+/*
+ * Flexible B-tree implementation. Supports reference counting for
+ * copy-on-write, user-defined node properties, and variable
+ * degree.
+ *
+ * This file is copyright 2001,2004 Simon Tatham.
+ *
+ * Permission is hereby granted, free of charge, to any person
+ * obtaining a copy of this software and associated documentation
+ * files (the "Software"), to deal in the Software without
+ * restriction, including without limitation the rights to use,
+ * copy, modify, merge, publish, distribute, sublicense, and/or
+ * sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following
+ * conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+ * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL SIMON TATHAM BE LIABLE FOR
+ * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
+ * CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+/*
+ * TODO:
+ *
+ * Possibly TODO in future, but may not be sensible in this code
+ * architecture:
+ *
+ * - user write properties.
+ * * this all happens during write_unlock(), I think. Except
+ * that we'll now need an _internal_ write_unlock() which
+ * does everything except user write properties. Sigh.
+ * * note that we also need a transform function for elements
+ * (rot13 will certainly require this, and reverse will
+ * require it if the elements themselves are in some way
+ * reversible).
+ *
+ * Still untested:
+ * - searching on user read properties.
+ * - user-supplied copy function.
+ * - bt_add when element already exists.
+ * - bt_del when element doesn't.
+ * - splitpos with before==TRUE.
+ * - split() on sorted elements (but it should be fine).
+ * - bt_replace, at all (it won't be useful until we get user read
+ * properties).
+ * - bt_index_w (won't make much sense until we start using
+ * user-supplied copy fn).
+ */
+
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+
+#ifdef TEST
+#include <stdio.h>
+#include <stdarg.h>
+#endif
+
+#include "btree.h"
+
+#ifdef TEST
+static void set_invalid_property(void *prop);
+#endif
+
+/* ----------------------------------------------------------------------
+ * Type definitions.
+ */
+
+typedef union nodecomponent nodecomponent;
+typedef nodecomponent *nodeptr;
+
+/*
+ * For type-checking purposes, and to ensure I don't accidentally
+ * confuse node_addr with node_ptr during implementation, I'll
+ * define node_addr for the in-memory case as being a struct
+ * containing only a nodeptr.
+ *
+ * This unfortunately needs to go in btree.h so that clients
+ * writing user properties can know about the nodecomponent
+ * structure.
+ */
+typedef struct {
+ nodeptr p;
+} node_addr;
+
+/*
+ * A B-tree node is a horrible thing when you're trying to be
+ * flexible. It is of variable size, and it contains a variety of
+ * distinct types of thing: nodes, elements, some counters, some
+ * user-defined properties ... it's a horrible thing. So we define
+ * it as an array of unions, each union being either an `int' or a
+ * `bt_element_t' or a `node_addr'...
+ */
+
+union nodecomponent {
+ int i;
+ node_addr na;
+ bt_element_t ep;
+};
+
+static const node_addr NODE_ADDR_NULL = { NULL };
+
+/*
+ * The array of nodecomponents will take the following form:
+ *
+ * - (maxdegree) child pointers.
+ * - (maxdegree-1) element pointers.
+ * - one subtree count (current number of child pointers that are
+ * valid; note that `valid' doesn't imply non-NULL).
+ * - one element count.
+ * - one reference count.
+ */
+
+struct btree {
+ int mindegree; /* min number of subtrees */
+ int maxdegree; /* max number of subtrees */
+ int depth; /* helps to store this explicitly */
+ node_addr root;
+ cmpfn_t cmp;
+ copyfn_t copy;
+ freefn_t freeelt;
+ int propsize, propalign, propoffset;
+ propmakefn_t propmake;
+ propmergefn_t propmerge;
+ void *userstate; /* passed to all user functions */
+};
+
+/* ----------------------------------------------------------------------
+ * Memory management routines and other housekeeping.
+ */
+#ifdef HAVE_ALLOCA
+# define ialloc(x) alloca(x)
+# define ifree(x)
+#else
+# define ialloc(x) smalloc(x)
+# define ifree(x) sfree(x)
+#endif
+
+#define new1(t) ( (t *) smalloc(sizeof(t)) )
+#define newn(t, n) ( (t *) smalloc((n) * sizeof(t)) )
+#define inew1(t) ( (t *) ialloc(sizeof(t)) )
+#define inewn(t, n) ( (t *) ialloc((n) * sizeof(t)) )
+
+static void *smalloc(size_t size)
+{
+ void *ret = malloc(size);
+ if (!ret)
+ abort();
+ return ret;
+}
+
+static void sfree(void *p)
+{
+ free(p);
+}
+
+#ifndef FALSE
+#define FALSE 0
+#endif
+#ifndef TRUE
+#define TRUE 1
+#endif
+
+/* We could probably do with more compiler-specific branches of this #if. */
+#if defined(__GNUC__)
+#define INLINE __inline
+#else
+#define INLINE
+#endif
+
+/* Hooks into the low-level code for test purposes. */
+#ifdef TEST
+void testlock(int write, int set, nodeptr n);
+#else
+#define testlock(w,s,n)
+#endif
+
+/* ----------------------------------------------------------------------
+ * Low-level helper routines, which understand the in-memory format
+ * of a node and know how to read-lock and write-lock.
+ */
+
+/*
+ * Read and write the node_addr of a child.
+ */
+static INLINE node_addr bt_child(btree *bt, nodeptr n, int index)
+{
+ return n[index].na;
+}
+static INLINE void bt_set_child(btree *bt, nodeptr n,
+ int index, node_addr value)
+{
+ n[index].na = value;
+}
+
+/*
+ * Read and write the address of an element.
+ */
+static INLINE bt_element_t bt_element(btree *bt, nodeptr n, int index)
+{
+ return n[bt->maxdegree + index].ep;
+}
+static INLINE void bt_set_element(btree *bt, nodeptr n,
+ int index, bt_element_t value)
+{
+ n[bt->maxdegree + index].ep = value;
+}
+
+/*
+ * Give the number of subtrees currently present in an element.
+ */
+static INLINE int bt_subtrees(btree *bt, nodeptr n)
+{
+ return n[bt->maxdegree*2-1].i;
+}
+#define bt_elements(bt,n) (bt_subtrees(bt,n) - 1)
+
+/*
+ * Give the minimum and maximum number of subtrees allowed in a
+ * node.
+ */
+static INLINE int bt_min_subtrees(btree *bt)
+{
+ return bt->mindegree;
+}
+static INLINE int bt_max_subtrees(btree *bt)
+{
+ return bt->maxdegree;
+}
+
+/*
+ * Return the count of items, and the user properties, in a
+ * particular subtree of a node.
+ *
+ * Note that in the in-memory form of the tree, this breaks the
+ * read-locking semantics, by reading the counts out of the child
+ * nodes without bothering to lock them. We're allowed to do this
+ * because this function is implemented at the same very low level
+ * as the implementation of bt_read_lock(), so we're allowed to
+ * know that read locking actually doesn't do anything.
+ */
+static INLINE int bt_child_count(btree *bt, nodeptr n, int index)
+{
+ if (n[index].na.p)
+ return n[index].na.p[bt->maxdegree*2].i;
+ else
+ return 0;
+}
+
+static INLINE void *bt_child_prop(btree *bt, nodeptr n, int index)
+{
+ if (n[index].na.p)
+ return (char *)n[index].na.p + bt->propoffset;
+ else
+ return NULL;
+}
+
+/*
+ * Return the count of items in a whole node.
+ */
+static INLINE int bt_node_count(btree *bt, nodeptr n)
+{
+ return n[bt->maxdegree*2].i;
+}
+
+/*
+ * Determine whether a node is a leaf node or not.
+ */
+static INLINE int bt_is_leaf(btree *bt, nodeptr n)
+{
+ return n[0].na.p == NULL;
+}
+
+/*
+ * Create a new write-locked node, and return a pointer to it.
+ */
+static INLINE nodeptr bt_new_node(btree *bt, int nsubtrees)
+{
+ nodeptr ret = (nodecomponent *)smalloc(bt->propoffset + bt->propsize);
+ ret[bt->maxdegree*2-1].i = nsubtrees;
+ ret[bt->maxdegree*2+1].i = 1; /* reference count 1 */
+#ifdef TEST
+ set_invalid_property(ret + bt->maxdegree * 2 + 2);
+#else
+ memset((char *)ret + bt->propoffset, 0, bt->propsize);
+#endif
+ testlock(TRUE, TRUE, ret);
+ return ret;
+}
+
+/*
+ * Destroy a node (must be write-locked).
+ */
+static INLINE void bt_destroy_node(btree *bt, nodeptr n)
+{
+ testlock(TRUE, FALSE, n);
+ /* Free the property. */
+ bt->propmerge(bt->userstate, NULL, NULL, n + bt->maxdegree * 2 + 2);
+ sfree(n);
+}
+
+/*
+ * Take an existing node and prepare to re-use it in a new context.
+ */
+static INLINE nodeptr bt_reuse_node(btree *bt, nodeptr n, int nsubtrees)
+{
+ testlock(TRUE, FALSE, n);
+ testlock(TRUE, TRUE, n);
+ n[bt->maxdegree*2-1].i = nsubtrees;
+ return n;
+}
+
+/*
+ * Return an extra reference to a node, for purposes of cloning. So
+ * we have to update its reference count as well.
+ */
+static INLINE node_addr bt_ref_node(btree *bt, node_addr n)
+{
+ if (n.p)
+ n.p[bt->maxdegree*2+1].i++;
+ return n;
+}
+
+/*
+ * Drop a node's reference count, for purposes of freeing. Returns
+ * the new reference count. Typically this will be tested against
+ * zero to see if the node needs to be physically freed; hence a
+ * NULL node_addr causes a return of 1 (because this isn't
+ * necessary).
+ */
+static INLINE int bt_unref_node(btree *bt, node_addr n)
+{
+ if (n.p) {
+ n.p[bt->maxdegree*2+1].i--;
+ return n.p[bt->maxdegree*2+1].i;
+ } else
+ return 1; /* a NULL node is considered OK */
+}
+
+/*
+ * Clone a node during write unlocking, if its reference count is
+ * more than one.
+ */
+static nodeptr bt_clone_node(btree *bt, nodeptr n)
+{
+ int i;
+ nodeptr ret = (nodecomponent *)smalloc(bt->propoffset + bt->propsize);
+ memcpy(ret, n, (bt->maxdegree*2+1) * sizeof(nodecomponent));
+ if (bt->copy) {
+ for (i = 0; i < bt_elements(bt, ret); i++) {
+ bt_element_t *e = bt_element(bt, ret, i);
+ bt_set_element(bt, ret, i, bt->copy(bt->userstate, e));
+ }
+ }
+ ret[bt->maxdegree*2+1].i = 1; /* clone has reference count 1 */
+ n[bt->maxdegree*2+1].i--; /* drop original's ref count by one */
+ /*
+ * At this low level, we're allowed to reach directly into the
+ * subtrees to fiddle with their reference counts without
+ * having to lock them.
+ */
+ for (i = 0; i < bt_subtrees(bt, ret); i++) {
+ node_addr na = bt_child(bt, ret, i);
+ if (na.p)
+ na.p[bt->maxdegree*2+1].i++; /* inc ref count of each child */
+ }
+ /*
+ * Copy the user property explicitly (in case it contains a
+ * pointer to an allocated area).
+ */
+ memset((char *)ret + bt->propoffset, 0, bt->propsize);
+ bt->propmerge(bt->userstate, NULL, n + bt->maxdegree * 2 + 2,
+ ret + bt->maxdegree * 2 + 2);
+ return ret;
+}
+
+/*
+ * Return the node_addr for a currently locked node. NB that this
+ * means node movement must take place during _locking_ rather than
+ * unlocking!
+ */
+static INLINE node_addr bt_node_addr(btree *bt, nodeptr n)
+{
+ node_addr ret;
+ ret.p = n;
+ return ret;
+}
+
+/*
+ * The bt_write_lock and bt_read_lock functions should gracefully
+ * handle being asked to write-lock a null node pointer, and just
+ * return a null nodeptr.
+ */
+static INLINE nodeptr bt_write_lock_child(btree *bt, nodeptr a, int index)
+{
+ node_addr addr = bt_child(bt, a, index);
+ if (addr.p && addr.p[bt->maxdegree*2+1].i > 1) {
+ nodeptr clone = bt_clone_node(bt, addr.p);
+ bt_set_child(bt, a, index, bt_node_addr(bt, clone));
+ testlock(TRUE, TRUE, clone);
+ return clone;
+ }
+ testlock(TRUE, TRUE, addr.p);
+ return addr.p;
+}
+static INLINE nodeptr bt_write_lock_root(btree *bt)
+{
+ node_addr addr = bt->root;
+ if (addr.p && addr.p[bt->maxdegree*2+1].i > 1) {
+ nodeptr clone = bt_clone_node(bt, addr.p);
+ bt->root = bt_node_addr(bt, clone);
+ testlock(TRUE, TRUE, clone);
+ return clone;
+ }
+ testlock(TRUE, TRUE, addr.p);
+ return addr.p;
+}
+static INLINE nodeptr bt_read_lock(btree *bt, node_addr a)
+{
+ testlock(FALSE, TRUE, a.p);
+ return a.p;
+}
+#define bt_read_lock_root(bt) (bt_read_lock(bt, (bt)->root))
+#define bt_read_lock_child(bt,a,index) (bt_read_lock(bt,bt_child(bt,a,index)))
+
+static INLINE void bt_write_relock(btree *bt, nodeptr n, int props)
+{
+ int i, ns, count;
+
+ /*
+ * Update the count in the node.
+ */
+ ns = bt_subtrees(bt, n);
+ count = ns-1; /* count the elements */
+ for (i = 0; i < ns; i++)
+ count += bt_child_count(bt, n, i);
+ n[bt->maxdegree*2].i = count;
+ testlock(TRUE, FALSE, n);
+ testlock(TRUE, TRUE, n);
+
+ /*
+ * Update user read properties.
+ */
+ if (props && bt->propsize) {
+ void *prevprop, *eltprop, *thisprop, *childprop;
+
+ prevprop = NULL;
+ eltprop = ialloc(bt->propsize);
+ thisprop = (void *)((char *)n + bt->propoffset);
+
+ for (i = 0; i < ns; i++) {
+ /* Merge a subtree's property into this one.
+ * Initially prevprop==NULL, meaning to just copy. */
+ if ( (childprop = bt_child_prop(bt, n, i)) != NULL ) {
+ bt->propmerge(bt->userstate, prevprop, childprop, thisprop);
+ prevprop = thisprop;
+ }
+
+ if (i < ns-1) {
+ /* Now merge in the separating element. */
+ bt->propmake(bt->userstate, bt_element(bt, n, i), eltprop);
+ bt->propmerge(bt->userstate, prevprop, eltprop, thisprop);
+ prevprop = thisprop;
+ }
+ }
+
+ ifree(eltprop);
+ }
+}
+
+static INLINE node_addr bt_write_unlock_internal(btree *bt, nodeptr n,
+ int props)
+{
+ node_addr ret;
+
+ bt_write_relock(bt, n, props);
+
+ testlock(TRUE, FALSE, n);
+
+ ret.p = n;
+ return ret;
+}
+
+static INLINE node_addr bt_write_unlock(btree *bt, nodeptr n)
+{
+ return bt_write_unlock_internal(bt, n, TRUE);
+}
+
+static INLINE void bt_read_unlock(btree *bt, nodeptr n)
+{
+ /*
+ * For trees in memory, we do nothing here, except run some
+ * optional testing.
+ */
+ testlock(FALSE, FALSE, n);
+}
+
+/* ----------------------------------------------------------------------
+ * Higher-level helper functions, which should be independent of
+ * the knowledge of precise node structure in the above code.
+ */
+
+/*
+ * Return the count of items below a node that appear before the
+ * start of a given subtree.
+ */
+static int bt_child_startpos(btree *bt, nodeptr n, int index)
+{
+ int pos = 0;
+
+ while (index > 0) {
+ index--;
+ pos += bt_child_count(bt, n, index) + 1; /* 1 for separating elt */
+ }
+ return pos;
+}
+
+/*
+ * Create a new root node for a tree.
+ */
+static void bt_new_root(btree *bt, node_addr left, node_addr right,
+ bt_element_t element)
+{
+ nodeptr n;
+ n = bt_new_node(bt, 2);
+ bt_set_child(bt, n, 0, left);
+ bt_set_child(bt, n, 1, right);
+ bt_set_element(bt, n, 0, element);
+ bt->root = bt_write_unlock(bt, n);
+ bt->depth++;
+}
+
+/*
+ * Discard the root node of a tree, and enshrine a new node as the
+ * root. Expects to be passed a write-locked nodeptr to the old
+ * root.
+ */
+static void bt_shift_root(btree *bt, nodeptr n, node_addr na)
+{
+ bt_destroy_node(bt, n);
+ bt->root = na;
+ bt->depth--;
+}
+
+/*
+ * Given a numeric index within a node, find which subtree we would
+ * descend to in order to find that index.
+ *
+ * Updates `pos' to give the numeric index within the subtree
+ * found. Also returns `ends' (if non-NULL), which has bit 0 set if
+ * the index is at the very left edge of the subtree, and/or bit 1
+ * if it's at the very right edge.
+ *
+ * Return value is the number of the subtree (0 upwards).
+ */
+#define ENDS_NONE 0
+#define ENDS_LEFT 1
+#define ENDS_RIGHT 2
+#define ENDS_BOTH 3
+static int bt_lookup_pos(btree *bt, nodeptr n, int *pos, int *ends)
+{
+ int child = 0;
+ int nchildren = bt_subtrees(bt, n);
+
+ while (child < nchildren) {
+ int count = bt_child_count(bt, n, child);
+ if (*pos <= count) {
+ if (ends) {
+ *ends = 0;
+ if (*pos == count)
+ *ends |= ENDS_RIGHT;
+ if (*pos == 0)
+ *ends |= ENDS_LEFT;
+ }
+ return child;
+ }
+ *pos -= count + 1; /* 1 for the separating element */
+ child++;
+ }
+ return -1; /* ran off the end; shouldn't happen */
+}
+
+/*
+ * Given an element to search for within a node, find either the
+ * element, or which subtree we would descend to to continue
+ * searching for that element.
+ *
+ * Return value is either the index of the element, or the index of
+ * the subtree (both 0 upwards). `is_elt' returns FALSE or TRUE
+ * respectively.
+ *
+ * Since this may be used by bt_find() with an alternative cmpfn_t,
+ * we always pass the input element as the first argument to cmp.
+ */
+static int bt_lookup_cmp(btree *bt, nodeptr n, bt_element_t element,
+ cmpfn_t cmp, int *is_elt)
+{
+ int mintree = 0, maxtree = bt_subtrees(bt, n)-1;
+
+ while (mintree < maxtree) {
+ int elt = (maxtree + mintree) / 2;
+ int c = cmp(bt->userstate, element, bt_element(bt, n, elt));
+
+ if (c == 0) {
+ *is_elt = TRUE;
+ return elt;
+ } else if (c < 0) {
+ /*
+ * `element' is less than element `elt'. So it can be
+ * in subtree number `elt' at the highest.
+ */
+ maxtree = elt;
+ } else { /* c > 0 */
+ /*
+ * `element' is greater than element `elt'. So it can
+ * be in subtree number (elt+1) at the lowest.
+ */
+ mintree = elt+1;
+ }
+ }
+
+ /*
+ * If we reach here without returning, we must have narrowed
+ * our search to the point where mintree = maxtree. So the
+ * element is not in the node itself and we know which subtree
+ * to search next.
+ */
+ assert(mintree == maxtree);
+ *is_elt = FALSE;
+ return mintree;
+}
+
+/*
+ * Generic transformations on B-tree nodes.
+ *
+ * This function divides essentially into an input side and an
+ * output side. The input side accumulates a list of items
+ * node,element,node,element,...,element,node; the output side
+ * writes those items into either one or two nodes.
+ *
+ * `intype' can be:
+ *
+ * - NODE_AS_IS. The input list is the contents of in1, followed
+ * by inelt, followed by the contents of in2. The `extra'
+ * parameters are unused, as is `inaux'.
+ *
+ * - NODE_ADD_ELT. `in2' is unused. The input list is the contents
+ * of `in1', but with subtree pointer number `inaux' replaced by
+ * extra1/inelt/extra2.
+ *
+ * - NODE_DEL_ELT. `in2' and `inelt' are unused, as is `extra2'.
+ * The input list is the contents of `in1', but with element
+ * pointer number `inaux' and its surrounding two subtrees
+ * replaced by extra1.
+ *
+ * Having obtained the input list, it is then written to one or two
+ * output nodes. If `splitpos' is NODE_JOIN, everything is written
+ * into one output node `out1'. Otherwise, `splitpos' is treated as
+ * an element index within the input list; that element is returned
+ * in `outelt', and the contents of the list is divided there and
+ * returned in nodes `out1' and `out2'.
+ *
+ * This function will re-use nodes in the `obvious' order. If two
+ * nodes are passed in and two nodes are output, they'll be the
+ * same nodes; if one node is passed in and one node output, it
+ * will be the same node too. If two are passed in and only one
+ * output, the first one will be used and the second destroyed; if
+ * one node is passed in and two are output, the one passed in will
+ * be the first of those returned, and the second will be new.
+ */
+#define NODE_AS_IS 1
+#define NODE_ADD_ELT 2
+#define NODE_DEL_ELT 3
+#define NODE_JOIN -1
+static void bt_xform(btree *bt, int intype, int inaux,
+ nodeptr in1, nodeptr in2, bt_element_t inelt,
+ node_addr extra1, node_addr extra2,
+ int splitpos, nodeptr *out1, nodeptr *out2,
+ bt_element_t *outelt)
+{
+ node_addr *nodes;
+ bt_element_t *elements;
+ nodeptr ret1, ret2;
+ int n1, n2, off2, i, j;
+
+ nodes = inewn(node_addr, 2 * bt_max_subtrees(bt));
+ elements = inewn(bt_element_t, 2 * bt_max_subtrees(bt));
+
+ /*
+ * Accumulate the input list.
+ */
+ switch(intype) {
+ case NODE_AS_IS:
+ n1 = bt_subtrees(bt, in1);
+ n2 = bt_subtrees(bt, in2);
+ off2 = 0;
+ break;
+ case NODE_ADD_ELT:
+ in2 = in1;
+ n1 = inaux+1;
+ n2 = bt_subtrees(bt, in1) - inaux;
+ off2 = inaux;
+ break;
+ case NODE_DEL_ELT:
+ in2 = in1;
+ n1 = inaux+1;
+ n2 = bt_subtrees(bt, in1) - inaux - 1;
+ off2 = inaux+1;
+ break;
+ }
+ i = j = 0;
+ while (j < n1) {
+ nodes[i] = bt_child(bt, in1, j);
+ if (j+1 < n1)
+ elements[i] = bt_element(bt, in1, j);
+ i++, j++;
+ }
+ if (intype == NODE_DEL_ELT) {
+ i--;
+ }
+ j = 0;
+ while (j < n2) {
+ nodes[i] = bt_child(bt, in2, off2+j);
+ if (j+1 < n2)
+ elements[i] = bt_element(bt, in2, off2+j);
+ i++, j++;
+ }
+ switch (intype) {
+ case NODE_AS_IS:
+ elements[n1-1] = inelt;
+ break;
+ case NODE_ADD_ELT:
+ nodes[n1-1] = extra1;
+ nodes[n1] = extra2;
+ elements[n1-1] = inelt;
+ break;
+ case NODE_DEL_ELT:
+ nodes[n1-1] = extra1;
+ break;
+ }
+
+ /*
+ * Now determine how many subtrees go in each output node, and
+ * actually create the nodes to be returned.
+ */
+ if (splitpos != NODE_JOIN) {
+ n1 = splitpos+1, n2 = i - splitpos - 1;
+ if (outelt)
+ *outelt = elements[splitpos];
+ } else {
+ n1 = i, n2 = 0;
+ }
+
+ ret1 = bt_reuse_node(bt, in1, n1);
+ if (intype == NODE_AS_IS && in2) {
+ /* We have a second input node. */
+ if (n2)
+ ret2 = bt_reuse_node(bt, in2, n2);
+ else
+ bt_destroy_node(bt, in2);
+ } else {
+ /* We have no second input node. */
+ if (n2)
+ ret2 = bt_new_node(bt, n2);
+ else
+ ret2 = NULL;
+ }
+
+ if (out1) *out1 = ret1;
+ if (out2) *out2 = ret2;
+
+ for (i = 0; i < n1; i++) {
+ bt_set_child(bt, ret1, i, nodes[i]);
+ if (i+1 < n1)
+ bt_set_element(bt, ret1, i, elements[i]);
+ }
+ if (n2) {
+ if (outelt) *outelt = elements[n1-1];
+ for (i = 0; i < n2; i++) {
+ bt_set_child(bt, ret2, i, nodes[n1+i]);
+ if (i+1 < n2)
+ bt_set_element(bt, ret2, i, elements[n1+i]);
+ }
+ }
+
+ ifree(nodes);
+ ifree(elements);
+}
+
+/*
+ * Fiddly little compare functions for use in special cases of
+ * findrelpos. One always returns +1 (a > b), the other always
+ * returns -1 (a < b).
+ */
+static int bt_cmp_greater(void *state,
+ const bt_element_t a, const bt_element_t b)
+{
+ return +1;
+}
+static int bt_cmp_less(void *state,
+ const bt_element_t a, const bt_element_t b)
+{
+ return -1;
+}
+
+/* ----------------------------------------------------------------------
+ * User-visible administration routines.
+ */
+
+btree *bt_new(cmpfn_t cmp, copyfn_t copy, freefn_t freeelt,
+ int propsize, int propalign, propmakefn_t propmake,
+ propmergefn_t propmerge, void *state, int mindegree)
+{
+ btree *ret;
+
+ ret = new1(btree);
+ ret->mindegree = mindegree;
+ ret->maxdegree = 2*mindegree;
+ ret->depth = 0; /* not even a root right now */
+ ret->root = NODE_ADDR_NULL;
+ ret->cmp = cmp;
+ ret->copy = copy;
+ ret->freeelt = freeelt;
+ ret->propsize = propsize;
+ ret->propalign = propalign;
+ ret->propoffset = sizeof(nodecomponent) * (ret->maxdegree*2 + 2);
+ if (propalign > 0) {
+ ret->propoffset += propalign - 1;
+ ret->propoffset -= ret->propoffset % propalign;
+ }
+ ret->propmake = propmake;
+ ret->propmerge = propmerge;
+ ret->userstate = state;
+
+ return ret;
+}
+
+static void bt_free_node(btree *bt, nodeptr n)
+{
+ int i;
+
+ for (i = 0; i < bt_subtrees(bt, n); i++) {
+ node_addr na;
+ nodeptr n2;
+
+ na = bt_child(bt, n, i);
+ if (!bt_unref_node(bt, na)) {
+ n2 = bt_write_lock_child(bt, n, i);
+ bt_free_node(bt, n2);
+ }
+ }
+
+ if (bt->freeelt) {
+ for (i = 0; i < bt_subtrees(bt, n)-1; i++)
+ bt->freeelt(bt->userstate, bt_element(bt, n, i));
+ }
+
+ bt_destroy_node(bt, n);
+}
+
+void bt_free(btree *bt)
+{
+ nodeptr n;
+
+ if (!bt_unref_node(bt, bt->root)) {
+ n = bt_write_lock_root(bt);
+ bt_free_node(bt, n);
+ }
+
+ sfree(bt);
+}
+
+btree *bt_clone(btree *bt)
+{
+ btree *bt2;
+
+ bt2 = bt_new(bt->cmp, bt->copy, bt->freeelt, bt->propsize, bt->propalign,
+ bt->propmake, bt->propmerge, bt->userstate, bt->mindegree);
+ bt2->depth = bt->depth;
+ bt2->root = bt_ref_node(bt, bt->root);
+ return bt2;
+}
+
+/*
+ * Nice simple function to count the size of a tree.
+ */
+int bt_count(btree *bt)
+{
+ int count;
+ nodeptr n;
+
+ n = bt_read_lock_root(bt);
+ if (n) {
+ count = bt_node_count(bt, n);
+ bt_read_unlock(bt, n);
+ return count;
+ } else {
+ return 0;
+ }
+}
+
+/* ----------------------------------------------------------------------
+ * Actual B-tree algorithms.
+ */
+
+/*
+ * Find an element by numeric index. bt_index_w is the same, but
+ * works with write locks instead of read locks, so it guarantees
+ * to return an element with only one reference to it. (You'd use
+ * this if you were using tree cloning, and wanted to modify the
+ * element once you'd found it.)
+ */
+bt_element_t bt_index(btree *bt, int index)
+{
+ nodeptr n, n2;
+ int child, ends;
+
+ n = bt_read_lock_root(bt);
+
+ if (index < 0 || index >= bt_node_count(bt, n)) {
+ bt_read_unlock(bt, n);
+ return NULL;
+ }
+
+ while (1) {
+ child = bt_lookup_pos(bt, n, &index, &ends);
+ if (ends & ENDS_RIGHT) {
+ bt_element_t ret = bt_element(bt, n, child);
+ bt_read_unlock(bt, n);
+ return ret;
+ }
+ n2 = bt_read_lock_child(bt, n, child);
+ bt_read_unlock(bt, n);
+ n = n2;
+ assert(n != NULL);
+ }
+}
+
+bt_element_t bt_index_w(btree *bt, int index)
+{
+ nodeptr n, n2;
+ int nnodes, child, ends;
+ nodeptr *nodes;
+ bt_element_t ret;
+
+ nodes = inewn(nodeptr, bt->depth+1);
+ nnodes = 0;
+
+ n = bt_write_lock_root(bt);
+
+ if (index < 0 || index >= bt_node_count(bt, n)) {
+ bt_write_unlock(bt, n);
+ return NULL;
+ }
+
+ while (1) {
+ nodes[nnodes++] = n;
+ child = bt_lookup_pos(bt, n, &index, &ends);
+ if (ends & ENDS_RIGHT) {
+ ret = bt_element(bt, n, child);
+ break;
+ }
+ n2 = bt_write_lock_child(bt, n, child);
+ n = n2;
+ assert(n != NULL);
+ }
+
+ while (nnodes-- > 0)
+ bt_write_unlock(bt, nodes[nnodes]);
+
+ return ret;
+}
+
+/*
+ * Search for an element by sorted order.
+ */
+bt_element_t bt_findrelpos(btree *bt, bt_element_t element, cmpfn_t cmp,
+ int relation, int *index)
+{
+ nodeptr n, n2;
+ int child, is_elt;
+ bt_element_t gotit;
+ int pos = 0;
+ int count;
+
+ if (!cmp) cmp = bt->cmp;
+
+ /*
+ * Special case: relation LT/GT and element NULL means get an
+ * extreme element of the tree. We do this by fudging the
+ * compare function so that our NULL element will be considered
+ * infinitely large or infinitely small.
+ */
+ if (element == NULL) {
+ assert(relation == BT_REL_LT || relation == BT_REL_GT);
+ if (relation == BT_REL_LT)
+ cmp = bt_cmp_greater; /* always returns a > b */
+ else
+ cmp = bt_cmp_less; /* always returns a < b */
+ }
+
+ gotit = NULL;
+ n = bt_read_lock_root(bt);
+ if (!n)
+ return NULL;
+ count = bt_node_count(bt, n);
+ while (n) {
+ child = bt_lookup_cmp(bt, n, element, cmp, &is_elt);
+ if (is_elt) {
+ pos += bt_child_startpos(bt, n, child+1) - 1;
+ gotit = bt_element(bt, n, child);
+ bt_read_unlock(bt, n);
+ break;
+ } else {
+ pos += bt_child_startpos(bt, n, child);
+ n2 = bt_read_lock_child(bt, n, child);
+ bt_read_unlock(bt, n);
+ n = n2;
+ }
+ }
+
+ /*
+ * Now all nodes are unlocked, and we are _either_ (a) holding
+ * an element in `gotit' whose index we have in `pos', _or_ (b)
+ * holding nothing in `gotit' but we know the index of the
+ * next-higher element.
+ */
+ if (gotit) {
+ /*
+ * We have the real element. For EQ, LE and GE relations we
+ * can now just return it; otherwise we must return the
+ * next element down or up.
+ */
+ if (relation == BT_REL_LT)
+ gotit = bt_index(bt, --pos);
+ else if (relation == BT_REL_GT)
+ gotit = bt_index(bt, ++pos);
+ } else {
+ /*
+ * We don't have the real element. For EQ relation we now
+ * just give up; for everything else we return the next
+ * element down or up.
+ */
+ if (relation == BT_REL_LT || relation == BT_REL_LE)
+ gotit = bt_index(bt, --pos);
+ else if (relation == BT_REL_GT || relation == BT_REL_GE)
+ gotit = bt_index(bt, pos);
+ }
+
+ if (gotit && index) *index = pos;
+ return gotit;
+}
+bt_element_t bt_findrel(btree *bt, bt_element_t element, cmpfn_t cmp,
+ int relation)
+{
+ return bt_findrelpos(bt, element, cmp, relation, NULL);
+}
+bt_element_t bt_findpos(btree *bt, bt_element_t element, cmpfn_t cmp,
+ int *index)
+{
+ return bt_findrelpos(bt, element, cmp, BT_REL_EQ, index);
+}
+bt_element_t bt_find(btree *bt, bt_element_t element, cmpfn_t cmp)
+{
+ return bt_findrelpos(bt, element, cmp, BT_REL_EQ, NULL);
+}
+
+/*
+ * Find an element by property-based search. Returns the element
+ * (if one is selected - the search can also terminate by
+ * descending to a nonexistent subtree of a leaf node, equivalent
+ * to selecting the _gap_ between two elements); also returns the
+ * index of either the element or the gap in `*index' if `index' is
+ * non-NULL.
+ */
+bt_element_t bt_propfind(btree *bt, searchfn_t search, void *sstate,
+ int *index)
+{
+ nodeptr n, n2;
+ int i, j, count, is_elt;
+ void **props;
+ int *counts;
+ bt_element_t *elts;
+ bt_element_t *e = NULL;
+
+ props = inewn(void *, bt->maxdegree);
+ counts = inewn(int, bt->maxdegree);
+ elts = inewn(bt_element_t, bt->maxdegree);
+
+ n = bt_read_lock_root(bt);
+
+ count = 0;
+
+ while (n) {
+ int ntrees = bt_subtrees(bt, n);
+
+ /*
+ * Prepare the arguments to the search function.
+ */
+ for (i = 0; i < ntrees; i++) {
+ props[i] = bt_child_prop(bt, n, i);
+ counts[i] = bt_child_count(bt, n, i);
+ if (i < ntrees-1)
+ elts[i] = bt_element(bt, n, i);
+ }
+
+ /*
+ * Call the search function.
+ */
+ i = search(bt->userstate, sstate, ntrees,
+ props, counts, elts, &is_elt);
+
+ if (!is_elt) {
+ /*
+ * Descend to subtree i. Update `count' to consider
+ * everything (both subtrees and elements) before that
+ * subtree.
+ */
+ for (j = 0; j < i; j++)
+ count += 1 + bt_child_count(bt, n, j);
+ n2 = bt_read_lock_child(bt, n, i);
+ bt_read_unlock(bt, n);
+ n = n2;
+ } else {
+ /*
+ * Return element i. Update `count' to consider
+ * everything (both subtrees and elements) before that
+ * element.
+ */
+ for (j = 0; j <= i; j++)
+ count += 1 + bt_child_count(bt, n, j);
+ count--; /* don't count element i itself */
+ e = bt_element(bt, n, i);
+ bt_read_unlock(bt, n);
+ break;
+ }
+ }
+
+ ifree(props);
+ ifree(counts);
+ ifree(elts);
+
+ if (index) *index = count;
+ return e;
+}
+
+/*
+ * Replace the element at a numeric index by a new element. Returns
+ * the old element.
+ *
+ * Can also be used when the new element is the _same_ as the old
+ * element, but has changed in some way that will affect user
+ * properties.
+ */
+bt_element_t bt_replace(btree *bt, bt_element_t element, int index)
+{
+ nodeptr n;
+ nodeptr *nodes;
+ bt_element_t ret;
+ int nnodes, child, ends;
+
+ nodes = inewn(nodeptr, bt->depth+1);
+ nnodes = 0;
+
+ n = bt_write_lock_root(bt);
+
+ if (index < 0 || index >= bt_node_count(bt, n)) {
+ bt_write_unlock(bt, n);
+ return NULL;
+ }
+
+ while (1) {
+ nodes[nnodes++] = n;
+ child = bt_lookup_pos(bt, n, &index, &ends);
+ if (ends & ENDS_RIGHT) {
+ ret = bt_element(bt, n, child);
+ bt_set_element(bt, n, child, element);
+ break;
+ }
+ n = bt_write_lock_child(bt, n, child);
+ assert(n != NULL);
+ }
+
+ while (nnodes-- > 0)
+ bt_write_unlock(bt, nodes[nnodes]);
+
+ return ret;
+}
+
+/*
+ * Add at a specific position. As we search down the tree we must
+ * write-lock every node we meet, since otherwise we might fail to
+ * clone nodes that will end up pointing to different things.
+ */
+void bt_addpos(btree *bt, bt_element_t element, int pos)
+{
+ nodeptr n;
+ node_addr left, right, single;
+ nodeptr *nodes;
+ int *childposns;
+ int nnodes, child;
+
+ /*
+ * Since in a reference-counted tree we can't have parent
+ * links, we will have to use O(depth) space to store the list
+ * of nodeptrs we have gone through, so we can un-write-lock
+ * them when we've finished. We also store the subtree index we
+ * descended to at each stage.
+ */
+ nodes = inewn(nodeptr, bt->depth+1);
+ childposns = inewn(int, bt->depth+1);
+ nnodes = 0;
+
+ n = bt_write_lock_root(bt);
+
+ assert(pos >= 0 && pos <= (n ? bt_node_count(bt, n) : 0));
+
+ /*
+ * Scan down the tree, write-locking nodes, until we find the
+ * empty subtree where we want to insert the item.
+ */
+ while (n) {
+ nodes[nnodes] = n;
+ child = bt_lookup_pos(bt, n, &pos, NULL);
+ childposns[nnodes] = child;
+ nnodes++;
+ n = bt_write_lock_child(bt, n, child);
+ }
+
+ left = right = NODE_ADDR_NULL;
+
+ /*
+ * Now nodes[nnodes-1] wants to have subtree index
+ * childposns[nnodes-1] replaced by the node/element/node triple
+ * (left,element,right). Propagate this up the tree until we
+ * can stop.
+ */
+ while (nnodes-- > 0) {
+ n = nodes[nnodes];
+ if (bt_subtrees(bt, n) == bt_max_subtrees(bt)) {
+ nodeptr lptr, rptr;
+ /* Split the node and carry on up. */
+ bt_xform(bt, NODE_ADD_ELT, childposns[nnodes],
+ n, NULL, element, left, right,
+ bt_min_subtrees(bt), &lptr, &rptr, &element);
+ left = bt_write_unlock(bt, lptr);
+ right = bt_write_unlock(bt, rptr);
+ } else {
+ bt_xform(bt, NODE_ADD_ELT, childposns[nnodes],
+ n, NULL, element, left, right,
+ NODE_JOIN, &n, NULL, NULL);
+ single = bt_write_unlock(bt, n);
+ break;
+ }
+ }
+
+ /*
+ * If nnodes < 0, we have just split the root and we need to
+ * build a new root node.
+ */
+ if (nnodes < 0) {
+ bt_new_root(bt, left, right, element);
+ } else {
+ /*
+ * Now nodes[nnodes-1] just wants to have child pointer
+ * child[nnodes-1] replaced by `single', in case the
+ * subtree was moved. Propagate this back up to the root,
+ * unlocking all nodes.
+ */
+ while (nnodes-- > 0) {
+ bt_set_child(bt, nodes[nnodes], childposns[nnodes], single);
+ single = bt_write_unlock(bt, nodes[nnodes]);
+ }
+ }
+
+ ifree(nodes);
+ ifree(childposns);
+}
+
+/*
+ * Add an element in sorted order. This is a wrapper on bt_addpos()
+ * which finds the numeric index to add the item at and then calls
+ * addpos. This isn't an optimal use of time, but it saves space by
+ * avoiding starting to clone multiply-linked nodes until it's
+ * known that the item _can_ be added to the tree (and isn't
+ * duplicated in it already).
+ */
+bt_element_t bt_add(btree *bt, bt_element_t element)
+{
+ nodeptr n, n2;
+ int child, is_elt;
+ int pos = 0;
+
+ n = bt_read_lock_root(bt);
+ while (n) {
+ child = bt_lookup_cmp(bt, n, element, bt->cmp, &is_elt);
+ if (is_elt) {
+ bt_read_unlock(bt, n);
+ return bt_element(bt, n, child); /* element exists already */
+ } else {
+ pos += bt_child_startpos(bt, n, child);
+ n2 = bt_read_lock_child(bt, n, child);
+ bt_read_unlock(bt, n);
+ n = n2;
+ }
+ }
+ bt_addpos(bt, element, pos);
+ return element;
+}
+
+/*
+ * Delete an element given its numeric position. Returns the
+ * element deleted.
+ */
+bt_element_t bt_delpos(btree *bt, int pos)
+{
+ nodeptr n, c, c2, saved_n;
+ nodeptr *nodes;
+ int nnodes, child, nroot, pos2, ends, st, splitpoint, saved_pos;
+ bt_element_t e, ret;
+
+ /*
+ * Just like in bt_add, we store the set of nodeptrs we
+ * write-locked on the way down, so we can unlock them on the
+ * way back up.
+ */
+ nodes = inewn(nodeptr, bt->depth+1);
+ nnodes = 0;
+
+ n = bt_write_lock_root(bt);
+ nroot = TRUE;
+ saved_n = NULL;
+
+ if (!n || pos < 0 || pos >= bt_node_count(bt, n)) {
+ if (n)
+ bt_write_unlock(bt, n);
+ return NULL;
+ }
+
+ while (1) {
+ nodes[nnodes++] = n;
+
+ /*
+ * Find out which subtree to descend to.
+ */
+ pos2 = pos;
+ child = bt_lookup_pos(bt, n, &pos, &ends);
+ c = bt_write_lock_child(bt, n, child);
+ if (c && bt_subtrees(bt, c) == bt_min_subtrees(bt)) {
+ /*
+ * We're trying to descend to a subtree that's of
+ * minimum size. Do something!
+ */
+ if (child > 0) {
+ /*
+ * Either move a subtree from the left sibling, or
+ * merge with it. (Traditionally we would only
+ * merge if we can't move a subtree from _either_
+ * sibling, but this way avoids too many extra
+ * write locks.)
+ */
+ c2 = c;
+ c = bt_write_lock_child(bt, n, child-1);
+ e = bt_element(bt, n, child-1);
+ st = bt_subtrees(bt, c);
+ if (st > bt_min_subtrees(bt))
+ splitpoint = st - 2;
+ else
+ splitpoint = NODE_JOIN;
+ child--;
+ } else {
+ /*
+ * Likewise on the right-hand side.
+ */
+ c2 = bt_write_lock_child(bt, n, child+1);
+ e = bt_element(bt, n, child);
+ st = bt_subtrees(bt, c2);
+ if (st > bt_min_subtrees(bt))
+ splitpoint = bt_min_subtrees(bt);
+ else
+ splitpoint = NODE_JOIN;
+ }
+
+ if (splitpoint == NODE_JOIN) {
+ /*
+ * So if we're merging nodes, go to it...
+ */
+ bt_xform(bt, NODE_AS_IS, 0,
+ c, c2, e, NODE_ADDR_NULL, NODE_ADDR_NULL,
+ NODE_JOIN, &c, NULL, NULL);
+ bt_xform(bt, NODE_DEL_ELT, child,
+ n, NULL, NULL, bt_node_addr(bt, c), NODE_ADDR_NULL,
+ NODE_JOIN, &n, NULL, NULL);
+ if (nroot && bt_subtrees(bt, n) == 1) {
+ /*
+ * Whoops, we just merged the last two children
+ * of the root. Better relocate the root.
+ */
+ bt_shift_root(bt, n, bt_node_addr(bt, c));
+ nnodes--; /* don't leave it in nodes[]! */
+ n = NULL;
+ bt_write_relock(bt, c, TRUE);
+ } else
+ bt_write_unlock(bt, c);
+ } else {
+ /*
+ * Or if we're redistributing subtrees, go to that.
+ */
+ bt_xform(bt, NODE_AS_IS, 0,
+ c, c2, e, NODE_ADDR_NULL, NODE_ADDR_NULL,
+ splitpoint, &c, &c2, &e);
+ bt_set_element(bt, n, child, e);
+ bt_write_unlock(bt, c);
+ bt_write_unlock(bt, c2);
+ }
+
+ if (n) {
+ /* Recompute the counts in n so we can do lookups again. */
+ bt_write_relock(bt, n, TRUE);
+
+ /* Having done the transform, redo the position lookup. */
+ pos = pos2;
+ child = bt_lookup_pos(bt, n, &pos, &ends);
+ c = bt_write_lock_child(bt, n, child);
+ } else {
+ pos = pos2;
+ }
+ }
+
+ /*
+ * Now see if this node contains the element we're
+ * looking for.
+ */
+ if (n && (ends & ENDS_RIGHT)) {
+ /*
+ * It does. Element number `child' is the element we
+ * want to delete. See if this is a leaf node...
+ */
+ if (!bt_is_leaf(bt, n)) {
+ /*
+ * It's not a leaf node. So we save the nodeptr and
+ * element index for later reference, and decrement
+ * `pos' so that we're searching for the element to its
+ * left, which _will_ be in a leaf node.
+ */
+ saved_n = n;
+ saved_pos = child;
+ pos--;
+ } else {
+ /*
+ * We've reached a leaf node. Check to see if an
+ * internal-node position was stored in saved_n and
+ * saved_pos, and move this element there if so.
+ */
+ if (saved_n) {
+ ret = bt_element(bt, saved_n, saved_pos);
+ bt_set_element(bt, saved_n, saved_pos,
+ bt_element(bt, n, child));
+ } else {
+ ret = bt_element(bt, n, child);
+ }
+ /* Then delete it from the leaf node. */
+ bt_xform(bt, NODE_DEL_ELT, child,
+ n, NULL, NULL, NODE_ADDR_NULL, NODE_ADDR_NULL,
+ NODE_JOIN, &n, NULL, NULL);
+ /*
+ * Final special case: if this is the root node and
+ * we've just deleted its last element, we should
+ * destroy it and leave a completely empty tree.
+ */
+ if (nroot && bt_subtrees(bt, n) == 1) {
+ bt_shift_root(bt, n, NODE_ADDR_NULL);
+ nnodes--; /* and take it out of nodes[] */
+ }
+ /* Now we're done */
+ break;
+ }
+ }
+
+ /* Descend to the child and go round again. */
+ n = c;
+ nroot = FALSE;
+ }
+
+ /*
+ * All done. Zip back up the tree un-write-locking nodes.
+ */
+ while (nnodes-- > 0)
+ bt_write_unlock(bt, nodes[nnodes]);
+
+ ifree(nodes);
+
+ return ret;
+}
+
+/*
+ * Delete an element in sorted order.
+ */
+bt_element_t bt_del(btree *bt, bt_element_t element)
+{
+ int index;
+ if (!bt_findrelpos(bt, element, NULL, BT_REL_EQ, &index))
+ return NULL; /* wasn't there */
+ return bt_delpos(bt, index);
+}
+
+/*
+ * Join two trees together, given their respective depths and a
+ * middle element. Puts the resulting tree in the root of `bt'.
+ *
+ * This internal routine assumes that the trees have the same
+ * degree.
+ *
+ * The input nodeptrs are assumed to be write-locked, but none of
+ * their children are yet write-locked.
+ */
+static void bt_join_internal(btree *bt, nodeptr lp, nodeptr rp,
+ bt_element_t sep, int ld, int rd)
+{
+ nodeptr *nodes;
+ int *childposns;
+ int nnodes, nodessize;
+ int lsub, rsub;
+
+ /*
+ * We will need to store parent nodes up to the difference
+ * between ld and rd.
+ */
+ nodessize = (ld < rd ? rd-ld : ld-rd);
+ if (nodessize) { /* we may not need _any_! */
+ nodes = inewn(nodeptr, nodessize);
+ childposns = inewn(int, nodessize);
+ }
+ nnodes = 0;
+
+ if (ld > rd) {
+ bt->root = bt_node_addr(bt, lp);
+ bt->depth = ld;
+ /* If the left tree is taller, search down its right-hand edge. */
+ while (ld > rd) {
+ int child = bt_subtrees(bt, lp) - 1;
+ nodeptr n = bt_write_lock_child(bt, lp, child);
+ nodes[nnodes] = lp;
+ childposns[nnodes] = child;
+ nnodes++;
+ lp = n;
+ ld--;
+ }
+ } else {
+ bt->root = bt_node_addr(bt, rp);
+ bt->depth = rd;
+ /* If the right tree is taller, search down its left-hand edge. */
+ while (rd > ld) {
+ nodeptr n = bt_write_lock_child(bt, rp, 0);
+ nodes[nnodes] = rp;
+ childposns[nnodes] = 0;
+ nnodes++;
+ rp = n;
+ rd--;
+ }
+ }
+
+ /*
+ * So we now want to combine nodes lp and rp into either one or
+ * two plausibly-sized nodes, whichever is feasible. We have a
+ * joining element `sep'.
+ */
+ lsub = (lp ? bt_subtrees(bt, lp) : 0);
+ rsub = (rp ? bt_subtrees(bt, rp) : 0);
+ if (lp && rp && lsub + rsub <= bt_max_subtrees(bt)) {
+ node_addr la;
+ /* Join the nodes into one. */
+ bt_xform(bt, NODE_AS_IS, 0, lp, rp, sep,
+ NODE_ADDR_NULL, NODE_ADDR_NULL,
+ NODE_JOIN, &lp, NULL, NULL);
+ /* Unlock the node. */
+ la = bt_write_unlock(bt, lp);
+ /* Update the child pointer in the next node up. */
+ if (nnodes > 0)
+ bt_set_child(bt, nodes[nnodes-1], childposns[nnodes-1], la);
+ else
+ bt->root = la;
+ } else {
+ node_addr la, ra;
+ if (!lp || !rp) {
+ la = NODE_ADDR_NULL;
+ ra = NODE_ADDR_NULL;
+ } else {
+ int lsize, rsize;
+ /* Re-split the nodes into two plausibly sized ones. */
+ lsize = lsub + rsub;
+ rsize = lsize / 2;
+ lsize -= rsize;
+ bt_xform(bt, NODE_AS_IS, 0, lp, rp, sep,
+ NODE_ADDR_NULL, NODE_ADDR_NULL,
+ lsize-1, &lp, &rp, &sep);
+ /* Unlock the nodes. */
+ la = bt_write_unlock(bt, lp);
+ ra = bt_write_unlock(bt, rp);
+ }
+
+ /*
+ * Now we have to do the addition thing: progress up the
+ * tree replacing a single subtree pointer with the
+ * la/sep/ra assembly, until no more nodes have to split as
+ * a result.
+ */
+ while (nnodes-- > 0) {
+ nodeptr n = nodes[nnodes];
+ if (bt_subtrees(bt, n) == bt_max_subtrees(bt)) {
+ /* Split the node and carry on up. */
+ bt_xform(bt, NODE_ADD_ELT, childposns[nnodes],
+ n, NULL, sep, la, ra,
+ bt_min_subtrees(bt), &lp, &rp, &sep);
+ la = bt_write_unlock(bt, lp);
+ ra = bt_write_unlock(bt, rp);
+ } else {
+ bt_xform(bt, NODE_ADD_ELT, childposns[nnodes],
+ n, NULL, sep, la, ra,
+ NODE_JOIN, &n, NULL, NULL);
+ bt_write_unlock(bt, n);
+ break;
+ }
+ }
+
+ /*
+ * If nnodes < 0, we have just split the root and we need
+ * to build a new root node.
+ */
+ if (nnodes < 0)
+ bt_new_root(bt, la, ra, sep);
+ }
+
+ /*
+ * Now we just need to go back up and unlock any remaining
+ * nodes. Also here we ensure the root points where it should.
+ */
+ while (nnodes-- > 0) {
+ node_addr na;
+ na = bt_write_unlock(bt, nodes[nnodes]);
+ if (nnodes == 0)
+ bt->root = na;
+ }
+
+ if (nodessize) {
+ ifree(nodes);
+ ifree(childposns);
+ }
+}
+
+/*
+ * External interfaces to the join functionality: join and joinr
+ * (differing only in which B-tree structure they leave without any
+ * elements, and which they return the combined tree in).
+ */
+btree *bt_join(btree *bt1, btree *bt2)
+{
+ nodeptr root1, root2;
+ int size2;
+
+ size2 = bt_count(bt2);
+ if (size2 > 0) {
+ bt_element_t sep;
+
+ if (bt1->cmp) {
+ /*
+ * The trees are ordered, so verify the ordering
+ * condition: ensure nothing in bt1 is greater than or
+ * equal to the minimum element in bt2.
+ */
+ sep = bt_index(bt2, 0);
+ sep = bt_findrelpos(bt1, sep, NULL, BT_REL_GE, NULL);
+ if (sep)
+ return NULL;
+ }
+
+ sep = bt_delpos(bt2, 0);
+ root1 = bt_write_lock_root(bt1);
+ root2 = bt_write_lock_root(bt2);
+ bt_join_internal(bt1, root1, root2, sep, bt1->depth, bt2->depth);
+ bt2->root = NODE_ADDR_NULL;
+ bt2->depth = 0;
+ }
+ return bt1;
+}
+
+btree *bt_joinr(btree *bt1, btree *bt2)
+{
+ nodeptr root1, root2;
+ int size1;
+
+ size1 = bt_count(bt1);
+ if (size1 > 0) {
+ bt_element_t sep;
+
+ if (bt2->cmp) {
+ /*
+ * The trees are ordered, so verify the ordering
+ * condition: ensure nothing in bt2 is less than or
+ * equal to the maximum element in bt1.
+ */
+ sep = bt_index(bt1, size1-1);
+ sep = bt_findrelpos(bt2, sep, NULL, BT_REL_LE, NULL);
+ if (sep)
+ return NULL;
+ }
+
+ sep = bt_delpos(bt1, size1-1);
+ root1 = bt_write_lock_root(bt1);
+ root2 = bt_write_lock_root(bt2);
+ bt_join_internal(bt2, root1, root2, sep, bt1->depth, bt2->depth);
+ bt1->root = NODE_ADDR_NULL;
+ bt1->depth = 0;
+ }
+ return bt2;
+}
+
+/*
+ * Perform the healing process after a tree has been split. `rhs'
+ * is set if the cut edge is the one on the right.
+ */
+static void bt_split_heal(btree *bt, int rhs)
+{
+ nodeptr n;
+ nodeptr *nodes;
+ int nnodes;
+
+ nodes = inewn(nodeptr, bt->depth);
+ nnodes = 0;
+
+ n = bt_write_lock_root(bt);
+
+ /*
+ * First dispense with completely trivial cases: a root node
+ * containing only one subtree can be thrown away instantly.
+ */
+ while (n && bt_subtrees(bt, n) == 1) {
+ nodeptr n2 = bt_write_lock_child(bt, n, 0);
+ bt_shift_root(bt, n, bt_node_addr(bt, n2));
+ n = n2;
+ }
+
+ /*
+ * Now we have a plausible root node. Start going down the cut
+ * edge looking for undersized or minimum nodes, and arranging
+ * for them to be above minimum size.
+ */
+ while (n) {
+ int edge, next, elt, size_e, size_n, size_total;
+ nodeptr ne, nn, nl, nr;
+ bt_element_t el;
+
+ nodes[nnodes++] = n;
+
+ if (rhs) {
+ edge = bt_subtrees(bt, n) - 1;
+ next = edge - 1;
+ elt = next;
+ } else {
+ edge = 0;
+ next = 1;
+ elt = edge;
+ }
+
+ ne = bt_write_lock_child(bt, n, edge);
+ if (!ne)
+ break;
+
+ size_e = bt_subtrees(bt, ne);
+
+ if (size_e <= bt_min_subtrees(bt)) {
+ nn = bt_write_lock_child(bt, n, next);
+ el = bt_element(bt, n, elt);
+ size_n = bt_subtrees(bt, nn);
+ if (edge < next)
+ nl = ne, nr = nn;
+ else
+ nl = nn, nr = ne;
+ size_total = size_e + size_n;
+ if (size_e + size_n <= bt_max_subtrees(bt)) {
+ /*
+ * Merge the edge node and its sibling together.
+ */
+ bt_xform(bt, NODE_AS_IS, 0, nl, nr, el,
+ NODE_ADDR_NULL, NODE_ADDR_NULL,
+ NODE_JOIN, &ne, NULL, NULL);
+ bt_xform(bt, NODE_DEL_ELT, elt, n, NULL, NULL,
+ bt_node_addr(bt, ne), NODE_ADDR_NULL,
+ NODE_JOIN, &n, NULL, NULL);
+ /*
+ * It's possible we've just trashed the root of the
+ * tree, again.
+ */
+ if (bt_subtrees(bt, n) == 1) {
+ bt_shift_root(bt, n, bt_node_addr(bt, ne));
+ nnodes--; /* and take it out of nodes[] */
+ }
+ } else {
+ /*
+ * Redistribute subtrees between the edge node and
+ * its sibling.
+ */
+ int split;
+ size_e = (size_total + 1) / 2;
+ assert(size_e > bt_min_subtrees(bt));
+ if (next < edge)
+ split = size_total - size_e - 1;
+ else
+ split = size_e - 1;
+ bt_xform(bt, NODE_AS_IS, 0, nl, nr, el,
+ NODE_ADDR_NULL, NODE_ADDR_NULL,
+ split, &nl, &nr, &el);
+ bt_write_unlock(bt, nn);
+ bt_set_element(bt, n, elt, el);
+ }
+ }
+
+ n = ne;
+ }
+
+ /*
+ * Now we just need to go back up and unlock any remaining
+ * nodes.
+ */
+ while (nnodes-- > 0)
+ bt_write_unlock(bt, nodes[nnodes]);
+
+ ifree(nodes);
+}
+
+/*
+ * Split a tree by numeric position. The new tree returned is the
+ * one on the right; the original tree contains the stuff on the
+ * left.
+ */
+static btree *bt_split_internal(btree *bt1, int index)
+{
+ btree *bt2;
+ nodeptr *lnodes, *rnodes;
+ nodeptr n1, n2, n;
+ int nnodes, child;
+
+ bt2 = bt_new(bt1->cmp, bt1->copy, bt1->freeelt, bt1->propsize,
+ bt1->propalign, bt1->propmake, bt1->propmerge,
+ bt1->userstate, bt1->mindegree);
+ bt2->depth = bt1->depth;
+
+ lnodes = inewn(nodeptr, bt1->depth);
+ rnodes = inewn(nodeptr, bt2->depth);
+ nnodes = 0;
+
+ n1 = bt_write_lock_root(bt1);
+ while (n1) {
+ child = bt_lookup_pos(bt1, n1, &index, NULL);
+ n = bt_write_lock_child(bt1, n1, child);
+ bt_xform(bt1, NODE_ADD_ELT, child, n1, NULL, NULL,
+ bt_node_addr(bt1, n), NODE_ADDR_NULL,
+ child, &n1, &n2, NULL);
+ lnodes[nnodes] = n1;
+ rnodes[nnodes] = n2;
+ if (nnodes > 0)
+ bt_set_child(bt2, rnodes[nnodes-1], 0, bt_node_addr(bt2, n2));
+ else
+ bt2->root = bt_node_addr(bt2, n2);
+ nnodes++;
+ n1 = n;
+ }
+
+ /*
+ * Now we go back up and unlock all the nodes. At this point we
+ * don't mess with user properties, because there's the danger
+ * of a node containing no subtrees _or_ elements and hence us
+ * having to invent a notation for an empty property. We're
+ * going to make a second healing pass in a moment anyway,
+ * which will sort all that out for us.
+ */
+ while (nnodes-- > 0) {
+ bt_write_unlock_internal(bt1, lnodes[nnodes], FALSE);
+ bt_write_unlock_internal(bt2, rnodes[nnodes], FALSE);
+ }
+
+ /*
+ * Then we make a healing pass down each side of the tree.
+ */
+ bt_split_heal(bt1, TRUE);
+ bt_split_heal(bt2, FALSE);
+
+ ifree(lnodes);
+ ifree(rnodes);
+
+ return bt2;
+}
+
+/*
+ * Split a tree at a numeric index.
+ */
+btree *bt_splitpos(btree *bt, int index, int before)
+{
+ btree *ret;
+ node_addr na;
+ int count, nd;
+ nodeptr n;
+
+ n = bt_read_lock_root(bt);
+ count = (n ? bt_node_count(bt, n) : 0);
+ bt_read_unlock(bt, n);
+
+ if (index < 0 || index > count)
+ return NULL;
+
+ ret = bt_split_internal(bt, index);
+ if (before) {
+ na = bt->root;
+ bt->root = ret->root;
+ ret->root = na;
+
+ nd = bt->depth;
+ bt->depth = ret->depth;
+ ret->depth = nd;
+ }
+ return ret;
+}
+
+/*
+ * Split a tree at a position dictated by the sorting order.
+ */
+btree *bt_split(btree *bt, bt_element_t element, cmpfn_t cmp, int rel)
+{
+ int before, index;
+
+ assert(rel != BT_REL_EQ); /* has to be an inequality */
+
+ if (rel == BT_REL_GT || rel == BT_REL_GE) {
+ before = TRUE;
+ rel = (rel == BT_REL_GT ? BT_REL_LE : BT_REL_LT);
+ } else {
+ before = FALSE;
+ }
+ if (!bt_findrelpos(bt, element, cmp, rel, &index))
+ index = -1;
+ return bt_splitpos(bt, index+1, before);
+}
+
+#ifdef TEST
+
+#define TEST_DEGREE 4
+#define BT_COPY bt_clone
+#define MAXTREESIZE 10000
+#define MAXLOCKS 100
+
+int errors;
+
+/*
+ * Error reporting function.
+ */
+void error(char *fmt, ...) {
+ va_list ap;
+ fprintf(stderr, "ERROR: ");
+ va_start(ap, fmt);
+ vfprintf(stderr, fmt, ap);
+ va_end(ap);
+ fprintf(stderr, "\n");
+ errors++;
+}
+
+/*
+ * See if a tree has a 2-element root node.
+ */
+static int bt_tworoot(btree *bt)
+{
+ nodeptr n;
+ int i;
+ n = bt_read_lock_root(bt);
+ i = bt_subtrees(bt, n);
+ bt_read_unlock(bt, n);
+ return (i == 2 ? TRUE : FALSE);
+}
+
+/*
+ * Physically copy an entire B-tree. (NB this appears as a test
+ * routine rather than a production one, since reference counting
+ * and bt_clone() provide a better way to do this for real code. If
+ * anyone really needs a genuine physical copy for anything other
+ * than testing reasons, I suppose they could always lift this into
+ * the admin section above.)
+ */
+
+static nodeptr bt_copy_node(btree *bt, nodeptr n)
+{
+ int i, children;
+ nodeptr ret;
+
+ children = bt_subtrees(bt, n);
+ ret = bt_new_node(bt, children);
+
+ for (i = 0; i < children; i++) {
+ nodeptr n2 = bt_read_lock_child(bt, n, i);
+ nodeptr n3;
+ if (n2) {
+ n3 = bt_copy_node(bt, n2);
+ bt_set_child(bt, ret, i, bt_write_unlock(bt, n3));
+ } else {
+ bt_set_child(bt, ret, i, NODE_ADDR_NULL);
+ }
+ bt_read_unlock(bt, n2);
+
+ if (i < children-1) {
+ bt_element_t e = bt_element(bt, n, i);
+ if (bt->copy)
+ e = bt->copy(bt->userstate, e);
+ bt_set_element(bt, ret, i, e);
+ }
+ }
+
+ return ret;
+}
+
+btree *bt_copy(btree *bt)
+{
+ nodeptr n;
+ btree *bt2;
+
+ bt2 = bt_new(bt->cmp, bt->copy, bt->freeelt, bt->propsize, bt->propalign,
+ bt->propmake, bt->propmerge, bt->userstate, bt->mindegree);
+ bt2->depth = bt->depth;
+
+ n = bt_read_lock_root(bt);
+ if (n)
+ bt2->root = bt_write_unlock(bt2, bt_copy_node(bt, n));
+ bt_read_unlock(bt, n);
+
+ return bt2;
+}
+
+/*
+ * This function is intended to be called from gdb when debugging
+ * things.
+ */
+void bt_dump_nodes(btree *bt, ...)
+{
+ int i, children;
+ va_list ap;
+ nodeptr n;
+
+ va_start(ap, bt);
+ while (1) {
+ n = va_arg(ap, nodeptr);
+ if (!n)
+ break;
+ printf("%p [%d]:", n, n[bt->maxdegree*2+1].i);
+ children = bt_subtrees(bt, n);
+ for (i = 0; i < children; i++) {
+ printf(" %p", bt_child(bt, n, i).p);
+ if (i < children-1)
+ printf(" %s", (char *)bt_element(bt, n, i));
+ }
+ printf("\n");
+ }
+ va_end(ap);
+}
+
+/*
+ * Verify a tree against an array. Checks that:
+ *
+ * - every node has a valid number of subtrees
+ * - subtrees are either all present (internal node) or all absent
+ * (leaf)
+ * - elements are all present
+ * - every leaf is at exactly the depth claimed by the tree
+ * - the tree represents the correct list of elements in the
+ * correct order. (This also tests the ordering constraint,
+ * assuming the array is correctly constructed.)
+ */
+
+void verifynode(btree *bt, nodeptr n, bt_element_t *array, int *arraypos,
+ int depth)
+{
+ int subtrees, min, max, i, before, after, count;
+
+ /* Check the subtree count. The root can have as few as 2 subtrees. */
+ subtrees = bt_subtrees(bt, n);
+ max = bt_max_subtrees(bt);
+ min = (depth == 1) ? 2 : bt_min_subtrees(bt);
+ if (subtrees > max)
+ error("node %p has too many subtrees (%d > %d)", n, subtrees, max);
+ if (subtrees < min)
+ error("node %p has too few subtrees (%d < %d)", n, subtrees, min);
+
+ /* Check that subtrees are present or absent as required. */
+ for (i = 0; i < subtrees; i++) {
+ node_addr child = bt_child(bt, n, i);
+ if (depth == bt->depth && child.p != NULL)
+ error("leaf node %p child %d is %p not NULL\n", n, i, child);
+ if (depth != bt->depth && child.p == NULL)
+ error("non-leaf node %p child %d is NULL\n", n, i);
+ }
+
+ /* Check that elements are all present. */
+ for (i = 0; i < subtrees-1; i++) {
+ bt_element_t elt = bt_element(bt, n, i);
+ if (elt == NULL)
+ error("node %p element %d is NULL\n", n, i);
+ }
+
+ before = *arraypos;
+
+ /* Now verify the subtrees, and simultaneously check the ordering. */
+ for (i = 0; i < subtrees; i++) {
+ if (depth < bt->depth) {
+ nodeptr child = bt_read_lock_child(bt, n, i);
+ verifynode(bt, child, array, arraypos, depth+1);
+ bt_read_unlock(bt, child);
+ }
+ if (i < subtrees-1) {
+ bt_element_t elt = bt_element(bt, n, i);
+ if (array[*arraypos] != elt) {
+ error("node %p element %d is \"%s\", but array[%d]=\"%s\"",
+ n, i, elt, *arraypos, array[*arraypos]);
+ }
+ (*arraypos)++;
+ }
+ }
+
+ after = *arraypos;
+
+ /* Check the node count. */
+ count = bt_node_count(bt, n);
+ if (count != after - before)
+ error("node %p count is %d, should be %d", n, count, after - before);
+
+ /*
+ * Check the user properties.
+ */
+ {
+ nodecomponent *prop;
+ int i;
+ int max = 0, total = 0;
+
+ prop = n + bt->maxdegree * 2 + 2;
+
+ for (i = before; i < after; i++) {
+ int c = (unsigned char)*(char *)array[i];
+
+ if (max < c) max = c;
+ total += c;
+ }
+
+ if (prop[0].i != total)
+ error("node %p total prop is %d, should be %d", n,
+ prop[0].i, total);
+ if (prop[1].i != max)
+ error("node %p max prop is %d, should be %d", n,
+ prop[1].i, max);
+ }
+}
+
+void verifytree(btree *bt, bt_element_t *array, int arraylen)
+{
+ nodeptr n;
+ int i = 0;
+ n = bt_read_lock_root(bt);
+ if (n) {
+ verifynode(bt, n, array, &i, 1);
+ bt_read_unlock(bt, n);
+ } else {
+ if (bt->depth != 0) {
+ error("tree has null root but depth is %d not zero", bt->depth);
+ }
+ }
+ if (i != arraylen)
+ error("tree contains %d elements, array contains %d",
+ i, arraylen);
+ testlock(-1, 0, NULL);
+}
+
+int mycmp(void *state, void *av, void *bv) {
+ char const *a = (char const *)av;
+ char const *b = (char const *)bv;
+ return strcmp(a, b);
+}
+
+static void set_invalid_property(void *propv)
+{
+ int *prop = (int *)propv;
+ prop[0] = prop[1] = -1;
+}
+
+void mypropmake(void *state, void *av, void *destv)
+{
+ char const *a = (char const *)av;
+ int *dest = (int *)destv;
+ dest[0] = dest[1] = (unsigned char)*a;
+}
+
+void mypropmerge(void *state, void *s1v, void *s2v, void *destv)
+{
+ int *s1 = (int *)s1v;
+ int *s2 = (int *)s2v;
+ int *dest = (int *)destv;
+ if (!s1v && !s2v) {
+ /* Special `destroy' case. */
+ set_invalid_property(destv);
+ return;
+ }
+ assert(s2[0] >= 0 && s2[1] >= 0);
+ assert(s1 == NULL || (s1[0] >= 0 && s1[1] >= 0));
+ dest[0] = s2[0] + (s1 ? s1[0] : 0);
+ dest[1] = (s1 && s1[1] > s2[1] ? s1[1] : s2[1]);
+}
+
+void array_addpos(bt_element_t *array, int *arraylen, bt_element_t e, int i)
+{
+ bt_element_t e2;
+ int len = *arraylen;
+
+ assert(len < MAXTREESIZE);
+
+ while (i < len) {
+ e2 = array[i];
+ array[i] = e;
+ e = e2;
+ i++;
+ }
+ array[len] = e;
+ *arraylen = len+1;
+}
+
+void array_add(bt_element_t *array, int *arraylen, bt_element_t e)
+{
+ int i;
+ int len = *arraylen;
+
+ for (i = 0; i < len; i++)
+ if (mycmp(NULL, array[i], e) >= 0)
+ break;
+ assert(i == len || mycmp(NULL, array[i], e) != 0);
+ array_addpos(array, arraylen, e, i);
+}
+
+void array_delpos(bt_element_t *array, int *arraylen, int i)
+{
+ int len = *arraylen;
+
+ while (i < len-1) {
+ array[i] = array[i+1];
+ i++;
+ }
+ *arraylen = len-1;
+}
+
+bt_element_t array_del(bt_element_t *array, int *arraylen, bt_element_t e)
+{
+ int i;
+ int len = *arraylen;
+ bt_element_t ret;
+
+ for (i = 0; i < len; i++)
+ if (mycmp(NULL, array[i], e) >= 0)
+ break;
+ if (i < len && mycmp(NULL, array[i], e) == 0) {
+ ret = array[i];
+ array_delpos(array, arraylen, i);
+ } else
+ ret = NULL;
+ return ret;
+}
+
+/* A sample data set and test utility. Designed for pseudo-randomness,
+ * and yet repeatability. */
+
+/*
+ * This random number generator uses the `portable implementation'
+ * given in ANSI C99 draft N869. It assumes `unsigned' is 32 bits;
+ * change it if not.
+ */
+int randomnumber(unsigned *seed) {
+ *seed *= 1103515245;
+ *seed += 12345;
+ return ((*seed) / 65536) % 32768;
+}
+
+#define lenof(x) ( sizeof((x)) / sizeof(*(x)) )
+
+char *strings[] = {
+ "0", "2", "3", "I", "K", "d", "H", "J", "Q", "N", "n", "q", "j", "i",
+ "7", "G", "F", "D", "b", "x", "g", "B", "e", "v", "V", "T", "f", "E",
+ "S", "8", "A", "k", "X", "p", "C", "R", "a", "o", "r", "O", "Z", "u",
+ "6", "1", "w", "L", "P", "M", "c", "U", "h", "9", "t", "5", "W", "Y",
+ "m", "s", "l", "4",
+};
+
+#define NSTR lenof(strings)
+
+void findtest(btree *tree, bt_element_t *array, int arraylen)
+{
+ static const int rels[] = {
+ BT_REL_EQ, BT_REL_GE, BT_REL_LE, BT_REL_LT, BT_REL_GT
+ };
+ static const char *const relnames[] = {
+ "EQ", "GE", "LE", "LT", "GT"
+ };
+ int i, j, rel, index;
+ char *p, *ret, *realret, *realret2;
+ int lo, hi, mid, c;
+
+ for (i = 0; i < (int)NSTR; i++) {
+ p = strings[i];
+ for (j = 0; j < (int)(sizeof(rels)/sizeof(*rels)); j++) {
+ rel = rels[j];
+
+ lo = 0; hi = arraylen-1;
+ while (lo <= hi) {
+ mid = (lo + hi) / 2;
+ c = strcmp(p, array[mid]);
+ if (c < 0)
+ hi = mid-1;
+ else if (c > 0)
+ lo = mid+1;
+ else
+ break;
+ }
+
+ if (c == 0) {
+ if (rel == BT_REL_LT)
+ ret = (mid > 0 ? array[--mid] : NULL);
+ else if (rel == BT_REL_GT)
+ ret = (mid < arraylen-1 ? array[++mid] : NULL);
+ else
+ ret = array[mid];
+ } else {
+ assert(lo == hi+1);
+ if (rel == BT_REL_LT || rel == BT_REL_LE) {
+ mid = hi;
+ ret = (hi >= 0 ? array[hi] : NULL);
+ } else if (rel == BT_REL_GT || rel == BT_REL_GE) {
+ mid = lo;
+ ret = (lo < arraylen ? array[lo] : NULL);
+ } else
+ ret = NULL;
+ }
+
+ realret = bt_findrelpos(tree, p, NULL, rel, &index);
+ testlock(-1, 0, NULL);
+ if (realret != ret) {
+ error("find(\"%s\",%s) gave %s should be %s",
+ p, relnames[j], realret, ret);
+ }
+ if (realret && index != mid) {
+ error("find(\"%s\",%s) gave %d should be %d",
+ p, relnames[j], index, mid);
+ }
+ if (realret && rel == BT_REL_EQ) {
+ realret2 = bt_index(tree, index);
+ if (realret2 != realret) {
+ error("find(\"%s\",%s) gave %s(%d) but %d -> %s",
+ p, relnames[j], realret, index, index, realret2);
+ }
+ }
+ }
+ }
+
+ realret = bt_findrelpos(tree, NULL, NULL, BT_REL_GT, &index);
+ testlock(-1, 0, NULL);
+ if (arraylen && (realret != array[0] || index != 0)) {
+ error("find(NULL,GT) gave %s(%d) should be %s(0)",
+ realret, index, array[0]);
+ } else if (!arraylen && (realret != NULL)) {
+ error("find(NULL,GT) gave %s(%d) should be NULL",
+ realret, index);
+ }
+
+ realret = bt_findrelpos(tree, NULL, NULL, BT_REL_LT, &index);
+ testlock(-1, 0, NULL);
+ if (arraylen && (realret != array[arraylen-1] || index != arraylen-1)) {
+ error("find(NULL,LT) gave %s(%d) should be %s(0)",
+ realret, index, array[arraylen-1]);
+ } else if (!arraylen && (realret != NULL)) {
+ error("find(NULL,LT) gave %s(%d) should be NULL",
+ realret, index);
+ }
+}
+
+void splittest(btree *tree, bt_element_t *array, int arraylen)
+{
+ int i;
+ btree *tree3, *tree4;
+ for (i = 0; i <= arraylen; i++) {
+ printf("splittest: %d\n", i);
+ tree3 = BT_COPY(tree);
+ testlock(-1, 0, NULL);
+ tree4 = bt_splitpos(tree3, i, 0);
+ testlock(-1, 0, NULL);
+ verifytree(tree3, array, i);
+ verifytree(tree4, array+i, arraylen-i);
+ bt_join(tree3, tree4);
+ testlock(-1, 0, NULL);
+ verifytree(tree4, NULL, 0);
+ bt_free(tree4); /* left empty by join */
+ testlock(-1, 0, NULL);
+ verifytree(tree3, array, arraylen);
+ bt_free(tree3);
+ testlock(-1, 0, NULL);
+ }
+}
+
+/*
+ * Called to track read and write locks on nodes.
+ */
+void testlock(int write, int set, nodeptr n)
+{
+ static nodeptr readlocks[MAXLOCKS], writelocks[MAXLOCKS];
+ static int nreadlocks = 0, nwritelocks = 0;
+
+ int i, rp, wp;
+
+ if (write == -1) {
+ /* Called after an operation to ensure all locks are unlocked. */
+ if (nreadlocks != 0 || nwritelocks != 0)
+ error("at least one left-behind lock exists!");
+ return;
+ }
+
+ /* Locking NULL does nothing. Unlocking it is an error. */
+ if (n == NULL) {
+ if (!set)
+ error("attempting to %s-unlock NULL", write ? "write" : "read");
+ return;
+ }
+
+ assert(nreadlocks < MAXLOCKS && nwritelocks < MAXLOCKS);
+
+ /* First look for the node in both lock lists. */
+ rp = wp = -1;
+ for (i = 0; i < nreadlocks; i++)
+ if (readlocks[i] == n)
+ rp = i;
+ for (i = 0; i < nwritelocks; i++)
+ if (writelocks[i] == n)
+ wp = i;
+
+ /* Now diverge based on what we're supposed to be up to. */
+ if (set) {
+ /* Setting a lock. Should not already be locked in either list. */
+ if (rp != -1 || wp != -1) {
+ error("attempt to %s-lock node %p, already %s-locked",
+ (write ? "write" : "read"), n, (rp==-1 ? "write" : "read"));
+ }
+ if (write)
+ writelocks[nwritelocks++] = n;
+ else
+ readlocks[nreadlocks++] = n;
+ } else {
+ /* Clearing a lock. Should exist in exactly the correct list. */
+ if (write && rp != -1)
+ error("attempt to write-unlock node %p which is read-locked", n);
+ if (!write && wp != -1)
+ error("attempt to read-unlock node %p which is write-locked", n);
+ if (wp != -1) {
+ nwritelocks--;
+ for (i = wp; i < nwritelocks; i++)
+ writelocks[i] = writelocks[i+1];
+ }
+ if (rp != -1) {
+ nreadlocks--;
+ for (i = rp; i < nreadlocks; i++)
+ readlocks[i] = readlocks[i+1];
+ }
+ }
+}
+
+int main(void) {
+ int in[NSTR];
+ int i, j, k;
+ int tworoot, tmplen;
+ unsigned seed = 0;
+ bt_element_t *array;
+ int arraylen;
+ bt_element_t ret, ret2, item;
+ btree *tree, *tree2, *tree3, *tree4;
+
+ setvbuf(stdout, NULL, _IOLBF, 0);
+ setvbuf(stderr, NULL, _IOLBF, 0);
+ errors = 0;
+
+ for (i = 0; i < (int)NSTR; i++) in[i] = 0;
+ array = newn(bt_element_t, MAXTREESIZE);
+ arraylen = 0;
+ tree = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+
+ verifytree(tree, array, arraylen);
+ for (i = 0; i < 10000; i++) {
+ j = randomnumber(&seed);
+ j %= NSTR;
+ printf("trial: %d\n", i);
+ if (in[j]) {
+ printf("deleting %s (%d)\n", strings[j], j);
+ ret2 = array_del(array, &arraylen, strings[j]);
+ ret = bt_del(tree, strings[j]);
+ testlock(-1, 0, NULL);
+ assert((bt_element_t)strings[j] == ret && ret == ret2);
+ verifytree(tree, array, arraylen);
+ in[j] = 0;
+ } else {
+ printf("adding %s (%d)\n", strings[j], j);
+ array_add(array, &arraylen, strings[j]);
+ ret = bt_add(tree, strings[j]);
+ testlock(-1, 0, NULL);
+ assert(strings[j] == ret);
+ verifytree(tree, array, arraylen);
+ in[j] = 1;
+ }
+ /* disptree(tree); */
+ findtest(tree, array, arraylen);
+ }
+
+ while (arraylen > 0) {
+ j = randomnumber(&seed);
+ j %= arraylen;
+ item = array[j];
+ ret2 = array_del(array, &arraylen, item);
+ ret = bt_del(tree, item);
+ testlock(-1, 0, NULL);
+ assert(ret2 == ret);
+ verifytree(tree, array, arraylen);
+ }
+
+ bt_free(tree);
+ testlock(-1, 0, NULL);
+
+ /*
+ * Now try an unsorted tree. We don't really need to test
+ * delpos because we know del is based on it, so it's already
+ * been tested in the above sorted-tree code; but for
+ * completeness we'll use it to tear down our unsorted tree
+ * once we've built it.
+ */
+ tree = bt_new(NULL, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+ verifytree(tree, array, arraylen);
+ for (i = 0; i < 1000; i++) {
+ printf("trial: %d\n", i);
+ j = randomnumber(&seed);
+ j %= NSTR;
+ k = randomnumber(&seed);
+ k %= bt_count(tree)+1;
+ testlock(-1, 0, NULL);
+ printf("adding string %s at index %d\n", strings[j], k);
+ array_addpos(array, &arraylen, strings[j], k);
+ bt_addpos(tree, strings[j], k);
+ testlock(-1, 0, NULL);
+ verifytree(tree, array, arraylen);
+ }
+
+ /*
+ * While we have this tree in its full form, we'll take a copy
+ * of it to use in split and join testing.
+ */
+ tree2 = BT_COPY(tree);
+ testlock(-1, 0, NULL);
+ verifytree(tree2, array, arraylen);/* check the copy is accurate */
+ /*
+ * Split tests. Split the tree at every possible point and
+ * check the resulting subtrees.
+ */
+ tworoot = bt_tworoot(tree2); /* see if it has a 2-root */
+ testlock(-1, 0, NULL);
+ splittest(tree2, array, arraylen);
+ /*
+ * Now do the split test again, but on a tree that has a 2-root
+ * (if the previous one didn't) or doesn't (if the previous one
+ * did).
+ */
+ tmplen = arraylen;
+ while (bt_tworoot(tree2) == tworoot) {
+ bt_delpos(tree2, --tmplen);
+ testlock(-1, 0, NULL);
+ }
+ printf("now trying splits on second tree\n");
+ splittest(tree2, array, tmplen);
+ bt_free(tree2);
+ testlock(-1, 0, NULL);
+
+ /*
+ * Back to the main testing of uncounted trees.
+ */
+ while (bt_count(tree) > 0) {
+ printf("cleanup: tree size %d\n", bt_count(tree));
+ j = randomnumber(&seed);
+ j %= bt_count(tree);
+ printf("deleting string %s from index %d\n", (char *)array[j], j);
+ ret = bt_delpos(tree, j);
+ testlock(-1, 0, NULL);
+ assert((bt_element_t)array[j] == ret);
+ array_delpos(array, &arraylen, j);
+ verifytree(tree, array, arraylen);
+ }
+ bt_free(tree);
+ testlock(-1, 0, NULL);
+
+ /*
+ * Finally, do some testing on split/join on _sorted_ trees. At
+ * the same time, we'll be testing split on very small trees.
+ */
+ tree = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+ arraylen = 0;
+ for (i = 0; i < 16; i++) {
+ array_add(array, &arraylen, strings[i]);
+ ret = bt_add(tree, strings[i]);
+ testlock(-1, 0, NULL);
+ assert(strings[i] == ret);
+ verifytree(tree, array, arraylen);
+ tree2 = BT_COPY(tree);
+ splittest(tree2, array, arraylen);
+ testlock(-1, 0, NULL);
+ bt_free(tree2);
+ testlock(-1, 0, NULL);
+ }
+ bt_free(tree);
+ testlock(-1, 0, NULL);
+
+ /*
+ * Test silly cases of join: join(emptytree, emptytree), and
+ * also ensure join correctly spots when sorted trees fail the
+ * ordering constraint.
+ */
+ tree = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+ tree2 = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+ tree3 = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+ tree4 = bt_new(mycmp, NULL, NULL, 2*sizeof(int), alignof(int),
+ mypropmake, mypropmerge, NULL, TEST_DEGREE);
+ assert(mycmp(NULL, strings[0], strings[1]) < 0); /* just in case :-) */
+ bt_add(tree2, strings[1]);
+ testlock(-1, 0, NULL);
+ bt_add(tree4, strings[0]);
+ testlock(-1, 0, NULL);
+ array[0] = strings[0];
+ array[1] = strings[1];
+ verifytree(tree, array, 0);
+ verifytree(tree2, array+1, 1);
+ verifytree(tree3, array, 0);
+ verifytree(tree4, array, 1);
+
+ /*
+ * So:
+ * - join(tree,tree3) should leave both tree and tree3 unchanged.
+ * - joinr(tree,tree2) should leave both tree and tree2 unchanged.
+ * - join(tree4,tree3) should leave both tree3 and tree4 unchanged.
+ * - join(tree, tree2) should move the element from tree2 to tree.
+ * - joinr(tree4, tree3) should move the element from tree4 to tree3.
+ * - join(tree,tree3) should return NULL and leave both unchanged.
+ * - join(tree3,tree) should work and create a bigger tree in tree3.
+ */
+ assert(tree == bt_join(tree, tree3));
+ testlock(-1, 0, NULL);
+ verifytree(tree, array, 0);
+ verifytree(tree3, array, 0);
+ assert(tree2 == bt_joinr(tree, tree2));
+ testlock(-1, 0, NULL);
+ verifytree(tree, array, 0);
+ verifytree(tree2, array+1, 1);
+ assert(tree4 == bt_join(tree4, tree3));
+ testlock(-1, 0, NULL);
+ verifytree(tree3, array, 0);
+ verifytree(tree4, array, 1);
+ assert(tree == bt_join(tree, tree2));
+ testlock(-1, 0, NULL);
+ verifytree(tree, array+1, 1);
+ verifytree(tree2, array, 0);
+ assert(tree3 == bt_joinr(tree4, tree3));
+ testlock(-1, 0, NULL);
+ verifytree(tree3, array, 1);
+ verifytree(tree4, array, 0);
+ assert(NULL == bt_join(tree, tree3));
+ testlock(-1, 0, NULL);
+ verifytree(tree, array+1, 1);
+ verifytree(tree3, array, 1);
+ assert(tree3 == bt_join(tree3, tree));
+ testlock(-1, 0, NULL);
+ verifytree(tree3, array, 2);
+ verifytree(tree, array, 0);
+
+ bt_free(tree);
+ testlock(-1, 0, NULL);
+ bt_free(tree2);
+ testlock(-1, 0, NULL);
+ bt_free(tree3);
+ testlock(-1, 0, NULL);
+ bt_free(tree4);
+ testlock(-1, 0, NULL);
+
+ sfree(array);
+
+ if (errors)
+ fprintf(stderr, "%d errors!\n", errors);
+ return (errors != 0 ? 1 : 0);
+}
+
+#endif