers.  Either way, all cells in apCell[]
  ** are alike.



  */
  nCell = 0;
  leafCorrection = pPage->leaf*4;
  leafData = pPage->leafData && pPage->leaf;
  for(i=0; i<nOld; i++){
    MemPage *pOld = apCopy[i];
    for(j=0; j<pOld->nCell; j++){
................................................................................
      apCell[nCell] = pOld->aCell[j];
      szCell[nCell] = cellSize(pOld, apCell[nCell]);
      nCell++;
    }
    if( i<nOld-1 ){
      int sz = cellSize(pParent, apDiv[i]);
      if( leafData ){





        dropCell(pParent, nxDiv, sz);
      }else{
        u8 *pTemp;
        szCell[nCell] = sz;
        pTemp = &aSpace[iSpace];
        iSpace += sz;
        assert( iSpace<=sizeof(aSpace) );
................................................................................
  /*
  ** Figure out the number of pages needed to hold all nCell cells.
  ** Store this number in "k".  Also compute szNew[] which is the total
  ** size of all cells on the i-th page and cntNew[] which is the index
  ** in apCell[] of the cell that divides page i from page i+1.  
  ** cntNew[k] should equal nCell.
  **
  ** This little patch of code is critical for keeping the tree
  ** balanced. 






  */
  usableSpace = pBt->usableSize - 10 + leafCorrection;
  for(subtotal=k=i=0; i<nCell; i++){
    subtotal += szCell[i];
    if( subtotal > usableSpace ){
      szNew[k] = subtotal - szCell[i];
      cntNew[k] = i;
................................................................................
      subtotal = 0;
      k++;
    }
  }
  szNew[k] = subtotal;
  cntNew[k] = nCell;
  k++;











  for(i=k-1; i>0; i--){
    while( szNew[i]<usableSpace/2 ){





      cntNew[i-1]--;




      assert( cntNew[i-1]>0 );
      szNew[i] += szCell[cntNew[i-1]];
      szNew[i-1] -= szCell[cntNew[i-1]-1];

    }


  }
  assert( cntNew[0]>0 );

  /*
  ** Allocate k new pages.  Reuse old pages where possible.
  */
  assert( pPage->pgno>1 );

** 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.
**
*************************************************************************
** $Id: btree.c,v 1.141 2004/05/16 16:24:37 drh Exp $
**
** This file implements a external (disk-based) database using BTrees.
** For a detailed discussion of BTrees, refer to
**
**     Donald E. Knuth, THE ART OF COMPUTER PROGRAMMING, Volume 3:
**     "Sorting And Searching", pages 473-480. Addison-Wesley
**     Publishing Company, Reading, Massachusetts.
................................................................................
  /* 
  ** Return without doing any work if pPage is neither overfull nor
  ** underfull.
  */
  assert( pPage->isInit );
  assert( sqlite3pager_iswriteable(pPage->aData) );
  pBt = pPage->pBt;
  if( !pPage->isOverfull && pPage->nFree<pBt->usableSize*2/3
        && pPage->nCell>=2){
    relinkCellList(pPage);
    return SQLITE_OK;
  }

  /*
  ** Find the parent of the page to be balanced.  If there is no parent,
  ** it means this page is the root page and special rules apply.
................................................................................
  ** Load pointers to all cells on sibling pages and the divider cells
  ** into the local apCell[] array.  Make copies of the divider cells
  ** into space obtained form aSpace[] and remove the the divider Cells
  ** from pParent.
  **
  ** If the siblings are on leaf pages, then the child pointers of the
  ** divider cells are stripped from the cells before they are copied
  ** into aSpace[].  In this way, all cells in apCell[] are without
  ** child pointers.  If siblings are not leaves, then all cell in
  ** apCell[] include child pointers.  Either way, all cells in apCell[]
  ** are alike.
  **
  ** leafCorrection:  4 if pPage is a leaf.  0 if pPage is not a leaf.
  **       leafData:  1 if pPage holds key+data and pParent holds only keys.
  */
  nCell = 0;
  leafCorrection = pPage->leaf*4;
  leafData = pPage->leafData && pPage->leaf;
  for(i=0; i<nOld; i++){
    MemPage *pOld = apCopy[i];
    for(j=0; j<pOld->nCell; j++){
................................................................................
      apCell[nCell] = pOld->aCell[j];
      szCell[nCell] = cellSize(pOld, apCell[nCell]);
      nCell++;
    }
    if( i<nOld-1 ){
      int sz = cellSize(pParent, apDiv[i]);
      if( leafData ){
        /* With the LEAFDATA flag, pParent cells hold only INTKEYs that
        ** are duplicates of keys on the child pages.  We need to remove
        ** the divider cells from pParent, but the dividers cells are not
        ** added to apCell[] because they are duplicates of child cells.
        */
        dropCell(pParent, nxDiv, sz);
      }else{
        u8 *pTemp;
        szCell[nCell] = sz;
        pTemp = &aSpace[iSpace];
        iSpace += sz;
        assert( iSpace<=sizeof(aSpace) );
................................................................................
  /*
  ** Figure out the number of pages needed to hold all nCell cells.
  ** Store this number in "k".  Also compute szNew[] which is the total
  ** size of all cells on the i-th page and cntNew[] which is the index
  ** in apCell[] of the cell that divides page i from page i+1.  
  ** cntNew[k] should equal nCell.
  **
  ** Values computed by this block:
  **
  **           k: The total number of sibling pages
  **    szNew[i]: Spaced used on the i-th sibling page.
  **   cntNew[i]: Index in apCell[] and szCell[] for the first cell to
  **              the right of the i-th sibling page.
  ** usableSpace: Number of bytes of space available on each sibling.
  ** 
  */
  usableSpace = pBt->usableSize - 10 + leafCorrection;
  for(subtotal=k=i=0; i<nCell; i++){
    subtotal += szCell[i];
    if( subtotal > usableSpace ){
      szNew[k] = subtotal - szCell[i];
      cntNew[k] = i;
................................................................................
      subtotal = 0;
      k++;
    }
  }
  szNew[k] = subtotal;
  cntNew[k] = nCell;
  k++;

  /*
  ** The packing computed by the previous block is biased toward the siblings
  ** on the left side.  The left siblings are always nearly full, while the
  ** right-most sibling might be nearly empty.  This block of code attempts
  ** to adjust the packing of siblings to get a better balance.
  **
  ** This adjustment is more than an optimization.  The packing above might
  ** be so out of balance as to be illegal.  For example, the right-most
  ** sibling might be completely empty.  This adjustment is not optional.
  */
  for(i=k-1; i>0; i--){

    int szRight = szNew[i];  /* Size of sibling on the right */
    int szLeft = szNew[i-1]; /* Size of sibling on the left */
    int r;              /* Index of right-most cell in left sibling */
    int d;              /* Index of first cell to the left of right sibling */

    r = cntNew[i-1] - 1;
    d = r + 1 - leafData;
    while( szRight==0 || szRight+szCell[d]<=szLeft-szCell[r] ){
      szRight += szCell[d];
      szLeft -= szCell[r];
      cntNew[i-1]--;
      r = cntNew[i-1] - 1;

      d = r + 1 - leafData;
    }
    szNew[i] = szRight;
    szNew[i-1] = szLeft;
  }
  assert( cntNew[0]>0 );

  /*
  ** Allocate k new pages.  Reuse old pages where possible.
  */
  assert( pPage->pgno>1 );