** 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 1.342 2007/03/26 22:05:01 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.
**
** The basic idea is that each page of the file contains N database
** entries and N+1 pointers to subpages.
**
**   ----------------------------------------------------------------
**   |  Ptr(0) | Key(0) | Ptr(1) | Key(1) | ... | Key(N) | Ptr(N+1) |
**   ----------------------------------------------------------------
**
** All of the keys on the page that Ptr(0) points to have values less
** than Key(0).  All of the keys on page Ptr(1) and its subpages have
** values greater than Key(0) and less than Key(1).  All of the keys
** on Ptr(N+1) and its subpages have values greater than Key(N).  And
** so forth.
**
** Finding a particular key requires reading O(log(M)) pages from the 
** disk where M is the number of entries in the tree.
**
** In this implementation, a single file can hold one or more separate 
** BTrees.  Each BTree is identified by the index of its root page.  The
** key and data for any entry are combined to form the "payload".  A
** fixed amount of payload can be carried directly on the database
** page.  If the payload is larger than the preset amount then surplus
** bytes are stored on overflow pages.  The payload for an entry
** and the preceding pointer are combined to form a "Cell".  Each 
** page has a small header which contains the Ptr(N+1) pointer and other
** information such as the size of key and data.
**
** FORMAT DETAILS
**
** The file is divided into pages.  The first page is called page 1,
** the second is page 2, and so forth.  A page number of zero indicates
** "no such page".  The page size can be anything between 512 and 65536.
................................................................................
**
**   OFFSET   SIZE     DESCRIPTION
**      0       1      Flags. 1: intkey, 2: zerodata, 4: leafdata, 8: leaf
**      1       2      byte offset to the first freeblock
**      3       2      number of cells on this page
**      5       2      first byte of the cell content area
**      7       1      number of fragmented free bytes
**      8       4      Right child (the Ptr(N+1) value).  Omitted on leaves.
**
** The flags define the format of this btree page.  The leaf flag means that
** this page has no children.  The zerodata flag means that this page carries
** only keys and no data.  The intkey flag means that the key is a integer
** which is stored in the key size entry of the cell header rather than in
** the payload area.
**

** 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 1.343 2007/03/27 14:05:23 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.
**
** The basic idea is that each page of the file contains N database
** entries and N+1 pointers to subpages.
**
**   ----------------------------------------------------------------
**   |  Ptr(0) | Key(0) | Ptr(1) | Key(1) | ... | Key(N-1) | Ptr(N) |
**   ----------------------------------------------------------------
**
** All of the keys on the page that Ptr(0) points to have values less
** than Key(0).  All of the keys on page Ptr(1) and its subpages have
** values greater than Key(0) and less than Key(1).  All of the keys
** on Ptr(N) and its subpages have values greater than Key(N-1).  And
** so forth.
**
** Finding a particular key requires reading O(log(M)) pages from the 
** disk where M is the number of entries in the tree.
**
** In this implementation, a single file can hold one or more separate 
** BTrees.  Each BTree is identified by the index of its root page.  The
** key and data for any entry are combined to form the "payload".  A
** fixed amount of payload can be carried directly on the database
** page.  If the payload is larger than the preset amount then surplus
** bytes are stored on overflow pages.  The payload for an entry
** and the preceding pointer are combined to form a "Cell".  Each 
** page has a small header which contains the Ptr(N) pointer and other
** information such as the size of key and data.
**
** FORMAT DETAILS
**
** The file is divided into pages.  The first page is called page 1,
** the second is page 2, and so forth.  A page number of zero indicates
** "no such page".  The page size can be anything between 512 and 65536.
................................................................................
**
**   OFFSET   SIZE     DESCRIPTION
**      0       1      Flags. 1: intkey, 2: zerodata, 4: leafdata, 8: leaf
**      1       2      byte offset to the first freeblock
**      3       2      number of cells on this page
**      5       2      first byte of the cell content area
**      7       1      number of fragmented free bytes
**      8       4      Right child (the Ptr(N) value).  Omitted on leaves.
**
** The flags define the format of this btree page.  The leaf flag means that
** this page has no children.  The zerodata flag means that this page carries
** only keys and no data.  The intkey flag means that the key is a integer
** which is stored in the key size entry of the cell header rather than in
** the payload area.
**