elib_malloc.c

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	x->parent->right = y;
    else {
	RBT_ASSERT(x == x->parent->left);
	x->parent->left = y;
    }
    y->right = x;
    x->parent = y;
}


/*
 * Replace node x with node y
 * NOTE: block header of y is not changed
 */
static ERTS_INLINE void
replace(RBTree_t **root, RBTree_t *x, RBTree_t *y)
{

    if (!x->parent) {
	RBT_ASSERT(*root == x);
	*root = y;
    }
    else if (x == x->parent->left)
	x->parent->left = y;
    else {
	RBT_ASSERT(x == x->parent->right);
	x->parent->right = y;
    }
    if (x->left) {
	RBT_ASSERT(x->left->parent == x);
	x->left->parent = y;
    }
    if (x->right) {
	RBT_ASSERT(x->right->parent == x);
	x->right->parent = y;
    }

    y->flags	= x->flags;
    y->parent	= x->parent;
    y->right	= x->right;
    y->left	= x->left;

    DESTROY_TREE_NODE(x);

}

static void
tree_insert_fixup(RBTree_t *blk)
{
    RBTree_t *x = blk, *y;

    /*
     * Rearrange the tree so that it satisfies the Red-Black Tree properties
     */

    RBT_ASSERT(x != root && IS_RED(x->parent));
    do {

	/*
	 * x and its parent are both red. Move the red pair up the tree
	 * until we get to the root or until we can separate them.
	 */

	RBT_ASSERT(IS_RED(x));
	RBT_ASSERT(IS_BLACK(x->parent->parent));
	RBT_ASSERT(x->parent->parent);

	if (x->parent == x->parent->parent->left) {
	    y = x->parent->parent->right;
	    if (IS_RED(y)) {
		SET_BLACK(y);
		x = x->parent;
		SET_BLACK(x);
		x = x->parent;
		SET_RED(x);
	    }
	    else {

		if (x == x->parent->right) {
		    x = x->parent;
		    left_rotate(&root, x);
		}

		RBT_ASSERT(x == x->parent->parent->left->left);
		RBT_ASSERT(IS_RED(x));
		RBT_ASSERT(IS_RED(x->parent));
		RBT_ASSERT(IS_BLACK(x->parent->parent));
		RBT_ASSERT(IS_BLACK(y));

		SET_BLACK(x->parent);
		SET_RED(x->parent->parent);
		right_rotate(&root, x->parent->parent);

		RBT_ASSERT(x == x->parent->left);
		RBT_ASSERT(IS_RED(x));
		RBT_ASSERT(IS_RED(x->parent->right));
		RBT_ASSERT(IS_BLACK(x->parent));
		break;
	    }
	}
	else {
	    RBT_ASSERT(x->parent == x->parent->parent->right);
	    y = x->parent->parent->left;
	    if (IS_RED(y)) {
		SET_BLACK(y);
		x = x->parent;
		SET_BLACK(x);
		x = x->parent;
		SET_RED(x);
	    }
	    else {

		if (x == x->parent->left) {
		    x = x->parent;
		    right_rotate(&root, x);
		}

		RBT_ASSERT(x == x->parent->parent->right->right);
		RBT_ASSERT(IS_RED(x));
		RBT_ASSERT(IS_RED(x->parent));
		RBT_ASSERT(IS_BLACK(x->parent->parent));
		RBT_ASSERT(IS_BLACK(y));

		SET_BLACK(x->parent);
		SET_RED(x->parent->parent);
		left_rotate(&root, x->parent->parent);

		RBT_ASSERT(x == x->parent->right);
		RBT_ASSERT(IS_RED(x));
		RBT_ASSERT(IS_RED(x->parent->left));
		RBT_ASSERT(IS_BLACK(x->parent));
		break;
	    }
	}
    } while (x != root && IS_RED(x->parent));

    SET_BLACK(root);
}

static void
unlink_free_block(Block_t *del)
{
    Uint spliced_is_black;
    RBTree_t *x, *y, *z = (RBTree_t *) del;
    RBTree_t null_x; /* null_x is used to get the fixup started when we
			splice out a node without children. */

    null_x.parent = NULL;

#ifdef HARD_DEBUG
    check_tree(0);
#endif

    /* Remove node from tree... */

    /* Find node to splice out */
    if (!z->left || !z->right)
	y = z;
    else
	/* Set y to z:s successor */
	for(y = z->right; y->left; y = y->left);
    /* splice out y */
    x = y->left ? y->left : y->right;
    spliced_is_black = IS_BLACK(y);
    if (x) {
	x->parent = y->parent;
    }
    else if (!x && spliced_is_black) {
	x = &null_x;
	x->flags = 0;
	SET_BLACK(x);
	x->right = x->left = NULL;
	x->parent = y->parent;
	y->left = x;
    }

    if (!y->parent) {
	RBT_ASSERT(root == y);
	root = x;
    }
    else if (y == y->parent->left)
	y->parent->left = x;
    else {
	RBT_ASSERT(y == y->parent->right);
	y->parent->right = x;
    }
    if (y != z) {
	/* We spliced out the successor of z; replace z by the successor */
	replace(&root, z, y);
    }

    if (spliced_is_black) {
	/* We removed a black node which makes the resulting tree
	   violate the Red-Black Tree properties. Fixup tree... */

	while (IS_BLACK(x) && x->parent) {

	    /*
	     * x has an "extra black" which we move up the tree
	     * until we reach the root or until we can get rid of it.
	     *
	     * y is the sibbling of x
	     */

	    if (x == x->parent->left) {
		y = x->parent->right;
		RBT_ASSERT(y);
		if (IS_RED(y)) {
		    RBT_ASSERT(y->right);
		    RBT_ASSERT(y->left);
		    SET_BLACK(y);
		    RBT_ASSERT(IS_BLACK(x->parent));
		    SET_RED(x->parent);
		    left_rotate(&root, x->parent);
		    y = x->parent->right;
		}
		RBT_ASSERT(y);
		RBT_ASSERT(IS_BLACK(y));
		if (IS_BLACK(y->left) && IS_BLACK(y->right)) {
		    SET_RED(y);
		    x = x->parent;
		}
		else {
		    if (IS_BLACK(y->right)) {
			SET_BLACK(y->left);
			SET_RED(y);
			right_rotate(&root, y);
			y = x->parent->right;
		    }
		    RBT_ASSERT(y);
		    if (IS_RED(x->parent)) {

			SET_BLACK(x->parent);
			SET_RED(y);
		    }
		    RBT_ASSERT(y->right);
		    SET_BLACK(y->right);
		    left_rotate(&root, x->parent);
		    x = root;
		    break;
		}
	    }
	    else {
		RBT_ASSERT(x == x->parent->right);
		y = x->parent->left;
		RBT_ASSERT(y);
		if (IS_RED(y)) {
		    RBT_ASSERT(y->right);
		    RBT_ASSERT(y->left);
		    SET_BLACK(y);
		    RBT_ASSERT(IS_BLACK(x->parent));
		    SET_RED(x->parent);
		    right_rotate(&root, x->parent);
		    y = x->parent->left;
		}
		RBT_ASSERT(y);
		RBT_ASSERT(IS_BLACK(y));
		if (IS_BLACK(y->right) && IS_BLACK(y->left)) {
		    SET_RED(y);
		    x = x->parent;
		}
		else {
		    if (IS_BLACK(y->left)) {
			SET_BLACK(y->right);
			SET_RED(y);
			left_rotate(&root, y);
			y = x->parent->left;
		    }
		    RBT_ASSERT(y);
		    if (IS_RED(x->parent)) {
			SET_BLACK(x->parent);
			SET_RED(y);
		    }
		    RBT_ASSERT(y->left);
		    SET_BLACK(y->left);
		    right_rotate(&root, x->parent);
		    x = root;
		    break;
		}
	    }
	}
	SET_BLACK(x);

	if (null_x.parent) {
	    if (null_x.parent->left == &null_x)
		null_x.parent->left = NULL;
	    else {
		RBT_ASSERT(null_x.parent->right == &null_x);
		null_x.parent->right = NULL;
	    }
	    RBT_ASSERT(!null_x.left);
	    RBT_ASSERT(!null_x.right);
	}
	else if (root == &null_x) {
	    root = NULL;
	    RBT_ASSERT(!null_x.left);
	    RBT_ASSERT(!null_x.right);
	}
    }


    DESTROY_TREE_NODE(del);

#ifdef HARD_DEBUG
    check_tree(0);
#endif

}

/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\
 * "Address order best fit" specific callbacks.                              *
\*                                                                           */

static void
link_free_block(Block_t *block)
{
    RBTree_t *blk = (RBTree_t *) block;
    Uint blk_sz = BLK_SZ(blk);

    blk->flags	= 0;
    blk->left	= NULL;
    blk->right	= NULL;

    if (!root) {
	blk->parent = NULL;
	SET_BLACK(blk);
	root = blk;
    } else {
	RBTree_t *x = root;
	while (1) {
	    Uint size;

	    size = BLK_SZ(x);

	    if (blk_sz < size || (blk_sz == size && blk < x)) {
		if (!x->left) {
		    blk->parent = x;
		    x->left = blk;
		    break;
		}
		x = x->left;
	    }
	    else {
		if (!x->right) {
		    blk->parent = x;
		    x->right = blk;
		    break;
		}
		x = x->right;
	    }

	}

	/* Insert block into size tree */
	RBT_ASSERT(blk->parent);

	SET_RED(blk);
	if (IS_RED(blk->parent)) {
	    tree_insert_fixup(blk);
	}
    }

#ifdef HARD_DEBUG
    check_tree(0);
#endif
}


static Block_t *
get_free_block(Uint size)
{
    RBTree_t *x = root;
    RBTree_t *blk = NULL;
    Uint blk_sz;

    while (x) {
	blk_sz = BLK_SZ(x);
	if (blk_sz < size) {
	    x = x->right;
	}
	else {
	    blk = x;
	    x = x->left;
	}
    }
    
    if (!blk)
	return NULL;

#ifdef HARD_DEBUG
    ASSERT(blk == check_tree(size));
#endif

    unlink_free_block((Block_t *) blk);

    return (Block_t *) blk;
}


/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\
 * Debug functions                                                           *
\*                                                                           */


#ifdef HARD_DEBUG

#define IS_LEFT_VISITED(FB)	((FB)->flags & LEFT_VISITED_FLG)
#define IS_RIGHT_VISITED(FB)	((FB)->flags & RIGHT_VISITED_FLG)

#define SET_LEFT_VISITED(FB)	((FB)->flags |= LEFT_VISITED_FLG)
#define SET_RIGHT_VISITED(FB)	((FB)->flags |= RIGHT_VISITED_FLG)

#define UNSET_LEFT_VISITED(FB)	((FB)->flags &= ~LEFT_VISITED_FLG)
#define UNSET_RIGHT_VISITED(FB)	((FB)->flags &= ~RIGHT_VISITED_FLG)


#if 0
#  define PRINT_TREE
#else
#  undef PRINT_TREE
#endif

#ifdef PRINT_TREE
static void print_tree(void);
#endif

/*
 * Checks that the order between parent and children are correct,
 * and that the Red-Black Tree properies are satisfied. if size > 0,
 * check_tree() returns a node that satisfies "best fit" resp.
 * "address order best fit".
 *
 * The Red-Black Tree properies are:
 *   1. Every node is either red or black.
 *   2. Every leaf (NIL) is black.
 *   3. If a node is red, then both its children are black.
 *   4. Every simple path from a node to a descendant leaf
 *      contains the same number of black nodes.
 */

static RBTree_t *
check_tree(Uint size)
{
    RBTree_t *res = NULL;
    Sint blacks;
    Sint curr_blacks;
    RBTree_t *x;

#ifdef PRINT_TREE
    print_tree();
#endif

    if (!root)
	return res;

    x = root;
    ASSERT(IS_BLACK(x));
    ASSERT(!x->parent);
    curr_blacks = 1;
    blacks = -1;

    while (x) {
	if (!IS_LEFT_VISITED(x)) {
	    SET_LEFT_VISITED(x);
	    if (x->left) {
		x = x->left;
		if (IS_BLACK(x))
		    curr_blacks++;
		continue;
	    }
	    else {
		if (blacks < 0)
		    blacks = curr_blacks;
		ASSERT(blacks == curr_blacks);
	    }
	}

	if (!IS_RIGHT_VISITED(x)) {
	    SET_RIGHT_VISITED(x);
	    if (x->right) {
		x = x->right;
		if (IS_BLACK(x))
		    curr_blacks++;
		continue;
	    }
	    else {
		if (blacks < 0)
		    blacks = curr_blacks;
		ASSERT(blacks == curr_blacks);
	    }
	}


	if (IS_RED(x)) {
	    ASSERT(IS_BLACK(x->right));
	    ASSERT(IS_BLACK(x->left));
	}

	ASSERT(x->parent || x == root);

	if (x->left) {
	    ASSERT(x->left->parent == x);
	    ASSERT(BLK_SZ(x->left) < BLK_SZ(x)
		   || (BLK_SZ(x->left) == BLK_SZ(x) && x->left < x));
	}

	if (x->right) {
	    ASSERT(x->right->parent == x);
	    ASSERT(BLK_SZ(x->right) > BLK_SZ(x)
		   || (BLK_SZ(x->right) == BLK_SZ(x) && x->right > x));
	}

	if (size && BLK_SZ(x) >= size) {
	    if (!res
		|| BLK_SZ(x) < BLK_SZ(res)
		|| (BLK_SZ(x) == BLK_SZ(res) && x < res))
		res = x;
	}

	UNSET_LEFT_VISITED(x);
	UNSET_RIGHT_VISITED(x);
	if (IS_BLACK(x))
	    curr_blacks--;
	x = x->parent;

    }

    ASSERT(curr_blacks == 0);

    UNSET_LEFT_VISITED(root);
    UNSET_RIGHT_VISITED(root);

    return res;

}


#ifdef PRINT_TREE
#define INDENT_STEP 2

#include <stdio.h>

static void
print_tree_aux(RBTree_t *x, int indent)
{
    int i;

    if (!x) {
	for (i = 0; i < indent; i++) {
	    putc(' ', stderr);
	}
	fprintf(stderr, "BLACK: nil\r\n");
    }
    else {
	print_tree_aux(x->right, indent + INDENT_STEP);
	for (i = 0; i < indent; i++) {
	    putc(' ', stderr);
	}
	fprintf(stderr, "%s: sz=%lu addr=0x%lx\r\n",
		IS_BLACK(x) ? "BLACK" : "RED",
		BLK_SZ(x),
		(Uint) x);
	print_tree_aux(x->left,  indent + INDENT_STEP);
    }
}


static void
print_tree(void)
{
    fprintf(stderr, " --- Size-Adress tree begin ---\r\n");
    print_tree_aux(root, 0);
    fprintf(stderr, " --- Size-Adress tree end ---\r\n");
}

#endif

#endif

#endif /* ENABLE_ELIB_MALLOC */