new tsearch implementation

Rewrote the AVL tree implementation:

- It is now non-recursive with fixed stack usage (large enough for
worst case tree height). twalk and tdestroy are still recursive as
that's smaller/simpler.

- Moved unrelated interfaces into separate translation units.

- The node structure is changed to use indexed children instead of
left/right pointers, this simplifies the balancing logic.

- Using void * pointers instead of struct node * in various places,
because this better fits the api (node address is passed in a void**
argument, so it is tempting to incorrectly cast it to struct node **).

- As a further performance improvement the rebalancing now stops
when it is not needed (subtree height is unchanged). Otherwise
the behaviour should be the same as before (checked over generated
random inputs that the resulting tree shape is equivalent).

- Removed the old copyright notice (including prng related one: it
should be licensed under the same terms as the rest of the project).

.text size of pic tsearch + tfind + tdelete + twalk:

   x86_64 i386 aarch64  arm mips powerpc ppc64le  sh4 m68k s390x
old   941  899    1220 1068 1852    1400    1600 1008 1008  1488
new   857  881    1040  976 1564    1192    1360  736  820  1408

COPYRIGHT

@@ -126,12 +126,6 @@ in jurisdictions that may not recognize the public domain.
 The smoothsort implementation (src/stdlib/qsort.c) is Copyright © 2011
 Valentin Ochs and is licensed under an MIT-style license.
 
-The BSD PRNG implementation (src/prng/random.c) and XSI search API
-(src/search/*.c) functions are Copyright © 2011 Szabolcs Nagy and
-licensed under following terms: "Permission to use, copy, modify,
-and/or distribute this code for any purpose with or without fee is
-hereby granted. There is no warranty."
-
 The x86_64 port was written by Nicholas J. Kain and is licensed under
 the standard MIT terms.
 

src/search/tdelete.c

@@ -0,0 +1,49 @@
+#include <stdlib.h>
+#include <search.h>
+#include "tsearch.h"
+
+void *tdelete(const void *restrict key, void **restrict rootp,
+	int(*cmp)(const void *, const void *))
+{
+	if (!rootp)
+		return 0;
+
+	void **a[MAXH+1];
+	struct node *n = *rootp;
+	struct node *parent;
+	struct node *child;
+	int i=0;
+	/* *a[0] is an arbitrary non-null pointer that is returned when
+	   the root node is deleted.  */
+	a[i++] = rootp;
+	a[i++] = rootp;
+	for (;;) {
+		if (!n)
+			return 0;
+		int c = cmp(key, n->key);
+		if (!c)
+			break;
+		a[i++] = &n->a[c>0];
+		n = n->a[c>0];
+	}
+	parent = *a[i-2];
+	if (n->a[0]) {
+		/* free the preceding node instead of the deleted one.  */
+		struct node *deleted = n;
+		a[i++] = &n->a[0];
+		n = n->a[0];
+		while (n->a[1]) {
+			a[i++] = &n->a[1];
+			n = n->a[1];
+		}
+		deleted->key = n->key;
+		child = n->a[0];
+	} else {
+		child = n->a[1];
+	}
+	/* freed node has at most one child, move it up and rebalance.  */
+	free(n);
+	*a[--i] = child;
+	while (--i && __tsearch_balance(a[i]));
+	return parent;
+}

src/search/tdestroy.c

@@ -1,12 +1,7 @@
 #define _GNU_SOURCE
 #include <stdlib.h>
 #include <search.h>
-
-struct node {
-	void *key;
-	struct node *left;
-	struct node *right;
-};
+#include "tsearch.h"
 
 void tdestroy(void *root, void (*freekey)(void *))
 {
@@ -14,8 +9,8 @@ void tdestroy(void *root, void (*freekey)(void *))
 
 	if (r == 0)
 		return;
-	tdestroy(r->left, freekey);
-	tdestroy(r->right, freekey);
-	if (freekey) freekey(r->key);
+	tdestroy(r->a[0], freekey);
+	tdestroy(r->a[1], freekey);
+	if (freekey) freekey((void *)r->key);
 	free(r);
 }

src/search/tfind.c

@@ -0,0 +1,20 @@
+#include <search.h>
+#include "tsearch.h"
+
+void *tfind(const void *key, void *const *rootp,
+	int(*cmp)(const void *, const void *))
+{
+	if (!rootp)
+		return 0;
+
+	struct node *n = *rootp;
+	for (;;) {
+		if (!n)
+			break;
+		int c = cmp(key, n->key);
+		if (!c)
+			break;
+		n = n->a[c>0];
+	}
+	return n;
+}

src/search/tsearch.c

@@ -0,0 +1,92 @@
+#include <stdlib.h>
+#include <search.h>
+#include "tsearch.h"
+
+static inline int height(struct node *n) { return n ? n->h : 0; }
+
+static int rot(void **p, struct node *x, int dir /* deeper side */)
+{
+	struct node *y = x->a[dir];
+	struct node *z = y->a[!dir];
+	int hx = x->h;
+	int hz = height(z);
+	if (hz > height(y->a[dir])) {
+		/*
+		 *   x
+		 *  / \ dir          z
+		 * A   y            / \
+		 *    / \   -->    x   y
+		 *   z   D        /|   |\
+		 *  / \          A B   C D
+		 * B   C
+		 */
+		x->a[dir] = z->a[!dir];
+		y->a[!dir] = z->a[dir];
+		z->a[!dir] = x;
+		z->a[dir] = y;
+		x->h = hz;
+		y->h = hz;
+		z->h = hz+1;
+	} else {
+		/*
+		 *   x               y
+		 *  / \             / \
+		 * A   y    -->    x   D
+		 *    / \         / \
+		 *   z   D       A   z
+		 */
+		x->a[dir] = z;
+		y->a[!dir] = x;
+		x->h = hz+1;
+		y->h = hz+2;
+		z = y;
+	}
+	*p = z;
+	return z->h - hx;
+}
+
+/* balance *p, return 0 if height is unchanged.  */
+int __tsearch_balance(void **p)
+{
+	struct node *n = *p;
+	int h0 = height(n->a[0]);
+	int h1 = height(n->a[1]);
+	if (h0 - h1 + 1u < 3u) {
+		int old = n->h;
+		n->h = h0<h1 ? h1+1 : h0+1;
+		return n->h - old;
+	}
+	return rot(p, n, h0<h1);
+}
+
+void *tsearch(const void *key, void **rootp,
+	int (*cmp)(const void *, const void *))
+{
+	if (!rootp)
+		return 0;
+
+	void **a[MAXH];
+	struct node *n = *rootp;
+	struct node *r;
+	int i=0;
+	a[i++] = rootp;
+	for (;;) {
+		if (!n)
+			break;
+		int c = cmp(key, n->key);
+		if (!c)
+			return n;
+		a[i++] = &n->a[c>0];
+		n = n->a[c>0];
+	}
+	r = malloc(sizeof *r);
+	if (!r)
+		return 0;
+	r->key = key;
+	r->a[0] = r->a[1] = 0;
+	r->h = 1;
+	/* insert new node, rebalance ancestors.  */
+	*a[--i] = r;
+	while (i && __tsearch_balance(a[--i]));
+	return r;
+}

src/search/tsearch.h

@@ -0,0 +1,13 @@
+#include <search.h>
+#include <features.h>
+
+/* AVL tree height < 1.44*log2(nodes+2)-0.3, MAXH is a safe upper bound.  */
+#define MAXH (sizeof(void*)*8*3/2)
+
+struct node {
+	const void *key;
+	void *a[2];
+	int h;
+};
+
+hidden int __tsearch_balance(void **);

src/search/tsearch_avl.c

@@ -1,204 +0,0 @@
-#include <stdlib.h>
-#include <search.h>
-
-/*
-avl tree implementation using recursive functions
-the height of an n node tree is less than 1.44*log2(n+2)-1
-(so the max recursion depth in case of a tree with 2^32 nodes is 45)
-*/
-
-struct node {
-	const void *key;
-	struct node *left;
-	struct node *right;
-	int height;
-};
-
-static int delta(struct node *n) {
-	return (n->left ? n->left->height:0) - (n->right ? n->right->height:0);
-}
-
-static void updateheight(struct node *n) {
-	n->height = 0;
-	if (n->left && n->left->height > n->height)
-		n->height = n->left->height;
-	if (n->right && n->right->height > n->height)
-		n->height = n->right->height;
-	n->height++;
-}
-
-static struct node *rotl(struct node *n) {
-	struct node *r = n->right;
-	n->right = r->left;
-	r->left = n;
-	updateheight(n);
-	updateheight(r);
-	return r;
-}
-
-static struct node *rotr(struct node *n) {
-	struct node *l = n->left;
-	n->left = l->right;
-	l->right = n;
-	updateheight(n);
-	updateheight(l);
-	return l;
-}
-
-static struct node *balance(struct node *n) {
-	int d = delta(n);
-
-	if (d < -1) {
-		if (delta(n->right) > 0)
-			n->right = rotr(n->right);
-		return rotl(n);
-	} else if (d > 1) {
-		if (delta(n->left) < 0)
-			n->left = rotl(n->left);
-		return rotr(n);
-	}
-	updateheight(n);
-	return n;
-}
-
-static struct node *find(struct node *n, const void *k,
-	int (*cmp)(const void *, const void *))
-{
-	int c;
-
-	if (!n)
-		return 0;
-	c = cmp(k, n->key);
-	if (c == 0)
-		return n;
-	if (c < 0)
-		return find(n->left, k, cmp);
-	else
-		return find(n->right, k, cmp);
-}
-
-static struct node *insert(struct node *n, const void *k,
-	int (*cmp)(const void *, const void *), struct node **found)
-{
-	struct node *r;
-	int c;
-
-	if (!n) {
-		n = malloc(sizeof *n);
-		if (n) {
-			n->key = k;
-			n->left = n->right = 0;
-			n->height = 1;
-		}
-		*found = n;
-		return n;
-	}
-	c = cmp(k, n->key);
-	if (c == 0) {
-		*found = n;
-		return 0;
-	}
-	r = insert(c < 0 ? n->left : n->right, k, cmp, found);
-	if (r) {
-		if (c < 0)
-			n->left = r;
-		else
-			n->right = r;
-		r = balance(n);
-	}
-	return r;
-}
-
-static struct node *remove_rightmost(struct node *n, struct node **rightmost)
-{
-	if (!n->right) {
-		*rightmost = n;
-		return n->left;
-	}
-	n->right = remove_rightmost(n->right, rightmost);
-	return balance(n);
-}
-
-static struct node *remove(struct node **n, const void *k,
-	int (*cmp)(const void *, const void *), struct node *parent)
-{
-	int c;
-
-	if (!*n)
-		return 0;
-	c = cmp(k, (*n)->key);
-	if (c == 0) {
-		struct node *r = *n;
-		if (r->left) {
-			r->left = remove_rightmost(r->left, n);
-			(*n)->left = r->left;
-			(*n)->right = r->right;
-			*n = balance(*n);
-		} else
-			*n = r->right;
-		free(r);
-		return parent;
-	}
-	if (c < 0)
-		parent = remove(&(*n)->left, k, cmp, *n);
-	else
-		parent = remove(&(*n)->right, k, cmp, *n);
-	if (parent)
-		*n = balance(*n);
-	return parent;
-}
-
-void *tdelete(const void *restrict key, void **restrict rootp,
-	int(*compar)(const void *, const void *))
-{
-	if (!rootp)
-		return 0;
-	struct node *n = *rootp;
-	struct node *ret;
-	/* last argument is arbitrary non-null pointer
-	   which is returned when the root node is deleted */
-	ret = remove(&n, key, compar, n);
-	*rootp = n;
-	return ret;
-}
-
-void *tfind(const void *key, void *const *rootp,
-	int(*compar)(const void *, const void *))
-{
-	if (!rootp)
-		return 0;
-	return find(*rootp, key, compar);
-}
-
-void *tsearch(const void *key, void **rootp,
-	int (*compar)(const void *, const void *))
-{
-	struct node *update;
-	struct node *ret;
-	if (!rootp)
-		return 0;
-	update = insert(*rootp, key, compar, &ret);
-	if (update)
-		*rootp = update;
-	return ret;
-}
-
-static void walk(const struct node *r, void (*action)(const void *, VISIT, int), int d)
-{
-	if (r == 0)
-		return;
-	if (r->left == 0 && r->right == 0)
-		action(r, leaf, d);
-	else {
-		action(r, preorder, d);
-		walk(r->left, action, d+1);
-		action(r, postorder, d);
-		walk(r->right, action, d+1);
-		action(r, endorder, d);
-	}
-}
-
-void twalk(const void *root, void (*action)(const void *, VISIT, int))
-{
-	walk(root, action, 0);
-}

src/search/twalk.c

@@ -0,0 +1,22 @@
+#include <search.h>
+#include "tsearch.h"
+
+static void walk(const struct node *r, void (*action)(const void *, VISIT, int), int d)
+{
+	if (!r)
+		return;
+	if (r->h == 1)
+		action(r, leaf, d);
+	else {
+		action(r, preorder, d);
+		walk(r->a[0], action, d+1);
+		action(r, postorder, d);
+		walk(r->a[1], action, d+1);
+		action(r, endorder, d);
+	}
+}
+
+void twalk(const void *root, void (*action)(const void *, VISIT, int))
+{
+	walk(root, action, 0);
+}