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sqlcipher/ext/rtree/rtree.c

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commit of sqlite 3.6.0
2008-07-30 13:15:43 +00:00
/*
** 2001 September 15
**
** 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 contains code for implementations of the r-tree and r*-tree
** algorithms packaged as an SQLite virtual table module.
**
** $Id: rtree.c,v 1.7 2008/07/16 14:43:35 drh Exp $
*/
#if !defined(SQLITE_CORE) || defined(SQLITE_ENABLE_RTREE)
/*
** This file contains an implementation of a couple of different variants
** of the r-tree algorithm. See the README file for further details. The
** same data-structure is used for all, but the algorithms for insert and
** delete operations vary. The variants used are selected at compile time
** by defining the following symbols:
*/
/* Either, both or none of the following may be set to activate
** r*tree variant algorithms.
*/
#define VARIANT_RSTARTREE_CHOOSESUBTREE 0
#define VARIANT_RSTARTREE_REINSERT 1
/*
** Exactly one of the following must be set to 1.
*/
#define VARIANT_GUTTMAN_QUADRATIC_SPLIT 0
#define VARIANT_GUTTMAN_LINEAR_SPLIT 0
#define VARIANT_RSTARTREE_SPLIT 1
#define VARIANT_GUTTMAN_SPLIT \
(VARIANT_GUTTMAN_LINEAR_SPLIT||VARIANT_GUTTMAN_QUADRATIC_SPLIT)
#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
#define PickNext QuadraticPickNext
#define PickSeeds QuadraticPickSeeds
#define AssignCells splitNodeGuttman
#endif
#if VARIANT_GUTTMAN_LINEAR_SPLIT
#define PickNext LinearPickNext
#define PickSeeds LinearPickSeeds
#define AssignCells splitNodeGuttman
#endif
#if VARIANT_RSTARTREE_SPLIT
#define AssignCells splitNodeStartree
#endif
#ifndef SQLITE_CORE
#include "sqlite3ext.h"
SQLITE_EXTENSION_INIT1
#else
#include "sqlite3.h"
#endif
#include <string.h>
#include <assert.h>
#ifndef SQLITE_AMALGAMATION
typedef sqlite3_int64 i64;
typedef unsigned char u8;
typedef unsigned int u32;
#endif
typedef struct Rtree Rtree;
typedef struct RtreeCursor RtreeCursor;
typedef struct RtreeNode RtreeNode;
typedef struct RtreeCell RtreeCell;
typedef struct RtreeConstraint RtreeConstraint;
typedef union RtreeCoord RtreeCoord;
/* The rtree may have between 1 and RTREE_MAX_DIMENSIONS dimensions. */
#define RTREE_MAX_DIMENSIONS 5
/* Size of hash table Rtree.aHash. This hash table is not expected to
** ever contain very many entries, so a fixed number of buckets is
** used.
*/
#define HASHSIZE 128
/*
** An rtree virtual-table object.
*/
struct Rtree {
sqlite3_vtab base;
sqlite3 *db; /* Host database connection */
int iNodeSize; /* Size in bytes of each node in the node table */
int nDim; /* Number of dimensions */
int nBytesPerCell; /* Bytes consumed per cell */
int iDepth; /* Current depth of the r-tree structure */
char *zDb; /* Name of database containing r-tree table */
char *zName; /* Name of r-tree table */
RtreeNode *aHash[HASHSIZE]; /* Hash table of in-memory nodes. */
int nBusy; /* Current number of users of this structure */
/* List of nodes removed during a CondenseTree operation. List is
** linked together via the pointer normally used for hash chains -
** RtreeNode.pNext. RtreeNode.iNode stores the depth of the sub-tree
** headed by the node (leaf nodes have RtreeNode.iNode==0).
*/
RtreeNode *pDeleted;
int iReinsertHeight; /* Height of sub-trees Reinsert() has run on */
/* Statements to read/write/delete a record from xxx_node */
sqlite3_stmt *pReadNode;
sqlite3_stmt *pWriteNode;
sqlite3_stmt *pDeleteNode;
/* Statements to read/write/delete a record from xxx_rowid */
sqlite3_stmt *pReadRowid;
sqlite3_stmt *pWriteRowid;
sqlite3_stmt *pDeleteRowid;
/* Statements to read/write/delete a record from xxx_parent */
sqlite3_stmt *pReadParent;
sqlite3_stmt *pWriteParent;
sqlite3_stmt *pDeleteParent;
int eCoordType;
};
/* Possible values for eCoordType: */
#define RTREE_COORD_REAL32 0
#define RTREE_COORD_INT32 1
/*
** The minimum number of cells allowed for a node is a third of the
** maximum. In Gutman's notation:
**
** m = M/3
**
** If an R*-tree "Reinsert" operation is required, the same number of
** cells are removed from the overfull node and reinserted into the tree.
*/
#define RTREE_MINCELLS(p) ((((p)->iNodeSize-4)/(p)->nBytesPerCell)/3)
#define RTREE_REINSERT(p) RTREE_MINCELLS(p)
#define RTREE_MAXCELLS 51
/*
** An rtree cursor object.
*/
struct RtreeCursor {
sqlite3_vtab_cursor base;
RtreeNode *pNode; /* Node cursor is currently pointing at */
int iCell; /* Index of current cell in pNode */
int iStrategy; /* Copy of idxNum search parameter */
int nConstraint; /* Number of entries in aConstraint */
RtreeConstraint *aConstraint; /* Search constraints. */
};
union RtreeCoord {
float f;
int i;
};
/*
** The argument is an RtreeCoord. Return the value stored within the RtreeCoord
** formatted as a double. This macro assumes that local variable pRtree points
** to the Rtree structure associated with the RtreeCoord.
*/
#define DCOORD(coord) ( \
(pRtree->eCoordType==RTREE_COORD_REAL32) ? \
((double)coord.f) : \
((double)coord.i) \
)
/*
** A search constraint.
*/
struct RtreeConstraint {
int iCoord; /* Index of constrained coordinate */
int op; /* Constraining operation */
double rValue; /* Constraint value. */
};
/* Possible values for RtreeConstraint.op */
#define RTREE_EQ 0x41
#define RTREE_LE 0x42
#define RTREE_LT 0x43
#define RTREE_GE 0x44
#define RTREE_GT 0x45
/*
** An rtree structure node.
**
** Data format (RtreeNode.zData):
**
** 1. If the node is the root node (node 1), then the first 2 bytes
** of the node contain the tree depth as a big-endian integer.
** For non-root nodes, the first 2 bytes are left unused.
**
** 2. The next 2 bytes contain the number of entries currently
** stored in the node.
**
** 3. The remainder of the node contains the node entries. Each entry
** consists of a single 8-byte integer followed by an even number
** of 4-byte coordinates. For leaf nodes the integer is the rowid
** of a record. For internal nodes it is the node number of a
** child page.
*/
struct RtreeNode {
RtreeNode *pParent; /* Parent node */
i64 iNode;
int nRef;
int isDirty;
u8 *zData;
RtreeNode *pNext; /* Next node in this hash chain */
};
#define NCELL(pNode) readInt16(&(pNode)->zData[2])
/*
** Structure to store a deserialized rtree record.
*/
struct RtreeCell {
i64 iRowid;
RtreeCoord aCoord[RTREE_MAX_DIMENSIONS*2];
};
#define MAX(x,y) ((x) < (y) ? (y) : (x))
#define MIN(x,y) ((x) > (y) ? (y) : (x))
/*
** Functions to deserialize a 16 bit integer, 32 bit real number and
** 64 bit integer. The deserialized value is returned.
*/
static int readInt16(u8 *p){
return (p[0]<<8) + p[1];
}
static void readCoord(u8 *p, RtreeCoord *pCoord){
u32 i = (
(((u32)p[0]) << 24) +
(((u32)p[1]) << 16) +
(((u32)p[2]) << 8) +
(((u32)p[3]) << 0)
);
*(u32 *)pCoord = i;
}
static i64 readInt64(u8 *p){
return (
(((i64)p[0]) << 56) +
(((i64)p[1]) << 48) +
(((i64)p[2]) << 40) +
(((i64)p[3]) << 32) +
(((i64)p[4]) << 24) +
(((i64)p[5]) << 16) +
(((i64)p[6]) << 8) +
(((i64)p[7]) << 0)
);
}
/*
** Functions to serialize a 16 bit integer, 32 bit real number and
** 64 bit integer. The value returned is the number of bytes written
** to the argument buffer (always 2, 4 and 8 respectively).
*/
static int writeInt16(u8 *p, int i){
p[0] = (i>> 8)&0xFF;
p[1] = (i>> 0)&0xFF;
return 2;
}
static int writeCoord(u8 *p, RtreeCoord *pCoord){
u32 i;
assert( sizeof(RtreeCoord)==4 );
assert( sizeof(u32)==4 );
i = *(u32 *)pCoord;
p[0] = (i>>24)&0xFF;
p[1] = (i>>16)&0xFF;
p[2] = (i>> 8)&0xFF;
p[3] = (i>> 0)&0xFF;
return 4;
}
static int writeInt64(u8 *p, i64 i){
p[0] = (i>>56)&0xFF;
p[1] = (i>>48)&0xFF;
p[2] = (i>>40)&0xFF;
p[3] = (i>>32)&0xFF;
p[4] = (i>>24)&0xFF;
p[5] = (i>>16)&0xFF;
p[6] = (i>> 8)&0xFF;
p[7] = (i>> 0)&0xFF;
return 8;
}
/*
** Increment the reference count of node p.
*/
static void nodeReference(RtreeNode *p){
if( p ){
p->nRef++;
}
}
/*
** Clear the content of node p (set all bytes to 0x00).
*/
static void nodeZero(Rtree *pRtree, RtreeNode *p){
if( p ){
memset(&p->zData[2], 0, pRtree->iNodeSize-2);
p->isDirty = 1;
}
}
/*
** Given a node number iNode, return the corresponding key to use
** in the Rtree.aHash table.
*/
static int nodeHash(i64 iNode){
return (
(iNode>>56) ^ (iNode>>48) ^ (iNode>>40) ^ (iNode>>32) ^
(iNode>>24) ^ (iNode>>16) ^ (iNode>> 8) ^ (iNode>> 0)
) % HASHSIZE;
}
/*
** Search the node hash table for node iNode. If found, return a pointer
** to it. Otherwise, return 0.
*/
static RtreeNode *nodeHashLookup(Rtree *pRtree, i64 iNode){
RtreeNode *p;
assert( iNode!=0 );
for(p=pRtree->aHash[nodeHash(iNode)]; p && p->iNode!=iNode; p=p->pNext);
return p;
}
/*
** Add node pNode to the node hash table.
*/
static void nodeHashInsert(Rtree *pRtree, RtreeNode *pNode){
if( pNode ){
int iHash;
assert( pNode->pNext==0 );
iHash = nodeHash(pNode->iNode);
pNode->pNext = pRtree->aHash[iHash];
pRtree->aHash[iHash] = pNode;
}
}
/*
** Remove node pNode from the node hash table.
*/
static void nodeHashDelete(Rtree *pRtree, RtreeNode *pNode){
RtreeNode **pp;
if( pNode->iNode!=0 ){
pp = &pRtree->aHash[nodeHash(pNode->iNode)];
for( ; (*pp)!=pNode; pp = &(*pp)->pNext){ assert(*pp); }
*pp = pNode->pNext;
pNode->pNext = 0;
}
}
/*
** Allocate and return new r-tree node. Initially, (RtreeNode.iNode==0),
** indicating that node has not yet been assigned a node number. It is
** assigned a node number when nodeWrite() is called to write the
** node contents out to the database.
*/
static RtreeNode *nodeNew(Rtree *pRtree, RtreeNode *pParent, int zero){
RtreeNode *pNode;
pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
if( pNode ){
memset(pNode, 0, sizeof(RtreeNode) + (zero?pRtree->iNodeSize:0));
pNode->zData = (u8 *)&pNode[1];
pNode->nRef = 1;
pNode->pParent = pParent;
pNode->isDirty = 1;
nodeReference(pParent);
}
return pNode;
}
/*
** Obtain a reference to an r-tree node.
*/
static int
nodeAcquire(
Rtree *pRtree, /* R-tree structure */
i64 iNode, /* Node number to load */
RtreeNode *pParent, /* Either the parent node or NULL */
RtreeNode **ppNode /* OUT: Acquired node */
){
int rc;
RtreeNode *pNode;
/* Check if the requested node is already in the hash table. If so,
** increase its reference count and return it.
*/
if( (pNode = nodeHashLookup(pRtree, iNode)) ){
assert( !pParent || !pNode->pParent || pNode->pParent==pParent );
if( pParent ){
pNode->pParent = pParent;
}
pNode->nRef++;
*ppNode = pNode;
return SQLITE_OK;
}
pNode = (RtreeNode *)sqlite3_malloc(sizeof(RtreeNode) + pRtree->iNodeSize);
if( !pNode ){
*ppNode = 0;
return SQLITE_NOMEM;
}
pNode->pParent = pParent;
pNode->zData = (u8 *)&pNode[1];
pNode->nRef = 1;
pNode->iNode = iNode;
pNode->isDirty = 0;
pNode->pNext = 0;
sqlite3_bind_int64(pRtree->pReadNode, 1, iNode);
rc = sqlite3_step(pRtree->pReadNode);
if( rc==SQLITE_ROW ){
const u8 *zBlob = sqlite3_column_blob(pRtree->pReadNode, 0);
memcpy(pNode->zData, zBlob, pRtree->iNodeSize);
nodeReference(pParent);
}else{
sqlite3_free(pNode);
pNode = 0;
}
*ppNode = pNode;
rc = sqlite3_reset(pRtree->pReadNode);
if( rc==SQLITE_OK && iNode==1 ){
pRtree->iDepth = readInt16(pNode->zData);
}
assert( (rc==SQLITE_OK && pNode) || (pNode==0 && rc!=SQLITE_OK) );
nodeHashInsert(pRtree, pNode);
return rc;
}
/*
** Overwrite cell iCell of node pNode with the contents of pCell.
*/
static void nodeOverwriteCell(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell,
int iCell
){
int ii;
u8 *p = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
p += writeInt64(p, pCell->iRowid);
for(ii=0; ii<(pRtree->nDim*2); ii++){
p += writeCoord(p, &pCell->aCoord[ii]);
}
pNode->isDirty = 1;
}
/*
** Remove cell the cell with index iCell from node pNode.
*/
static void nodeDeleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell){
u8 *pDst = &pNode->zData[4 + pRtree->nBytesPerCell*iCell];
u8 *pSrc = &pDst[pRtree->nBytesPerCell];
int nByte = (NCELL(pNode) - iCell - 1) * pRtree->nBytesPerCell;
memmove(pDst, pSrc, nByte);
writeInt16(&pNode->zData[2], NCELL(pNode)-1);
pNode->isDirty = 1;
}
/*
** Insert the contents of cell pCell into node pNode. If the insert
** is successful, return SQLITE_OK.
**
** If there is not enough free space in pNode, return SQLITE_FULL.
*/
static int
nodeInsertCell(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell
){
int nCell; /* Current number of cells in pNode */
int nMaxCell; /* Maximum number of cells for pNode */
nMaxCell = (pRtree->iNodeSize-4)/pRtree->nBytesPerCell;
nCell = NCELL(pNode);
assert(nCell<=nMaxCell);
if( nCell<nMaxCell ){
nodeOverwriteCell(pRtree, pNode, pCell, nCell);
writeInt16(&pNode->zData[2], nCell+1);
pNode->isDirty = 1;
}
return (nCell==nMaxCell);
}
/*
** If the node is dirty, write it out to the database.
*/
static int
nodeWrite(Rtree *pRtree, RtreeNode *pNode){
int rc = SQLITE_OK;
if( pNode->isDirty ){
sqlite3_stmt *p = pRtree->pWriteNode;
if( pNode->iNode ){
sqlite3_bind_int64(p, 1, pNode->iNode);
}else{
sqlite3_bind_null(p, 1);
}
sqlite3_bind_blob(p, 2, pNode->zData, pRtree->iNodeSize, SQLITE_STATIC);
sqlite3_step(p);
pNode->isDirty = 0;
rc = sqlite3_reset(p);
if( pNode->iNode==0 && rc==SQLITE_OK ){
pNode->iNode = sqlite3_last_insert_rowid(pRtree->db);
nodeHashInsert(pRtree, pNode);
}
}
return rc;
}
/*
** Release a reference to a node. If the node is dirty and the reference
** count drops to zero, the node data is written to the database.
*/
static int
nodeRelease(Rtree *pRtree, RtreeNode *pNode){
int rc = SQLITE_OK;
if( pNode ){
assert( pNode->nRef>0 );
pNode->nRef--;
if( pNode->nRef==0 ){
if( pNode->iNode==1 ){
pRtree->iDepth = -1;
}
if( pNode->pParent ){
rc = nodeRelease(pRtree, pNode->pParent);
}
if( rc==SQLITE_OK ){
rc = nodeWrite(pRtree, pNode);
}
nodeHashDelete(pRtree, pNode);
sqlite3_free(pNode);
}
}
return rc;
}
/*
** Return the 64-bit integer value associated with cell iCell of
** node pNode. If pNode is a leaf node, this is a rowid. If it is
** an internal node, then the 64-bit integer is a child page number.
*/
static i64 nodeGetRowid(
Rtree *pRtree,
RtreeNode *pNode,
int iCell
){
assert( iCell<NCELL(pNode) );
return readInt64(&pNode->zData[4 + pRtree->nBytesPerCell*iCell]);
}
/*
** Return coordinate iCoord from cell iCell in node pNode.
*/
static void nodeGetCoord(
Rtree *pRtree,
RtreeNode *pNode,
int iCell,
int iCoord,
RtreeCoord *pCoord /* Space to write result to */
){
readCoord(&pNode->zData[12 + pRtree->nBytesPerCell*iCell + 4*iCoord], pCoord);
}
/*
** Deserialize cell iCell of node pNode. Populate the structure pointed
** to by pCell with the results.
*/
static void nodeGetCell(
Rtree *pRtree,
RtreeNode *pNode,
int iCell,
RtreeCell *pCell
){
int ii;
pCell->iRowid = nodeGetRowid(pRtree, pNode, iCell);
for(ii=0; ii<pRtree->nDim*2; ii++){
nodeGetCoord(pRtree, pNode, iCell, ii, &pCell->aCoord[ii]);
}
}
/* Forward declaration for the function that does the work of
** the virtual table module xCreate() and xConnect() methods.
*/
static int rtreeInit(
sqlite3 *, void *, int, const char *const*, sqlite3_vtab **, char **, int, int
);
/*
** Rtree virtual table module xCreate method.
*/
static int rtreeCreate(
sqlite3 *db,
void *pAux,
int argc, const char *const*argv,
sqlite3_vtab **ppVtab,
char **pzErr
){
return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 1, (int)pAux);
}
/*
** Rtree virtual table module xConnect method.
*/
static int rtreeConnect(
sqlite3 *db,
void *pAux,
int argc, const char *const*argv,
sqlite3_vtab **ppVtab,
char **pzErr
){
return rtreeInit(db, pAux, argc, argv, ppVtab, pzErr, 0, (int)pAux);
}
/*
** Increment the r-tree reference count.
*/
static void rtreeReference(Rtree *pRtree){
pRtree->nBusy++;
}
/*
** Decrement the r-tree reference count. When the reference count reaches
** zero the structure is deleted.
*/
static void rtreeRelease(Rtree *pRtree){
pRtree->nBusy--;
if( pRtree->nBusy==0 ){
sqlite3_finalize(pRtree->pReadNode);
sqlite3_finalize(pRtree->pWriteNode);
sqlite3_finalize(pRtree->pDeleteNode);
sqlite3_finalize(pRtree->pReadRowid);
sqlite3_finalize(pRtree->pWriteRowid);
sqlite3_finalize(pRtree->pDeleteRowid);
sqlite3_finalize(pRtree->pReadParent);
sqlite3_finalize(pRtree->pWriteParent);
sqlite3_finalize(pRtree->pDeleteParent);
sqlite3_free(pRtree);
}
}
/*
** Rtree virtual table module xDisconnect method.
*/
static int rtreeDisconnect(sqlite3_vtab *pVtab){
rtreeRelease((Rtree *)pVtab);
return SQLITE_OK;
}
/*
** Rtree virtual table module xDestroy method.
*/
static int rtreeDestroy(sqlite3_vtab *pVtab){
Rtree *pRtree = (Rtree *)pVtab;
int rc;
char *zCreate = sqlite3_mprintf(
"DROP TABLE '%q'.'%q_node';"
"DROP TABLE '%q'.'%q_rowid';"
"DROP TABLE '%q'.'%q_parent';",
pRtree->zDb, pRtree->zName,
pRtree->zDb, pRtree->zName,
pRtree->zDb, pRtree->zName
);
if( !zCreate ){
rc = SQLITE_NOMEM;
}else{
rc = sqlite3_exec(pRtree->db, zCreate, 0, 0, 0);
sqlite3_free(zCreate);
}
if( rc==SQLITE_OK ){
rtreeRelease(pRtree);
}
return rc;
}
/*
** Rtree virtual table module xOpen method.
*/
static int rtreeOpen(sqlite3_vtab *pVTab, sqlite3_vtab_cursor **ppCursor){
int rc = SQLITE_NOMEM;
RtreeCursor *pCsr;
pCsr = (RtreeCursor *)sqlite3_malloc(sizeof(RtreeCursor));
if( pCsr ){
memset(pCsr, 0, sizeof(RtreeCursor));
pCsr->base.pVtab = pVTab;
rc = SQLITE_OK;
}
*ppCursor = (sqlite3_vtab_cursor *)pCsr;
return rc;
}
/*
** Rtree virtual table module xClose method.
*/
static int rtreeClose(sqlite3_vtab_cursor *cur){
Rtree *pRtree = (Rtree *)(cur->pVtab);
int rc;
RtreeCursor *pCsr = (RtreeCursor *)cur;
sqlite3_free(pCsr->aConstraint);
rc = nodeRelease(pRtree, pCsr->pNode);
sqlite3_free(pCsr);
return rc;
}
/*
** Rtree virtual table module xEof method.
**
** Return non-zero if the cursor does not currently point to a valid
** record (i.e if the scan has finished), or zero otherwise.
*/
static int rtreeEof(sqlite3_vtab_cursor *cur){
RtreeCursor *pCsr = (RtreeCursor *)cur;
return (pCsr->pNode==0);
}
/*
** Cursor pCursor currently points to a cell in a non-leaf page.
** Return true if the sub-tree headed by the cell is filtered
** (excluded) by the constraints in the pCursor->aConstraint[]
** array, or false otherwise.
*/
static int testRtreeCell(Rtree *pRtree, RtreeCursor *pCursor){
RtreeCell cell;
int ii;
int bRes = 0;
nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
for(ii=0; bRes==0 && ii<pCursor->nConstraint; ii++){
RtreeConstraint *p = &pCursor->aConstraint[ii];
double cell_min = DCOORD(cell.aCoord[(p->iCoord>>1)*2]);
double cell_max = DCOORD(cell.aCoord[(p->iCoord>>1)*2+1]);
assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE
|| p->op==RTREE_GT || p->op==RTREE_EQ
);
switch( p->op ){
case RTREE_LE: case RTREE_LT: bRes = p->rValue<cell_min; break;
case RTREE_GE: case RTREE_GT: bRes = p->rValue>cell_max; break;
case RTREE_EQ:
bRes = (p->rValue>cell_max || p->rValue<cell_min);
break;
}
}
return bRes;
}
/*
** Return true if the cell that cursor pCursor currently points to
** would be filtered (excluded) by the constraints in the
** pCursor->aConstraint[] array, or false otherwise.
**
** This function assumes that the cell is part of a leaf node.
*/
static int testRtreeEntry(Rtree *pRtree, RtreeCursor *pCursor){
RtreeCell cell;
int ii;
nodeGetCell(pRtree, pCursor->pNode, pCursor->iCell, &cell);
for(ii=0; ii<pCursor->nConstraint; ii++){
RtreeConstraint *p = &pCursor->aConstraint[ii];
double coord = DCOORD(cell.aCoord[p->iCoord]);
int res;
assert(p->op==RTREE_LE || p->op==RTREE_LT || p->op==RTREE_GE
|| p->op==RTREE_GT || p->op==RTREE_EQ
);
switch( p->op ){
case RTREE_LE: res = (coord<=p->rValue); break;
case RTREE_LT: res = (coord<p->rValue); break;
case RTREE_GE: res = (coord>=p->rValue); break;
case RTREE_GT: res = (coord>p->rValue); break;
case RTREE_EQ: res = (coord==p->rValue); break;
}
if( !res ) return 1;
}
return 0;
}
/*
** Cursor pCursor currently points at a node that heads a sub-tree of
** height iHeight (if iHeight==0, then the node is a leaf). Descend
** to point to the left-most cell of the sub-tree that matches the
** configured constraints.
*/
static int descendToCell(
Rtree *pRtree,
RtreeCursor *pCursor,
int iHeight,
int *pEof /* OUT: Set to true if cannot descend */
){
int isEof;
int rc;
int ii;
RtreeNode *pChild;
sqlite3_int64 iRowid;
RtreeNode *pSavedNode = pCursor->pNode;
int iSavedCell = pCursor->iCell;
assert( iHeight>=0 );
if( iHeight==0 ){
isEof = testRtreeEntry(pRtree, pCursor);
}else{
isEof = testRtreeCell(pRtree, pCursor);
}
if( isEof || iHeight==0 ){
*pEof = isEof;
return SQLITE_OK;
}
iRowid = nodeGetRowid(pRtree, pCursor->pNode, pCursor->iCell);
rc = nodeAcquire(pRtree, iRowid, pCursor->pNode, &pChild);
if( rc!=SQLITE_OK ){
return rc;
}
nodeRelease(pRtree, pCursor->pNode);
pCursor->pNode = pChild;
isEof = 1;
for(ii=0; isEof && ii<NCELL(pChild); ii++){
pCursor->iCell = ii;
rc = descendToCell(pRtree, pCursor, iHeight-1, &isEof);
if( rc!=SQLITE_OK ){
return rc;
}
}
if( isEof ){
assert( pCursor->pNode==pChild );
nodeReference(pSavedNode);
nodeRelease(pRtree, pChild);
pCursor->pNode = pSavedNode;
pCursor->iCell = iSavedCell;
}
*pEof = isEof;
return SQLITE_OK;
}
/*
** One of the cells in node pNode is guaranteed to have a 64-bit
** integer value equal to iRowid. Return the index of this cell.
*/
static int nodeRowidIndex(Rtree *pRtree, RtreeNode *pNode, i64 iRowid){
int ii;
for(ii=0; nodeGetRowid(pRtree, pNode, ii)!=iRowid; ii++){
assert( ii<(NCELL(pNode)-1) );
}
return ii;
}
/*
** Return the index of the cell containing a pointer to node pNode
** in its parent. If pNode is the root node, return -1.
*/
static int nodeParentIndex(Rtree *pRtree, RtreeNode *pNode){
RtreeNode *pParent = pNode->pParent;
if( pParent ){
return nodeRowidIndex(pRtree, pParent, pNode->iNode);
}
return -1;
}
/*
** Rtree virtual table module xNext method.
*/
static int rtreeNext(sqlite3_vtab_cursor *pVtabCursor){
Rtree *pRtree = (Rtree *)(pVtabCursor->pVtab);
RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
int rc = SQLITE_OK;
if( pCsr->iStrategy==1 ){
/* This "scan" is a direct lookup by rowid. There is no next entry. */
nodeRelease(pRtree, pCsr->pNode);
pCsr->pNode = 0;
}
else if( pCsr->pNode ){
/* Move to the next entry that matches the configured constraints. */
int iHeight = 0;
while( pCsr->pNode ){
RtreeNode *pNode = pCsr->pNode;
int nCell = NCELL(pNode);
for(pCsr->iCell++; pCsr->iCell<nCell; pCsr->iCell++){
int isEof;
rc = descendToCell(pRtree, pCsr, iHeight, &isEof);
if( rc!=SQLITE_OK || !isEof ){
return rc;
}
}
pCsr->pNode = pNode->pParent;
pCsr->iCell = nodeParentIndex(pRtree, pNode);
nodeReference(pCsr->pNode);
nodeRelease(pRtree, pNode);
iHeight++;
}
}
return rc;
}
/*
** Rtree virtual table module xRowid method.
*/
static int rtreeRowid(sqlite3_vtab_cursor *pVtabCursor, sqlite_int64 *pRowid){
Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
assert(pCsr->pNode);
*pRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
return SQLITE_OK;
}
/*
** Rtree virtual table module xColumn method.
*/
static int rtreeColumn(sqlite3_vtab_cursor *cur, sqlite3_context *ctx, int i){
Rtree *pRtree = (Rtree *)cur->pVtab;
RtreeCursor *pCsr = (RtreeCursor *)cur;
if( i==0 ){
i64 iRowid = nodeGetRowid(pRtree, pCsr->pNode, pCsr->iCell);
sqlite3_result_int64(ctx, iRowid);
}else{
RtreeCoord c;
nodeGetCoord(pRtree, pCsr->pNode, pCsr->iCell, i-1, &c);
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
sqlite3_result_double(ctx, c.f);
}else{
assert( pRtree->eCoordType==RTREE_COORD_INT32 );
sqlite3_result_int(ctx, c.i);
}
}
return SQLITE_OK;
}
/*
** Use nodeAcquire() to obtain the leaf node containing the record with
** rowid iRowid. If successful, set *ppLeaf to point to the node and
** return SQLITE_OK. If there is no such record in the table, set
** *ppLeaf to 0 and return SQLITE_OK. If an error occurs, set *ppLeaf
** to zero and return an SQLite error code.
*/
static int findLeafNode(Rtree *pRtree, i64 iRowid, RtreeNode **ppLeaf){
int rc;
*ppLeaf = 0;
sqlite3_bind_int64(pRtree->pReadRowid, 1, iRowid);
if( sqlite3_step(pRtree->pReadRowid)==SQLITE_ROW ){
i64 iNode = sqlite3_column_int64(pRtree->pReadRowid, 0);
rc = nodeAcquire(pRtree, iNode, 0, ppLeaf);
sqlite3_reset(pRtree->pReadRowid);
}else{
rc = sqlite3_reset(pRtree->pReadRowid);
}
return rc;
}
/*
** Rtree virtual table module xFilter method.
*/
static int rtreeFilter(
sqlite3_vtab_cursor *pVtabCursor,
int idxNum, const char *idxStr,
int argc, sqlite3_value **argv
){
Rtree *pRtree = (Rtree *)pVtabCursor->pVtab;
RtreeCursor *pCsr = (RtreeCursor *)pVtabCursor;
RtreeNode *pRoot = 0;
int ii;
int rc = SQLITE_OK;
rtreeReference(pRtree);
sqlite3_free(pCsr->aConstraint);
pCsr->aConstraint = 0;
pCsr->iStrategy = idxNum;
if( idxNum==1 ){
/* Special case - lookup by rowid. */
RtreeNode *pLeaf; /* Leaf on which the required cell resides */
i64 iRowid = sqlite3_value_int64(argv[0]);
rc = findLeafNode(pRtree, iRowid, &pLeaf);
pCsr->pNode = pLeaf;
if( pLeaf && rc==SQLITE_OK ){
pCsr->iCell = nodeRowidIndex(pRtree, pLeaf, iRowid);
}
}else{
/* Normal case - r-tree scan. Set up the RtreeCursor.aConstraint array
** with the configured constraints.
*/
if( argc>0 ){
pCsr->aConstraint = sqlite3_malloc(sizeof(RtreeConstraint)*argc);
pCsr->nConstraint = argc;
if( !pCsr->aConstraint ){
rc = SQLITE_NOMEM;
}else{
assert( (idxStr==0 && argc==0) || strlen(idxStr)==argc*2 );
for(ii=0; ii<argc; ii++){
RtreeConstraint *p = &pCsr->aConstraint[ii];
p->op = idxStr[ii*2];
p->iCoord = idxStr[ii*2+1]-'a';
p->rValue = sqlite3_value_double(argv[ii]);
}
}
}
if( rc==SQLITE_OK ){
pCsr->pNode = 0;
rc = nodeAcquire(pRtree, 1, 0, &pRoot);
}
if( rc==SQLITE_OK ){
int isEof = 1;
int nCell = NCELL(pRoot);
pCsr->pNode = pRoot;
for(pCsr->iCell=0; rc==SQLITE_OK && pCsr->iCell<nCell; pCsr->iCell++){
assert( pCsr->pNode==pRoot );
rc = descendToCell(pRtree, pCsr, pRtree->iDepth, &isEof);
if( !isEof ){
break;
}
}
if( rc==SQLITE_OK && isEof ){
assert( pCsr->pNode==pRoot );
nodeRelease(pRtree, pRoot);
pCsr->pNode = 0;
}
assert( rc!=SQLITE_OK || !pCsr->pNode || pCsr->iCell<NCELL(pCsr->pNode) );
}
}
rtreeRelease(pRtree);
return rc;
}
/*
** Rtree virtual table module xBestIndex method. There are three
** table scan strategies to choose from (in order from most to
** least desirable):
**
** idxNum idxStr Strategy
** ------------------------------------------------
** 1 Unused Direct lookup by rowid.
** 2 See below R-tree query.
** 3 Unused Full table scan.
** ------------------------------------------------
**
** If strategy 1 or 3 is used, then idxStr is not meaningful. If strategy
** 2 is used, idxStr is formatted to contain 2 bytes for each
** constraint used. The first two bytes of idxStr correspond to
** the constraint in sqlite3_index_info.aConstraintUsage[] with
** (argvIndex==1) etc.
**
** The first of each pair of bytes in idxStr identifies the constraint
** operator as follows:
**
** Operator Byte Value
** ----------------------
** = 0x41 ('A')
** <= 0x42 ('B')
** < 0x43 ('C')
** >= 0x44 ('D')
** > 0x45 ('E')
** ----------------------
**
** The second of each pair of bytes identifies the coordinate column
** to which the constraint applies. The leftmost coordinate column
** is 'a', the second from the left 'b' etc.
*/
static int rtreeBestIndex(sqlite3_vtab *tab, sqlite3_index_info *pIdxInfo){
int rc = SQLITE_OK;
int ii, cCol;
int iIdx = 0;
char zIdxStr[RTREE_MAX_DIMENSIONS*8+1];
memset(zIdxStr, 0, sizeof(zIdxStr));
assert( pIdxInfo->idxStr==0 );
for(ii=0; ii<pIdxInfo->nConstraint; ii++){
struct sqlite3_index_constraint *p = &pIdxInfo->aConstraint[ii];
if( p->usable && p->iColumn==0 && p->op==SQLITE_INDEX_CONSTRAINT_EQ ){
/* We have an equality constraint on the rowid. Use strategy 1. */
int jj;
for(jj=0; jj<ii; jj++){
pIdxInfo->aConstraintUsage[jj].argvIndex = 0;
pIdxInfo->aConstraintUsage[jj].omit = 0;
}
pIdxInfo->idxNum = 1;
pIdxInfo->aConstraintUsage[ii].argvIndex = 1;
pIdxInfo->aConstraintUsage[jj].omit = 1;
return SQLITE_OK;
}
if( p->usable && p->iColumn>0 ){
u8 op = 0;
switch( p->op ){
case SQLITE_INDEX_CONSTRAINT_EQ: op = RTREE_EQ; break;
case SQLITE_INDEX_CONSTRAINT_GT: op = RTREE_GT; break;
case SQLITE_INDEX_CONSTRAINT_LE: op = RTREE_LE; break;
case SQLITE_INDEX_CONSTRAINT_LT: op = RTREE_LT; break;
case SQLITE_INDEX_CONSTRAINT_GE: op = RTREE_GE; break;
}
if( op ){
/* Make sure this particular constraint has not been used before.
** If it has been used before, ignore it.
**
** A <= or < can be used if there is a prior >= or >.
** A >= or > can be used if there is a prior < or <=.
** A <= or < is disqualified if there is a prior <=, <, or ==.
** A >= or > is disqualified if there is a prior >=, >, or ==.
** A == is disqualifed if there is any prior constraint.
*/
int j, opmsk;
static const unsigned char compatible[] = { 0, 0, 1, 1, 2, 2 };
assert( compatible[RTREE_EQ & 7]==0 );
assert( compatible[RTREE_LT & 7]==1 );
assert( compatible[RTREE_LE & 7]==1 );
assert( compatible[RTREE_GT & 7]==2 );
assert( compatible[RTREE_GE & 7]==2 );
cCol = p->iColumn - 1 + 'a';
opmsk = compatible[op & 7];
for(j=0; j<iIdx; j+=2){
if( zIdxStr[j+1]==cCol && (compatible[zIdxStr[j] & 7] & opmsk)!=0 ){
op = 0;
break;
}
}
}
if( op ){
assert( iIdx<sizeof(zIdxStr)-1 );
zIdxStr[iIdx++] = op;
zIdxStr[iIdx++] = cCol;
pIdxInfo->aConstraintUsage[ii].argvIndex = (iIdx/2);
pIdxInfo->aConstraintUsage[ii].omit = 1;
}
}
}
pIdxInfo->idxNum = 2;
pIdxInfo->needToFreeIdxStr = 1;
if( iIdx>0 && 0==(pIdxInfo->idxStr = sqlite3_mprintf("%s", zIdxStr)) ){
return SQLITE_NOMEM;
}
return rc;
}
/*
** Return the N-dimensional volumn of the cell stored in *p.
*/
static float cellArea(Rtree *pRtree, RtreeCell *p){
float area = 1.0;
int ii;
for(ii=0; ii<(pRtree->nDim*2); ii+=2){
area = area * (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
}
return area;
}
/*
** Return the margin length of cell p. The margin length is the sum
** of the objects size in each dimension.
*/
static float cellMargin(Rtree *pRtree, RtreeCell *p){
float margin = 0.0;
int ii;
for(ii=0; ii<(pRtree->nDim*2); ii+=2){
margin += (DCOORD(p->aCoord[ii+1]) - DCOORD(p->aCoord[ii]));
}
return margin;
}
/*
** Store the union of cells p1 and p2 in p1.
*/
static void cellUnion(Rtree *pRtree, RtreeCell *p1, RtreeCell *p2){
int ii;
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
for(ii=0; ii<(pRtree->nDim*2); ii+=2){
p1->aCoord[ii].f = MIN(p1->aCoord[ii].f, p2->aCoord[ii].f);
p1->aCoord[ii+1].f = MAX(p1->aCoord[ii+1].f, p2->aCoord[ii+1].f);
}
}else{
for(ii=0; ii<(pRtree->nDim*2); ii+=2){
p1->aCoord[ii].i = MIN(p1->aCoord[ii].i, p2->aCoord[ii].i);
p1->aCoord[ii+1].i = MAX(p1->aCoord[ii+1].i, p2->aCoord[ii+1].i);
}
}
}
/*
** Return the amount cell p would grow by if it were unioned with pCell.
*/
static float cellGrowth(Rtree *pRtree, RtreeCell *p, RtreeCell *pCell){
float area;
RtreeCell cell;
memcpy(&cell, p, sizeof(RtreeCell));
area = cellArea(pRtree, &cell);
cellUnion(pRtree, &cell, pCell);
return (cellArea(pRtree, &cell)-area);
}
#if VARIANT_RSTARTREE_CHOOSESUBTREE || VARIANT_RSTARTREE_SPLIT
static float cellOverlap(
Rtree *pRtree,
RtreeCell *p,
RtreeCell *aCell,
int nCell,
int iExclude
){
int ii;
float overlap = 0.0;
for(ii=0; ii<nCell; ii++){
if( ii!=iExclude ){
int jj;
float o = 1.0;
for(jj=0; jj<(pRtree->nDim*2); jj+=2){
double x1;
double x2;
x1 = MAX(DCOORD(p->aCoord[jj]), DCOORD(aCell[ii].aCoord[jj]));
x2 = MIN(DCOORD(p->aCoord[jj+1]), DCOORD(aCell[ii].aCoord[jj+1]));
if( x2<x1 ){
o = 0.0;
break;
}else{
o = o * (x2-x1);
}
}
overlap += o;
}
}
return overlap;
}
#endif
#if VARIANT_RSTARTREE_CHOOSESUBTREE
static float cellOverlapEnlargement(
Rtree *pRtree,
RtreeCell *p,
RtreeCell *pInsert,
RtreeCell *aCell,
int nCell,
int iExclude
){
float before;
float after;
before = cellOverlap(pRtree, p, aCell, nCell, iExclude);
cellUnion(pRtree, p, pInsert);
after = cellOverlap(pRtree, p, aCell, nCell, iExclude);
return after-before;
}
#endif
/*
** This function implements the ChooseLeaf algorithm from Gutman[84].
** ChooseSubTree in r*tree terminology.
*/
static int ChooseLeaf(
Rtree *pRtree, /* Rtree table */
RtreeCell *pCell, /* Cell to insert into rtree */
int iHeight, /* Height of sub-tree rooted at pCell */
RtreeNode **ppLeaf /* OUT: Selected leaf page */
){
int rc;
int ii;
RtreeNode *pNode;
rc = nodeAcquire(pRtree, 1, 0, &pNode);
for(ii=0; rc==SQLITE_OK && ii<(pRtree->iDepth-iHeight); ii++){
int iCell;
sqlite3_int64 iBest;
float fMinGrowth;
float fMinArea;
float fMinOverlap;
int nCell = NCELL(pNode);
RtreeCell cell;
RtreeNode *pChild;
RtreeCell *aCell = 0;
#if VARIANT_RSTARTREE_CHOOSESUBTREE
if( ii==(pRtree->iDepth-1) ){
int jj;
aCell = sqlite3_malloc(sizeof(RtreeCell)*nCell);
if( !aCell ){
rc = SQLITE_NOMEM;
nodeRelease(pRtree, pNode);
pNode = 0;
continue;
}
for(jj=0; jj<nCell; jj++){
nodeGetCell(pRtree, pNode, jj, &aCell[jj]);
}
}
#endif
/* Select the child node which will be enlarged the least if pCell
** is inserted into it. Resolve ties by choosing the entry with
** the smallest area.
*/
for(iCell=0; iCell<nCell; iCell++){
float growth;
float area;
float overlap = 0.0;
nodeGetCell(pRtree, pNode, iCell, &cell);
growth = cellGrowth(pRtree, &cell, pCell);
area = cellArea(pRtree, &cell);
#if VARIANT_RSTARTREE_CHOOSESUBTREE
if( ii==(pRtree->iDepth-1) ){
overlap = cellOverlapEnlargement(pRtree,&cell,pCell,aCell,nCell,iCell);
}
#endif
if( (iCell==0)
|| (overlap<fMinOverlap)
|| (overlap==fMinOverlap && growth<fMinGrowth)
|| (overlap==fMinOverlap && growth==fMinGrowth && area<fMinArea)
){
fMinOverlap = overlap;
fMinGrowth = growth;
fMinArea = area;
iBest = cell.iRowid;
}
}
sqlite3_free(aCell);
rc = nodeAcquire(pRtree, iBest, pNode, &pChild);
nodeRelease(pRtree, pNode);
pNode = pChild;
}
*ppLeaf = pNode;
return rc;
}
/*
** A cell with the same content as pCell has just been inserted into
** the node pNode. This function updates the bounding box cells in
** all ancestor elements.
*/
static void AdjustTree(
Rtree *pRtree, /* Rtree table */
RtreeNode *pNode, /* Adjust ancestry of this node. */
RtreeCell *pCell /* This cell was just inserted */
){
RtreeNode *p = pNode;
while( p->pParent ){
RtreeCell cell;
RtreeNode *pParent = p->pParent;
int iCell = nodeParentIndex(pRtree, p);
nodeGetCell(pRtree, pParent, iCell, &cell);
if( cellGrowth(pRtree, &cell, pCell)>0.0 ){
cellUnion(pRtree, &cell, pCell);
nodeOverwriteCell(pRtree, pParent, &cell, iCell);
}
p = pParent;
}
}
/*
** Write mapping (iRowid->iNode) to the <rtree>_rowid table.
*/
static int rowidWrite(Rtree *pRtree, sqlite3_int64 iRowid, sqlite3_int64 iNode){
sqlite3_bind_int64(pRtree->pWriteRowid, 1, iRowid);
sqlite3_bind_int64(pRtree->pWriteRowid, 2, iNode);
sqlite3_step(pRtree->pWriteRowid);
return sqlite3_reset(pRtree->pWriteRowid);
}
/*
** Write mapping (iNode->iPar) to the <rtree>_parent table.
*/
static int parentWrite(Rtree *pRtree, sqlite3_int64 iNode, sqlite3_int64 iPar){
sqlite3_bind_int64(pRtree->pWriteParent, 1, iNode);
sqlite3_bind_int64(pRtree->pWriteParent, 2, iPar);
sqlite3_step(pRtree->pWriteParent);
return sqlite3_reset(pRtree->pWriteParent);
}
static int rtreeInsertCell(Rtree *, RtreeNode *, RtreeCell *, int);
#if VARIANT_GUTTMAN_LINEAR_SPLIT
/*
** Implementation of the linear variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *LinearPickNext(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeCell *pLeftBox,
RtreeCell *pRightBox,
int *aiUsed
){
int ii;
for(ii=0; aiUsed[ii]; ii++);
aiUsed[ii] = 1;
return &aCell[ii];
}
/*
** Implementation of the linear variant of the PickSeeds() function from
** Guttman[84].
*/
static void LinearPickSeeds(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
int *piLeftSeed,
int *piRightSeed
){
int i;
int iLeftSeed = 0;
int iRightSeed = 1;
float maxNormalInnerWidth = 0.0;
/* Pick two "seed" cells from the array of cells. The algorithm used
** here is the LinearPickSeeds algorithm from Gutman[1984]. The
** indices of the two seed cells in the array are stored in local
** variables iLeftSeek and iRightSeed.
*/
for(i=0; i<pRtree->nDim; i++){
float x1 = aCell[0].aCoord[i*2];
float x2 = aCell[0].aCoord[i*2+1];
float x3 = x1;
float x4 = x2;
int jj;
int iCellLeft = 0;
int iCellRight = 0;
for(jj=1; jj<nCell; jj++){
float left = aCell[jj].aCoord[i*2];
float right = aCell[jj].aCoord[i*2+1];
if( left<x1 ) x1 = left;
if( right>x4 ) x4 = right;
if( left>x3 ){
x3 = left;
iCellRight = jj;
}
if( right<x2 ){
x2 = right;
iCellLeft = jj;
}
}
if( x4!=x1 ){
float normalwidth = (x3 - x2) / (x4 - x1);
if( normalwidth>maxNormalInnerWidth ){
iLeftSeed = iCellLeft;
iRightSeed = iCellRight;
}
}
}
*piLeftSeed = iLeftSeed;
*piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_LINEAR_SPLIT */
#if VARIANT_GUTTMAN_QUADRATIC_SPLIT
/*
** Implementation of the quadratic variant of the PickNext() function from
** Guttman[84].
*/
static RtreeCell *QuadraticPickNext(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeCell *pLeftBox,
RtreeCell *pRightBox,
int *aiUsed
){
#define FABS(a) ((a)<0.0?-1.0*(a):(a))
int iSelect = -1;
float fDiff;
int ii;
for(ii=0; ii<nCell; ii++){
if( aiUsed[ii]==0 ){
float left = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
float right = cellGrowth(pRtree, pLeftBox, &aCell[ii]);
float diff = FABS(right-left);
if( iSelect<0 || diff>fDiff ){
fDiff = diff;
iSelect = ii;
}
}
}
aiUsed[iSelect] = 1;
return &aCell[iSelect];
}
/*
** Implementation of the quadratic variant of the PickSeeds() function from
** Guttman[84].
*/
static void QuadraticPickSeeds(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
int *piLeftSeed,
int *piRightSeed
){
int ii;
int jj;
int iLeftSeed = 0;
int iRightSeed = 1;
float fWaste = 0.0;
for(ii=0; ii<nCell; ii++){
for(jj=ii+1; jj<nCell; jj++){
float right = cellArea(pRtree, &aCell[jj]);
float growth = cellGrowth(pRtree, &aCell[ii], &aCell[jj]);
float waste = growth - right;
if( waste>fWaste ){
iLeftSeed = ii;
iRightSeed = jj;
fWaste = waste;
}
}
}
*piLeftSeed = iLeftSeed;
*piRightSeed = iRightSeed;
}
#endif /* VARIANT_GUTTMAN_QUADRATIC_SPLIT */
/*
** Arguments aIdx, aDistance and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to the indexed values in aDistance. For
** example, assuming the inputs:
**
** aIdx = { 0, 1, 2, 3 }
** aDistance = { 5.0, 2.0, 7.0, 6.0 }
**
** this function sets the aIdx array to contain:
**
** aIdx = { 0, 1, 2, 3 }
**
** The aSpare array is used as temporary working space by the
** sorting algorithm.
*/
static void SortByDistance(
int *aIdx,
int nIdx,
float *aDistance,
int *aSpare
){
if( nIdx>1 ){
int iLeft = 0;
int iRight = 0;
int nLeft = nIdx/2;
int nRight = nIdx-nLeft;
int *aLeft = aIdx;
int *aRight = &aIdx[nLeft];
SortByDistance(aLeft, nLeft, aDistance, aSpare);
SortByDistance(aRight, nRight, aDistance, aSpare);
memcpy(aSpare, aLeft, sizeof(int)*nLeft);
aLeft = aSpare;
while( iLeft<nLeft || iRight<nRight ){
if( iLeft==nLeft ){
aIdx[iLeft+iRight] = aRight[iRight];
iRight++;
}else if( iRight==nRight ){
aIdx[iLeft+iRight] = aLeft[iLeft];
iLeft++;
}else{
float fLeft = aDistance[aLeft[iLeft]];
float fRight = aDistance[aRight[iRight]];
if( fLeft<fRight ){
aIdx[iLeft+iRight] = aLeft[iLeft];
iLeft++;
}else{
aIdx[iLeft+iRight] = aRight[iRight];
iRight++;
}
}
}
#if 0
/* Check that the sort worked */
{
int jj;
for(jj=1; jj<nIdx; jj++){
float left = aDistance[aIdx[jj-1]];
float right = aDistance[aIdx[jj]];
assert( left<=right );
}
}
#endif
}
}
/*
** Arguments aIdx, aCell and aSpare all point to arrays of size
** nIdx. The aIdx array contains the set of integers from 0 to
** (nIdx-1) in no particular order. This function sorts the values
** in aIdx according to dimension iDim of the cells in aCell. The
** minimum value of dimension iDim is considered first, the
** maximum used to break ties.
**
** The aSpare array is used as temporary working space by the
** sorting algorithm.
*/
static void SortByDimension(
Rtree *pRtree,
int *aIdx,
int nIdx,
int iDim,
RtreeCell *aCell,
int *aSpare
){
if( nIdx>1 ){
int iLeft = 0;
int iRight = 0;
int nLeft = nIdx/2;
int nRight = nIdx-nLeft;
int *aLeft = aIdx;
int *aRight = &aIdx[nLeft];
SortByDimension(pRtree, aLeft, nLeft, iDim, aCell, aSpare);
SortByDimension(pRtree, aRight, nRight, iDim, aCell, aSpare);
memcpy(aSpare, aLeft, sizeof(int)*nLeft);
aLeft = aSpare;
while( iLeft<nLeft || iRight<nRight ){
double xleft1 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2]);
double xleft2 = DCOORD(aCell[aLeft[iLeft]].aCoord[iDim*2+1]);
double xright1 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2]);
double xright2 = DCOORD(aCell[aRight[iRight]].aCoord[iDim*2+1]);
if( (iLeft!=nLeft) && ((iRight==nRight)
|| (xleft1<xright1)
|| (xleft1==xright1 && xleft2<xright2)
)){
aIdx[iLeft+iRight] = aLeft[iLeft];
iLeft++;
}else{
aIdx[iLeft+iRight] = aRight[iRight];
iRight++;
}
}
#if 0
/* Check that the sort worked */
{
int jj;
for(jj=1; jj<nIdx; jj++){
float xleft1 = aCell[aIdx[jj-1]].aCoord[iDim*2];
float xleft2 = aCell[aIdx[jj-1]].aCoord[iDim*2+1];
float xright1 = aCell[aIdx[jj]].aCoord[iDim*2];
float xright2 = aCell[aIdx[jj]].aCoord[iDim*2+1];
assert( xleft1<=xright1 && (xleft1<xright1 || xleft2<=xright2) );
}
}
#endif
}
}
#if VARIANT_RSTARTREE_SPLIT
/*
** Implementation of the R*-tree variant of SplitNode from Beckman[1990].
*/
static int splitNodeStartree(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeNode *pLeft,
RtreeNode *pRight,
RtreeCell *pBboxLeft,
RtreeCell *pBboxRight
){
int **aaSorted;
int *aSpare;
int ii;
int iBestDim;
int iBestSplit;
float fBestMargin;
int nByte = (pRtree->nDim+1)*(sizeof(int*)+nCell*sizeof(int));
aaSorted = (int **)sqlite3_malloc(nByte);
if( !aaSorted ){
return SQLITE_NOMEM;
}
aSpare = &((int *)&aaSorted[pRtree->nDim])[pRtree->nDim*nCell];
memset(aaSorted, 0, nByte);
for(ii=0; ii<pRtree->nDim; ii++){
int jj;
aaSorted[ii] = &((int *)&aaSorted[pRtree->nDim])[ii*nCell];
for(jj=0; jj<nCell; jj++){
aaSorted[ii][jj] = jj;
}
SortByDimension(pRtree, aaSorted[ii], nCell, ii, aCell, aSpare);
}
for(ii=0; ii<pRtree->nDim; ii++){
float margin = 0.0;
float fBestOverlap;
float fBestArea;
int iBestLeft;
int nLeft;
for(
nLeft=RTREE_MINCELLS(pRtree);
nLeft<=(nCell-RTREE_MINCELLS(pRtree));
nLeft++
){
RtreeCell left;
RtreeCell right;
int kk;
float overlap;
float area;
memcpy(&left, &aCell[aaSorted[ii][0]], sizeof(RtreeCell));
memcpy(&right, &aCell[aaSorted[ii][nCell-1]], sizeof(RtreeCell));
for(kk=1; kk<(nCell-1); kk++){
if( kk<nLeft ){
cellUnion(pRtree, &left, &aCell[aaSorted[ii][kk]]);
}else{
cellUnion(pRtree, &right, &aCell[aaSorted[ii][kk]]);
}
}
margin += cellMargin(pRtree, &left);
margin += cellMargin(pRtree, &right);
overlap = cellOverlap(pRtree, &left, &right, 1, -1);
area = cellArea(pRtree, &left) + cellArea(pRtree, &right);
if( (nLeft==RTREE_MINCELLS(pRtree))
|| (overlap<fBestOverlap)
|| (overlap==fBestOverlap && area<fBestArea)
){
iBestLeft = nLeft;
fBestOverlap = overlap;
fBestArea = area;
}
}
if( ii==0 || margin<fBestMargin ){
iBestDim = ii;
fBestMargin = margin;
iBestSplit = iBestLeft;
}
}
memcpy(pBboxLeft, &aCell[aaSorted[iBestDim][0]], sizeof(RtreeCell));
memcpy(pBboxRight, &aCell[aaSorted[iBestDim][iBestSplit]], sizeof(RtreeCell));
for(ii=0; ii<nCell; ii++){
RtreeNode *pTarget = (ii<iBestSplit)?pLeft:pRight;
RtreeCell *pBbox = (ii<iBestSplit)?pBboxLeft:pBboxRight;
RtreeCell *pCell = &aCell[aaSorted[iBestDim][ii]];
nodeInsertCell(pRtree, pTarget, pCell);
cellUnion(pRtree, pBbox, pCell);
}
sqlite3_free(aaSorted);
return SQLITE_OK;
}
#endif
#if VARIANT_GUTTMAN_SPLIT
/*
** Implementation of the regular R-tree SplitNode from Guttman[1984].
*/
static int splitNodeGuttman(
Rtree *pRtree,
RtreeCell *aCell,
int nCell,
RtreeNode *pLeft,
RtreeNode *pRight,
RtreeCell *pBboxLeft,
RtreeCell *pBboxRight
){
int iLeftSeed = 0;
int iRightSeed = 1;
int *aiUsed;
int i;
aiUsed = sqlite3_malloc(sizeof(int)*nCell);
memset(aiUsed, 0, sizeof(int)*nCell);
PickSeeds(pRtree, aCell, nCell, &iLeftSeed, &iRightSeed);
memcpy(pBboxLeft, &aCell[iLeftSeed], sizeof(RtreeCell));
memcpy(pBboxRight, &aCell[iRightSeed], sizeof(RtreeCell));
nodeInsertCell(pRtree, pLeft, &aCell[iLeftSeed]);
nodeInsertCell(pRtree, pRight, &aCell[iRightSeed]);
aiUsed[iLeftSeed] = 1;
aiUsed[iRightSeed] = 1;
for(i=nCell-2; i>0; i--){
RtreeCell *pNext;
pNext = PickNext(pRtree, aCell, nCell, pBboxLeft, pBboxRight, aiUsed);
float diff =
cellGrowth(pRtree, pBboxLeft, pNext) -
cellGrowth(pRtree, pBboxRight, pNext)
;
if( (RTREE_MINCELLS(pRtree)-NCELL(pRight)==i)
|| (diff>0.0 && (RTREE_MINCELLS(pRtree)-NCELL(pLeft)!=i))
){
nodeInsertCell(pRtree, pRight, pNext);
cellUnion(pRtree, pBboxRight, pNext);
}else{
nodeInsertCell(pRtree, pLeft, pNext);
cellUnion(pRtree, pBboxLeft, pNext);
}
}
sqlite3_free(aiUsed);
return SQLITE_OK;
}
#endif
static int updateMapping(
Rtree *pRtree,
i64 iRowid,
RtreeNode *pNode,
int iHeight
){
int (*xSetMapping)(Rtree *, sqlite3_int64, sqlite3_int64);
xSetMapping = ((iHeight==0)?rowidWrite:parentWrite);
if( iHeight>0 ){
RtreeNode *pChild = nodeHashLookup(pRtree, iRowid);
if( pChild ){
nodeRelease(pRtree, pChild->pParent);
nodeReference(pNode);
pChild->pParent = pNode;
}
}
return xSetMapping(pRtree, iRowid, pNode->iNode);
}
static int SplitNode(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell,
int iHeight
){
int i;
int newCellIsRight = 0;
int rc = SQLITE_OK;
int nCell = NCELL(pNode);
RtreeCell *aCell;
int *aiUsed;
RtreeNode *pLeft = 0;
RtreeNode *pRight = 0;
RtreeCell leftbbox;
RtreeCell rightbbox;
/* Allocate an array and populate it with a copy of pCell and
** all cells from node pLeft. Then zero the original node.
*/
aCell = sqlite3_malloc((sizeof(RtreeCell)+sizeof(int))*(nCell+1));
if( !aCell ){
rc = SQLITE_NOMEM;
goto splitnode_out;
}
aiUsed = (int *)&aCell[nCell+1];
memset(aiUsed, 0, sizeof(int)*(nCell+1));
for(i=0; i<nCell; i++){
nodeGetCell(pRtree, pNode, i, &aCell[i]);
}
nodeZero(pRtree, pNode);
memcpy(&aCell[nCell], pCell, sizeof(RtreeCell));
nCell++;
if( pNode->iNode==1 ){
pRight = nodeNew(pRtree, pNode, 1);
pLeft = nodeNew(pRtree, pNode, 1);
pRtree->iDepth++;
pNode->isDirty = 1;
writeInt16(pNode->zData, pRtree->iDepth);
}else{
pLeft = pNode;
pRight = nodeNew(pRtree, pLeft->pParent, 1);
nodeReference(pLeft);
}
if( !pLeft || !pRight ){
rc = SQLITE_NOMEM;
goto splitnode_out;
}
memset(pLeft->zData, 0, pRtree->iNodeSize);
memset(pRight->zData, 0, pRtree->iNodeSize);
rc = AssignCells(pRtree, aCell, nCell, pLeft, pRight, &leftbbox, &rightbbox);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
/* Ensure both child nodes have node numbers assigned to them. */
if( (0==pRight->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pRight)))
|| (0==pLeft->iNode && SQLITE_OK!=(rc = nodeWrite(pRtree, pLeft)))
){
goto splitnode_out;
}
rightbbox.iRowid = pRight->iNode;
leftbbox.iRowid = pLeft->iNode;
if( pNode->iNode==1 ){
rc = rtreeInsertCell(pRtree, pLeft->pParent, &leftbbox, iHeight+1);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
}else{
RtreeNode *pParent = pLeft->pParent;
int iCell = nodeParentIndex(pRtree, pLeft);
nodeOverwriteCell(pRtree, pParent, &leftbbox, iCell);
AdjustTree(pRtree, pParent, &leftbbox);
}
if( (rc = rtreeInsertCell(pRtree, pRight->pParent, &rightbbox, iHeight+1)) ){
goto splitnode_out;
}
for(i=0; i<NCELL(pRight); i++){
i64 iRowid = nodeGetRowid(pRtree, pRight, i);
rc = updateMapping(pRtree, iRowid, pRight, iHeight);
if( iRowid==pCell->iRowid ){
newCellIsRight = 1;
}
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
}
if( pNode->iNode==1 ){
for(i=0; i<NCELL(pLeft); i++){
i64 iRowid = nodeGetRowid(pRtree, pLeft, i);
rc = updateMapping(pRtree, iRowid, pLeft, iHeight);
if( rc!=SQLITE_OK ){
goto splitnode_out;
}
}
}else if( newCellIsRight==0 ){
rc = updateMapping(pRtree, pCell->iRowid, pLeft, iHeight);
}
if( rc==SQLITE_OK ){
rc = nodeRelease(pRtree, pRight);
pRight = 0;
}
if( rc==SQLITE_OK ){
rc = nodeRelease(pRtree, pLeft);
pLeft = 0;
}
splitnode_out:
nodeRelease(pRtree, pRight);
nodeRelease(pRtree, pLeft);
sqlite3_free(aCell);
return rc;
}
static int fixLeafParent(Rtree *pRtree, RtreeNode *pLeaf){
int rc = SQLITE_OK;
if( pLeaf->iNode!=1 && pLeaf->pParent==0 ){
sqlite3_bind_int64(pRtree->pReadParent, 1, pLeaf->iNode);
if( sqlite3_step(pRtree->pReadParent)==SQLITE_ROW ){
i64 iNode = sqlite3_column_int64(pRtree->pReadParent, 0);
rc = nodeAcquire(pRtree, iNode, 0, &pLeaf->pParent);
}else{
rc = SQLITE_ERROR;
}
sqlite3_reset(pRtree->pReadParent);
if( rc==SQLITE_OK ){
rc = fixLeafParent(pRtree, pLeaf->pParent);
}
}
return rc;
}
static int deleteCell(Rtree *, RtreeNode *, int, int);
static int removeNode(Rtree *pRtree, RtreeNode *pNode, int iHeight){
int rc;
RtreeNode *pParent;
int iCell;
assert( pNode->nRef==1 );
/* Remove the entry in the parent cell. */
iCell = nodeParentIndex(pRtree, pNode);
pParent = pNode->pParent;
pNode->pParent = 0;
if( SQLITE_OK!=(rc = deleteCell(pRtree, pParent, iCell, iHeight+1))
|| SQLITE_OK!=(rc = nodeRelease(pRtree, pParent))
){
return rc;
}
/* Remove the xxx_node entry. */
sqlite3_bind_int64(pRtree->pDeleteNode, 1, pNode->iNode);
sqlite3_step(pRtree->pDeleteNode);
if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteNode)) ){
return rc;
}
/* Remove the xxx_parent entry. */
sqlite3_bind_int64(pRtree->pDeleteParent, 1, pNode->iNode);
sqlite3_step(pRtree->pDeleteParent);
if( SQLITE_OK!=(rc = sqlite3_reset(pRtree->pDeleteParent)) ){
return rc;
}
/* Remove the node from the in-memory hash table and link it into
** the Rtree.pDeleted list. Its contents will be re-inserted later on.
*/
nodeHashDelete(pRtree, pNode);
pNode->iNode = iHeight;
pNode->pNext = pRtree->pDeleted;
pNode->nRef++;
pRtree->pDeleted = pNode;
return SQLITE_OK;
}
static void fixBoundingBox(Rtree *pRtree, RtreeNode *pNode){
RtreeNode *pParent = pNode->pParent;
if( pParent ){
int ii;
int nCell = NCELL(pNode);
RtreeCell box; /* Bounding box for pNode */
nodeGetCell(pRtree, pNode, 0, &box);
for(ii=1; ii<nCell; ii++){
RtreeCell cell;
nodeGetCell(pRtree, pNode, ii, &cell);
cellUnion(pRtree, &box, &cell);
}
box.iRowid = pNode->iNode;
ii = nodeParentIndex(pRtree, pNode);
nodeOverwriteCell(pRtree, pParent, &box, ii);
fixBoundingBox(pRtree, pParent);
}
}
/*
** Delete the cell at index iCell of node pNode. After removing the
** cell, adjust the r-tree data structure if required.
*/
static int deleteCell(Rtree *pRtree, RtreeNode *pNode, int iCell, int iHeight){
int rc;
if( SQLITE_OK!=(rc = fixLeafParent(pRtree, pNode)) ){
return rc;
}
/* Remove the cell from the node. This call just moves bytes around
** the in-memory node image, so it cannot fail.
*/
nodeDeleteCell(pRtree, pNode, iCell);
/* If the node is not the tree root and now has less than the minimum
** number of cells, remove it from the tree. Otherwise, update the
** cell in the parent node so that it tightly contains the updated
** node.
*/
if( pNode->iNode!=1 ){
RtreeNode *pParent = pNode->pParent;
if( (pParent->iNode!=1 || NCELL(pParent)!=1)
&& (NCELL(pNode)<RTREE_MINCELLS(pRtree))
){
rc = removeNode(pRtree, pNode, iHeight);
}else{
fixBoundingBox(pRtree, pNode);
}
}
return rc;
}
static int Reinsert(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell,
int iHeight
){
int *aOrder;
int *aSpare;
RtreeCell *aCell;
float *aDistance;
int nCell;
float aCenterCoord[RTREE_MAX_DIMENSIONS];
int iDim;
int ii;
int rc = SQLITE_OK;
memset(aCenterCoord, 0, sizeof(float)*RTREE_MAX_DIMENSIONS);
nCell = NCELL(pNode)+1;
/* Allocate the buffers used by this operation. The allocation is
** relinquished before this function returns.
*/
aCell = (RtreeCell *)sqlite3_malloc(nCell * (
sizeof(RtreeCell) + /* aCell array */
sizeof(int) + /* aOrder array */
sizeof(int) + /* aSpare array */
sizeof(float) /* aDistance array */
));
if( !aCell ){
return SQLITE_NOMEM;
}
aOrder = (int *)&aCell[nCell];
aSpare = (int *)&aOrder[nCell];
aDistance = (float *)&aSpare[nCell];
for(ii=0; ii<nCell; ii++){
if( ii==(nCell-1) ){
memcpy(&aCell[ii], pCell, sizeof(RtreeCell));
}else{
nodeGetCell(pRtree, pNode, ii, &aCell[ii]);
}
aOrder[ii] = ii;
for(iDim=0; iDim<pRtree->nDim; iDim++){
aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2]);
aCenterCoord[iDim] += DCOORD(aCell[ii].aCoord[iDim*2+1]);
}
}
for(iDim=0; iDim<pRtree->nDim; iDim++){
aCenterCoord[iDim] = aCenterCoord[iDim]/((float)nCell*2.0);
}
for(ii=0; ii<nCell; ii++){
aDistance[ii] = 0.0;
for(iDim=0; iDim<pRtree->nDim; iDim++){
float coord = DCOORD(aCell[ii].aCoord[iDim*2+1]) -
DCOORD(aCell[ii].aCoord[iDim*2]);
aDistance[ii] += (coord-aCenterCoord[iDim])*(coord-aCenterCoord[iDim]);
}
}
SortByDistance(aOrder, nCell, aDistance, aSpare);
nodeZero(pRtree, pNode);
for(ii=0; rc==SQLITE_OK && ii<(nCell-(RTREE_MINCELLS(pRtree)+1)); ii++){
RtreeCell *p = &aCell[aOrder[ii]];
nodeInsertCell(pRtree, pNode, p);
if( p->iRowid==pCell->iRowid ){
if( iHeight==0 ){
rc = rowidWrite(pRtree, p->iRowid, pNode->iNode);
}else{
rc = parentWrite(pRtree, p->iRowid, pNode->iNode);
}
}
}
if( rc==SQLITE_OK ){
fixBoundingBox(pRtree, pNode);
}
for(; rc==SQLITE_OK && ii<nCell; ii++){
/* Find a node to store this cell in. pNode->iNode currently contains
** the height of the sub-tree headed by the cell.
*/
RtreeNode *pInsert;
RtreeCell *p = &aCell[aOrder[ii]];
rc = ChooseLeaf(pRtree, p, iHeight, &pInsert);
if( rc==SQLITE_OK ){
int rc2;
rc = rtreeInsertCell(pRtree, pInsert, p, iHeight);
rc2 = nodeRelease(pRtree, pInsert);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
}
sqlite3_free(aCell);
return rc;
}
/*
** Insert cell pCell into node pNode. Node pNode is the head of a
** subtree iHeight high (leaf nodes have iHeight==0).
*/
static int rtreeInsertCell(
Rtree *pRtree,
RtreeNode *pNode,
RtreeCell *pCell,
int iHeight
){
int rc = SQLITE_OK;
if( iHeight>0 ){
RtreeNode *pChild = nodeHashLookup(pRtree, pCell->iRowid);
if( pChild ){
nodeRelease(pRtree, pChild->pParent);
nodeReference(pNode);
pChild->pParent = pNode;
}
}
if( nodeInsertCell(pRtree, pNode, pCell) ){
#if VARIANT_RSTARTREE_REINSERT
if( iHeight<=pRtree->iReinsertHeight || pNode->iNode==1){
rc = SplitNode(pRtree, pNode, pCell, iHeight);
}else{
pRtree->iReinsertHeight = iHeight;
rc = Reinsert(pRtree, pNode, pCell, iHeight);
}
#else
rc = SplitNode(pRtree, pNode, pCell, iHeight);
#endif
}else{
AdjustTree(pRtree, pNode, pCell);
if( iHeight==0 ){
rc = rowidWrite(pRtree, pCell->iRowid, pNode->iNode);
}else{
rc = parentWrite(pRtree, pCell->iRowid, pNode->iNode);
}
}
return rc;
}
static int reinsertNodeContent(Rtree *pRtree, RtreeNode *pNode){
int ii;
int rc = SQLITE_OK;
int nCell = NCELL(pNode);
for(ii=0; rc==SQLITE_OK && ii<nCell; ii++){
RtreeNode *pInsert;
RtreeCell cell;
nodeGetCell(pRtree, pNode, ii, &cell);
/* Find a node to store this cell in. pNode->iNode currently contains
** the height of the sub-tree headed by the cell.
*/
rc = ChooseLeaf(pRtree, &cell, pNode->iNode, &pInsert);
if( rc==SQLITE_OK ){
int rc2;
rc = rtreeInsertCell(pRtree, pInsert, &cell, pNode->iNode);
rc2 = nodeRelease(pRtree, pInsert);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
}
return rc;
}
/*
** Select a currently unused rowid for a new r-tree record.
*/
static int newRowid(Rtree *pRtree, i64 *piRowid){
int rc;
sqlite3_bind_null(pRtree->pWriteRowid, 1);
sqlite3_bind_null(pRtree->pWriteRowid, 2);
sqlite3_step(pRtree->pWriteRowid);
rc = sqlite3_reset(pRtree->pWriteRowid);
*piRowid = sqlite3_last_insert_rowid(pRtree->db);
return rc;
}
#ifndef NDEBUG
static int hashIsEmpty(Rtree *pRtree){
int ii;
for(ii=0; ii<HASHSIZE; ii++){
assert( !pRtree->aHash[ii] );
}
return 1;
}
#endif
/*
** The xUpdate method for rtree module virtual tables.
*/
int rtreeUpdate(
sqlite3_vtab *pVtab,
int nData,
sqlite3_value **azData,
sqlite_int64 *pRowid
){
Rtree *pRtree = (Rtree *)pVtab;
int rc = SQLITE_OK;
rtreeReference(pRtree);
assert(nData>=1);
assert(hashIsEmpty(pRtree));
/* If azData[0] is not an SQL NULL value, it is the rowid of a
** record to delete from the r-tree table. The following block does
** just that.
*/
if( sqlite3_value_type(azData[0])!=SQLITE_NULL ){
i64 iDelete; /* The rowid to delete */
RtreeNode *pLeaf; /* Leaf node containing record iDelete */
int iCell; /* Index of iDelete cell in pLeaf */
RtreeNode *pRoot;
/* Obtain a reference to the root node to initialise Rtree.iDepth */
rc = nodeAcquire(pRtree, 1, 0, &pRoot);
/* Obtain a reference to the leaf node that contains the entry
** about to be deleted.
*/
if( rc==SQLITE_OK ){
iDelete = sqlite3_value_int64(azData[0]);
rc = findLeafNode(pRtree, iDelete, &pLeaf);
}
/* Delete the cell in question from the leaf node. */
if( rc==SQLITE_OK ){
int rc2;
iCell = nodeRowidIndex(pRtree, pLeaf, iDelete);
rc = deleteCell(pRtree, pLeaf, iCell, 0);
rc2 = nodeRelease(pRtree, pLeaf);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
/* Delete the corresponding entry in the <rtree>_rowid table. */
if( rc==SQLITE_OK ){
sqlite3_bind_int64(pRtree->pDeleteRowid, 1, iDelete);
sqlite3_step(pRtree->pDeleteRowid);
rc = sqlite3_reset(pRtree->pDeleteRowid);
}
/* Check if the root node now has exactly one child. If so, remove
** it, schedule the contents of the child for reinsertion and
** reduce the tree height by one.
**
** This is equivalent to copying the contents of the child into
** the root node (the operation that Gutman's paper says to perform
** in this scenario).
*/
if( rc==SQLITE_OK && pRtree->iDepth>0 ){
if( rc==SQLITE_OK && NCELL(pRoot)==1 ){
RtreeNode *pChild;
i64 iChild = nodeGetRowid(pRtree, pRoot, 0);
rc = nodeAcquire(pRtree, iChild, pRoot, &pChild);
if( rc==SQLITE_OK ){
rc = removeNode(pRtree, pChild, pRtree->iDepth-1);
}
if( rc==SQLITE_OK ){
pRtree->iDepth--;
writeInt16(pRoot->zData, pRtree->iDepth);
pRoot->isDirty = 1;
}
}
}
/* Re-insert the contents of any underfull nodes removed from the tree. */
for(pLeaf=pRtree->pDeleted; pLeaf; pLeaf=pRtree->pDeleted){
if( rc==SQLITE_OK ){
rc = reinsertNodeContent(pRtree, pLeaf);
}
pRtree->pDeleted = pLeaf->pNext;
sqlite3_free(pLeaf);
}
/* Release the reference to the root node. */
if( rc==SQLITE_OK ){
rc = nodeRelease(pRtree, pRoot);
}else{
nodeRelease(pRtree, pRoot);
}
}
/* If the azData[] array contains more than one element, elements
** (azData[2]..azData[argc-1]) contain a new record to insert into
** the r-tree structure.
*/
if( rc==SQLITE_OK && nData>1 ){
/* Insert a new record into the r-tree */
RtreeCell cell;
int ii;
RtreeNode *pLeaf;
/* Populate the cell.aCoord[] array. The first coordinate is azData[3]. */
assert( nData==(pRtree->nDim*2 + 3) );
if( pRtree->eCoordType==RTREE_COORD_REAL32 ){
for(ii=0; ii<(pRtree->nDim*2); ii+=2){
cell.aCoord[ii].f = (float)sqlite3_value_double(azData[ii+3]);
cell.aCoord[ii+1].f = (float)sqlite3_value_double(azData[ii+4]);
if( cell.aCoord[ii].f>cell.aCoord[ii+1].f ){
rc = SQLITE_CONSTRAINT;
goto constraint;
}
}
}else{
for(ii=0; ii<(pRtree->nDim*2); ii+=2){
cell.aCoord[ii].i = sqlite3_value_int(azData[ii+3]);
cell.aCoord[ii+1].i = sqlite3_value_int(azData[ii+4]);
if( cell.aCoord[ii].i>cell.aCoord[ii+1].i ){
rc = SQLITE_CONSTRAINT;
goto constraint;
}
}
}
/* Figure out the rowid of the new row. */
if( sqlite3_value_type(azData[2])==SQLITE_NULL ){
rc = newRowid(pRtree, &cell.iRowid);
}else{
cell.iRowid = sqlite3_value_int64(azData[2]);
sqlite3_bind_int64(pRtree->pReadRowid, 1, cell.iRowid);
if( SQLITE_ROW==sqlite3_step(pRtree->pReadRowid) ){
sqlite3_reset(pRtree->pReadRowid);
rc = SQLITE_CONSTRAINT;
goto constraint;
}
rc = sqlite3_reset(pRtree->pReadRowid);
}
if( rc==SQLITE_OK ){
rc = ChooseLeaf(pRtree, &cell, 0, &pLeaf);
}
if( rc==SQLITE_OK ){
int rc2;
pRtree->iReinsertHeight = -1;
rc = rtreeInsertCell(pRtree, pLeaf, &cell, 0);
rc2 = nodeRelease(pRtree, pLeaf);
if( rc==SQLITE_OK ){
rc = rc2;
}
}
}
constraint:
rtreeRelease(pRtree);
return rc;
}
/*
** The xRename method for rtree module virtual tables.
*/
static int rtreeRename(sqlite3_vtab *pVtab, const char *zNewName){
Rtree *pRtree = (Rtree *)pVtab;
int rc = SQLITE_NOMEM;
char *zSql = sqlite3_mprintf(
"ALTER TABLE %Q.'%q_node' RENAME TO \"%w_node\";"
"ALTER TABLE %Q.'%q_parent' RENAME TO \"%w_parent\";"
"ALTER TABLE %Q.'%q_rowid' RENAME TO \"%w_rowid\";"
, pRtree->zDb, pRtree->zName, zNewName
, pRtree->zDb, pRtree->zName, zNewName
, pRtree->zDb, pRtree->zName, zNewName
);
if( zSql ){
rc = sqlite3_exec(pRtree->db, zSql, 0, 0, 0);
sqlite3_free(zSql);
}
return rc;
}
static sqlite3_module rtreeModule = {
0, /* iVersion */
rtreeCreate, /* xCreate - create a table */
rtreeConnect, /* xConnect - connect to an existing table */
rtreeBestIndex, /* xBestIndex - Determine search strategy */
rtreeDisconnect, /* xDisconnect - Disconnect from a table */
rtreeDestroy, /* xDestroy - Drop a table */
rtreeOpen, /* xOpen - open a cursor */
rtreeClose, /* xClose - close a cursor */
rtreeFilter, /* xFilter - configure scan constraints */
rtreeNext, /* xNext - advance a cursor */
rtreeEof, /* xEof */
rtreeColumn, /* xColumn - read data */
rtreeRowid, /* xRowid - read data */
rtreeUpdate, /* xUpdate - write data */
0, /* xBegin - begin transaction */
0, /* xSync - sync transaction */
0, /* xCommit - commit transaction */
0, /* xRollback - rollback transaction */
0, /* xFindFunction - function overloading */
rtreeRename /* xRename - rename the table */
};
static int rtreeSqlInit(
Rtree *pRtree,
sqlite3 *db,
const char *zDb,
const char *zPrefix,
int isCreate
){
int rc = SQLITE_OK;
#define N_STATEMENT 9
static const char *azSql[N_STATEMENT] = {
/* Read and write the xxx_node table */
"SELECT data FROM '%q'.'%q_node' WHERE nodeno = :1",
"INSERT OR REPLACE INTO '%q'.'%q_node' VALUES(:1, :2)",
"DELETE FROM '%q'.'%q_node' WHERE nodeno = :1",
/* Read and write the xxx_rowid table */
"SELECT nodeno FROM '%q'.'%q_rowid' WHERE rowid = :1",
"INSERT OR REPLACE INTO '%q'.'%q_rowid' VALUES(:1, :2)",
"DELETE FROM '%q'.'%q_rowid' WHERE rowid = :1",
/* Read and write the xxx_parent table */
"SELECT parentnode FROM '%q'.'%q_parent' WHERE nodeno = :1",
"INSERT OR REPLACE INTO '%q'.'%q_parent' VALUES(:1, :2)",
"DELETE FROM '%q'.'%q_parent' WHERE nodeno = :1"
};
sqlite3_stmt **appStmt[N_STATEMENT];
int i;
pRtree->db = db;
if( isCreate ){
char *zCreate = sqlite3_mprintf(
"CREATE TABLE \"%w\".\"%w_node\"(nodeno INTEGER PRIMARY KEY, data BLOB);"
"CREATE TABLE \"%w\".\"%w_rowid\"(rowid INTEGER PRIMARY KEY, nodeno INTEGER);"
"CREATE TABLE \"%w\".\"%w_parent\"(nodeno INTEGER PRIMARY KEY, parentnode INTEGER);"
"INSERT INTO '%q'.'%q_node' VALUES(1, zeroblob(%d))",
zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, zDb, zPrefix, pRtree->iNodeSize
);
if( !zCreate ){
return SQLITE_NOMEM;
}
rc = sqlite3_exec(db, zCreate, 0, 0, 0);
sqlite3_free(zCreate);
if( rc!=SQLITE_OK ){
return rc;
}
}
appStmt[0] = &pRtree->pReadNode;
appStmt[1] = &pRtree->pWriteNode;
appStmt[2] = &pRtree->pDeleteNode;
appStmt[3] = &pRtree->pReadRowid;
appStmt[4] = &pRtree->pWriteRowid;
appStmt[5] = &pRtree->pDeleteRowid;
appStmt[6] = &pRtree->pReadParent;
appStmt[7] = &pRtree->pWriteParent;
appStmt[8] = &pRtree->pDeleteParent;
for(i=0; i<N_STATEMENT && rc==SQLITE_OK; i++){
char *zSql = sqlite3_mprintf(azSql[i], zDb, zPrefix);
if( zSql ){
rc = sqlite3_prepare_v2(db, zSql, -1, appStmt[i], 0);
}else{
rc = SQLITE_NOMEM;
}
sqlite3_free(zSql);
}
return rc;
}
/*
** This routine queries database handle db for the page-size used by
** database zDb. If successful, the page-size in bytes is written to
** *piPageSize and SQLITE_OK returned. Otherwise, and an SQLite error
** code is returned.
*/
static int getPageSize(sqlite3 *db, const char *zDb, int *piPageSize){
int rc = SQLITE_NOMEM;
char *zSql;
sqlite3_stmt *pStmt = 0;
zSql = sqlite3_mprintf("PRAGMA %Q.page_size", zDb);
if( !zSql ){
return SQLITE_NOMEM;
}
rc = sqlite3_prepare_v2(db, zSql, -1, &pStmt, 0);
sqlite3_free(zSql);
if( rc!=SQLITE_OK ){
return rc;
}
if( SQLITE_ROW==sqlite3_step(pStmt) ){
*piPageSize = sqlite3_column_int(pStmt, 0);
}
return sqlite3_finalize(pStmt);
}
/*
** This function is the implementation of both the xConnect and xCreate
** methods of the r-tree virtual table.
**
** argv[0] -> module name
** argv[1] -> database name
** argv[2] -> table name
** argv[...] -> column names...
*/
static int rtreeInit(
sqlite3 *db, /* Database connection */
void *pAux, /* Pointer to head of rtree list */
int argc, const char *const*argv, /* Parameters to CREATE TABLE statement */
sqlite3_vtab **ppVtab, /* OUT: New virtual table */
char **pzErr, /* OUT: Error message, if any */
int isCreate, /* True for xCreate, false for xConnect */
int eCoordType /* One of the RTREE_COORD_* constants */
){
int rc = SQLITE_OK;
int iPageSize = 0;
Rtree *pRtree;
int nDb; /* Length of string argv[1] */
int nName; /* Length of string argv[2] */
const char *aErrMsg[] = {
0, /* 0 */
"Wrong number of columns for an rtree table", /* 1 */
"Too few columns for an rtree table", /* 2 */
"Too many columns for an rtree table" /* 3 */
};
int iErr = (argc<6) ? 2 : argc>(RTREE_MAX_DIMENSIONS*2+4) ? 3 : argc%2;
if( aErrMsg[iErr] ){
*pzErr = sqlite3_mprintf("%s", aErrMsg[iErr]);
return SQLITE_ERROR;
}
rc = getPageSize(db, argv[1], &iPageSize);
if( rc!=SQLITE_OK ){
return rc;
}
/* Allocate the sqlite3_vtab structure */
nDb = strlen(argv[1]);
nName = strlen(argv[2]);
pRtree = (Rtree *)sqlite3_malloc(sizeof(Rtree)+nDb+nName+2);
if( !pRtree ){
return SQLITE_NOMEM;
}
memset(pRtree, 0, sizeof(Rtree)+nDb+nName+2);
pRtree->nBusy = 1;
pRtree->base.pModule = &rtreeModule;
pRtree->zDb = (char *)&pRtree[1];
pRtree->zName = &pRtree->zDb[nDb+1];
pRtree->nDim = (argc-4)/2;
pRtree->nBytesPerCell = 8 + pRtree->nDim*4*2;
pRtree->eCoordType = eCoordType;
memcpy(pRtree->zDb, argv[1], nDb);
memcpy(pRtree->zName, argv[2], nName);
/* Figure out the node size to use. By default, use 64 bytes less than
** the database page-size. This ensures that each node is stored on
** a single database page.
**
** If the databasd page-size is so large that more than RTREE_MAXCELLS
** entries would fit in a single node, use a smaller node-size.
*/
pRtree->iNodeSize = iPageSize-64;
if( (4+pRtree->nBytesPerCell*RTREE_MAXCELLS)<pRtree->iNodeSize ){
pRtree->iNodeSize = 4+pRtree->nBytesPerCell*RTREE_MAXCELLS;
}
/* Create/Connect to the underlying relational database schema. If
** that is successful, call sqlite3_declare_vtab() to configure
** the r-tree table schema.
*/
if( (rc = rtreeSqlInit(pRtree, db, argv[1], argv[2], isCreate)) ){
*pzErr = sqlite3_mprintf("%s", sqlite3_errmsg(db));
}else{
char *zSql = sqlite3_mprintf("CREATE TABLE x(%s", argv[3]);
char *zTmp;
int ii;
for(ii=4; zSql && ii<argc; ii++){
zTmp = zSql;
zSql = sqlite3_mprintf("%s, %s", zTmp, argv[ii]);
sqlite3_free(zTmp);
}
if( zSql ){
zTmp = zSql;
zSql = sqlite3_mprintf("%s);", zTmp);
sqlite3_free(zTmp);
}
if( !zSql || sqlite3_declare_vtab(db, zSql) ){
rc = SQLITE_NOMEM;
}
sqlite3_free(zSql);
}
if( rc==SQLITE_OK ){
*ppVtab = (sqlite3_vtab *)pRtree;
}else{
rtreeRelease(pRtree);
}
return rc;
}
/*
** Implementation of a scalar function that decodes r-tree nodes to
** human readable strings. This can be used for debugging and analysis.
**
** The scalar function takes two arguments, a blob of data containing
** an r-tree node, and the number of dimensions the r-tree indexes.
** For a two-dimensional r-tree structure called "rt", to deserialize
** all nodes, a statement like:
**
** SELECT rtreenode(2, data) FROM rt_node;
**
** The human readable string takes the form of a Tcl list with one
** entry for each cell in the r-tree node. Each entry is itself a
** list, containing the 8-byte rowid/pageno followed by the
** <num-dimension>*2 coordinates.
*/
static void rtreenode(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
char *zText = 0;
RtreeNode node;
Rtree tree;
int ii;
memset(&node, 0, sizeof(RtreeNode));
memset(&tree, 0, sizeof(Rtree));
tree.nDim = sqlite3_value_int(apArg[0]);
tree.nBytesPerCell = 8 + 8 * tree.nDim;
node.zData = (u8 *)sqlite3_value_blob(apArg[1]);
for(ii=0; ii<NCELL(&node); ii++){
char zCell[512];
int nCell = 0;
RtreeCell cell;
int jj;
nodeGetCell(&tree, &node, ii, &cell);
sqlite3_snprintf(512-nCell,&zCell[nCell],"%d", cell.iRowid);
nCell = strlen(zCell);
for(jj=0; jj<tree.nDim*2; jj++){
sqlite3_snprintf(512-nCell,&zCell[nCell]," %f",(double)cell.aCoord[jj].f);
nCell = strlen(zCell);
}
if( zText ){
char *zTextNew = sqlite3_mprintf("%s {%s}", zText, zCell);
sqlite3_free(zText);
zText = zTextNew;
}else{
zText = sqlite3_mprintf("{%s}", zCell);
}
}
sqlite3_result_text(ctx, zText, -1, sqlite3_free);
}
static void rtreedepth(sqlite3_context *ctx, int nArg, sqlite3_value **apArg){
if( sqlite3_value_type(apArg[0])!=SQLITE_BLOB
|| sqlite3_value_bytes(apArg[0])<2
){
sqlite3_result_error(ctx, "Invalid argument to rtreedepth()", -1);
}else{
u8 *zBlob = (u8 *)sqlite3_value_blob(apArg[0]);
sqlite3_result_int(ctx, readInt16(zBlob));
}
}
/*
** Register the r-tree module with database handle db. This creates the
** virtual table module "rtree" and the debugging/analysis scalar
** function "rtreenode".
*/
int sqlite3RtreeInit(sqlite3 *db){
int rc = SQLITE_OK;
if( rc==SQLITE_OK ){
int utf8 = SQLITE_UTF8;
rc = sqlite3_create_function(db, "rtreenode", 2, utf8, 0, rtreenode, 0, 0);
}
if( rc==SQLITE_OK ){
int utf8 = SQLITE_UTF8;
rc = sqlite3_create_function(db, "rtreedepth", 1, utf8, 0,rtreedepth, 0, 0);
}
if( rc==SQLITE_OK ){
void *c = (void *)RTREE_COORD_REAL32;
rc = sqlite3_create_module_v2(db, "rtree", &rtreeModule, c, 0);
}
if( rc==SQLITE_OK ){
void *c = (void *)RTREE_COORD_INT32;
rc = sqlite3_create_module_v2(db, "rtree_i32", &rtreeModule, c, 0);
}
return rc;
}
#if !SQLITE_CORE
int sqlite3_extension_init(
sqlite3 *db,
char **pzErrMsg,
const sqlite3_api_routines *pApi
){
SQLITE_EXTENSION_INIT2(pApi)
return sqlite3RtreeInit(db);
}
#endif
#endif